Effects of mutation, truncation and temperature on the folding kinetics of a WW domain

PubMed Central

Maisuradze, Gia G.; Zhou, Rui; Liwo, Adam; Xiao, Yi; Scheraga, Harold A.

2013-01-01

The purpose of this work is to show how mutation, truncation and change of temperature can influence the folding kinetics of a protein. This is accomplished by principal component analysis (PCA) of molecular dynamics (MD)-generated folding trajectories of the triple β-strand WW domain from the Formin binding protein 28 (FBP) [PDB: 1E0L] and its full-size, and singly- and doubly-truncated mutants at temperatures below and very close to the melting point. The reasons for biphasic folding kinetics [i.e., coexistence of slow (three-state) and fast (two-state) phases], including the involvement of a solvent-exposed hydrophobic cluster and another delocalized hydrophobic core in the folding kinetics, are discussed. New folding pathways are identified in free-energy landscapes determined in terms of principal components for full-size mutants. Three-state folding is found to be a main mechanism for folding FBP28 WW domain and most of the full-size and truncated mutants. The results from the theoretical analysis are compared to those from experiment. Agreements and discrepancies between the theoretical and experimental results are discussed. Because of its importance in understanding protein kinetics and function, the diffusive mechanism by which FBP28 WW domain and its full-size and truncated mutants explore their conformational space is examined in terms of the mean-square displacement, (MSD), and PCA eigenvalue spectrum analyses. Subdiffusive behavior is observed for all studied systems. PMID:22560992

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

PubMed Central

Wang, Jin; Oliveira, Ronaldo J.; Chu, Xiakun; Whitford, Paul C.; Chahine, Jorge; Han, Wei; Wang, Erkang; Onuchic, José N.; Leite, Vitor B.P.

2012-01-01

The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles δE, the energetic roughness ΔE, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system accurately predicts the thermodynamics, as well as the kinetics of folding. Large Λ implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio Λ is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, Λ also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements. PMID:23019359

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics.

PubMed

Bisaria, Namita; Greenfeld, Max; Limouse, Charles; Mabuchi, Hideo; Herschlag, Daniel

2017-09-12

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔG align , the probability of aligning tertiary contact partners, and ΔG tert , the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔG HJH ) or from changes in the electrostatic environment (ΔG +/- ) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔG tert ). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔG tert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

Kinetic studies of the folding of heterodimeric monellin: evidence for switching between alternative parallel pathways.

PubMed

Aghera, Nilesh; Udgaonkar, Jayant B

2012-07-13

Determining whether or not a protein uses multiple pathways to fold is an important goal in protein folding studies. When multiple pathways are present, defined by transition states that differ in their compactness and structure but not significantly in energy, they may manifest themselves by causing the dependence on denaturant concentration of the logarithm of the observed rate constant of folding to have an upward curvature. In this study, the folding mechanism of heterodimeric monellin [double-chain monellin (dcMN)] has been studied over a range of protein and guanidine hydrochloride (GdnHCl) concentrations, using the intrinsic tryptophan fluorescence of the protein as the probe for the folding reaction. Refolding is shown to occur in multiple kinetic phases. In the first stage of refolding, which is silent to any change in intrinsic fluorescence, the two chains of monellin bind to one another to form an encounter complex. Interrupted folding experiments show that the initial encounter complex folds to native dcMN via two folding routes. A productive folding intermediate population is identified on one route but not on both of these routes. Two intermediate subpopulations appear to form in a fast kinetic phase, and native dcMN forms in a slow kinetic phase. The chevron arms for both the fast and slow phases of refolding are shown to have upward curvatures, suggesting that at least two pathways each defined by a different intermediate are operational during these kinetic phases of structure formation. Refolding switches from one pathway to the other as the GdnHCl concentration is increased. Copyright © 2012 Elsevier Ltd. All rights reserved.

How Kinetics within the Unfolded State Affects Protein Folding: an Analysis Based on Markov State Models and an Ultra-Long MD Trajectory

PubMed Central

Deng, Nan-jie; Dai, Wei

2013-01-01

Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultra-long MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤ 40 ns, compared with the folding time of ≈ 5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90 % of the unfolded states are sampled within the first 40 μs of the ultra-long MD trajectory, which on average explores ~27 % of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into “tubes”, and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with non-uniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently leading to non-exponential kinetics. A kinetic partition of

Fast protein folding kinetics

PubMed Central

Gelman, Hannah; Gruebele, Martin

2014-01-01

Fast folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast folding proteins has provided insight into the mechanisms which allow some proteins to find their native conformation well less than 1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even “slow” folding processes: fast folders are small, relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast folding proteins and provides an overview of the major findings of fast folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general as well as some work that is left to do. PMID:24641816

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements

PubMed Central

Zhou, Rui; Maisuradze, Gia G.; Suñol, David; Todorovski, Toni; Macias, Maria J.; Xiao, Yi; Scheraga, Harold A.; Czaplewski, Cezary; Liwo, Adam

2014-01-01

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecond-timescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed. The folding mechanisms obtained from the simulated folding kinetics are in agreement with experimental results, with a few discrepancies for which we have accounted. The origins of single- and double-exponential kinetics and their correlations with two- and three-state folding scenarios are shown to be related to the relative barrier heights between the various states. The rate constants obtained from time profiles of the fractions of the native, intermediate, and unfolded structures, and the kinetic equations fitted to them, correlate with the experimental values; however, they are about three orders of magnitude larger than the experimental ones for most of the systems. These differences are in agreement with the timescale extension derived by scaling down the friction of water and averaging out the fast degrees of freedom when passing from all-atom to a coarse-grained representation. Our results indicate that the UNRES force field can provide accurate predictions of folding kinetics of these WW domains, often used as models for the study of the mechanisms of proein folding. PMID:25489078

Folding kinetics of WW domains with the united residue force field for bridging microscopic motions and experimental measurements.

PubMed

Zhou, Rui; Maisuradze, Gia G; Suñol, David; Todorovski, Toni; Macias, Maria J; Xiao, Yi; Scheraga, Harold A; Czaplewski, Cezary; Liwo, Adam

2014-12-23

To demonstrate the utility of the coarse-grained united-residue (UNRES) force field to compare experimental and computed kinetic data for folding proteins, we have performed long-time millisecond-timescale canonical Langevin molecular dynamics simulations of the triple β-strand from the Formin binding protein 28 WW domain and six nonnatural variants, using UNRES. The results have been compared with available experimental data in both a qualitative and a quantitative manner. Complexities of the folding pathways, which cannot be determined experimentally, were revealed. The folding mechanisms obtained from the simulated folding kinetics are in agreement with experimental results, with a few discrepancies for which we have accounted. The origins of single- and double-exponential kinetics and their correlations with two- and three-state folding scenarios are shown to be related to the relative barrier heights between the various states. The rate constants obtained from time profiles of the fractions of the native, intermediate, and unfolded structures, and the kinetic equations fitted to them, correlate with the experimental values; however, they are about three orders of magnitude larger than the experimental ones for most of the systems. These differences are in agreement with the timescale extension derived by scaling down the friction of water and averaging out the fast degrees of freedom when passing from all-atom to a coarse-grained representation. Our results indicate that the UNRES force field can provide accurate predictions of folding kinetics of these WW domains, often used as models for the study of the mechanisms of proein folding.

A lattice protein with an amyloidogenic latent state: stability and folding kinetics.

PubMed

Palyanov, Andrey Yu; Krivov, Sergei V; Karplus, Martin; Chekmarev, Sergei F

2007-03-15

We have designed a model lattice protein that has two stable folded states, the lower free energy native state and a latent state of somewhat higher energy. The two states have a sizable part of their structures in common (two "alpha-helices") and differ in the content of "alpha-helices" and "beta-strands" in the rest of their structures; i.e. for the native state, this part is alpha-helical, and for the latent state it is composed of beta-strands. Thus, the lattice protein free energy surface mimics that of amyloidogenic proteins that form well organized fibrils under appropriate conditions. A Go-like potential was used and the folding process was simulated with a Monte Carlo method. To gain insight into the equilibrium free energy surface and the folding kinetics, we have combined standard approaches (reduced free energy surfaces, contact maps, time-dependent populations of the characteristic states, and folding time distributions) with a new approach. The latter is based on a principal coordinate analysis of the entire set of contacts, which makes possible the introduction of unbiased reaction coordinates and the construction of a kinetic network for the folding process. The system is found to have four characteristic basins, namely a semicompact globule, an on-pathway intermediate (the bifurcation basin), and the native and latent states. The bifurcation basin is shallow and consists of the structure common to the native and latent states, with the rest disorganized. On the basis of the simulation results, a simple kinetic model describing the transitions between the characteristic states was developed, and the rate constants for the essential transitions were estimated. During the folding process the system dwells in the bifurcation basin for a relatively short time before it proceeds to the native or latent state. We suggest that such a bifurcation may occur generally for proteins in which native and latent states have a sizable part of their structures in

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage.

PubMed

Linhananta, Apichart; Boer, Jesse; MacKay, Ian

2005-03-15

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.

Kinetic pathway for folding of the Tetrahymena ribozyme revealed by three UV-inducible crosslinks.

PubMed Central

Downs, W D; Cech, T R

1996-01-01

The kinetics of RNA folding were examined in the L-21 ribozyme, an RNA enzyme derived from the self-splicing Tetrahymena intron. Three UV-inducible crosslinks were mapped, characterized, and used as indicators for the folded state of the ribozyme. Together these data suggest that final structures are adopted first by the P4-P6 independently folding domain and only later in a region that positions the P1 helix (including the 5' splice site), a region whose folding is linked to that of a portion of the catalytic core. At intermediate times, a non-native structure forms in the region of the triple helical scaffold, which connects the major folding domains. At 30 degrees C, the unfolded ribozyme passes through these stages with a half-life of 2 min from the time magnesium cations are provided. At higher temperatures, the half-life is shortened but the order of events is unchanged. Thermal melting of the fully folded ribozyme also revealed a multi-stage process in which the steps of folding are reversed: the kinetically slowest structure is the least stable and melts first. These structures of the ribozyme also bind Mg2+ cooperatively and their relative affinity for binding seems to be a major determinant in the order of events during folding. Na+ can also substitute for Mg2+ to give rise to the same crosslinkable structures, but only at much higher concentrations. Specific binding sites for Mg2+ may make this cation particularly efficient at electrostatic stabilization during folding of these ribozyme structures. PMID:8756414

Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Y Mikata

2006-08-22

This paper treats approximate solutions for a self-folding problem of carbon nanotubes. It has been observed in the molecular dynamics calculations [1] that a carbon nanotube with a large aspect ratio can self-fold due to van der Waals force between the parts of the same carbon nanotube. The main issue in the self-folding problem is to determine the minimum threshold length of the carbon nanotube at which it becomes possible for the carbon nanotube to self-fold due to the van der Waals force. An approximate mathematical model based on the force method is constructed for the self-folding problem of carbonmore » nanotubes, and it is solved exactly as an elastica problem using elliptic functions. Additionally, three other mathematical models are constructed based on the energy method. As a particular example, the lower and upper estimates for the critical threshold (minimum) length are determined based on both methods for the (5,5) armchair carbon nanotube.« less

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

PubMed Central

Prentiss, Michael C.; Wales, David J.; Wolynes, Peter G.

2010-01-01

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N or C terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N terminus portion of the knot and a rate-determining step where the C terminus is incorporated. The low-lying minima with the N terminus knotted and the C terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N and C termini into the knot occurs late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly. PMID:20617197

A Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations

PubMed Central

Marinelli, Fabrizio; Pietrucci, Fabio; Laio, Alessandro; Piana, Stefano

2009-01-01

Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins. Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For the Trp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap. Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at of 4.4 Å from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the and chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data. PMID:19662155

A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations.

PubMed

Marinelli, Fabrizio; Pietrucci, Fabio; Laio, Alessandro; Piana, Stefano

2009-08-01

Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins.Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For theTrp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap.Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at Calpha-RMSD of 4.4 A from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the Pro12-delta3 and Gly11-alpha3 chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data.

The equilibrium properties and folding kinetics of an all-atom Go xAF model of the Trp-cage

NASA Astrophysics Data System (ADS)

Linhananta, Apichart; Boer, Jesse; MacKay, Ian

2005-03-01

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go ¯ model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial α-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.

A new model for approximating RNA folding trajectories and population kinetics

NASA Astrophysics Data System (ADS)

Kirkpatrick, Bonnie; Hajiaghayi, Monir; Condon, Anne

2013-01-01

RNA participates both in functional aspects of the cell and in gene regulation. The interactions of these molecules are mediated by their secondary structure which can be viewed as a planar circle graph with arcs for all the chemical bonds between pairs of bases in the RNA sequence. The problem of predicting RNA secondary structure, specifically the chemically most probable structure, has many useful and efficient algorithms. This leaves RNA folding, the problem of predicting the dynamic behavior of RNA structure over time, as the main open problem. RNA folding is important for functional understanding because some RNA molecules change secondary structure in response to interactions with the environment. The full RNA folding model on at most O(3n) secondary structures is the gold standard. We present a new subset approximation model for the full model, give methods to analyze its accuracy and discuss the relative merits of our model as compared with a pre-existing subset approximation. The main advantage of our model is that it generates Monte Carlo folding pathways with the same probabilities with which they are generated under the full model. The pre-existing subset approximation does not have this property.

Impact of ion binding on poly-L-lysine (un)folding energy landscape and kinetics.

PubMed

Xiong, Kan; Asher, Sanford A

2012-06-21

We utilize T-jump UV resonance Raman spectroscopy (UVRR) to study the impact of ion binding on the equilibrium energy landscape and on (un)folding kinetics of poly-L-lysine (PLL). We observe that the relaxation rates of the folded conformations (including π-helix (bulge), pure α-helix, and turns) of PLL are slower than those of short alanine-based peptides. The PLL pure α-helix folding time is similar to that of short alanine-based peptides. We for the first time have directly observed that turn conformations are α-helix and π-helix (bulge) unfolding intermediates. ClO(4)(-) binding to the Lys side chain -NH(3)(+) groups and the peptide backbone slows the α-helix unfolding rate compared to that in pure water, but little impacts the folding rate, resulting in an increased α-helix stability. ClO(4)(-) binding significantly increases the PLL unfolding activation barrier but little impacts the folding barrier. Thus, the PLL folding coordinate(s) differs from the unfolding coordinate(s). The-π helix (bulge) unfolding and folding coordinates do not directly go through the α-helix energy well. Our results clearly demonstrate that PLL (un)folding is not a two-state process.

Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding.

PubMed

Radford, Isolde H; Fersht, Alan R; Settanni, Giovanni

2011-06-09

Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

Thermodynamics and kinetics of protein folding on the ribosome: Alteration in energy landscapes, denatured state, and transition state ensembles

NASA Astrophysics Data System (ADS)

O'Brien, Edward; Vendruscolo, Michele; Dobson, Christopher

2010-03-01

In vitro experiments examining cotranslational folding utilize ribosome-nascent chain complexes (RNCs) in which the nascent chain is stalled at different points of its biosynthesis on the ribosome. We investigate the thermodynamics, kinetics, and structural properties of RNCs containing five different globular and repeat proteins stalled at ten different nascent chain lengths using coarse grained replica exchange simulations. We find that when the proteins are stalled near the ribosome exit tunnel opening they exhibit altered folding coopserativity, quantified by the van't Hoff enthalpy criterion; a significantly altered denatured state ensemble, in terms of Rg and shape parameters (Rg tensor); and the appearance of partially folded intermediates during cotranslation, evidenced by the appearance of a third basin in the free energy profile. These trends are due in part to excluded volume (crowding) interactions between the ribosome and nascent chain. We perform in silico temperature-jump experiments on the RNCs and examine nascent chain folding kinetics and structural changes in the transition state ensemble at various stall lengths.

Computational design of RNA parts, devices, and transcripts with kinetic folding algorithms implemented on multiprocessor clusters.

PubMed

Thimmaiah, Tim; Voje, William E; Carothers, James M

2015-01-01

With progress toward inexpensive, large-scale DNA assembly, the demand for simulation tools that allow the rapid construction of synthetic biological devices with predictable behaviors continues to increase. By combining engineered transcript components, such as ribosome binding sites, transcriptional terminators, ligand-binding aptamers, catalytic ribozymes, and aptamer-controlled ribozymes (aptazymes), gene expression in bacteria can be fine-tuned, with many corollaries and applications in yeast and mammalian cells. The successful design of genetic constructs that implement these kinds of RNA-based control mechanisms requires modeling and analyzing kinetically determined co-transcriptional folding pathways. Transcript design methods using stochastic kinetic folding simulations to search spacer sequence libraries for motifs enabling the assembly of RNA component parts into static ribozyme- and dynamic aptazyme-regulated expression devices with quantitatively predictable functions (rREDs and aREDs, respectively) have been described (Carothers et al., Science 334:1716-1719, 2011). Here, we provide a detailed practical procedure for computational transcript design by illustrating a high throughput, multiprocessor approach for evaluating spacer sequences and generating functional rREDs. This chapter is written as a tutorial, complete with pseudo-code and step-by-step instructions for setting up a computational cluster with an Amazon, Inc. web server and performing the large numbers of kinefold-based stochastic kinetic co-transcriptional folding simulations needed to design functional rREDs and aREDs. The method described here should be broadly applicable for designing and analyzing a variety of synthetic RNA parts, devices and transcripts.

Energetics, kinetics, and pathway of SNARE folding and assembly revealed by optical tweezers.

PubMed

Zhang, Yongli

2017-07-01

Soluble N-ethylmaleimide-sensitive factor attachment protein receptors (SNAREs) are universal molecular engines that drive membrane fusion. Particularly, synaptic SNAREs mediate fast calcium-triggered fusion of neurotransmitter-containing vesicles with plasma membranes for synaptic transmission, the basis of all thought and action. During membrane fusion, complementary SNAREs located on two apposed membranes (often called t- and v-SNAREs) join together to assemble into a parallel four-helix bundle, releasing the energy to overcome the energy barrier for fusion. A long-standing hypothesis suggests that SNAREs act like a zipper to draw the two membranes into proximity and thereby force them to fuse. However, a quantitative test of this SNARE zippering hypothesis was hindered by difficulties to determine the energetics and kinetics of SNARE assembly and to identify the relevant folding intermediates. Here, we first review different approaches that have been applied to study SNARE assembly and then focus on high-resolution optical tweezers. We summarize the folding energies, kinetics, and pathways of both wild-type and mutant SNARE complexes derived from this new approach. These results show that synaptic SNAREs assemble in four distinct stages with different functions: slow N-terminal domain association initiates SNARE assembly; a middle domain suspends and controls SNARE assembly; and rapid sequential zippering of the C-terminal domain and the linker domain directly drive membrane fusion. In addition, the kinetics and pathway of the stagewise assembly are shared by other SNARE complexes. These measurements prove the SNARE zippering hypothesis and suggest new mechanisms for SNARE assembly regulated by other proteins. © 2017 The Protein Society.

Practical Approaches to Protein Folding and Assembly

PubMed Central

Walters, Jad; Milam, Sara L.; Clark, A. Clay

2009-01-01

We describe here the use of several spectroscopies, such as fluorescence emission, circular dichroism, and differential quenching by acrylamide, in examining the equilibrium and kinetic folding of proteins. The first section regarding equilibrium techniques provides practical information for determining the conformational stability of a protein. In addition, several equilibrium-folding models are discussed, from two-state monomer to four-state homodimer, providing a comprehensive protocol for interpretation of folding curves. The second section focuses on the experimental design and interpretation of kinetic data, such as burst-phase analysis and exponential fits, used in elucidating kinetic folding pathways. In addition, simulation programs are used routinely to support folding models generated by kinetic experiments, and the fundamentals of simulations are covered. PMID:19289201

Ultrafast microfluidic mixer for tracking the early folding kinetics of human telomere G-quadruplex.

PubMed

Li, Ying; Liu, Chao; Feng, Xiaojun; Xu, Youzhi; Liu, Bi-Feng

2014-05-06

The folding of G-quadruplex is hypothesized to undergo a complex process, from the formation of a hairpin structure to a triplex intermediate and to the final G-quadruplex. Currently, no experimental evidence has been found for the hairpin formation, because it folds in the time regime of 10-100 μs, entailing the development of microfluidic mixers with a mixing time of less than 10 μs. In this paper, we reported an ultrarapid micromixer with a mixing time of 5.5 μs, which represents the fastest turbulent micromixer to our best knowledge. Evaluations of the micromixer were conducted to confirm its mixing efficiency for small molecules and macromolecules. This new micromixer enabled us to interrogate the hairpin formation in the early folding process of human telomere G-quadruplex. The experimental kinetic evidence for the formation of hairpin was obtained for the first time.

Kinetic Dissection of the Pre-existing Conformational Equilibrium in the Trypsin Fold*

PubMed Central

Vogt, Austin D.; Chakraborty, Pradipta; Di Cera, Enrico

2015-01-01

Structural biology has recently documented the conformational plasticity of the trypsin fold for both the protease and zymogen in terms of a pre-existing equilibrium between closed (E*) and open (E) forms of the active site region. How such plasticity is manifested in solution and affects ligand recognition by the protease and zymogen is poorly understood in quantitative terms. Here we dissect the E*-E equilibrium with stopped-flow kinetics in the presence of excess ligand or macromolecule. Using the clotting protease thrombin and its zymogen precursor prethrombin-2 as relevant models we resolve the relative distribution of the E* and E forms and the underlying kinetic rates for their interconversion. In the case of thrombin, the E* and E forms are distributed in a 1:4 ratio and interconvert on a time scale of 45 ms. In the case of prethrombin-2, the equilibrium is shifted strongly (10:1 ratio) in favor of the closed E* form and unfolds over a faster time scale of 4.5 ms. The distribution of E* and E forms observed for thrombin and prethrombin-2 indicates that zymogen activation is linked to a significant shift in the pre-existing equilibrium between closed and open conformations that facilitates ligand binding to the active site. These findings broaden our mechanistic understanding of how conformational transitions control ligand recognition by thrombin and its zymogen precursor prethrombin-2 and have direct relevance to other members of the trypsin fold. PMID:26216877

Guiding the folding pathway of DNA origami

NASA Astrophysics Data System (ADS)

Dunn, Katherine E.; Dannenberg, Frits; Ouldridge, Thomas E.; Kwiatkowska, Marta; Turberfield, Andrew J.; Bath, Jonathan

2015-09-01

DNA origami is a robust assembly technique that folds a single-stranded DNA template into a target structure by annealing it with hundreds of short `staple' strands. Its guiding design principle is that the target structure is the single most stable configuration. The folding transition is cooperative and, as in the case of proteins, is governed by information encoded in the polymer sequence. A typical origami folds primarily into the desired shape, but misfolded structures can kinetically trap the system and reduce the yield. Although adjusting assembly conditions or following empirical design rules can improve yield, well-folded origami often need to be separated from misfolded structures. The problem could in principle be avoided if assembly pathway and kinetics were fully understood and then rationally optimized. To this end, here we present a DNA origami system with the unusual property of being able to form a small set of distinguishable and well-folded shapes that represent discrete and approximately degenerate energy minima in a vast folding landscape, thus allowing us to probe the assembly process. The obtained high yield of well-folded origami structures confirms the existence of efficient folding pathways, while the shape distribution provides information about individual trajectories through the folding landscape. We find that, similarly to protein folding, the assembly of DNA origami is highly cooperative; that reversible bond formation is important in recovering from transient misfoldings; and that the early formation of long-range connections can very effectively enforce particular folds. We use these insights to inform the design of the system so as to steer assembly towards desired structures. Expanding the rational design process to include the assembly pathway should thus enable more reproducible synthesis, particularly when targeting more complex structures. We anticipate that this expansion will be essential if DNA origami is to continue its

Guiding the folding pathway of DNA origami.

PubMed

Dunn, Katherine E; Dannenberg, Frits; Ouldridge, Thomas E; Kwiatkowska, Marta; Turberfield, Andrew J; Bath, Jonathan

2015-09-03

DNA origami is a robust assembly technique that folds a single-stranded DNA template into a target structure by annealing it with hundreds of short 'staple' strands. Its guiding design principle is that the target structure is the single most stable configuration. The folding transition is cooperative and, as in the case of proteins, is governed by information encoded in the polymer sequence. A typical origami folds primarily into the desired shape, but misfolded structures can kinetically trap the system and reduce the yield. Although adjusting assembly conditions or following empirical design rules can improve yield, well-folded origami often need to be separated from misfolded structures. The problem could in principle be avoided if assembly pathway and kinetics were fully understood and then rationally optimized. To this end, here we present a DNA origami system with the unusual property of being able to form a small set of distinguishable and well-folded shapes that represent discrete and approximately degenerate energy minima in a vast folding landscape, thus allowing us to probe the assembly process. The obtained high yield of well-folded origami structures confirms the existence of efficient folding pathways, while the shape distribution provides information about individual trajectories through the folding landscape. We find that, similarly to protein folding, the assembly of DNA origami is highly cooperative; that reversible bond formation is important in recovering from transient misfoldings; and that the early formation of long-range connections can very effectively enforce particular folds. We use these insights to inform the design of the system so as to steer assembly towards desired structures. Expanding the rational design process to include the assembly pathway should thus enable more reproducible synthesis, particularly when targeting more complex structures. We anticipate that this expansion will be essential if DNA origami is to continue its

Equilibrium and kinetic folding of rabbit muscle triosephosphate isomerase by hydrogen exchange mass spectrometry.

PubMed

Pan, Hai; Raza, Ashraf S; Smith, David L

2004-03-05

Unfolding and refolding of rabbit muscle triosephosphate isomerase (TIM), a model for (betaalpha)8-barrel proteins, has been studied by amide hydrogen exchange/mass spectrometry. Unfolding was studied by destabilizing the protein in guanidine hydrochloride (GdHCl) or urea, pulse-labeling with 2H2O and analyzing the intact protein by HPLC electrospray ionization mass spectrometry. Bimodal isotope patterns were found in the mass spectra of the labeled protein, indicating two-state unfolding behavior. Refolding experiments were performed by diluting solutions of TIM unfolded in GdHCl or urea and pulse-labeling with 2H2O at different times. Mass spectra of the intact protein labeled after one to two minutes had three envelopes of isotope peaks, indicating population of an intermediate. Kinetic modeling indicates that the stability of the folding intermediate in water is only 1.5 kcal/mol. Failure to detect the intermediate in the unfolding experiments was attributed to its low stability and the high concentrations of denaturant required for unfolding experiments. The folding status of each segment of the polypeptide backbone was determined from the deuterium levels found in peptic fragments of the labeled protein. Analysis of these spectra showed that the C-terminal half folds to form the intermediate, which then forms native TIM with folding of the N-terminal half. These results show that TIM folding fits the (4+4) model for folding of (betaalpha)8-barrel proteins. Results of a double-jump experiment indicate that proline isomerization does not contribute to the rate-limiting step in the folding of TIM.

Comparative analysis of the folding dynamics and kinetics of an engineered knotted protein and its variants derived from HP0242 of Helicobacter pylori

NASA Astrophysics Data System (ADS)

Wang, Liang-Wei; Liu, Yu-Nan; Lyu, Ping-Chiang; Jackson, Sophie E.; Hsu, Shang-Te Danny

2015-09-01

Understanding the mechanism by which a polypeptide chain thread itself spontaneously to attain a knotted conformation has been a major challenge in the field of protein folding. HP0242 is a homodimeric protein from Helicobacter pylori with intertwined helices to form a unique pseudo-knotted folding topology. A tandem HP0242 repeat has been constructed to become the first engineered trefoil-knotted protein. Its small size renders it a model system for computational analyses to examine its folding and knotting pathways. Here we report a multi-parametric study on the folding stability and kinetics of a library of HP0242 variants, including the trefoil-knotted tandem HP0242 repeat, using far-UV circular dichroism and fluorescence spectroscopy. Equilibrium chemical denaturation of HP0242 variants shows the presence of highly populated dimeric and structurally heterogeneous folding intermediates. Such equilibrium folding intermediates retain significant amount of helical structures except those at the N- and C-terminal regions in the native structure. Stopped-flow fluorescence measurements of HP0242 variants show that spontaneous refolding into knotted structures can be achieved within seconds, which is several orders of magnitude faster than previously observed for other knotted proteins. Nevertheless, the complex chevron plots indicate that HP0242 variants are prone to misfold into kinetic traps, leading to severely rolled-over refolding arms. The experimental observations are in general agreement with the previously reported molecular dynamics simulations. Based on our results, kinetic folding pathways are proposed to qualitatively describe the complex folding processes of HP0242 variants.

Collapse kinetics and chevron plots from simulations of denaturant-dependent folding of globular proteins

PubMed Central

Liu, Zhenxing; Reddy, Govardhan; O’Brien, Edward P.; Thirumalai, D.

2011-01-01

Quantitative description of how proteins fold under experimental conditions remains a challenging problem. Experiments often use urea and guanidinium chloride to study folding whereas the natural variable in simulations is temperature. To bridge the gap, we use the molecular transfer model that combines measured denaturant-dependent transfer free energies for the peptide group and amino acid residues, and a coarse-grained Cα-side chain model for polypeptide chains to simulate the folding of src SH3 domain. Stability of the native state decreases linearly as [C] (the concentration of guanidinium chloride) increases with the slope, m, that is in excellent agreement with experiments. Remarkably, the calculated folding rate at [C] = 0 is only 16-fold larger than the measured value. Most importantly ln kobs (kobs is the sum of folding and unfolding rates) as a function of [C] has the characteristic V (chevron) shape. In every folding trajectory, the times for reaching the native state, interactions stabilizing all the substructures, and global collapse coincide. The value of (mf is the slope of the folding arm of the chevron plot) is identical to the fraction of buried solvent accessible surface area in the structures of the transition state ensemble. In the dominant transition state, which does not vary significantly at low [C], the core of the protein and certain loops are structured. Besides solving the long-standing problem of computing the chevron plot, our work lays the foundation for incorporating denaturant effects in a physically transparent manner either in all-atom or coarse-grained simulations. PMID:21512127

Collapse kinetics and chevron plots from simulations of denaturant-dependent folding of globular proteins.

PubMed

Liu, Zhenxing; Reddy, Govardhan; O'Brien, Edward P; Thirumalai, D

2011-05-10

Quantitative description of how proteins fold under experimental conditions remains a challenging problem. Experiments often use urea and guanidinium chloride to study folding whereas the natural variable in simulations is temperature. To bridge the gap, we use the molecular transfer model that combines measured denaturant-dependent transfer free energies for the peptide group and amino acid residues, and a coarse-grained C(α)-side chain model for polypeptide chains to simulate the folding of src SH(3) domain. Stability of the native state decreases linearly as [C] (the concentration of guanidinium chloride) increases with the slope, m, that is in excellent agreement with experiments. Remarkably, the calculated folding rate at [C] = 0 is only 16-fold larger than the measured value. Most importantly ln k(obs) (k(obs) is the sum of folding and unfolding rates) as a function of [C] has the characteristic V (chevron) shape. In every folding trajectory, the times for reaching the native state, interactions stabilizing all the substructures, and global collapse coincide. The value of (m(f) is the slope of the folding arm of the chevron plot) is identical to the fraction of buried solvent accessible surface area in the structures of the transition state ensemble. In the dominant transition state, which does not vary significantly at low [C], the core of the protein and certain loops are structured. Besides solving the long-standing problem of computing the chevron plot, our work lays the foundation for incorporating denaturant effects in a physically transparent manner either in all-atom or coarse-grained simulations.

The initial value problem in Lagrangian drift kinetic theory

NASA Astrophysics Data System (ADS)

Burby, J. W.

2016-06-01

> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.

Determination of protein folding kinetic types using sequence and predicted secondary structure and solvent accessibility.

PubMed

Zhang, Hua; Zhang, Tuo; Gao, Jianzhao; Ruan, Jishou; Shen, Shiyi; Kurgan, Lukasz

2012-01-01

Proteins fold through a two-state (TS), with no visible intermediates, or a multi-state (MS), via at least one intermediate, process. We analyze sequence-derived factors that determine folding types by introducing a novel sequence-based folding type predictor called FOKIT. This method implements a logistic regression model with six input features which hybridize information concerning amino acid composition and predicted secondary structure and solvent accessibility. FOKIT provides predictions with average Matthews correlation coefficient (MCC) between 0.58 and 0.91 measured using out-of-sample tests on four benchmark datasets. These results are shown to be competitive or better than results of four modern predictors. We also show that FOKIT outperforms these methods when predicting chains that share low similarity with the chains used to build the model, which is an important advantage given the limited number of annotated chains. We demonstrate that inclusion of solvent accessibility helps in discrimination of the folding kinetic types and that three of the features constitute statistically significant markers that differentiate TS and MS folders. We found that the increased content of exposed Trp and buried Leu are indicative of the MS folding, which implies that the exposure/burial of certain hydrophobic residues may play important role in the formation of the folding intermediates. Our conclusions are supported by two case studies.

Identification of a key structural element for protein folding within beta-hairpin turns.

PubMed

Kim, Jaewon; Brych, Stephen R; Lee, Jihun; Logan, Timothy M; Blaber, Michael

2003-05-09

Specific residues in a polypeptide may be key contributors to the stability and foldability of the unique native structure. Identification and prediction of such residues is, therefore, an important area of investigation in solving the protein folding problem. Atypical main-chain conformations can help identify strains within a folded protein, and by inference, positions where unique amino acids may have a naturally high frequency of occurrence due to favorable contributions to stability and folding. Non-Gly residues located near the left-handed alpha-helical region (L-alpha) of the Ramachandran plot are a potential indicator of structural strain. Although many investigators have studied mutations at such positions, no consistent energetic or kinetic contributions to stability or folding have been elucidated. Here we report a study of the effects of Gly, Ala and Asn substitutions found within the L-alpha region at a characteristic position in defined beta-hairpin turns within human acidic fibroblast growth factor, and demonstrate consistent effects upon stability and folding kinetics. The thermodynamic and kinetic data are compared to available data for similar mutations in other proteins, with excellent agreement. The results have identified that Gly at the i+3 position within a subset of beta-hairpin turns is a key contributor towards increasing the rate of folding to the native state of the polypeptide while leaving the rate of unfolding largely unchanged.

Rapid three-dimensional microfluidic mixer for high viscosity solutions to unravel earlier folding kinetics of G-quadruplex under molecular crowding conditions.

PubMed

Liu, Chao; Li, Ying; Li, Yiwei; Chen, Peng; Feng, Xiaojun; Du, Wei; Liu, Bi-Feng

2016-01-01

Rapid mixing of highly viscous solutions is a great challenge, which helps to analyze the reaction kinetics in viscous liquid phase, particularly to discover the folding kinetics of macromolecules under molecular crowding conditions mimicking the conditions inside cells. Here, we demonstrated a novel microfluidic mixer based on Dean flows with three-dimensional (3D) microchannel configuration for fast mixing of high-viscosity fluids. The main structure contained three consecutive subunits, each consisting of a "U"-type channel followed by a chamber with different width and height. Thus, the two solutions injected from the two inlets would undergo a mixing in the first "U"-type channel due to the Dean flow effect, and simultaneous vortices expansions in both horizontal and vertical directions in the following chamber. Numerical simulations and experimental characterizations confirmed that the micromixer could achieve a mixing time of 122.4μs for solutions with viscosities about 33.6 times that of pure water. It was the fastest micromixer for high viscosity solutions compared with previous reports. With this highly efficient 3D microfluidic mixer, we further characterized the early folding kinetics of human telomere G-quadruplex under molecular crowding conditions, and unravelled a new folding process within 550μs. Copyright © 2015 Elsevier B.V. All rights reserved.

A one-dimensional free energy surface does not account for two-probe folding kinetics of protein alpha(3)D.

PubMed

Liu, Feng; Dumont, Charles; Zhu, Yongjin; DeGrado, William F; Gai, Feng; Gruebele, Martin

2009-02-14

We present fluorescence-detected measurements of the temperature-jump relaxation kinetics of the designed three-helix bundle protein alpha(3)D taken under solvent conditions identical to previous infrared-detected kinetics. The fluorescence-detected rate is similar to the IR-detected rate only at the lowest temperature where we could measure it (326 K). The fluorescence-detected rate decreases by a factor of 3 over the 326-344 K temperature range, whereas the IR-detected rate remains nearly constant over the same range. To investigate this probe dependence, we tested an extensive set of physically reasonable one-dimensional (1D) free energy surfaces by Langevin dynamics simulation. The simulations included coordinate- and temperature-dependent roughness, diffusion coefficients, and IR/fluorescence spectroscopic signatures. None of these can reproduce the IR and fluorescence data simultaneously, forcing us to the conclusion that a 1D free energy surface cannot accurately describe the folding of alpha(3)D. This supports the hypothesis that alpha(3)D has a multidimensional free energy surface conducive to downhill folding at 326 K, and that it is already an incipient downhill folder with probe-dependent kinetics near its melting point.

Principal component analysis for protein folding dynamics.

PubMed

Maisuradze, Gia G; Liwo, Adam; Scheraga, Harold A

2009-01-09

Protein folding is considered here by studying the dynamics of the folding of the triple beta-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.

Aromatic residues engineered into the beta-turn nucleation site of ubiquitin lead to a complex folding landscape, non-native side-chain interactions, and kinetic traps.

PubMed

Rea, Anita M; Simpson, Emma R; Meldrum, Jill K; Williams, Huw E L; Searle, Mark S

2008-12-02

The fast folding of small proteins is likely to be the product of evolutionary pressures that balance the search for native-like contacts in the transition state with the minimum number of stable non-native interactions that could lead to partially folded states prone to aggregation and amyloid formation. We have investigated the effects of non-native interactions on the folding landscape of yeast ubiquitin by introducing aromatic substitutions into the beta-turn region of the N-terminal beta-hairpin, using both the native G-bulged type I turn sequence (TXTGK) as well as an engineered 2:2 XNGK type I' turn sequence. The N-terminal beta-hairpin is a recognized folding nucleation site in ubiquitin. The folding kinetics for wt-Ub (TLTGK) and the type I' turn mutant (TNGK) reveal only a weakly populated intermediate, however, substitution with X = Phe or Trp in either context results in a high propensity to form a stable compact intermediate where the initial U-->I collapse is visible as a distinct kinetic phase. The introduction of Trp into either of the two host turn sequences results in either complex multiphase kinetics with the possibility of parallel folding pathways, or formation of a highly compact I-state stabilized by non-native interactions that must unfold before refolding. Sequence substitutions with aromatic residues within a localized beta-turn capable of forming non-native hydrophobic contacts in both the native state and partially folded states has the undesirable consequence that folding is frustrated by the formation of stable compact intermediates that evolutionary pressures at the sequence level may have largely eliminated.

The Complexity of Folding Self-Folding Origami

NASA Astrophysics Data System (ADS)

Stern, Menachem; Pinson, Matthew B.; Murugan, Arvind

2017-10-01

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of "distractor" folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. We show that seeding successful folding in this way can be understood in terms of subpatterns that fold when cut out ("folding islands"). Besides providing guidelines for the placement of active hinges in origami applications, our results point to fundamental limits on the programmability of energy landscapes in sheets.

Single molecule RNA folding studied with optical trapping

NASA Astrophysics Data System (ADS)

Vieregg, Jeffrey Robert

The RNA folding problem (predicting the equilibrium structure and folding pathway of an RNA molecule from its sequence) is one of the classic problems of biophysics. Recent discoveries of many new functions for RNA have increased its importance, and new instrumental techniques have provided new ways to characterize molecular behavior. In particular, optical trapping (optical tweezers) allows controlled mechanical force to be applied to single RNA molecules while their end-to-end extension is monitored in real time. This enables characterization of RNA folding dynamics at a level unreachable by traditional bulk methods. Furthermore, recent advances in statistical mechanics make it possible to recover equilibrium quantities such as free energy from reactions which occur away from equilibrium. This dissertation describes the application of optical trapping and non-equilibrium statistical mechanics to quantitatively characterize folding of RNA secondary structures. By measuring the folding free energy of several specially designed hairpins in solutions containing various amounts of sodium and potassium, we were able to determine that RNA secondary structure thermodynamics depends not only on monovalent cation concentration but also surprisingly, on species. We also investigated the temperature dependence of hairpin folding thermodynamics and kinetics, which provided a direct measurement of enthalpy and entropy for RNA folding at physiological temperatures. We found that the folding pathway was quite sensitive to both salt and temperature, as measured by the folding success rate of a biologically important hairpin from the HIV-1 viral genome. Finally, I discuss modeling of force-induced RNA folding and unfolding, as well as a series of efforts which have dramatically improved the performance of our optical trapping instrument.

Transiently disordered tails accelerate folding of globular proteins.

PubMed

Mallik, Saurav; Ray, Tanaya; Kundu, Sudip

2017-07-01

Numerous biological proteins exhibit intrinsic disorder at their termini, which are associated with multifarious functional roles. Here, we show the surprising result that an increased percentage of terminal short transiently disordered regions with enhanced flexibility (TstDREF) is associated with accelerated folding rates of globular proteins. Evolutionary conservation of predicted disorder at TstDREFs and drastic alteration of folding rates upon point-mutations suggest critical regulatory role(s) of TstDREFs in shaping the folding kinetics. TstDREFs are associated with long-range intramolecular interactions and the percentage of native secondary structural elements physically contacted by TstDREFs exhibit another surprising positive correlation with folding kinetics. These results allow us to infer probable molecular mechanisms behind the TstDREF-mediated regulation of folding kinetics that challenge protein biochemists to assess by direct experimental testing. © 2017 Federation of European Biochemical Societies.

Renormalized Hamiltonian for a peptide chain: Digitalizing the protein folding problem

NASA Astrophysics Data System (ADS)

Fernández, Ariel; Colubri, Andrés

2000-05-01

A renormalized Hamiltonian for a flexible peptide chain is derived to generate the long-time limit dynamics compatible with a coarsening of torsional conformation space. The renormalization procedure is tailored taking into account the coarse graining imposed by the backbone torsional constraints due to the local steric hindrance and the local backbone-side-group interactions. Thus, the torsional degrees of freedom for each residue are resolved modulo basins of attraction in its so-called Ramachandran map. This Ramachandran renormalization (RR) procedure is implemented so that the chain is energetically driven to form contact patterns as their respective collective topological constraints are fulfilled within the coarse description. In this way, the torsional dynamics are digitalized and become codified as an evolving pattern in a binary matrix. Each accepted Monte Carlo step in a canonical ensemble simulation is correlated with the real mean first passage time it takes to reach the destination coarse topological state. This real-time correlation enables us to test the RR dynamics by comparison with experimentally probed kinetic bottlenecks along the dominant folding pathway. Such intermediates are scarcely populated at any given time, but they determine the kinetic funnel leading to the active structure. This landscape region is reached through kinetically controlled steps needed to overcome the conformational entropy of the random coil. The results are specialized for the bovine pancreatic trypsin inhibitor, corroborating the validity of our method.

PREFACE Protein folding: lessons learned and new frontiers Protein folding: lessons learned and new frontiers

NASA Astrophysics Data System (ADS)

Pappu, Rohit V.; Nussinov, Ruth

2009-03-01

In appropriate physiological milieux proteins spontaneously fold into their functional three-dimensional structures. The amino acid sequences of functional proteins contain all the information necessary to specify the folds. This remarkable observation has spawned research aimed at answering two major questions. (1) Of all the conceivable structures that a protein can adopt, why is the ensemble of native-like structures the most favorable? (2) What are the paths by which proteins manage to robustly and reproducibly fold into their native structures? Anfinsen's thermodynamic hypothesis has guided the pursuit of answers to the first question whereas Levinthal's paradox has influenced the development of models for protein folding dynamics. Decades of work have led to significant advances in the folding problem. Mean-field models have been developed to capture our current, coarse grain understanding of the driving forces for protein folding. These models are being used to predict three-dimensional protein structures from sequence and stability profiles as a function of thermodynamic and chemical perturbations. Impressive strides have also been made in the field of protein design, also known as the inverse folding problem, thereby testing our understanding of the determinants of the fold specificities of different sequences. Early work on protein folding pathways focused on the specific sequence of events that could lead to a simplification of the search process. However, unifying principles proved to be elusive. Proteins that show reversible two-state folding-unfolding transitions turned out to be a gift of natural selection. Focusing on these simple systems helped researchers to uncover general principles regarding the origins of cooperativity in protein folding thermodynamics and kinetics. On the theoretical front, concepts borrowed from polymer physics and the physics of spin glasses led to the development of a framework based on energy landscape theories. These

Characterization of the kinetic and thermodynamic landscape of RNA folding using a novel application of isothermal titration calorimetry

PubMed Central

Vander Meulen, Kirk A.; Butcher, Samuel E.

2012-01-01

A novel isothermal titration calorimetry (ITC) method was applied to investigate RNA helical packing driven by the GAAA tetraloop–receptor interaction in magnesium and potassium solutions. Both the kinetics and thermodynamics were obtained in individual ITC experiments, and analysis of the kinetic data over a range of temperatures provided Arrhenius activation energies (ΔH‡) and Eyring transition state entropies (ΔS‡). The resulting rich dataset reveals strongly contrasting kinetic and thermodynamic profiles for this RNA folding system when stabilized by potassium versus magnesium. In potassium, association is highly exothermic (ΔH25°C = −41.6 ± 1.2 kcal/mol in 150 mM KCl) and the transition state is enthalpically barrierless (ΔH‡ = −0.6 ± 0.5). These parameters are sigificantly positively shifted in magnesium (ΔH25°C = −20.5 ± 2.1 kcal/mol, ΔH‡ = 7.3 ± 2.2 kcal/mol in 0.5 mM MgCl2). Mixed salt solutions approximating physiological conditions exhibit an intermediate thermodynamic character. The cation-dependent thermodynamic landscape may reflect either a salt-dependent unbound receptor conformation, or alternatively and more generally, it may reflect a small per-cation enthalpic penalty associated with folding-coupled magnesium uptake. PMID:22058128

Protein folding simulations: from coarse-grained model to all-atom model.

PubMed

Zhang, Jian; Li, Wenfei; Wang, Jun; Qin, Meng; Wu, Lei; Yan, Zhiqiang; Xu, Weixin; Zuo, Guanghong; Wang, Wei

2009-06-01

Protein folding is an important and challenging problem in molecular biology. During the last two decades, molecular dynamics (MD) simulation has proved to be a paramount tool and was widely used to study protein structures, folding kinetics and thermodynamics, and structure-stability-function relationship. It was also used to help engineering and designing new proteins, and to answer even more general questions such as the minimal number of amino acid or the evolution principle of protein families. Nowadays, the MD simulation is still undergoing rapid developments. The first trend is to toward developing new coarse-grained models and studying larger and more complex molecular systems such as protein-protein complex and their assembling process, amyloid related aggregations, and structure and motion of chaperons, motors, channels and virus capsides; the second trend is toward building high resolution models and explore more detailed and accurate pictures of protein folding and the associated processes, such as the coordination bond or disulfide bond involved folding, the polarization, charge transfer and protonate/deprotonate process involved in metal coupled folding, and the ion permeation and its coupling with the kinetics of channels. On these new territories, MD simulations have given many promising results and will continue to offer exciting views. Here, we review several new subjects investigated by using MD simulations as well as the corresponding developments of appropriate protein models. These include but are not limited to the attempt to go beyond the topology based Gō-like model and characterize the energetic factors in protein structures and dynamics, the study of the thermodynamics and kinetics of disulfide bond involved protein folding, the modeling of the interactions between chaperonin and the encapsulated protein and the protein folding under this circumstance, the effort to clarify the important yet still elusive folding mechanism of protein BBL

Folding of guanine quadruplex molecules-funnel-like mechanism or kinetic partitioning? An overview from MD simulation studies.

PubMed

Šponer, Jiří; Bussi, Giovanni; Stadlbauer, Petr; Kührová, Petra; Banáš, Pavel; Islam, Barira; Haider, Shozeb; Neidle, Stephen; Otyepka, Michal

2017-05-01

Guanine quadruplexes (GQs) play vital roles in many cellular processes and are of much interest as drug targets. In contrast to the availability of many structural studies, there is still limited knowledge on GQ folding. We review recent molecular dynamics (MD) simulation studies of the folding of GQs, with an emphasis paid to the human telomeric DNA GQ. We explain the basic principles and limitations of all types of MD methods used to study unfolding and folding in a way accessible to non-specialists. We discuss the potential role of G-hairpin, G-triplex and alternative GQ intermediates in the folding process. We argue that, in general, folding of GQs is fundamentally different from funneled folding of small fast-folding proteins, and can be best described by a kinetic partitioning (KP) mechanism. KP is a competition between at least two (but often many) well-separated and structurally different conformational ensembles. The KP mechanism is the only plausible way to explain experiments reporting long time-scales of GQ folding and the existence of long-lived sub-states. A significant part of the natural partitioning of the free energy landscape of GQs comes from the ability of the GQ-forming sequences to populate a large number of syn-anti patterns in their G-tracts. The extreme complexity of the KP of GQs typically prevents an appropriate description of the folding landscape using just a few order parameters or collective variables. We reconcile available computational and experimental studies of GQ folding and formulate basic principles characterizing GQ folding landscapes. This article is part of a Special Issue entitled "G-quadruplex" Guest Editor: Dr. Concetta Giancola and Dr. Daniela Montesarchio. Copyright © 2016 Elsevier B.V. All rights reserved.

Structural analysis of kinetic folding intermediates for a TIM barrel protein, indole-3-glycerol phosphate synthase, by hydrogen exchange mass spectrometry and Gō-model simulation

PubMed Central

Gu, Zhenyu; Rao, Maithreyi K.; Forsyth, William R.

2009-01-01

The structures of partially-folded states appearing during the folding of a (βα)8 TIM barrel protein, the indole-3-glycerol phosphate synthase from S. solfataricus (sIGPS), was assessed by hydrogen exchange mass spectrometry (HX-MS) and Gō-model simulations. HX-MS analysis of the peptic peptides derived from the pulse-labeled product of the sub-millisecond folding reaction from the urea-denatured state revealed strong protection in the (βα)4 region, modest protection in the neighboring (βα)1–3 and (βα)5β6 segments and no significant protection in the remaining N- and C-terminal segments. These results demonstrate that this species is not a collapsed form of the unfolded state under native-favoring conditions nor is it the native state formed via fast-track folding. However, the striking contrast of these results with the strong protection observed in the (βα)2–5β6 region after 5 s of folding demonstrates that these species represent kinetically-distinct folding intermediates that are not identical as previously thought. A re-examination of the kinetic folding mechanism by chevron analysis of fluorescence data confirmed distinct roles for these two species: the burst-phase intermediate is predicted to be a misfolded, off-pathway intermediate while the subsequent 5 s intermediate corresponds to an on-pathway equilibrium intermediate. Comparison with the predictions using a Cα Gō-model simulation of the kinetic folding reaction for sIGPS shows good agreement with the core of structure offering protection against exchange in the on-pathway intermediate(s). Because the native-centric Gō-model simulations do not explicitly include sequence-specific information, the simulation results support the hypothesis that the topology of TIM barrel proteins is a primary determinant of the folding free energy surface for the productive folding reaction. The early misfolding reaction must involve aspects of non-native structure not detected by the G�

Redesigning the type II' β-turn in green fluorescent protein to type I': implications for folding kinetics and stability.

PubMed

Madan, Bharat; Sokalingam, Sriram; Raghunathan, Govindan; Lee, Sun-Gu

2014-10-01

Both Type I' and Type II' β-turns have the same sense of the β-turn twist that is compatible with the β-sheet twist. They occur predominantly in two residue β-hairpins, but the occurrence of Type I' β-turns is two times higher than Type II' β-turns. This suggests that Type I' β-turns may be more stable than Type II' β-turns, and Type I' β-turn sequence and structure can be more favorable for protein folding than Type II' β-turns. Here, we redesigned the native Type II' β-turn in GFP to Type I' β-turn, and investigated its effect on protein folding and stability. The Type I' β-turns were designed based on the statistical analysis of residues in natural Type I' β-turns. The substitution of the native "GD" sequence of i+1 and i+2 residues with Type I' preferred "(N/D)G" sequence motif increased the folding rate by 50% and slightly improved the thermodynamic stability. Despite the enhancement of in vitro refolding kinetics and stability of the redesigned mutants, they showed poor soluble expression level compared to wild type. To overcome this problem, i and i + 3 residues of the designed Type I' β-turn were further engineered. The mutation of Thr to Lys at i + 3 could restore the in vivo soluble expression of the Type I' mutant. This study indicates that Type II' β-turns in natural β-hairpins can be further optimized by converting the sequence to Type I'. © 2014 Wiley Periodicals, Inc.

Pressure-jump small-angle x-ray scattering detected kinetics of staphylococcal nuclease folding.

PubMed Central

Woenckhaus, J; Köhling, R; Thiyagarajan, P; Littrell, K C; Seifert, S; Royer, C A; Winter, R

2001-01-01

The kinetics of chain disruption and collapse of staphylococcal nuclease after positive or negative pressure jumps was monitored by real-time small-angle x-ray scattering under pressure. We used this method to probe the overall conformation of the protein by measuring its radius of gyration and pair-distance-distribution function p(r) which are sensitive to the spatial extent and shape of the particle. At all pressures and temperatures tested, the relaxation profiles were well described by a single exponential function. No fast collapse was observed, indicating that the rate limiting step for chain collapse is the same as that for secondary and tertiary structure formation. Whereas refolding at low pressures occurred in a few seconds, at high pressures the relaxation was quite slow, approximately 1 h, due to a large positive activation volume for the rate-limiting step for chain collapse. A large increase in the system volume upon folding implies significant dehydration of the transition state and a high degree of similarity in terms of the packing density between the native and transition states in this system. This study of the time-dependence of the tertiary structure in pressure-induced folding/unfolding reactions demonstrates that novel information about the nature of protein folding transitions and transition states can be obtained from a combination of small-angle x-ray scattering using high intensity synchrotron radiation with the high pressure perturbation technique. PMID:11222312

Co-Translational Folding Trajectory of the HemK Helical Domain.

PubMed

Mercier, Evan; Rodnina, Marina V

2018-06-26

Protein folding begins co-translationally within the restricted space of the peptide exit tunnel of the ribosome. We have already shown that the N-terminal α-helical domain of the universally conserved N 5 -glutamine methyltransferase HemK is compacted within the exit tunnel and rearranges into the native fold upon emerging from the ribosome. However, the exact folding pathway of the domain remained unclear. Here we analyzed the rapid kinetics of translation and folding monitored by fluorescence resonance energy transfer and photoinduced electron transfer using global fitting to a model for synthesis of the 112-amino acid HemK fragment. Our results suggest that the co-translational folding trajectory of HemK starts within the tunnel and passes through four kinetically distinct folding intermediates that may represent sequential docking of helices to a growing compact core. The kinetics of the process is defined entirely by translation. The results show how analysis of ensemble kinetic data can be used to dissect complex trajectories of rapid conformational rearrangements in multicomponent systems.

Solvent Effects on Protein Folding/Unfolding

NASA Astrophysics Data System (ADS)

García, A. E.; Hillson, N.; Onuchic, J. N.

Pressure effects on the hydrophobic potential of mean force led Hummer et al. to postulate a model for pressure denaturation of proteins in which denaturation occurs by means of water penetration into the protein interior, rather than by exposing the protein hydrophobic core to the solvent --- commonly used to describe temperature denaturation. We study the effects of pressure in protein folding/unfolding kinetics in an off-lattice minimalist model of a protein in which pressure effects have been incorporated by means of the pair-wise potential of mean force of hydrophobic groups in water. We show that pressure slows down the kinetics of folding by decreasing the reconfigurational diffusion coefficient and moves the location of the folding transition state.

Free Energy Landscape and Multiple Folding Pathways of an H-Type RNA Pseudoknot

PubMed Central

Bian, Yunqiang; Zhang, Jian; Wang, Jun; Wang, Jihua; Wang, Wei

2015-01-01

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA. PMID:26030098

How interfaces affect hydrophobically driven polymer folding.

PubMed

Jamadagni, Sumanth N; Godawat, Rahul; Dordick, Jonathan S; Garde, Shekhar

2009-04-02

Studies of folding-unfolding of hydrophobic polymers in water provide an excellent starting point to probe manybody hydrophobic interactions in the context of realistic self-assembly processes. Such studies in bulk water have highlighted the similarities between thermodynamics of polymer collapse and of protein folding, and emphasized the role of hydration-water structure, density, and fluctuations-in the folding kinetics. Hydrophobic polymers are interfacially active-that is, they prefer locations at aqueous interfaces relative to bulk water-consistent with their low solubility. How does the presence of a hydrophobic solid surface or an essentially hydrophobic vapor-water interface affect the structural, thermodynamic, and kinetic aspects of polymer folding? Using extensive molecular dynamics simulations, we show that the large hydrophobic driving force for polymer collapse in bulk water is reduced at a solid alkane-water interface and further reduced at a vapor-water interface. As a result, at the solid-water interface, folded structures are marginally stable, whereas the vapor-liquid interface unfolds polymers completely. Structural sampling is also significantly affected by the interface. For example, at the solid-water interface, polymer conformations are quasi-2- dimensional, with folded states being pancake-like structures. At the vapor-water interface, the hydrophobic polymer is significantly excluded from the water phase and freely samples a broad range of compact to extended structures. Interestingly, although the driving force for folding is considerably lower, kinetics of folding are faster at both interfaces, highlighting the role of enhanced water fluctuations and dynamics at a hydrophobic interface.

Soft Computing Techniques for the Protein Folding Problem on High Performance Computing Architectures.

PubMed

Llanes, Antonio; Muñoz, Andrés; Bueno-Crespo, Andrés; García-Valverde, Teresa; Sánchez, Antonia; Arcas-Túnez, Francisco; Pérez-Sánchez, Horacio; Cecilia, José M

2016-01-01

The protein-folding problem has been extensively studied during the last fifty years. The understanding of the dynamics of global shape of a protein and the influence on its biological function can help us to discover new and more effective drugs to deal with diseases of pharmacological relevance. Different computational approaches have been developed by different researchers in order to foresee the threedimensional arrangement of atoms of proteins from their sequences. However, the computational complexity of this problem makes mandatory the search for new models, novel algorithmic strategies and hardware platforms that provide solutions in a reasonable time frame. We present in this revision work the past and last tendencies regarding protein folding simulations from both perspectives; hardware and software. Of particular interest to us are both the use of inexact solutions to this computationally hard problem as well as which hardware platforms have been used for running this kind of Soft Computing techniques.

Energy landscape of knotted protein folding

PubMed Central

Sułkowska, Joanna I.; Noel, Jeffrey K.; Onuchic, Jose N.

2012-01-01

Recent experiments have conclusively shown that proteins are able to fold from an unknotted, denatured polypeptide to the knotted, native state without the aid of chaperones. These experiments are consistent with a growing body of theoretical work showing that a funneled, minimally frustrated energy landscape is sufficient to fold small proteins with complex topologies. Here, we present a theoretical investigation of the folding of a knotted protein, 2ouf, engineered in the laboratory by a domain fusion that mimics an evolutionary pathway for knotted proteins. Unlike a previously studied knotted protein of similar length, we see reversible folding/knotting and a surprising lack of deep topological traps with a coarse-grained structure-based model. Our main interest is to investigate how evolution might further select the geometry and stiffness of the threading region of the newly fused protein. We compare the folding of the wild-type protein to several mutants. Similarly to the wild-type protein, all mutants show robust and reversible folding, and knotting coincides with the transition state ensemble. As observed experimentally, our simulations show that the knotted protein folds about ten times slower than an unknotted construct with an identical contact map. Simulated folding kinetics reflect the experimentally observed rollover in the folding limbs of chevron plots. Successful folding of the knotted protein is restricted to a narrow range of temperature as compared to the unknotted protein and fits of the kinetic folding data below folding temperature suggest slow, nondiffusive dynamics for the knotted protein. PMID:22891304

Fragility of Liquids, Polyamorphism, Nucleation, and Folding Directions, in the Landscape Paradigm

NASA Astrophysics Data System (ADS)

Angell, C. A.

1998-03-01

folding problem. The possibility exists that in certain cases an aberrant step in the nucleation event, facilitated by mutant nucleotide sequences or by third agents (heterogeneous nucleating agents), will trigger folding down an alternative and pathogenic route to a second stable state. This possibility should be evaluated, using nucleation kinetics analysis techniques, as an approach to understanding the initiation of ``mad cow" disease cerebral pathology.

Sampling the multiple folding mechanisms of Trp-cage in explicit solvent

PubMed Central

Juraszek, J.; Bolhuis, P. G.

2006-01-01

We investigate the kinetic pathways of folding and unfolding of the designed miniprotein Trp- cage in explicit solvent. Straightforward molecular dynamics and replica exchange methods both have severe convergence problems, whereas transition path sampling allows us to sample unbiased dynamical pathways between folded and unfolded states and leads to deeper understanding of the mechanisms of (un)folding. In contrast to previous predictions employing an implicit solvent, we find that Trp-cage folds primarily (80% of the paths) via a pathway forming the tertiary contacts and the salt bridge, before helix formation. The remaining 20% of the paths occur in the opposite order, by first forming the helix. The transition states of the rate-limiting steps are solvated native-like structures. Water expulsion is found to be the last step upon folding for each route. Committor analysis suggests that the dynamics of the solvent is not part of the reaction coordinate. Nevertheless, during the transition, specific water molecules are strongly bound and can play a structural role in the folding. PMID:17035504

An overlapping region between the two terminal folding units of the outer surface protein A (OspA) controls its folding behavior.

PubMed

Makabe, Koki; Nakamura, Takashi; Dhar, Debanjan; Ikura, Teikichi; Koide, Shohei; Kuwajima, Kunihiro

2018-04-27

Although many naturally occurring proteins consist of multiple domains, most studies on protein folding to date deal with single-domain proteins or isolated domains of multi-domain proteins. Studies of multi-domain protein folding are required for further advancing our understanding of protein folding mechanisms. Borrelia outer surface protein A (OspA) is a β-rich two-domain protein, in which two globular domains are connected by a rigid and stable single-layer β-sheet. Thus, OspA is particularly suited as a model system for studying the interplays of domains in protein folding. Here, we studied the equilibria and kinetics of the urea-induced folding-unfolding reactions of OspA probed with tryptophan fluorescence and ultraviolet circular dichroism. Global analysis of the experimental data revealed compelling lines of evidence for accumulation of an on-pathway intermediate during kinetic refolding and for the identity between the kinetic intermediate and a previously described equilibrium unfolding intermediate. The results suggest that the intermediate has the fully native structure in the N-terminal domain and the single layer β-sheet, with the C-terminal domain still unfolded. The observation of the productive on-pathway folding intermediate clearly indicates substantial interactions between the two domains mediated by the single-layer β-sheet. We propose that a rigid and stable intervening region between two domains creates an overlap between two folding units and can energetically couple their folding reactions. Copyright © 2018. Published by Elsevier Ltd.

A hybrid MD-kMC algorithm for folding proteins in explicit solvent.

PubMed

Peter, Emanuel Karl; Shea, Joan-Emma

2014-04-14

We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.

Structure of the beta 2 homodimer of bacterial luciferase from Vibrio harveyi: X-ray analysis of a kinetic protein folding trap.

PubMed Central

Thoden, J. B.; Holden, H. M.; Fisher, A. J.; Sinclair, J. F.; Wesenberg, G.; Baldwin, T. O.; Rayment, I.

1997-01-01

Luciferase, as isolated from Vibrio harveyi, is an alpha beta heterodimer. When allowed to fold in the absence of the alpha subunit, either in vitro or in vivo, the beta subunit of enzyme will form a kinetically stable homodimer that does not unfold even after prolonged incubation in 5 M urea at pH 7.0 and 18 degrees C. This form of the beta subunit, arising via kinetic partitioning on the folding pathway, appears to constitute a kinetically trapped alternative to the heterodimeric enzyme (Sinclair JF, Ziegler MM, Baldwin TO. 1994. Kinetic partitioning during protein folding yields multiple native states. Nature Struct Biol 1: 320-326). Here we describe the X-ray crystal structure of the beta 2 homodimer of luciferase from V. harveyi determined and refined at 1.95 A resolution. Crystals employed in the investigational belonged to the orthorhombic space group P2(1)2(1)2(1) with unit cell dimensions of a = 58.8 A, b = 62.0 A, and c = 218.2 A and contained one dimer per asymmetric unit. Like that observed in the functional luciferase alpha beta heterodimer, the major tertiary structural motif of each beta subunit consists of an (alpha/beta)8 barrel (Fisher AJ, Raushel FM, Baldwin TO, Rayment I. 1995. Three-dimensional structure of bacterial luciferase from Vibrio harveyi at 2.4 A resolution. Biochemistry 34: 6581-6586). The root-mean-square deviation of the alpha-carbon coordinates between the beta subunits of the hetero- and homodimers is 0.7 A. This high resolution X-ray analysis demonstrated that "domain" or "loop" swapping has not occurred upon formation of the beta 2 homodimer and thus the stability of the beta 2 species to denaturation cannot be explained in such simple terms. In fact, the subunit:subunit interfaces observed in both the beta 2 homodimer and alpha beta heterodimer are remarkably similar in hydrogen-bonding patterns and buried surface areas. PMID:9007973

Rough energy landscapes in protein folding: dimeric E. coli Trp repressor folds through three parallel channels.

PubMed

Gloss, L M; Simler, B R; Matthews, C R

2001-10-05

The folding mechanism of the dimeric Escherichia coli Trp repressor (TR) is a kinetically complex process that involves three distinguishable stages of development. Following the formation of a partially folded, monomeric ensemble of species, within 5 ms, folding to the native dimer is controlled by three kinetic phases. The rate-limiting step in each phase is either a non-proline isomerization reaction or a dimerization reaction, depending on the final denaturant concentration. Two approaches have been employed to test the previously proposed folding mechanism of TR through three parallel channels: (1) unfolding double-jump experiments demonstrate that all three folding channels lead directly to native dimer; and (2) the differential stabilization of the transition state for the final step in folding and the native dimer, by the addition of salt, shows that all three channels involve isomerization of a dimeric species. A refined model for the folding of Trp repressor is presented, in which all three channels involve a rapid dimerization reaction between partially folded monomers followed by the isomerization of the dimeric intermediates to yield native dimer. The ensemble of partially folded monomers can be captured at equilibrium by low pH; one-dimensional proton NMR spectra at pH 2.5 demonstrate that monomers exist in two distinct, slowly interconverting conformations. These data provide a potential structural explanation for the three-channel folding mechanism of TR: random association of two different monomeric forms, which are distinguished by alternative packing modes of the core dimerization domain and the DNA-binding, helix-turn-helix, domain. One, perhaps both, of these packing modes contains non-native contacts. Copyright 2001 Academic Press.

Exploration of the folding dynamics of human telomeric G-quadruplex with a hybrid atomistic structure-based model

NASA Astrophysics Data System (ADS)

Bian, Yunqiang; Ren, Weitong; Song, Feng; Yu, Jiafeng; Wang, Jihua

2018-05-01

Structure-based models or Gō-like models, which are built from one or multiple particular experimental structures, have been successfully applied to the folding of proteins and RNAs. Recently, a variant termed the hybrid atomistic model advances the description of backbone and side chain interactions of traditional structure-based models, by borrowing the description of local interactions from classical force fields. In this study, we assessed the validity of this model in the folding problem of human telomeric DNA G-quadruplex, where local dihedral terms play important roles. A two-state model was developed and a set of molecular dynamics simulations was conducted to study the folding dynamics of sequence Htel24, which was experimentally validated to adopt two different (3 + 1) hybrid G-quadruplex topologies in K+ solution. Consistent with the experimental observations, the hybrid-1 conformation was found to be more stable and the hybrid-2 conformation was kinetically more favored. The simulations revealed that the hybrid-2 conformation folded in a higher cooperative manner, which may be the reason why it was kinetically more accessible. Moreover, by building a Markov state model, a two-quartet G-quadruplex state and a misfolded state were identified as competing states to complicate the folding process of Htel24. Besides, the simulations also showed that the transition between hybrid-1 and hybrid-2 conformations may proceed an ensemble of hairpin structures. The hybrid atomistic structure-based model reproduced the kinetic partitioning folding dynamics of Htel24 between two different folds, and thus can be used to study the complex folding processes of other G-quadruplex structures.

Learning To Fold Proteins Using Energy Landscape Theory

PubMed Central

Schafer, N.P.; Kim, B.L.; Zheng, W.; Wolynes, P.G.

2014-01-01

This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation. PMID:25308991

Understanding the mechanical properties of DNA origami tiles and controlling the kinetics of their folding and unfolding reconfiguration.

PubMed

Chen, Haorong; Weng, Te-Wei; Riccitelli, Molly M; Cui, Yi; Irudayaraj, Joseph; Choi, Jong Hyun

2014-05-14

DNA origami represents a class of highly programmable macromolecules that can go through conformational changes in response to external signals. Here we show that a two-dimensional origami rectangle can be effectively folded into a short, cylindrical tube by connecting the two opposite edges through the hybridization of linker strands and that this process can be efficiently reversed via toehold-mediated strand displacement. The reconfiguration kinetics was experimentally studied as a function of incubation temperature, initial origami concentration, missing staples, and origami geometry. A kinetic model was developed by introducing the j factor to describe the reaction rates in the cyclization process. We found that the cyclization efficiency (j factor) increases sharply with temperature and depends strongly on the structural flexibility and geometry. A simple mechanical model was used to correlate the observed cyclization efficiency with origami structure details. The mechanical analysis suggests two sources of the energy barrier for DNA origami folding: overcoming global twisting and bending the structure into a circular conformation. It also provides the first semiquantitative estimation of the rigidity of DNA interhelix crossovers, an essential element in structural DNA nanotechnology. This work demonstrates efficient DNA origami reconfiguration, advances our understanding of the dynamics and mechanical properties of self-assembled DNA structures, and should be valuable to the field of DNA nanotechnology.

SeqRate: sequence-based protein folding type classification and rates prediction

PubMed Central

2010-01-01

Background Protein folding rate is an important property of a protein. Predicting protein folding rate is useful for understanding protein folding process and guiding protein design. Most previous methods of predicting protein folding rate require the tertiary structure of a protein as an input. And most methods do not distinguish the different kinetic nature (two-state folding or multi-state folding) of the proteins. Here we developed a method, SeqRate, to predict both protein folding kinetic type (two-state versus multi-state) and real-value folding rate using sequence length, amino acid composition, contact order, contact number, and secondary structure information predicted from only protein sequence with support vector machines. Results We systematically studied the contributions of individual features to folding rate prediction. On a standard benchmark dataset, the accuracy of folding kinetic type classification is 80%. The Pearson correlation coefficient and the mean absolute difference between predicted and experimental folding rates (sec-1) in the base-10 logarithmic scale are 0.81 and 0.79 for two-state protein folders, and 0.80 and 0.68 for three-state protein folders. SeqRate is the first sequence-based method for protein folding type classification and its accuracy of fold rate prediction is improved over previous sequence-based methods. Its performance can be further enhanced with additional information, such as structure-based geometric contacts, as inputs. Conclusions Both the web server and software of predicting folding rate are publicly available at http://casp.rnet.missouri.edu/fold_rate/index.html. PMID:20438647

Kinetic network study of the diversity and temperature dependence of Trp-Cage folding pathways: combining transition path theory with stochastic simulations.

PubMed

Zheng, Weihua; Gallicchio, Emilio; Deng, Nanjie; Andrec, Michael; Levy, Ronald M

2011-02-17

We present a new approach to study a multitude of folding pathways and different folding mechanisms for the 20-residue mini-protein Trp-Cage using the combined power of replica exchange molecular dynamics (REMD) simulations for conformational sampling, transition path theory (TPT) for constructing folding pathways, and stochastic simulations for sampling the pathways in a high dimensional structure space. REMD simulations of Trp-Cage with 16 replicas at temperatures between 270 and 566 K are carried out with an all-atom force field (OPLSAA) and an implicit solvent model (AGBNP). The conformations sampled from all temperatures are collected. They form a discretized state space that can be used to model the folding process. The equilibrium population for each state at a target temperature can be calculated using the weighted-histogram-analysis method (WHAM). By connecting states with similar structures and creating edges satisfying detailed balance conditions, we construct a kinetic network that preserves the equilibrium population distribution of the state space. After defining the folded and unfolded macrostates, committor probabilities (P(fold)) are calculated by solving a set of linear equations for each node in the network and pathways are extracted together with their fluxes using the TPT algorithm. By clustering the pathways into folding "tubes", a more physically meaningful picture of the diversity of folding routes emerges. Stochastic simulations are carried out on the network, and a procedure is developed to project sampled trajectories onto the folding tubes. The fluxes through the folding tubes calculated from the stochastic trajectories are in good agreement with the corresponding values obtained from the TPT analysis. The temperature dependence of the ensemble of Trp-Cage folding pathways is investigated. Above the folding temperature, a large number of diverse folding pathways with comparable fluxes flood the energy landscape. At low temperature

Extreme Folding

NASA Astrophysics Data System (ADS)

Demaine, Erik

2012-02-01

Our understanding of the mathematics and algorithms behind paper folding, and geometric folding in general, has increased dramatically over the past several years. These developments have found a surprisingly broad range of applications. In the art of origami, it has helped spur the technical origami revolution. In engineering and science, it has helped solve problems in areas such as manufacturing, robotics, graphics, and protein folding. On the recreational side, it has led to new kinds of folding puzzles and magic. I will give an overview of the mathematics and algorithms of folding, with a focus on new mathematics and sculpture.

How Four Scientists Integrate Thermodynamic and Kinetic Theory, Context, Analogies, and Methods in Protein-Folding and Dynamics Research: Implications for Biochemistry Instruction

ERIC Educational Resources Information Center

Jeffery, Kathleen A.; Pelaez, Nancy; Anderson, Trevor R.

2018-01-01

To keep biochemistry instruction current and relevant, it is crucial to expose students to cutting-edge scientific research and how experts reason about processes governed by thermodynamics and kinetics such as protein folding and dynamics. This study focuses on how experts explain their research into this topic with the intention of informing…

Impact of hydrodynamic interactions on protein folding rates depends on temperature

NASA Astrophysics Data System (ADS)

Zegarra, Fabio C.; Homouz, Dirar; Eliaz, Yossi; Gasic, Andrei G.; Cheung, Margaret S.

2018-03-01

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue α /β chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue β -barrel α -spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a "crossover" behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

Influence of Glu/Arg, Asp/Arg, and Glu/Lys Salt Bridges on α-Helical Stability and Folding Kinetics.

PubMed

Meuzelaar, Heleen; Vreede, Jocelyne; Woutersen, Sander

2016-06-07

Using a combination of ultraviolet circular dichroism, temperature-jump transient-infrared spectroscopy, and molecular dynamics simulations, we investigate the effect of salt bridges between different types of charged amino-acid residue pairs on α-helix folding. We determine the stability and the folding and unfolding rates of 12 alanine-based α-helical peptides, each of which has a nearly identical composition containing three pairs of positively and negatively charged residues (either Glu(-)/Arg(+), Asp(-)/Arg(+), or Glu(-)/Lys(+)). Within each set of peptides, the distance and order of the oppositely charged residues in the peptide sequence differ, such that they have different capabilities of forming salt bridges. Our results indicate that stabilizing salt bridges (in which the interacting residues are spaced and ordered such that they favor helix formation) speed up α-helix formation by up to 50% and slow down the unfolding of the α-helix, whereas salt bridges with an unfavorable geometry have the opposite effect. Comparing the peptides with different types of charge pairs, we observe that salt bridges between side chains of Glu(-) and Arg(+) are most favorable for the speed of folding, probably because of the larger conformational space of the salt-bridging Glu(-)/Arg(+) rotamer pairs compared to Asp(-)/Arg(+) and Glu(-)/Lys(+). We speculate that the observed impact of salt bridges on the folding kinetics might explain why some proteins contain salt bridges that do not stabilize the final, folded conformation. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Influence of the native topology on the folding barrier for small proteins

NASA Astrophysics Data System (ADS)

Prieto, Lidia; Rey, Antonio

2007-11-01

The possibility of downhill instead of two-state folding for proteins has been a very controversial topic which arose from recent experimental studies. From the theoretical side, this question has also been accomplished in different ways. Given the experimental observation that a relationship exists between the native structure topology of a protein and the kinetic and thermodynamic properties of its folding process, Gō-type potentials are an appropriate way to approach this problem. In this work, we employ an interaction potential from this family to get a better insight on the topological characteristics of the native state that may somehow determine the presence of a thermodynamic barrier in the folding pathway. The results presented here show that, indeed, the native topology of a small protein has a great influence on its folding behavior, mostly depending on the proportion of local and long range contacts the protein has in its native structure. Furthermore, when all the interactions present contribute in a balanced way, the transition results to be cooperative. Otherwise, the tendency to a downhill folding behavior increases.

Folding and unfolding single RNA molecules under tension

PubMed Central

Woodside, Michael T; García-García, Cuauhtémoc; Block, Steven M

2010-01-01

Single-molecule force spectroscopy constitutes a powerful method for probing RNA folding: it allows the kinetic, energetic, and structural properties of intermediate and transition states to be determined quantitatively, yielding new insights into folding pathways and energy landscapes. Recent advances in experimental and theoretical methods, including fluctuation theorems, kinetic theories, novel force clamps, and ultrastable instruments, have opened new avenues for study. These tools have been used to probe folding in simple model systems, for example, RNA and DNA hairpins. Knowledge gained from such systems is helping to build our understanding of more complex RNA structures composed of multiple elements, as well as how nucleic acids interact with proteins involved in key cellular activities, such as transcription and translation. PMID:18786653

Ab initio RNA folding by discrete molecular dynamics: From structure prediction to folding mechanisms

PubMed Central

Ding, Feng; Sharma, Shantanu; Chalasani, Poornima; Demidov, Vadim V.; Broude, Natalia E.; Dokholyan, Nikolay V.

2008-01-01

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 Å deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNAPhe, pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses. PMID:18456842

Folding mechanism of an extremely thermostable (βα)(8)-barrel enzyme: a high kinetic barrier protects the protein from denaturation.

PubMed

Carstensen, Linn; Zoldák, Gabriel; Schmid, Franz-Xaver; Sterner, Reinhard

2012-04-24

HisF, the cyclase subunit of imidazole glycerol phosphate synthase (ImGPS) from Thermotoga maritima, is an extremely thermostable (βα)(8)-barrel protein. We elucidated the unfolding and refolding mechanism of HisF. Its unfolding transition is reversible and adequately described by the two-state model, but 6 weeks is necessary to reach equilibrium (at 25 °C). During refolding, initially a burst-phase off-pathway intermediate is formed. The subsequent productive folding occurs in two kinetic phases with time constants of ~3 and ~20 s. They reflect a sequential process via an on-pathway intermediate, as revealed by stopped-flow double-mixing experiments. The final step leads to native HisF, which associates with the glutaminase subunit HisH to form the functional ImGPS complex. The conversion of the on-pathway intermediate to the native protein results in a 10(6)-fold increase of the time constant for unfolding from 89 ms to 35 h (at 4.0 M GdmCl) and thus establishes a high energy barrier to denaturation. We conclude that the extra stability of HisF is used for kinetic protection against unfolding. In its refolding mechanism, HisF resembles other (βα)(8)-barrel proteins.

The folding pathways and thermodynamics of semiflexible polymers

NASA Astrophysics Data System (ADS)

Wu, Jing; Cheng, Chenqian; Liu, Gaoyuan; Zhang, Ping; Chen, Tao

2018-05-01

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Kinetic and thermodynamic framework for P4-P6 RNA reveals tertiary motif modularity and modulation of the folding preferred pathway

PubMed Central

Bisaria, Namita; Greenfeld, Max; Limouse, Charles; Pavlichin, Dmitri S.; Mabuchi, Hideo; Herschlag, Daniel

2016-01-01

The past decade has seen a wealth of 3D structural information about complex structured RNAs and identification of functional intermediates. Nevertheless, developing a complete and predictive understanding of the folding and function of these RNAs in biology will require connection of individual rate and equilibrium constants to structural changes that occur in individual folding steps and further relating these steps to the properties and behavior of isolated, simplified systems. To accomplish these goals we used the considerable structural knowledge of the folded, unfolded, and intermediate states of P4-P6 RNA. We enumerated structural states and possible folding transitions and determined rate and equilibrium constants for the transitions between these states using single-molecule FRET with a series of mutant P4-P6 variants. Comparisons with simplified constructs containing an isolated tertiary contact suggest that a given tertiary interaction has a stereotyped rate for breaking that may help identify structural transitions within complex RNAs and simplify the prediction of folding kinetics and thermodynamics for structured RNAs from their parts. The preferred folding pathway involves initial formation of the proximal tertiary contact. However, this preference was only ∼10 fold and could be reversed by a single point mutation, indicating that a model akin to a protein-folding contact order model will not suffice to describe RNA folding. Instead, our results suggest a strong analogy with a modified RNA diffusion-collision model in which tertiary elements within preformed secondary structures collide, with the success of these collisions dependent on whether the tertiary elements are in their rare binding-competent conformations. PMID:27493222

Kinetic Network Study of the Diversity and Temperature Dependence of Trp-Cage Folding Pathways: Combining Transition Path Theory with Stochastic Simulations

PubMed Central

Zheng, Weihua; Gallicchio, Emilio; Deng, Nanjie; Andrec, Michael; Levy, Ronald M.

2011-01-01

We present a new approach to study a multitude of folding pathways and different folding mechanisms for the 20-residue mini-protein Trp-Cage using the combined power of replica exchange molecular dynamics (REMD) simulations for conformational sampling, Transition Path Theory (TPT) for constructing folding pathways and stochastic simulations for sampling the pathways in a high dimensional structure space. REMD simulations of Trp-Cage with 16 replicas at temperatures between 270K and 566K are carried out with an all-atom force field (OPLSAA) and an implicit solvent model (AGBNP). The conformations sampled from all temperatures are collected. They form a discretized state space that can be used to model the folding process. The equilibrium population for each state at a target temperature can be calculated using the Weighted-Histogram-Analysis Method (WHAM). By connecting states with similar structures and creating edges satisfying detailed balance conditions, we construct a kinetic network that preserves the equilibrium population distribution of the state space. After defining the folded and unfolded macrostates, committor probabilities (Pfold) are calculated by solving a set of linear equations for each node in the network and pathways are extracted together with their fluxes using the TPT algorithm. By clustering the pathways into folding “tubes”, a more physically meaningful picture of the diversity of folding routes emerges. Stochastic simulations are carried out on the network and a procedure is developed to project sampled trajectories onto the folding tubes. The fluxes through the folding tubes calculated from the stochastic trajectories are in good agreement with the corresponding values obtained from the TPT analysis. The temperature dependence of the ensemble of Trp-Cage folding pathways is investigated. Above the folding temperature, a large number of diverse folding pathways with comparable fluxes flood the energy landscape. At low temperature

Self-catalyzed growth of S layers via an amorphous-to-crystalline transition limited by folding kinetics.

PubMed

Chung, Sungwook; Shin, Seong-Ho; Bertozzi, Carolyn R; De Yoreo, James J

2010-09-21

The importance of nonclassical, multistage crystallization pathways is increasingly evident from theoretical studies on colloidal systems and experimental investigations of proteins and biomineral phases. Although theoretical predictions suggest that proteins follow these pathways as a result of fluctuations that create unstable dense-liquid states, microscopic studies indicate these states are long-lived. Using in situ atomic force microscopy to follow 2D assembly of S-layer proteins on supported lipid bilayers, we have obtained a molecular-scale picture of multistage protein crystallization that reveals the importance of conformational transformations in directing the pathway of assembly. We find that monomers with an extended conformation first form a mobile adsorbed phase, from which they condense into amorphous clusters. These clusters undergo a phase transition through S-layer folding into crystalline clusters composed of compact tetramers. Growth then proceeds by formation of new tetramers exclusively at cluster edges, implying tetramer formation is autocatalytic. Analysis of the growth kinetics leads to a quantitative model in which tetramer creation is rate limiting. However, the estimated barrier is much smaller than expected for folding of isolated S-layer proteins, suggesting an energetic rationale for this multistage pathway.

FROM FOLDING THEORIES TO FOLDING PROTEINS: A Review and Assessment of Simulation Studies of Protein Folding and Unfolding

NASA Astrophysics Data System (ADS)

Shea, Joan-Emma; Brooks, Charles L., III

2001-10-01

Beginning with simplified lattice and continuum "minimalist" models and progressing to detailed atomic models, simulation studies have augmented and directed development of the modern landscape perspective of protein folding. In this review we discuss aspects of detailed atomic simulation methods applied to studies of protein folding free energy surfaces, using biased-sampling free energy methods and temperature-induced protein unfolding. We review studies from each on systems of particular experimental interest and assess the strengths and weaknesses of each approach in the context of "exact" results for both free energies and kinetics of a minimalist model for a beta-barrel protein. We illustrate in detail how each approach is implemented and discuss analysis methods that have been developed as components of these studies. We describe key insights into the relationship between protein topology and the folding mechanism emerging from folding free energy surface calculations. We further describe the determination of detailed "pathways" and models of folding transition states that have resulted from unfolding studies. Our assessment of the two methods suggests that both can provide, often complementary, details of folding mechanism and thermodynamics, but this success relies on (a) adequate sampling of diverse conformational regions for the biased-sampling free energy approach and (b) many trajectories at multiple temperatures for unfolding studies. Furthermore, we find that temperature-induced unfolding provides representatives of folding trajectories only when the topology and sequence (energy) provide a relatively funneled landscape and "off-pathway" intermediates do not exist.

Trp zipper folding kinetics by molecular dynamics and temperature-jump spectroscopy

NASA Astrophysics Data System (ADS)

Snow, Christopher D.; Qiu, Linlin; Du, Deguo; Gai, Feng; Hagen, Stephen J.; Pande, Vijay S.

2004-03-01

We studied the microsecond folding dynamics of three hairpins (Trp zippers 1-3, TZ1-TZ3) by using temperature-jump fluorescence and atomistic molecular dynamics in implicit solvent. In addition, we studied TZ2 by using time-resolved IR spectroscopy. By using distributed computing, we obtained an aggregate simulation time of 22 ms. The simulations included 150, 212, and 48 folding events at room temperature for TZ1, TZ2, and TZ3, respectively. The all-atom optimized potentials for liquid simulations (OPLSaa) potential set predicted TZ1 and TZ2 properties well; the estimated folding rates agreed with the experimentally determined folding rates and native conformations were the global potential-energy minimum. The simulations also predicted reasonable unfolding activation enthalpies. This work, directly comparing large simulated folding ensembles with multiple spectroscopic probes, revealed both the surprising predictive ability of current models as well as their shortcomings. Specifically, for TZ1-TZ3, OPLS for united atom models had a nonnative free-energy minimum, and the folding rate for OPLSaa TZ3 was sensitive to the initial conformation. Finally, we characterized the transition state; all TZs fold by means of similar, native-like transition-state conformations.

Accurate prediction of cellular co-translational folding indicates proteins can switch from post- to co-translational folding

PubMed Central

Nissley, Daniel A.; Sharma, Ajeet K.; Ahmed, Nabeel; Friedrich, Ulrike A.; Kramer, Günter; Bukau, Bernd; O'Brien, Edward P.

2016-01-01

The rates at which domains fold and codons are translated are important factors in determining whether a nascent protein will co-translationally fold and function or misfold and malfunction. Here we develop a chemical kinetic model that calculates a protein domain's co-translational folding curve during synthesis using only the domain's bulk folding and unfolding rates and codon translation rates. We show that this model accurately predicts the course of co-translational folding measured in vivo for four different protein molecules. We then make predictions for a number of different proteins in yeast and find that synonymous codon substitutions, which change translation-elongation rates, can switch some protein domains from folding post-translationally to folding co-translationally—a result consistent with previous experimental studies. Our approach explains essential features of co-translational folding curves and predicts how varying the translation rate at different codon positions along a transcript's coding sequence affects this self-assembly process. PMID:26887592

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures

Constructive methods of invariant manifolds for kinetic problems

NASA Astrophysics Data System (ADS)

Gorban, Alexander N.; Karlin, Iliya V.; Zinovyev, Andrei Yu.

2004-06-01

The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space ( the invariance equation). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn∼1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.

Trp zipper folding kinetics by molecular dynamics and temperature-jump spectroscopy

PubMed Central

Snow, Christopher D.; Qiu, Linlin; Du, Deguo; Gai, Feng; Hagen, Stephen J.; Pande, Vijay S.

2004-01-01

We studied the microsecond folding dynamics of three β hairpins (Trp zippers 1–3, TZ1–TZ3) by using temperature-jump fluorescence and atomistic molecular dynamics in implicit solvent. In addition, we studied TZ2 by using time-resolved IR spectroscopy. By using distributed computing, we obtained an aggregate simulation time of 22 ms. The simulations included 150, 212, and 48 folding events at room temperature for TZ1, TZ2, and TZ3, respectively. The all-atom optimized potentials for liquid simulations (OPLSaa) potential set predicted TZ1 and TZ2 properties well; the estimated folding rates agreed with the experimentally determined folding rates and native conformations were the global potential-energy minimum. The simulations also predicted reasonable unfolding activation enthalpies. This work, directly comparing large simulated folding ensembles with multiple spectroscopic probes, revealed both the surprising predictive ability of current models as well as their shortcomings. Specifically, for TZ1–TZ3, OPLS for united atom models had a nonnative free-energy minimum, and the folding rate for OPLSaa TZ3 was sensitive to the initial conformation. Finally, we characterized the transition state; all TZs fold by means of similar, native-like transition-state conformations. PMID:15020773

Atomic-level description of ubiquitin folding

PubMed Central

Piana, Stefano; Lindorff-Larsen, Kresten; Shaw, David E.

2013-01-01

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins. PMID:23503848

Does proline isomerization shape the folding funnel of the wild type and mutant staphylococcal nuclease?

NASA Astrophysics Data System (ADS)

Tsong, Tian Yow; Su, Zheng-Ding

1999-10-01

Cis/trans isomerization of proline residues is known to exhibit high activation energies. These kinetic barriers often dominate the energy landscape of protein folding. There are 6 proline residues (at positions 11, 31, 42, 47, 56 and 117) in staphylococcal nuclease (SNase) [EC 3.1.31.1]. Stopped-flow CD222nm measuring the evolution of the secondary structure of protein has detected 5 kinetic barriers in SNase folding (ΔG≠ for τfr<15, τf1 16.9, τf2 18.5, τf3 19.5, and τfs 21.8 kcal/mol) and 3 kinetic barriers in unfolding (ΔG≠ for τur<15, τu1 17.4, τus 21.6 kcal/mol). To investigate systematically how individual proline residues and 6 proline residues in toto can shape the folding funnel we have expediently constructed 7 proline mutants for study. They are 6 single-proline-substituted mutants (P11A, P31A, P42A, P47A, P56A and P117A) and 1 proline-free mutant (PallA). Study of equilibrium folding/unfolding and stopped-flow kinetics of the wildtype and the 7 mutants of SNase have allowed us to identify sources of 3 main kinetic barriers in the SNase folding. The highest barrier (ΔG≠=21.8 kcal) belongs to the cis/trans isomerization of Pro117. The next barrier (ΔG≠=19.5 kcal) involves synergetic effects of proline residues which limits the rate of folding of the oligonucleotide binding (OB) domain in all 7 proline-containing SNase. For the proline-free mutant (PallA) the OB domain folds rapidly. Furthermore, we have found that the equilibrium folding/unfolding properties of these proline mutants are remarkably similar to that of the wildtype despite their startlingly different folding/unfolding kinetics. These results lead us to conclude that while free energy of folding (ΔGF=-4.5 kcal/mol) provides the driving force, it is the activation energy that forms a conduit or shapes a kinetic funnel for SNase folding. The landscape for SNase folding is extremely rugged. Data support our previously proposed Least Activation Path (LAP) model for protein

Finessing filter scarcity problem in face recognition via multi-fold filter convolution

NASA Astrophysics Data System (ADS)

Low, Cheng-Yaw; Teoh, Andrew Beng-Jin

2017-06-01

The deep convolutional neural networks for face recognition, from DeepFace to the recent FaceNet, demand a sufficiently large volume of filters for feature extraction, in addition to being deep. The shallow filter-bank approaches, e.g., principal component analysis network (PCANet), binarized statistical image features (BSIF), and other analogous variants, endure the filter scarcity problem that not all PCA and ICA filters available are discriminative to abstract noise-free features. This paper extends our previous work on multi-fold filter convolution (ℳ-FFC), where the pre-learned PCA and ICA filter sets are exponentially diversified by ℳ folds to instantiate PCA, ICA, and PCA-ICA offspring. The experimental results unveil that the 2-FFC operation solves the filter scarcity state. The 2-FFC descriptors are also evidenced to be superior to that of PCANet, BSIF, and other face descriptors, in terms of rank-1 identification rate (%).

Identification of kinetically hot residues in proteins.

PubMed Central

Demirel, M. C.; Atilgan, A. R.; Jernigan, R. L.; Erman, B.; Bahar, I.

1998-01-01

A number of recent studies called attention to the presence of kinetically important residues underlying the formation and stabilization of folding nuclei in proteins, and to the possible existence of a correlation between conserved residues and those participating in the folding nuclei. Here, we use the Gaussian network model (GNM), which recently proved useful in describing the dynamic characteristics of proteins for identifying the kinetically hot residues in folded structures. These are the residues involved in the highest frequency fluctuations near the native state coordinates. Their high frequency is a manifestation of the steepness of the energy landscape near their native state positions. The theory is applied to a series of proteins whose kinetically important residues have been extensively explored: chymotrypsin inhibitor 2, cytochrome c, and related C2 proteins. Most of the residues previously pointed out to underlie the folding process of these proteins, and to be critically important for the stabilization of the tertiary fold, are correctly identified, indicating a correlation between the kinetic hot spots and the early forming structural elements in proteins. Additionally, a strong correlation between kinetically hot residues and loci of conserved residues is observed. Finally, residues that may be important for the stability of the tertiary structure of CheY are proposed. PMID:9865946

Integration of Inhibition Kinetics and Molecular Dynamics Simulations: A Urea-Mediated Folding Study on Acetaldehyde Dehydrogenase 1.

PubMed

Xu, Yingying; Lee, Jinhyuk; Lü, Zhi-Rong; Mu, Hang; Zhang, Qian; Park, Yong-Doo

2016-07-01

Understanding the mechanism of acetaldehyde dehydrogenase 1 (ALDH1) folding is important because this enzyme is directly involved in several types of cancers and other diseases. We investigated the urea-mediated unfolding of ALDH1 by integrating kinetic inhibition studies with computational molecular dynamics (MD) simulations. Conformational changes in the enzyme structure were also analyzed using intrinsic and 1-anilinonaphthalene-8-sulfonate (ANS)-binding fluorescence measurements. Kinetic studies revealed that the direct binding of urea to ALDH1 induces inactivation of ALDH1 in a manner of mixed-type inhibition. Tertiary structural changes associated with regional hydrophobic exposure of the active site were observed. The urea binding regions on ALDH1 were predicted by docking simulations and were partly shared with active site residues of ALDH1 and with interface residues of the oligomerization domain for tetramer formation. The docking results suggest that urea prevents formation of the ALDH1 normal shape for the tetramer state as well as entrance of the substrate into the active site. Our study provides insight into the structural changes that accompany urea-mediated unfolding of ALDH1 and the catalytic role associated with conformational changes.

Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations.

PubMed

Biyun, Shi; Cho, Samuel S; Thirumalai, D

2011-12-21

Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single

Protein folding by NMR.

PubMed

Zhuravleva, Anastasia; Korzhnev, Dmitry M

2017-05-01

Protein folding is a highly complex process proceeding through a number of disordered and partially folded nonnative states with various degrees of structural organization. These transiently and sparsely populated species on the protein folding energy landscape play crucial roles in driving folding toward the native conformation, yet some of these nonnative states may also serve as precursors for protein misfolding and aggregation associated with a range of devastating diseases, including neuro-degeneration, diabetes and cancer. Therefore, in vivo protein folding is often reshaped co- and post-translationally through interactions with the ribosome, molecular chaperones and/or other cellular components. Owing to developments in instrumentation and methodology, solution NMR spectroscopy has emerged as the central experimental approach for the detailed characterization of the complex protein folding processes in vitro and in vivo. NMR relaxation dispersion and saturation transfer methods provide the means for a detailed characterization of protein folding kinetics and thermodynamics under native-like conditions, as well as modeling high-resolution structures of weakly populated short-lived conformational states on the protein folding energy landscape. Continuing development of isotope labeling strategies and NMR methods to probe high molecular weight protein assemblies, along with advances of in-cell NMR, have recently allowed protein folding to be studied in the context of ribosome-nascent chain complexes and molecular chaperones, and even inside living cells. Here we review solution NMR approaches to investigate the protein folding energy landscape, and discuss selected applications of NMR methodology to studying protein folding in vitro and in vivo. Together, these examples highlight a vast potential of solution NMR in providing atomistic insights into molecular mechanisms of protein folding and homeostasis in health and disease. Copyright © 2016 Elsevier B.V. All

Protein folding and misfolding: mechanism and principles

PubMed Central

Englander, S. Walter; Mayne, Leland; Krishna, Mallela M. G.

2012-01-01

Two fundamentally different views of how proteins fold are now being debated. Do proteins fold through multiple unpredictable routes directed only by the energetically downhill nature of the folding landscape or do they fold through specific intermediates in a defined pathway that systematically puts predetermined pieces of the target native protein into place? It has now become possible to determine the structure of protein folding intermediates, evaluate their equilibrium and kinetic parameters, and establish their pathway relationships. Results obtained for many proteins have serendipitously revealed a new dimension of protein structure. Cooperative structural units of the native protein, called foldons, unfold and refold repeatedly even under native conditions. Much evidence obtained by hydrogen exchange and other methods now indicates that cooperative foldon units and not individual amino acids account for the unit steps in protein folding pathways. The formation of foldons and their ordered pathway assembly systematically puts native-like foldon building blocks into place, guided by a sequential stabilization mechanism in which prior native-like structure templates the formation of incoming foldons with complementary structure. Thus the same propensities and interactions that specify the final native state, encoded in the amino-acid sequence of every protein, determine the pathway for getting there. Experimental observations that have been interpreted differently, in terms of multiple independent pathways, appear to be due to chance misfolding errors that cause different population fractions to block at different pathway points, populate different pathway intermediates, and fold at different rates. This paper summarizes the experimental basis for these three determining principles and their consequences. Cooperative native-like foldon units and the sequential stabilization process together generate predetermined stepwise pathways. Optional misfolding errors

SVM-Fold: a tool for discriminative multi-class protein fold and superfamily recognition

PubMed Central

Melvin, Iain; Ie, Eugene; Kuang, Rui; Weston, Jason; Stafford, William Noble; Leslie, Christina

2007-01-01

Background Predicting a protein's structural class from its amino acid sequence is a fundamental problem in computational biology. Much recent work has focused on developing new representations for protein sequences, called string kernels, for use with support vector machine (SVM) classifiers. However, while some of these approaches exhibit state-of-the-art performance at the binary protein classification problem, i.e. discriminating between a particular protein class and all other classes, few of these studies have addressed the real problem of multi-class superfamily or fold recognition. Moreover, there are only limited software tools and systems for SVM-based protein classification available to the bioinformatics community. Results We present a new multi-class SVM-based protein fold and superfamily recognition system and web server called SVM-Fold, which can be found at . Our system uses an efficient implementation of a state-of-the-art string kernel for sequence profiles, called the profile kernel, where the underlying feature representation is a histogram of inexact matching k-mer frequencies. We also employ a novel machine learning approach to solve the difficult multi-class problem of classifying a sequence of amino acids into one of many known protein structural classes. Binary one-vs-the-rest SVM classifiers that are trained to recognize individual structural classes yield prediction scores that are not comparable, so that standard "one-vs-all" classification fails to perform well. Moreover, SVMs for classes at different levels of the protein structural hierarchy may make useful predictions, but one-vs-all does not try to combine these multiple predictions. To deal with these problems, our method learns relative weights between one-vs-the-rest classifiers and encodes information about the protein structural hierarchy for multi-class prediction. In large-scale benchmark results based on the SCOP database, our code weighting approach significantly improves

Electrostatically Accelerated Coupled Binding and Folding of Intrinsically Disordered Proteins

PubMed Central

Ganguly, Debabani; Otieno, Steve; Waddell, Brett; Iconaru, Luigi; Kriwacki, Richard W.; Chen, Jianhan

2012-01-01

Intrinsically disordered proteins (IDPs) are now recognized to be prevalent in biology, and many potential functional benefits have been discussed. However, the frequent requirement of peptide folding in specific interactions of IDPs could impose a kinetic bottleneck, which could be overcome only by efficient folding upon encounter. Intriguingly, existing kinetic data suggest that specific binding of IDPs is generally no slower than that of globular proteins. Here, we exploited the cell cycle regulator p27Kip1 (p27) as a model system to understand how IDPs might achieve efficient folding upon encounter for facile recognition. Combining experiments and coarse-grained modeling, we demonstrate that long-range electrostatic interactions between enriched charges on p27 and near its binding site on cyclin A not only enhance the encounter rate (i.e., electrostatic steering), but also promote folding-competent topologies in the encounter complexes, allowing rapid subsequent formation of short-range native interactions en route to the specific complex. In contrast, nonspecific hydrophobic interactions, while hardly affecting the encounter rate, can significantly reduce the efficiency of folding upon encounter and lead to slower binding kinetics. Further analysis of charge distributions in a set of known IDP complexes reveals that, although IDP binding sites tend to be more hydrophobic compared to the rest of the target surface, their vicinities are frequently enriched with charges to complement those on IDPs. This observation suggests that electrostatically accelerated encounter and induced folding might represent a prevalent mechanism for promoting facile IDP recognition. PMID:22721951

Proline Can Have Opposite Effects on Fast and Slow Protein Folding Phases

PubMed Central

Osváth, Szabolcs; Gruebele, Martin

2003-01-01

Proline isomerization is well known to cause additional slow phases during protein refolding. We address a new question: does the presence of prolines significantly affect the very fast kinetics that lead to the formation of folding intermediates? We examined both the very slow (10–100 min) and very fast (4 μs–2.5 ms) folding kinetics of the two-domain enzyme yeast phosphoglycerate kinase by temperature-jump relaxation. Phosphoglycerate kinase contains a conserved cis-proline in position 204, in addition to several trans-prolines. Native cis-prolines have the largest effect on folding kinetics because the unfolded state favors trans isomerization, so we compared the kinetics of a P204H mutant with the wild-type as a proof of principle. The presence of Pro-204 causes an additional slow phase upon refolding from the cold denatured state, as reported in the literature. Contrary to this, the fast folding events are sped up in the presence of the cis-proline, probably by restriction of the conformational space accessible to the molecule. The wild-type and Pro204His mutant would be excellent models for off-lattice simulations probing the effects of conformational restriction on short timescales. PMID:12885665

How Fast is Collapse of Proteins During Folding?

NASA Astrophysics Data System (ADS)

Chahine, J.; Onuchic, J. N.; Socci, N. D.

1998-03-01

Recent experiments in fast folding proteins are now starting to address the question of how fast is collapse relative to the total folding time. Using minimalist models, we are able to investigate the way in which different scenarios of folding can arise depending on the interplay between the collapse order parameter and the order parameter sensitive to specific tertiary contacts. Most of our earlier studies have focused on the limit that collapse is very fast compared to the total folding time. In this work we focus on the opposite limit, i.e., at the folding temperature, collapse and folding occurs simultaneously. The folding mechanism becomes very different in this limit. Particularly, the non-specific collapse transition, that occurs at temperatures higher than the folding temperature for the fast collapse limit, now occurs between the folding and the glass temperature. We show how this transition can be identified and its consequences for the folding kinetics.

Hidden complexity of free energy surfaces for peptide (protein) folding.

PubMed

Krivov, Sergei V; Karplus, Martin

2004-10-12

An understanding of the thermodynamics and kinetics of protein folding requires a knowledge of the free energy surface governing the motion of the polypeptide chain. Because of the many degrees of freedom involved, surfaces projected on only one or two progress variables are generally used in descriptions of the folding reaction. Such projections result in relatively smooth surfaces, but they could mask the complexity of the unprojected surface. Here we introduce an approach to determine the actual (unprojected) free energy surface and apply it to the second beta-hairpin of protein G, which has been used as a model system for protein folding. The surface is represented by a disconnectivity graph calculated from a long equilibrium folding-unfolding trajectory. The denatured state is found to have multiple low free energy basins. Nevertheless, the peptide shows exponential kinetics in folding to the native basin. Projected surfaces obtained from the present analysis have a simple form in agreement with other studies of the beta-hairpin. The hidden complexity found for the beta-hairpin surface suggests that the standard funnel picture of protein folding should be revisited.

Electrostatically Accelerated Encounter and Folding for Facile Recognition of Intrinsically Disordered Proteins

PubMed Central

Ganguly, Debabani; Zhang, Weihong; Chen, Jianhan

2013-01-01

Achieving facile specific recognition is essential for intrinsically disordered proteins (IDPs) that are involved in cellular signaling and regulation. Consideration of the physical time scales of protein folding and diffusion-limited protein-protein encounter has suggested that the frequent requirement of protein folding for specific IDP recognition could lead to kinetic bottlenecks. How IDPs overcome such potential kinetic bottlenecks to viably function in signaling and regulation in general is poorly understood. Our recent computational and experimental study of cell-cycle regulator p27 (Ganguly et al., J. Mol. Biol. (2012)) demonstrated that long-range electrostatic forces exerted on enriched charges of IDPs could accelerate protein-protein encounter via “electrostatic steering” and at the same time promote “folding-competent” encounter topologies to enhance the efficiency of IDP folding upon encounter. Here, we further investigated the coupled binding and folding mechanisms and the roles of electrostatic forces in the formation of three IDP complexes with more complex folded topologies. The surface electrostatic potentials of these complexes lack prominent features like those observed for the p27/Cdk2/cyclin A complex to directly suggest the ability of electrostatic forces to facilitate folding upon encounter. Nonetheless, similar electrostatically accelerated encounter and folding mechanisms were consistently predicted for all three complexes using topology-based coarse-grained simulations. Together with our previous analysis of charge distributions in known IDP complexes, our results support a prevalent role of electrostatic interactions in promoting efficient coupled binding and folding for facile specific recognition. These results also suggest that there is likely a co-evolution of IDP folded topology, charge characteristics, and coupled binding and folding mechanisms, driven at least partially by the need to achieve fast association kinetics for

How Does Your Protein Fold? Elucidating the Apomyoglobin Folding Pathway

PubMed Central

Dyson, H. Jane; Wright, Peter E.

2017-01-01

, and the conformational ensembles formed in the presence of denaturing agents and low pH can be characterized as models for the unfolded states of the protein. Newer NMR techniques such as measurement of residual dipolar couplings in the various partly folded states, and relaxation dispersion measurements to probe invisible states present at low concentrations, have contributed to providing a detailed picture of the apomyoglobin folding pathway. The research summarized in this review was aimed at characterizing and comparing the equilibrium and kinetic intermediates both structurally and dynamically, as well as delineating the complete folding pathway at a residue-specific level, in order to answer the question “What is it about the amino acid sequence that causes each molecule in the unfolded protein ensemble to start folding, and, once started, to proceed towards the formation of the correctly folded three-dimensional structure?” PMID:28032989

Understanding the kinetic mechanism of RNA single base pair formation

PubMed Central

Xu, Xiaojun; Yu, Tao; Chen, Shi-Jie

2016-01-01

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model. PMID:26699466

Numerical impact simulation of gradually increased kinetic energy transfer has the potential to break up folded protein structures resulting in cytotoxic brain tissue edema.

PubMed

von Holst, Hans; Li, Xiaogai

2013-07-01

Although the consequences of traumatic brain injury (TBI) and its treatment have been improved, there is still a substantial lack of understanding the mechanisms. Numerical simulation of the impact can throw further lights on site and mechanism of action. A finite element model of the human head and brain tissue was used to simulate TBI. The consequences of gradually increased kinetic energy transfer was analyzed by evaluating the impact intracranial pressure (ICP), strain level, and their potential influences on binding forces in folded protein structures. The gradually increased kinetic energy was found to have the potential to break apart bonds of Van der Waals in all impacts and hydrogen bonds at simulated impacts from 6 m/s and higher, thereby superseding the energy in folded protein structures. Further, impacts below 6 m/s showed none or very slight increase in impact ICP and strain levels, whereas impacts of 6 m/s or higher showed a gradual increase of the impact ICP and strain levels reaching over 1000 KPa and over 30%, respectively. The present simulation study shows that the free kinetic energy transfer, impact ICP, and strain levels all have the potential to initiate cytotoxic brain tissue edema by unfolding protein structures. The definition of mild, moderate, and severe TBI should thus be looked upon as the same condition and separated only by a gradual severity of impact.

How cooperative are protein folding and unfolding transitions?

PubMed Central

Malhotra, Pooja

2016-01-01

Abstract A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding. PMID:27522064

Folding of multidomain proteins: biophysical consequences of tethering even in apparently independent folding.

PubMed

Arviv, Oshrit; Levy, Yaakov

2012-12-01

Most eukaryotic and a substantial fraction of prokaryotic proteins are composed of more than one domain. The tethering of these evolutionary, structural, and functional units raises, among others, questions regarding the folding process of conjugated domains. Studying the folding of multidomain proteins in silico enables one to identify and isolate the tethering-induced biophysical determinants that govern crosstalks generated between neighboring domains. For this purpose, we carried out coarse-grained and atomistic molecular dynamics simulations of two two-domain constructs from the immunoglobulin-like β-sandwich fold. Each of these was experimentally shown to behave as the "sum of its parts," that is, the thermodynamic and kinetic folding behavior of the constituent domains of these constructs seems to occur independently, with the folding of each domain uncoupled from the folding of its partner in the two-domain construct. We show that the properties of the individual domains can be significantly affected by conjugation to another domain. The tethering may be accompanied by stabilizing as well as destabilizing factors whose magnitude depends on the size of the interface, the length, and the flexibility of the linker, and the relative stability of the domains. Accordingly, the folding of a multidomain protein should not be viewed as the sum of the folding patterns of each of its parts, but rather, it involves abrogating several effects that lead to this outcome. An imbalance between these effects may result in either stabilization or destabilization owing to the tethering. Copyright © 2012 Wiley Periodicals, Inc.

On the Role of Entropy in the Protein Folding Process

NASA Astrophysics Data System (ADS)

Hoppe, Travis

2011-12-01

A protein's ultimate function and activity is determined by the unique three-dimensional structure taken by the folding process. Protein malfunction due to misfolding is the culprit of many clinical disorders, such as abnormal protein aggregations. This leads to neurodegenerative disorders like Huntington's and Alzheimer's disease. We focus on a subset of the folding problem, exploring the role and effects of entropy on the process of protein folding. Four major concepts and models are developed and each pertains to a specific aspect of the folding process: entropic forces, conformational states under crowding, aggregation, and macrostate kinetics from microstate trajectories. The exclusive focus on entropy is well-suited for crowding studies, as many interactions are nonspecific. We show how a stabilizing entropic force can arise purely from the motion of crowders in solution. In addition we are able to make a a quantitative prediction of the crowding effect with an implicit crowding approximation using an aspherical scaled-particle theory. In order to investigate the effects of aggregation, we derive a new operator expansion method to solve the Ising/Potts model with external fields over an arbitrary graph. Here the external fields are representative of the entropic forces. We show that this method reduces the problem of calculating the partition function to the solution of recursion relations. Many of the methods employed are coarse-grained approximations. As such, it is useful to have a viable method for extracting macrostate information from time series data. We develop a method to cluster the microstates into physically meaningful macrostates by grouping similar relaxation times from a transition matrix. Overall, the studied topics allow us to understand deeper the complicated process involving proteins.

Improvements in Mixing Time and Mixing Uniformity in Devices Designed for Studies of Protein Folding Kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yao, Shuhuai; Bakajin, Olgica

2007-08-01

Using a microfluidic laminar flow mixer designed for studies of protein folding kinetics, we demonstrate a mixing time of 1 +/- 1 micros with sample consumption on the order of femtomoles. We recognize two limitations of previously proposed designs: (1) size and shape of the mixing region, which limits mixing uniformity and (2) the formation of Dean vortices at high flow rates, which limits the mixing time. We address these limitations by using a narrow shape-optimized nozzle and by reducing the bend of the side channel streamlines. The final design, which combines both of these features, achieves the best performance.more » We quantified the mixing performance of the different designs by numerical simulation of coupled Navier-Stokes and convection-diffusion equations and experiments using fluorescence resonance energy-transfer (FRET)-labeled DNA.« less

Development and Application of a High Throughput Protein Unfolding Kinetic Assay

PubMed Central

Wang, Qiang; Waterhouse, Nicklas; Feyijinmi, Olusegun; Dominguez, Matthew J.; Martinez, Lisa M.; Sharp, Zoey; Service, Rachel; Bothe, Jameson R.; Stollar, Elliott J.

2016-01-01

The kinetics of folding and unfolding underlie protein stability and quantification of these rates provides important insights into the folding process. Here, we present a simple high throughput protein unfolding kinetic assay using a plate reader that is applicable to the studies of the majority of 2-state folding proteins. We validate the assay by measuring kinetic unfolding data for the SH3 (Src Homology 3) domain from Actin Binding Protein 1 (AbpSH3) and its stabilized mutants. The results of our approach are in excellent agreement with published values. We further combine our kinetic assay with a plate reader equilibrium assay, to obtain indirect estimates of folding rates and use these approaches to characterize an AbpSH3-peptide hybrid. Our high throughput protein unfolding kinetic assays allow accurate screening of libraries of mutants by providing both kinetic and equilibrium measurements and provide a means for in-depth ϕ-value analyses. PMID:26745729

Folding mechanism of β-hairpin trpzip2: heterogeneity, transition state and folding pathways.

PubMed

Xiao, Yi; Chen, Changjun; He, Yi

2009-06-22

We review the studies on the folding mechanism of the beta-hairpin tryptophan zipper 2 (trpzip2) and present some additional computational results to refine the picture of folding heterogeneity and pathways. We show that trpzip2 can have a two-state or a multi-state folding pattern, depending on whether it folds within the native basin or through local state basins on the high-dimensional free energy surface; Trpzip2 can fold along different pathways according to the packing order of tryptophan pairs. We also point out some important problems related to the folding mechanism of trpzip2 that still need clarification, e.g., a wide distribution of the computed conformations for the transition state ensemble.

Principles of protein folding--a perspective from simple exact models.

PubMed Central

Dill, K. A.; Bromberg, S.; Yue, K.; Fiebig, K. M.; Yee, D. P.; Thomas, P. D.; Chan, H. S.

1995-01-01

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse. PMID:7613459

RNAslider: a faster engine for consecutive windows folding and its application to the analysis of genomic folding asymmetry.

PubMed

Horesh, Yair; Wexler, Ydo; Lebenthal, Ilana; Ziv-Ukelson, Michal; Unger, Ron

2009-03-04

Scanning large genomes with a sliding window in search of locally stable RNA structures is a well motivated problem in bioinformatics. Given a predefined window size L and an RNA sequence S of size N (L < N), the consecutive windows folding problem is to compute the minimal free energy (MFE) for the folding of each of the L-sized substrings of S. The consecutive windows folding problem can be naively solved in O(NL3) by applying any of the classical cubic-time RNA folding algorithms to each of the N-L windows of size L. Recently an O(NL2) solution for this problem has been described. Here, we describe and implement an O(NLpsi(L)) engine for the consecutive windows folding problem, where psi(L) is shown to converge to O(1) under the assumption of a standard probabilistic polymer folding model, yielding an O(L) speedup which is experimentally confirmed. Using this tool, we note an intriguing directionality (5'-3' vs. 3'-5') folding bias, i.e. that the minimal free energy (MFE) of folding is higher in the native direction of the DNA than in the reverse direction of various genomic regions in several organisms including regions of the genomes that do not encode proteins or ncRNA. This bias largely emerges from the genomic dinucleotide bias which affects the MFE, however we see some variations in the folding bias in the different genomic regions when normalized to the dinucleotide bias. We also present results from calculating the MFE landscape of a mouse chromosome 1, characterizing the MFE of the long ncRNA molecules that reside in this chromosome. The efficient consecutive windows folding engine described in this paper allows for genome wide scans for ncRNA molecules as well as large-scale statistics. This is implemented here as a software tool, called RNAslider, and applied to the scanning of long chromosomes, leading to the observation of features that are visible only on a large scale.

How the folding rates of two- and multistate proteins depend on the amino acid properties.

PubMed

Huang, Jitao T; Huang, Wei; Huang, Shanran R; Li, Xin

2014-10-01

Proteins fold by either two-state or multistate kinetic mechanism. We observe that amino acids play different roles in different mechanism. Many residues that are easy to form regular secondary structures (α helices, β sheets and turns) can promote the two-state folding reactions of small proteins. Most of hydrophilic residues can speed up the multistate folding reactions of large proteins. Folding rates of large proteins are equally responsive to the flexibility of partial amino acids. Other properties of amino acids (including volume, polarity, accessible surface, exposure degree, isoelectric point, and phase transfer energy) have contributed little to folding kinetics of the proteins. Cysteine is a special residue, it triggers two-state folding reaction and but inhibits multistate folding reaction. These findings not only provide a new insight into protein structure prediction, but also could be used to direct the point mutations that can change folding rate. © 2014 Wiley Periodicals, Inc.

Folding pathway of a multidomain protein depends on its topology of domain connectivity

PubMed Central

Inanami, Takashi; Terada, Tomoki P.; Sasai, Masaki

2014-01-01

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant. PMID:25267632

Maximizing RNA folding rates: a balancing act.

PubMed Central

Thirumalai, D; Woodson, S A

2000-01-01

Large ribozymes typically require very long times to refold into their active conformation in vitro, because the RNA is easily trapped in metastable misfolded structures. Theoretical models show that the probability of misfolding is reduced when local and long-range interactions in the RNA are balanced. Using the folding kinetics of the Tetrahymena ribozyme as an example, we propose that folding rates are maximized when the free energies of forming independent domains are similar to each other. A prediction is that the folding pathway of the ribozyme can be reversed by inverting the relative stability of the tertiary domains. This result suggests strategies for optimizing ribozyme sequences for therapeutics and structural studies. PMID:10864039

Circuit topology of self-interacting chains: implications for folding and unfolding dynamics.

PubMed

Mugler, Andrew; Tans, Sander J; Mashaghi, Alireza

2014-11-07

Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, the topology is preserved when continuously stretching the chain while maintaining the contact arrangement. Here we investigate how the folding and unfolding of linear chains with binary contacts is guided by the topology of contact arrangements. We formalize the topology by describing the relations between any two contacts in the structure, which for a linear chain can either be in parallel, in series, or crossing each other. We show that even when other determinants of folding rate such as contact order and size are kept constant, this 'circuit' topology determines folding kinetics. In particular, we find that the folding rate increases with the fractions of parallel and crossed relations. Moreover, we show how circuit topology constrains the conformational phase space explored during folding and unfolding: the number of forbidden unfolding transitions is found to increase with the fraction of parallel relations and to decrease with the fraction of series relations. Finally, we find that circuit topology influences whether distinct intermediate states are present, with crossed contacts being the key factor. The approach presented here can be more generally applied to questions on molecular dynamics, evolutionary biology, molecular engineering, and single-molecule biophysics.

Physics of protein folding

NASA Astrophysics Data System (ADS)

Finkelstein, A. V.; Galzitskaya, O. V.

2004-04-01

Protein physics is grounded on three fundamental experimental facts: protein, this long heteropolymer, has a well defined compact three-dimensional structure; this structure can spontaneously arise from the unfolded protein chain in appropriate environment; and this structure is separated from the unfolded state of the chain by the “all-or-none” phase transition, which ensures robustness of protein structure and therefore of its action. The aim of this review is to consider modern understanding of physical principles of self-organization of protein structures and to overview such important features of this process, as finding out the unique protein structure among zillions alternatives, nucleation of the folding process and metastable folding intermediates. Towards this end we will consider the main experimental facts and simple, mostly phenomenological theoretical models. We will concentrate on relatively small (single-domain) water-soluble globular proteins (whose structure and especially folding are much better studied and understood than those of large or membrane and fibrous proteins) and consider kinetic and structural aspects of transition of initially unfolded protein chains into their final solid (“native”) 3D structures.

Protein folding: Over half a century lasting quest. Comment on "There and back again: Two views on the protein folding puzzle" by Alexei V. Finkelstein et al.

NASA Astrophysics Data System (ADS)

Krokhotin, Andrey; Dokholyan, Nikolay V.

2017-07-01

Most proteins fold into unique three-dimensional (3D) structures that determine their biological functions, such as catalytic activity or macromolecular binding. Misfolded proteins can pose a threat through aberrant interactions with other proteins leading to a number of diseases including Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis [1,2]. What does determine 3D structure of proteins? The first clue to this question came more than fifty years ago when Anfinsen demonstrated that unfolded proteins can spontaneously fold to their native 3D structures [3,4]. Anfinsen's experiments lead to the conclusion that proteins fold to unique native structure corresponding to the stable and kinetically accessible free energy minimum, and protein native structure is solely determined by its amino acid sequence. The question of how exactly proteins find their free energy minimum proved to be a difficult problem. One of the puzzles, initially pointed out by Levinthal, was an inconsistency between observed protein folding times and theoretical estimates. A self-avoiding polymer model of a globular protein of 100-residues length on a cubic lattice can sample at least 1047 states. Based on the assumption that conformational sampling occurs at the highest vibrational mode of proteins (∼picoseconds), predicted folding time by searching among all the possible conformations leads to ∼1027 years (much larger than the age of the universe) [5]. In contrast, observed protein folding time range from microseconds to minutes. Due to tremendous theoretical progress in protein folding field that has been achieved in past decades, the source of this inconsistency is currently understood that is thoroughly described in the review by Finkelstein et al. [6].

Thermodynamic properties of an extremely rapid protein folding reaction.

PubMed

Schindler, T; Schmid, F X

1996-12-24

The cold-shock protein CspB from Bacillus subtilis is a very small beta-barrel protein, which folds with a time constant of 1 ms (at 25 degrees C) in a U reversible N two-state reaction. To elucidate the energetics of this extremely fast reaction we investigated the folding kinetics of CspB as a function of both temperature and denaturant concentration between 2 and 45 degrees C and between 1 and 8 M urea. Under all these conditions unfolding and refolding were reversible monoexponential reactions. By using transition state theory, data from 327 kinetic curves were jointly analyzed to determine the thermodynamic activation parameters delta H H2O++, delta S H2O++, delta G H2O++, and delta C p H2O++ for unfolding and refolding and their dependences on the urea concentration. 90% of the total change in heat capacity and 96% of the change in the m value (m = d delta G/d[urea]) occur between the unfolded state and the activated state. This suggests that for CspB the activated state of folding is unusually well structured and almost equivalent to the native protein in its interactions with the solvent. As a consequence of this native-like activated state a strong temperature-dependent enthalpy/entropy compensation is observed for the refolding kinetics, and the barrier to refolding shifts from being largely enthalpic at low temperature to largely entropic at high temperature. This shift originates not from the changes in the folding protein chains itself, but from the changes in the protein-solvent interactions. We speculate that the absence of intermediates and the native-like activated state in the folding of CspB are correlated with the small size and the structural type of this protein. The stabilization of a small beta-sheet as in CspB requires extensive non-local interactions, and therefore incomplete sheets are unstable. As a consequence, the critical activated state is reached only very late in folding. The instability of partially folded structure is a means to

Using enzyme folding to explore the mechanism of therapeutic touch: a feasibility study.

PubMed

Strickland, Mallory L; Boylan, Helen M

2010-07-01

The goal of this research is to design a novel model using protein folding to study Therapeutic Touch, a noncontact form of energy manipulation healing. Presented is a feasibility study suggesting that the denaturation path of ribonuclease A may be a useful model to study the energy exchange underlying therapeutic touch. The folding of ribonuclease A serves as a controlled energy-requiring system in which energy manipulation can be measured by the degree of folding achieved. A kinetic assay and fluorescence spectroscopy are used to assess the enzyme-folding state. The data suggest that the kinetic assay is a useful means of assessing the degree of refolding, and specifically, the enzyme function. However, fluorescence spectroscopy was not shown to be an effective measurement of enzyme structure for the purposes of this work. More research is needed to assess the underlying mechanism of therapeutic touch to complement the existing studies. An enzyme-folding model may provide a useful means of studying the energy exchange in therapeutic touch.

Hydrophobic folding units derived from dissimilar monomer structures and their interactions.

PubMed

Tsai, C J; Nussinov, R

1997-01-01

We have designed an automated procedure to cut a protein into compact hydrophobic folding units. The hydrophobic units are large enough to contain tertiary non-local interactions, reflecting potential nucleation sites during protein folding. The quality of a hydrophobic folding unit is evaluated by four criteria. The first two correspond to visual characterization of a structural domain, namely, compactness and extent of isolation. We use the definition of Zehfus and Rose (Zehfus MH, Rose GD, 1986, Biochemistry 25:35-340) to calculate the compactness of a cut protein unit. The isolation of a unit is based on the solvent accessible surface area (ASA) originally buried in the interior and exposed to the solvent after cutting. The third quantity is the hydrophobicity, equivalent to the fraction of the buried non-polar ASA with respect to the total non-polar ASA. The last criterion in the evaluation of a folding unit is the number of segments it includes. To conform with the rationale of obtaining hydrophobic units, which may relate to early folding events, the hydrophobic interactions are implicitly and explicitly applied in their generation and assessment. We follow Holm and Sander (Holm L, Sander C, 1994, Proteins 19:256-268) to reduce the multiple cutting-point problem to a one-dimensional search for all reasonable trial cuts. However, as here we focus on the hydrophobic cores, the contact matrix used to obtain the first non-trivial eigenvector contains only hydrophobic contracts, rather than all, hydrophobic and hydrophilic, interactions. This dataset of hydrophobic folding units, derived from structurally dissimilar single chain monomers, is particularly useful for investigations of the mechanism of protein folding. For cases where there are kinetic data, the one or more hydrophobic folding units generated for a protein correlate with the two or with the three-state folding process observed. We carry out extensive amino acid sequence order independent structural

Phi-value analysis of apo-azurin folding: comparison between experiment and theory.

PubMed

Zong, Chenghang; Wilson, Corey J; Shen, Tongye; Wolynes, Peter G; Wittung-Stafshede, Pernilla

2006-05-23

Pseudomonas aeruginosa azurin is a 128-residue beta-sandwich metalloprotein; in vitro kinetic experiments have shown that it folds in a two-state reaction. Here, we used a variational free energy functional to calculate the characteristics of the transition state ensemble (TSE) for folding of the apo-form of P. aeruginosa azurin and investigate how it responds to thermal and mutational changes. The variational method directly yields predicted chevron plots for wild-type and mutant apo-forms of azurin. In parallel, we performed in vitro kinetic-folding experiments on the same set of azurin variants using chemical perturbation. Like the wild-type protein, all apo-variants fold in apparent two-state reactions both in calculations and in stopped-flow mixing experiments. Comparisons of phi (phi) values determined from the experimental and theoretical chevron parameters reveal an excellent agreement for most positions, indicating a polarized, highly structured TSE for folding of P. aeruginosa apo-azurin. We also demonstrate that careful analysis of side-chain interactions is necessary for appropriate theoretical description of core mutants.

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 3: Illustrative test problems

NASA Technical Reports Server (NTRS)

Bittker, David A.; Radhakrishnan, Krishnan

1994-01-01

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 3 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 3 explains the kinetics and kinetics-plus-sensitivity analysis problems supplied with LSENS and presents sample results. These problems illustrate the various capabilities of, and reaction models that can be solved by, the code and may provide a convenient starting point for the user to construct the problem data file required to execute LSENS. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Protein Folding Mechanism of the Dimeric AmphiphysinII/Bin1 N-BAR Domain

PubMed Central

Gruber, Tobias; Balbach, Jochen

2015-01-01

The human AmphyphisinII/Bin1 N-BAR domain belongs to the BAR domain superfamily, whose members sense and generate membrane curvatures. The N-BAR domain is a 57 kDa homodimeric protein comprising a six helix bundle. Here we report the protein folding mechanism of this protein as a representative of this protein superfamily. The concentration dependent thermodynamic stability was studied by urea equilibrium transition curves followed by fluorescence and far-UV CD spectroscopy. Kinetic unfolding and refolding experiments, including rapid double and triple mixing techniques, allowed to unravel the complex folding behavior of N-BAR. The equilibrium unfolding transition curve can be described by a two-state process, while the folding kinetics show four refolding phases, an additional burst reaction and two unfolding phases. All fast refolding phases show a rollover in the chevron plot but only one of these phases depends on the protein concentration reporting the dimerization step. Secondary structure formation occurs during the three fast refolding phases. The slowest phase can be assigned to a proline isomerization. All kinetic experiments were also followed by fluorescence anisotropy detection to verify the assignment of the dimerization step to the respective folding phase. Based on these experiments we propose for N-BAR two parallel folding pathways towards the homodimeric native state depending on the proline conformation in the unfolded state. PMID:26368922

Molecular dynamics studies of protein folding and aggregation

NASA Astrophysics Data System (ADS)

Ding, Feng

This thesis applies molecular dynamics simulations and statistical mechanics to study: (i) protein folding; and (ii) protein aggregation. Most small proteins fold into their native states via a first-order-like phase transition with a major free energy barrier between the folded and unfolded states. A set of protein conformations corresponding to the free energy barrier, Delta G >> kBT, are the folding transition state ensemble (TSE). Due to their evasive nature, TSE conformations are hard to capture (probability ∝ exp(-DeltaG/k BT)) and characterize. A coarse-grained discrete molecular dynamics model with realistic steric constraints is constructed to reproduce the experimentally observed two-state folding thermodynamics. A kinetic approach is proposed to identify the folding TSE. A specific set of contacts, common to the TSE conformations, is identified as the folding nuclei which are necessary to be formed in order for the protein to fold. Interestingly, the amino acids at the site of the identified folding nuclei are highly conserved for homologous proteins sharing the same structures. Such conservation suggests that amino acids that are important for folding kinetics are under selective pressure to be preserved during the course of molecular evolution. In addition, studies of the conformations close to the transition states uncover the importance of topology in the construction of order parameter for protein folding transition. Misfolded proteins often form insoluble aggregates, amyloid fibrils, that deposit in the extracellular space and lead to a type of disease known as amyloidosis. Due to its insoluble and non-crystalline nature, the aggregation structure and, thus the aggregation mechanism, has yet to be uncovered. Discrete molecular dynamics studies reveal an aggregate structure with the same structural signatures as in experimental observations and show a nucleation aggregation scenario. The simulations also suggest a generic aggregation mechanism

How Four Scientists Integrate Thermodynamic and Kinetic Theory, Context, Analogies, and Methods in Protein-Folding and Dynamics Research: Implications for Biochemistry Instruction.

PubMed

Jeffery, Kathleen A; Pelaez, Nancy; Anderson, Trevor R

2018-01-01

To keep biochemistry instruction current and relevant, it is crucial to expose students to cutting-edge scientific research and how experts reason about processes governed by thermodynamics and kinetics such as protein folding and dynamics. This study focuses on how experts explain their research into this topic with the intention of informing instruction. Previous research has modeled how expert biologists incorporate research methods, social or biological context, and analogies when they talk about their research on mechanisms. We used this model as a guiding framework to collect and analyze interview data from four experts. The similarities and differences that emerged from analysis indicate that all experts integrated theoretical knowledge with their research context, methods, and analogies when they explained how phenomena operate, in particular by mapping phenomena to mathematical models; they explored different processes depending on their explanatory aims, but readily transitioned between different perspectives and explanatory models; and they explained thermodynamic and kinetic concepts of relevance to protein folding in different ways that aligned with their particular research methods. We discuss how these findings have important implications for teaching and future educational research. © 2018 K. A. Jeffery et al. CBE—Life Sciences Education © 2018 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Functional modulation of a protein folding landscape via side-chain distortion

PubMed Central

Kelch, Brian A.; Salimi, Neema L.; Agard, David A.

2012-01-01

Ultrahigh-resolution (< 1.0 Å) structures have revealed unprecedented and unexpected details of molecular geometry, such as the deformation of aromatic rings from planarity. However, the functional utility of such energetically costly strain is unknown. The 0.83 Å structure of α-lytic protease (αLP) indicated that residues surrounding a conserved Phe side-chain dictate a rotamer which results in a ∼6° distortion along the side-chain, estimated to cost 4 kcal/mol. By contrast, in the closely related protease Streptomyces griseus Protease B (SGPB), the equivalent Phe adopts a different rotamer and is undistorted. Here, we report that the αLP Phe side-chain distortion is both functional and conserved in proteases with large pro regions. Sequence analysis of the αLP serine protease family reveals a bifurcation separating those sequences expected to induce distortion and those that would not, which correlates with the extent of kinetic stability. Structural and folding kinetics analyses of family members suggest that distortion of this side-chain plays a role in increasing kinetic stability within the αLP family members that use a large Pro region. Additionally, structural and kinetic folding studies of mutants demonstrate that strain alters the folding free energy landscape by destabilizing the transition state (TS) relative to the native state (N). Although side-chain distortion comes at a cost of foldability, it suppresses the rate of unfolding, thereby enhancing kinetic stability and increasing protein longevity under harsh extracellular conditions. This ability of a structural distortion to enhance function is unlikely to be unique to αLP family members and may be relevant in other proteins exhibiting side-chain distortions. PMID:22635267

Inflationary magneto-(non)genesis, increasing kinetic couplings, and the strong coupling problem

NASA Astrophysics Data System (ADS)

Bazrafshan Moghaddam, Hossein; McDonough, Evan; Namba, Ryo; Brandenberger, Robert H.

2018-05-01

We study the generation of magnetic fields during inflation making use of a coupling of the inflaton and moduli fields to electromagnetism via the photon kinetic term, and assuming that the coupling is an increasing function of time. We demonstrate that the strong coupling problem of inflationary magnetogenesis can be avoided by incorporating the destabilization of moduli fields after inflation. The magnetic field always dominates over the electric one, and thus the severe constraints on the latter from backreaction, which are the demanding obstacles in the case of a decreasing coupling function, do not apply to the current scenario. However, we show that this loophole to the strong coupling problem comes at a price: the normalization of the amplitude of magnetic fields is determined by this coupling term and is therefore suppressed by a large factor after the moduli destabilization completes. From this we conclude that there is no self-consistent and generic realization of primordial magnetogenesis producing scale-invariant fields in the case of an increasing kinetic coupling.

Folding and Unfolding Pathways of the Human Telomeric G-Quadruplex

PubMed Central

Gray, Robert D.; Trent, John O.; Chaires, Jonathan B.

2014-01-01

Sequence analogues of human telomeric DNA such as d[AGGG(TTAGGG)3] (Tel22) fold into monomeric quadruplex structures in the presence of a suitable cation. To investigate the pathway for unimolecular quadruplex formation, we monitored the kinetics of K+-induced folding of Tel22 by circular dichroism (CD), intrinsic 2-aminopurine fluorescence, and fluorescence resonance energy transfer (FRET). The results are consistent with a four-step pathway U ↔ I1 ↔ I2 ↔ I3 ↔ F where U and F represent unfolded and folded conformational ensembles, and I1, I2, and I3 are intermediates. Previous kinetic studies have shown that I1 is formed in a rapid pre-equilibrium and may consist of an ensemble of “prefolded” hairpin structures brought about by cation-induced electrostatic collapse of the DNA. The current study shows that I1 converts to I2 with a relaxation time τ1 = 0.1 s at 25 °C in 25 mM KCl. The CD spectrum of I2 is characteristic of an antiparallel quadruplex that could form as a result of intra-molecular fold-over of the I1 hairpins. I3 is relatively slowly formed (τ2 ≈ 3700 s) and has CD and FRET properties consistent with those expected of a triplex structure as previously observed in equilibrium melting studies. I3 converts to F with τ3 ≈ 750 s. Identical pathways with different kinetic constants involving a rapidly formed antiparallel intermediate were observed with oligonucleotides forming mixed parallel/antiparallel hybrid-1 and hybrid-2 topologies (e.g. d[TTGGG(TTAGGG)3A and d[TAGGG(TTAGGG)3TT]). Aspects of the kinetics of unfolding were also monitored by the spectroscopic methods listed above and by time-resolved fluorescence lifetime measurements using a complementary strand trap assay. These experiments reveal a slow, rate-limiting step along the unfolding pathway. PMID:24487181

Folding of viscous sheets and filaments

NASA Astrophysics Data System (ADS)

Skorobogatiy, M.; Mahadevan, L.

2000-12-01

We consider the nonlinear folding behavior of a viscous filament or a sheet under the influence of an external force such as gravity. Everyday examples of this phenomenon are provided by the periodic folding of a sheet of honey as it impinges on toast, or the folding of a stream of shampoo as it falls on one's hand. To understand the evolution of a fold, we formulate and solve a free-boundary problem for the phenomenon, give scaling laws for the size of the folds and the frequency with which they are laid out, and verify these experimentally.

Programmed folding of DNA origami structures through single-molecule force control.

PubMed

Bae, Wooli; Kim, Kipom; Min, Duyoung; Ryu, Je-Kyung; Hyeon, Changbong; Yoon, Tae-Young

2014-12-03

Despite the recent development in the design of DNA origami, its folding yet relies on thermal or chemical annealing methods. We here demonstrate mechanical folding of the DNA origami structure via a pathway that has not been accessible to thermal annealing. Using magnetic tweezers, we stretch a single scaffold DNA with mechanical tension to remove its secondary structures, followed by base pairing of the stretched DNA with staple strands. When the force is subsequently quenched, folding of the DNA nanostructure is completed through displacement between the bound staple strands. Each process in the mechanical folding is well defined and free from kinetic traps, enabling us to complete folding within 10 min. We also demonstrate parallel folding of DNA nanostructures through multiplexed manipulation of the scaffold DNAs. Our results suggest a path towards programmability of the folding pathway of DNA nanostructures.

Amyloid Polymorphism in the Protein Folding and Aggregation Energy Landscape.

PubMed

Adamcik, Jozef; Mezzenga, Raffaele

2018-02-15

Protein folding involves a large number of steps and conformations in which the folding protein samples different thermodynamic states characterized by local minima. Kinetically trapped on- or off-pathway intermediates are metastable folding intermediates towards the lowest absolute energy minima, which have been postulated to be the natively folded state where intramolecular interactions dominate, and the amyloid state where intermolecular interactions dominate. However, this view largely neglects the rich polymorphism found within amyloid species. We review the protein folding energy landscape in view of recent findings identifying specific transition routes among different amyloid polymorphs. Observed transitions such as twisted ribbon→crystal or helical ribbon→nanotube, and forbidden transitions such helical ribbon↛crystal, are discussed and positioned within the protein folding and aggregation energy landscape. Finally, amyloid crystals are identified as the ground state of the protein folding and aggregation energy landscape. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Polymer Uncrossing and Knotting in Protein Folding, and Their Role in Minimal Folding Pathways

PubMed Central

Mohazab, Ali R.; Plotkin, Steven S.

2013-01-01

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold , , , and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation “alignment”. The consensus minimal pathway is constructed and shown schematically for representative cases of an , , and knotted protein. An overlap parameter is defined between pathways; we find that proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding. PMID:23365638

Kinetics from Replica Exchange Molecular Dynamics Simulations.

PubMed

Stelzl, Lukas S; Hummer, Gerhard

2017-08-08

Transitions between metastable states govern many fundamental processes in physics, chemistry and biology, from nucleation events in phase transitions to the folding of proteins. The free energy surfaces underlying these processes can be obtained from simulations using enhanced sampling methods. However, their altered dynamics makes kinetic and mechanistic information difficult or impossible to extract. Here, we show that, with replica exchange molecular dynamics (REMD), one can not only sample equilibrium properties but also extract kinetic information. For systems that strictly obey first-order kinetics, the procedure to extract rates is rigorous. For actual molecular systems whose long-time dynamics are captured by kinetic rate models, accurate rate coefficients can be determined from the statistics of the transitions between the metastable states at each replica temperature. We demonstrate the practical applicability of the procedure by constructing master equation (Markov state) models of peptide and RNA folding from REMD simulations.

There and back again: Two views on the protein folding puzzle

NASA Astrophysics Data System (ADS)

Finkelstein, Alexei V.; Badretdin, Azat J.; Galzitskaya, Oxana V.; Ivankov, Dmitry N.; Bogatyreva, Natalya S.; Garbuzynskiy, Sergiy O.

2017-07-01

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: ;U-to-N; and ;N-to-U;. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the ;N-to-U; transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical ;detailed balance; principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the ;N-to-U; transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the ;U-to-N; transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the

Cleavage Mapping the Topology of Protein Folding Intermediates

DTIC Science & Technology

1995-03-13

1993). 29. Nakano, T., Antonino , L. C, Fox, R. O. & Fink, A. L. Effect of proline mutation on the stability and kinetics of folding of...Biochem. 62, 653-683. Nakano, T., Antonino , L. C., Fox, R. O., & Fink, A. L. (1993) Biochemistry 32, 2534-2541. Nozaki, Y. (1972) Methods Enzymol. 26, 43

On the role of conformational geometry in protein folding

NASA Astrophysics Data System (ADS)

Du, Rose; Pande, Vijay S.; Grosberg, Alexander Yu.; Tanaka, Toyoichi; Shakhnovich, Eugene

1999-12-01

Using a lattice model of protein folding, we find that once certain native contacts have been formed, folding to the native state is inevitable, even if the only energetic bias in the system is nonspecific, homopolymeric attraction to a collapsed state. These conformations can be quite geometrically unrelated to the native state (with as low as only 53% of the native contacts formed). We demonstrate these results by examining the Monte Carlo kinetics of both heteropolymers under Go interactions and homopolymers, with the folding of both types of polymers to the native state of the heteropolymer. Although we only consider a 48-mer lattice model, our findings shed light on the effects of geometrical restrictions, including those of chain connectivity and steric excluded volume, on protein folding. These effects play a complementary role to that of the rugged energy landscape. In addition, the results of this work can aid in the interpretation of experiments and computer simulations of protein folding performed at elevated temperatures.

Oxidative Folding and N-terminal Cyclization of Onconase+

PubMed Central

Welker, Ervin; Hathaway, Laura; Xu, Guoqiang; Narayan, Mahesh; Pradeep, Lovy; Shin, Hang-Cheol; Scheraga, Harold A.

2008-01-01

Cyclization of the N-terminal glutamine residue to pyroglutamic acid in onconase, an anti-cancer chemotherapeutic agent, increases the activity and stability of the protein. Here, we examine the correlated effects of the folding/unfolding process and the formation of this N-terminal pyroglutamic acid. The results in this study indicate that cyclization of the N-terminal glutamine has no significant effect on the rate of either reductive unfolding or oxidative folding of the protein. Both the cyclized and uncyclized proteins seem to follow the same oxidative folding pathways; however, cyclization altered the relative flux of the protein in these two pathways by increasing the rate of formation of a kinetically trapped intermediate. Glutaminyl cyclase (QC) catalyzed the cyclization of the unfolded, reduced protein, but had no effect on the disulfide-intact, uncyclized, folded protein. The structured intermediates of uncyclized onconase were also resistant to QC-catalysis, consistent with their having a native-like fold. These observations suggest that, in vivo, cyclization takes place during the initial stages of oxidative folding, specifically, before the formation of structured intermediates. The competition between oxidative folding and QC-mediated cyclization suggests that QC-catalyzed cyclization of the N-terminal glutamine in onconase occurs in the endoplasmic reticulum, probably co-translationally. PMID:17439243

Landscapes with megabasins: Polyamorphism in liquids and biopolymers and the role of nucleation in folding and folding diseases

NASA Astrophysics Data System (ADS)

Angell, C. A.

1997-02-01

We show how energy landscape concepts can rationalize the observations on glassforming liquids over the whole range of behavior, strong to fragile. In particular, we show how the existence of landscapes with both strong and fragile megabasins can provide a basis for understanding the nature of quasi-first-order transitions between amorphous states such as those observed to occur in the glassy states of “strong” glassformers. We show how this propensity originates in the liquid state and then emphasize the analogy provided, at the mesoscopic level, by the folding transition in proteins. Recognition that the folding transition is an equilibrium first-order transition between polyamorphic forms of a complex system implies recognition of the need for a nucleation step in the process. When nucleated phase transitions are kinetically retarded, their probability can be influenced by time-temperature history and by the presence of nucleating agents. Nucleation events are statistically rare in mesoscopic systems, hence the ability to fold rapidly should require special features in the folding molecular structure or the presence of nucleating agents. We propose that the unwanted folding events leading to pathogenic forms of certain proteins (prions) can be stimulated by nucleating agents, which thus may be the unidentified infectious agents in “mad cow” disease and related maladies.

Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy.

PubMed

Borgia, Alessandro; Wensley, Beth G; Soranno, Andrea; Nettels, Daniel; Borgia, Madeleine B; Hoffmann, Armin; Pfeil, Shawn H; Lipman, Everett A; Clarke, Jane; Schuler, Benjamin

2012-01-01

Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes.

Engineering diverse changes in beta-turn propensities in the N-terminal beta-hairpin of ubiquitin reveals significant effects on stability and kinetics but a robust folding transition state.

PubMed

Simpson, Emma R; Meldrum, Jill K; Searle, Mark S

2006-04-04

Using the N-terminal 17-residue beta-hairpin of ubiquitin as a "host" for mutational studies, we have investigated the influence of the beta-turn sequence on protein stability and folding kinetics by replacing the native G-bulged turn (TLTGK) with more flexible analogues (TG3K and TG5K) and a series of four-residue type I' beta-turn sequences, commonly found in beta-hairpins. Although a statistical analysis of type I' turns demonstrates residue preferences at specific sites, the frequency of occurrence appears to only broadly correlate with experimentally determined protein stabilities. The subsequent engineering of context-dependent non-native tertiary contacts involving turn residues is shown to produce large changes in stability. Relatively few point mutations have been described that probe secondary structure formation in ubiquitin in a manner that is independent of tertiary contacts. To this end, we have used the more rigorous rate-equilibrium free energy relationship (Leffler analysis), rather than the two-point phi value analysis, to show for a family of engineered beta-turn mutants that stability (range of approximately 20 kJ/mol) and folding kinetics (190-fold variation in refolding rate) are linearly correlated (alpha(f) = 0.74 +/- 0.08). The data are consistent with a transition state that is robust with regard to a wide range of statistically favored and disfavored beta-turn mutations and implicate a loosely assembled beta-hairpin as a key template in transition state stabilization with the beta-turn playing a central role.

Probing the kinetic stabilities of Friedreich's ataxia clinical variants using a solid phase GroEL chaperonin capture platform.

PubMed

Correia, Ana R; Naik, Subhashchandra; Fisher, Mark T; Gomes, Cláudio M

2014-10-20

Numerous human diseases are caused by protein folding defects where the protein may become more susceptible to degradation or aggregation. Aberrant protein folding can affect the kinetic stability of the proteins even if these proteins appear to be soluble in vivo. Experimental discrimination between functional properly folded and misfolded nonfunctional conformers is not always straightforward at near physiological conditions. The differences in the kinetic behavior of two initially folded frataxin clinical variants were examined using a high affinity chaperonin kinetic trap approach at 25 °C. The kinetically stable wild type frataxin (FXN) shows no visible partitioning onto the chaperonin. In contrast, the clinical variants FXN-p.Asp122Tyr and FXN-p.Ile154Phe kinetically populate partial folded forms that tightly bind the GroEL chaperonin platform. The initially soluble FXN-p.Ile154Phe variant partitions onto GroEL more rapidly and is more kinetically liable. These differences in kinetic stability were confirmed using differential scanning fluorimetry. The kinetic and aggregation stability differences of these variants may lead to the distinct functional impairments described in Friedreich's ataxia, the neurodegenerative disease associated to frataxin functional deficiency. This chaperonin platform approach may be useful for identifying small molecule stabilizers since stabilizing ligands to frataxin variants should lead to a concomitant decrease in chaperonin binding.

Evolution, Energy Landscapes and the Paradoxes of Protein Folding

PubMed Central

Wolynes, Peter G.

2014-01-01

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signalling a beautiful confluence of genomics and chemical physics. PMID:25530262

Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy

PubMed Central

Borgia, Alessandro; Wensley, Beth G.; Soranno, Andrea; Nettels, Daniel; Borgia, Madeleine B.; Hoffmann, Armin; Pfeil, Shawn H.; Lipman, Everett A.; Clarke, Jane; Schuler, Benjamin

2012-01-01

Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes. PMID:23149740

A stoichiometry driven universal spatial organization of backbones of folded proteins: are there Chargaff's rules for protein folding?

PubMed

Mittal, A; Jayaram, B; Shenoy, Sandhya; Bawa, Tejdeep Singh

2010-10-01

Protein folding is at least a six decade old problem, since the times of Pauling and Anfinsen. However, rules of protein folding remain elusive till date. In this work, rigorous analyses of several thousand crystal structures of folded proteins reveal a surprisingly simple unifying principle of backbone organization in protein folding. We find that protein folding is a direct consequence of a narrow band of stoichiometric occurrences of amino-acids in primary sequences, regardless of the size and the fold of a protein. We observe that "preferential interactions" between amino-acids do not drive protein folding, contrary to all prevalent views. We dedicate our discovery to the seminal contribution of Chargaff which was one of the major keys to elucidation of the stoichiometry-driven spatially organized double helical structure of DNA.

Context-dependent effects of asparagine glycosylation on Pin WW folding kinetics and thermodynamics.

PubMed

Price, Joshua L; Shental-Bechor, Dalit; Dhar, Apratim; Turner, Maurice J; Powers, Evan T; Gruebele, Martin; Levy, Yaakov; Kelly, Jeffery W

2010-11-03

Asparagine glycosylation is one of the most common and important post-translational modifications of proteins in eukaryotic cells. N-glycosylation occurs when a triantennary glycan precursor is transferred en bloc to a nascent polypeptide (harboring the N-X-T/S sequon) as the peptide is cotranslationally translocated into the endoplasmic reticulum (ER). In addition to facilitating binding interactions with components of the ER proteostasis network, N-glycans can also have intrinsic effects on protein folding by directly altering the folding energy landscape. Previous work from our laboratories (Hanson et al. Proc. Natl. Acad. Sci. U.S.A. 2009, 109, 3131-3136; Shental-Bechor, D.; Levy, Y. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 8256-8261) suggested that the three sugar residues closest to the protein are sufficient for accelerating protein folding and stabilizing the resulting structure in vitro; even a monosaccharide can have a dramatic effect. The highly conserved nature of these three proximal sugars in N-glycans led us to speculate that introducing an N-glycosylation site into a protein that is not normally glycosylated would stabilize the protein and increase its folding rate in a manner that does not depend on the presence of specific stabilizing protein-saccharide interactions. Here, we test this hypothesis experimentally and computationally by incorporating an N-linked GlcNAc residue at various positions within the Pin WW domain, a small β-sheet-rich protein. The results show that an increased folding rate and enhanced thermodynamic stability are not general, context-independent consequences of N-glycosylation. Comparison between computational predictions and experimental observations suggests that generic glycan-based excluded volume effects are responsible for the destabilizing effect of glycosylation at highly structured positions. However, this reasoning does not adequately explain the observed destabilizing effect of glycosylation within flexible

Investigation of RNA Hairpin Loop Folding with Time-Resolved Infrared Spectroscopy

NASA Astrophysics Data System (ADS)

Stancik, Aaron Lee

Ribonucleic acids (RNAs) are a group of functional biopolymers central to the molecular underpinnings of life. To complete the many processes they mediate, RNAs must fold into precise three-dimensional structures. Hairpin loops are the most ubiquitous and basic structural elements present in all folded RNAs, and are the foundation upon which all complex tertiary structures are built. A hairpin loop forms when a single stranded RNA molecule folds back on itself creating a helical stem of paired bases capped by a loop. This work investigates the formation of UNCG hairpin loops with the sequence 5'-GC(UNCG)GC-3' (N = A, U, G, or C) using both equilibrium infrared (IR) and time-resolved IR spectroscopy. Equilibrium IR melting data were used to determine thermodynamic parameters. Melting temperatures ranged from 50 to 60°C, and enthalpies of unfolding were on the order of 100 kJ/mol. In the time-resolved work, temperature jumps of up to 20°C at 2.5°C increments were obtained with transient relaxation kinetics spanning nanoseconds to hundreds of microseconds. The relaxation kinetics for all of the oligomers studied were fit to first or second order exponentials. Multiple vibrational transitions were probed on each oligomer for fully folded and partially denatured structures. In the time-resolved limit, in contrast to equilibrium melting, RNA does not fold according to two-state behavior. These results are some of the first to show that RNA hairpins fold according to a rugged energy landscape, which contradicts their relatively simple nature. In addition, this work has proven that time-resolved IR spectroscopy is a powerful and novel tool for investigating the earliest events of RNA folding, the formation of the hairpin loop.

There and back again: Two views on the protein folding puzzle.

PubMed

Finkelstein, Alexei V; Badretdin, Azat J; Galzitskaya, Oxana V; Ivankov, Dmitry N; Bogatyreva, Natalya S; Garbuzynskiy, Sergiy O

2017-07-01

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the

[Temperament of children with vocal fold nodules].

PubMed

Wei, Youhua; Wang, Zhinan; Xu, Zhongqiang; Chen, Ping; Hao, Lili

2009-11-01

To examine the temperament of children with vocal fold nodules. To compare the temperament dimension and temperamental types of 42 children with vocal fold nodules with 46 vocally normal children, using Chinese children's Temperament Problem Screening system (CCTPSs). The children with vocal fold nodules differed significantly from the comparison group in their temperament dimension's adaptability, intensity of reaction, mood value, persistency and temperamental types. There are more difficult and slow-to-warm-up children in patients with vocal fold nodules than vocally normal children.

Intermediates and the folding of proteins L and G

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Scott; Head-Gordon, Teresa

We use a minimalist protein model, in combination with a sequence design strategy, to determine differences in primary structure for proteins L and G that are responsible for the two proteins folding through distinctly different folding mechanisms. We find that the folding of proteins L and G are consistent with a nucleation-condensation mechanism, each of which is described as helix-assisted {beta}-1 and {beta}-2 hairpin formation, respectively. We determine that the model for protein G exhibits an early intermediate that precedes the rate-limiting barrier of folding and which draws together misaligned secondary structure elements that are stabilized by hydrophobic core contactsmore » involving the third {beta}-strand, and presages the later transition state in which the correct strand alignment of these same secondary structure elements is restored. Finally the validity of the targeted intermediate ensemble for protein G was analyzed by fitting the kinetic data to a two-step first order reversible reaction, proving that protein G folding involves an on-pathway early intermediate, and should be populated and therefore observable by experiment.« less

Intermediates and the folding of proteins L and G

PubMed Central

Brown, Scott; Head-Gordon, Teresa

2004-01-01

We use a minimalist protein model, in combination with a sequence design strategy, to determine differences in primary structure for proteins L and G, which are responsible for the two proteins folding through distinctly different folding mechanisms. We find that the folding of proteins L and G are consistent with a nucleation-condensation mechanism, each of which is described as helix-assisted β-1 and β-2 hairpin formation, respectively. We determine that the model for protein G exhibits an early intermediate that precedes the rate-limiting barrier of folding, and which draws together misaligned secondary structure elements that are stabilized by hydrophobic core contacts involving the third β-strand, and presages the later transition state in which the correct strand alignment of these same secondary structure elements is restored. Finally, the validity of the targeted intermediate ensemble for protein G was analyzed by fitting the kinetic data to a two-step first-order reversible reaction, proving that protein G folding involves an on-pathway early intermediate, and should be populated and therefore observable by experiment. PMID:15044729

Proteome-level interplay between folding and aggregation propensities of proteins.

PubMed

Tartaglia, Gian Gaetano; Vendruscolo, Michele

2010-10-08

With the advent of proteomics, there is an increasing need of tools for predicting the properties of large numbers of proteins by using the information provided by their amino acid sequences, even in the absence of the knowledge of their structures. One of the most important types of predictions concerns whether proteins will fold or aggregate. Here, we study the competition between these two processes by analyzing the relationship between the folding and aggregation propensity profiles for the human and Escherichia coli proteomes. These profiles are calculated, respectively, using the CamFold method, which we introduce in this work, and the Zyggregator method. Our results indicate that the kinetic behavior of proteins is, to a large extent, determined by the interplay between regions of low folding and high aggregation propensities. Copyright © 2010. Published by Elsevier Ltd.

Visualizing chaperone-assisted protein folding

DOE PAGES

Horowitz, Scott; Salmon, Loïc; Koldewey, Philipp; ...

2016-05-30

We present that challenges in determining the structures of heterogeneous and dynamic protein complexes have greatly hampered past efforts to obtain a mechanistic understanding of many important biological processes. One such process is chaperone-assisted protein folding. Obtaining structural ensembles of chaperone–substrate complexes would ultimately reveal how chaperones help proteins fold into their native state. To address this problem, we devised a new structural biology approach based on X-ray crystallography, termed residual electron and anomalous density (READ). READ enabled us to visualize even sparsely populated conformations of the substrate protein immunity protein 7 (Im7) in complex with the Escherichia coli chaperonemore » Spy, and to capture a series of snapshots depicting the various folding states of Im7 bound to Spy. The ensemble shows that Spy-associated Im7 samples conformations ranging from unfolded to partially folded to native-like states and reveals how a substrate can explore its folding landscape while being bound to a chaperone.« less

An adaptive bias - hybrid MD/kMC algorithm for protein folding and aggregation.

PubMed

Peter, Emanuel K; Shea, Joan-Emma

2017-07-05

In this paper, we present a novel hybrid Molecular Dynamics/kinetic Monte Carlo (MD/kMC) algorithm and apply it to protein folding and aggregation in explicit solvent. The new algorithm uses a dynamical definition of biases throughout the MD component of the simulation, normalized in relation to the unbiased forces. The algorithm guarantees sampling of the underlying ensemble in dependency of one average linear coupling factor 〈α〉 τ . We test the validity of the kinetics in simulations of dialanine and compare dihedral transition kinetics with long-time MD-simulations. We find that for low 〈α〉 τ values, kinetics are in good quantitative agreement. In folding simulations of TrpCage and TrpZip4 in explicit solvent, we also find good quantitative agreement with experimental results and prior MD/kMC simulations. Finally, we apply our algorithm to study growth of the Alzheimer Amyloid Aβ 16-22 fibril by monomer addition. We observe two possible binding modes, one at the extremity of the fibril (elongation) and one on the surface of the fibril (lateral growth), on timescales ranging from ns to 8 μs.

Kinetics and thermodynamics of the thermal inactivation and chaperone assisted folding of zebrafish dihydrofolate reductase.

PubMed

Thapliyal, Charu; Jain, Neha; Rashid, Naira; Chaudhuri Chattopadhyay, Pratima

2018-01-01

The maintenance of thermal stability is a major issue in protein engineering as many proteins tend to form inactive aggregates at higher temperatures. Zebrafish DHFR, an essential protein for the survival of cells, shows irreversible thermal unfolding transition. The protein exhibits complete unfolding and loss of activity at 50 °C as monitored by UV-Visible, fluorescence and far UV-CD spectroscopy. The heat induced inactivation of zDHFR follows first-order kinetics and Arrhenius law. The variation in the value of inactivation rate constant, k with increasing temperatures depicts faster inactivation at elevated temperatures. We have attempted to study the chaperoning ability of a shorter variant of GroEL (minichaperone) and compared it with that of conventional GroEL-GroES chaperone system. Both the chaperone system prevented the aggregation and assisted in refolding of zDHFR. The rate of thermal inactivation was significantly retarded in the presence of chaperones which indicate that it enhances the thermal stability of the enzyme. As minichaperone is less complex, and does not require high energy co-factors like ATP, for its function as compared to conventional GroEL-GroES system, it can act as a very good in vitro as well as in vivo chaperone model for monitoring assisted protein folding phenomenon. Copyright © 2017 Elsevier Inc. All rights reserved.

Probing the cytochrome c' folding landscape.

PubMed

Pletneva, Ekaterina V; Zhao, Ziqing; Kimura, Tetsunari; Petrova, Krastina V; Gray, Harry B; Winkler, Jay R

2007-11-01

The folding kinetics of R. palustris cytochrome c' (cyt c') have been monitored by heme absorption and native Trp72 fluorescence at pH 5. The Trp72 fluorescence burst signal suggests early compaction of the polypeptide ensemble. Analysis of heme transient absorption spectra reveals deviations from two-state behavior, including a prominent slow phase that is accelerated by the prolyl isomerase cyclophilin. A nonnative proline configuration (Pro21) likely interferes with the formation of the helical bundle surrounding the heme.

Time-resolved distance determination by tryptophan fluorescence quenching: probing intermediates in membrane protein folding.

PubMed

Kleinschmidt, J H; Tamm, L K

1999-04-20

The mechanism of insertion and folding of an integral membrane protein has been investigated with the beta-barrel forming outer membrane protein A (OmpA) of Escherichia coli. This work describes a new approach to this problem by combining structural information obtained from tryptophan fluorescence quenching at different depths in the lipid bilayer with the kinetics of the refolding process. Experiments carried out over a temperature range between 2 and 40 degrees C allowed us to detect, trap, and characterize previously unidentified folding intermediates on the pathway of OmpA insertion and folding into lipid bilayers. Three membrane-bound intermediates were found in which the average distances of the Trps were 14-16, 10-11, and 0-5 A, respectively, from the bilayer center. The first folding intermediate is stable at 2 degrees C for at least 1 h. A second intermediate has been isolated at temperatures between 7 and 20 degrees C. The Trps move 4-5 A closer to the center of the bilayer at this stage. Subsequently, in an intermediate that is observable at 26-28 degrees C, the Trps move another 5-10 A closer to the center of the bilayer. The final (native) structure is observed at higher temperatures of refolding. In this structure, the Trps are located on average about 9-10 A from the bilayer center. Monitoring the evolution of Trp fluorescence quenching by a set of brominated lipids during refolding at various temperatures therefore allowed us to identify and characterize intermediate states in the folding process of an integral membrane protein.

Review of chemical-kinetic problems of future NASA missions. I - Earth entries

NASA Technical Reports Server (NTRS)

Park, Chul

1993-01-01

A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

NASA Astrophysics Data System (ADS)

Polotto, Franciele; Drigo Filho, Elso; Chahine, Jorge; Oliveira, Ronaldo Junio de

2018-03-01

This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker-Planck equation is mapped onto a Schrödinger-type equation due to the well-known solutions of the latter. Through a semi-analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein Tm CSP was simulated at a Cα level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of Tm CSP having the well-known 'U' shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems.

Frustration Sculpts the Early Stages of Protein Folding.

PubMed

Di Silvio, Eva; Brunori, Maurizio; Gianni, Stefano

2015-09-07

The funneled energy landscape theory implies that protein structures are minimally frustrated. Yet, because of the divergent demands between folding and function, regions of frustrated patterns are present at the active site of proteins. To understand the effects of such local frustration in dictating the energy landscape of proteins, here we compare the folding mechanisms of the two alternative spliced forms of a PDZ domain (PDZ2 and PDZ2as) that share a nearly identical sequence and structure, while displaying different frustration patterns. The analysis, based on the kinetic characterization of a large number of site-directed mutants, reveals that although the late stages for folding are very robust and biased by native topology, the early stages are more malleable and dominated by local frustration. The results are briefly discussed in the context of the energy-landscape theory. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Extreme Mechanics: Self-Folding Origami

NASA Astrophysics Data System (ADS)

Santangelo, Christian D.

2017-03-01

Origami has emerged as a tool for designing three-dimensional structures from flat films. Because they can be fabricated by lithographic or roll-to-roll processing techniques, they have great potential for the manufacture of complicated geometries and devices. This article discusses the mechanics of origami and kirigami with a view toward understanding how to design self-folding origami structures. Whether an origami structure can be made to fold autonomously depends strongly on the geometry and kinematics of the origami fold pattern. This article collects some of the results on origami rigidity into a single framework, and discusses how these aspects affect the foldability of origami. Despite recent progress, most problems in origami and origami design remain completely open.

Chaperonin-based biolayer interferometry to assess the kinetic stability of metastable, aggregation-prone proteins

PubMed Central

Lea, Wendy A.; Naik, Subhashchandra; Chaudhri, Tapan; Machen, Alexandra J.; O’Neil, Pierce T.; McGinn-Straub, Wesley; Tischer, Alexander; Auton, Matthew T.; Burns, Joshua R.; Baldwin, Michael R.; Khar, Karen R.; Karanicolas, John; Fisher, Mark T.

2017-01-01

Stabilizing the folded state of metastable and/or aggregation-prone proteins through exogenous ligand binding is an appealing strategy to decrease disease pathologies brought on by protein folding defects or deleterious kinetic transitions. Current methods of examining ligand binding to these marginally stable native states are limited, because protein aggregation typically interferes with analysis. Here, we describe a rapid method for assessing the kinetic stability of folded proteins and monitoring the effects of ligand stabilization for both intrinsically stable proteins (monomers, oligomers, multi-domain) and metastable proteins (e.g. low Tm) that uses a new GroEL chaperonin-based biolayer interferometry (BLI) denaturant-pulse platform. A kinetically controlled denaturation isotherm is generated by exposing a target protein immobilized on a BLI biosensor to increasing denaturant concentrations (urea or GnHCl) in a pulsatile manner to induce partial or complete unfolding of the attached protein population. Following the rapid removal of the denaturant, the extent of hydrophobic unfolded/partially folded species that remain is detected by increased GroEL binding. Since this kinetic denaturant pulse is brief, the amplitude of the GroEL binding to the immobilized protein depends on the duration of exposure to denaturant, the concentration of denaturant, wash times, and the underlying protein unfolding/refolding kinetics; fixing all other parameters and plotting GroEL binding amplitude versus denaturant pulse concentration results in a kinetically controlled denaturation isotherm. When folding osmolytes or stabilizing ligands are added to the immobilized target proteins before and during the denaturant pulse, the diminished population of unfolded/partially folded protein is manifested by a decreased GroEL binding and/or a marked shift in these kinetically controlled denaturation profiles to higher denaturant concentrations. This particular platform approach can be

PyFolding: Open-Source Graphing, Simulation, and Analysis of the Biophysical Properties of Proteins.

PubMed

Lowe, Alan R; Perez-Riba, Albert; Itzhaki, Laura S; Main, Ewan R G

2018-02-06

For many years, curve-fitting software has been heavily utilized to fit simple models to various types of biophysical data. Although such software packages are easy to use for simple functions, they are often expensive and present substantial impediments to applying more complex models or for the analysis of large data sets. One field that is reliant on such data analysis is the thermodynamics and kinetics of protein folding. Over the past decade, increasingly sophisticated analytical models have been generated, but without simple tools to enable routine analysis. Consequently, users have needed to generate their own tools or otherwise find willing collaborators. Here we present PyFolding, a free, open-source, and extensible Python framework for graphing, analysis, and simulation of the biophysical properties of proteins. To demonstrate the utility of PyFolding, we have used it to analyze and model experimental protein folding and thermodynamic data. Examples include: 1) multiphase kinetic folding fitted to linked equations, 2) global fitting of multiple data sets, and 3) analysis of repeat protein thermodynamics with Ising model variants. Moreover, we demonstrate how PyFolding is easily extensible to novel functionality beyond applications in protein folding via the addition of new models. Example scripts to perform these and other operations are supplied with the software, and we encourage users to contribute notebooks and models to create a community resource. Finally, we show that PyFolding can be used in conjunction with Jupyter notebooks as an easy way to share methods and analysis for publication and among research teams. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Single-molecule studies highlight conformational heterogeneity in the early folding steps of a large ribozyme

PubMed Central

Xie, Zheng; Srividya, Narayanan; Sosnick, Tobin R.; Pan, Tao; Scherer, Norbert F.

2004-01-01

The equilibrium folding of the catalytic domain of Bacillus subtilis RNase P RNA is investigated by single-molecule fluorescence resonance energy transfer (FRET). Previous ensemble studies of this 255-nucleotide ribozyme described the equilibrium folding with two transitions, U-to-Ieq-to-N, and focused on the Ieq-to-N transition. The present study focuses on the U-to-Ieq transition. Comparative ensemble measurements of the ribozyme construct labeled with fluorescein at the 5′ end and Cy3 at the 3′ end show that modifications required for labeling do not interfere with folding and help to define the Mg2+ concentration range for the U-to-Ieq transition. Histogram analysis of the Mg2+-dependent single-molecule FRET efficiency reveals two previously undetermined folding intermediates. The single-molecule FRET trajectories exhibit non-two-state and nonergodic behaviors at intermediate Mg2+ concentrations on the time scale of seconds. The trajectories at intermediate Mg2+ concentrations are classified into five classes based on three FRET levels and their dynamics of interconversion within the measured time range. This heterogeneity, together with the observation of “nonsudden jump” FRET transitions, indicates that the early folding steps of this ribozyme involve a series of intermediates with different degrees of kinetic isolation and that folding occurs under kinetic control and involves many “local” conformational switches. A free energy contour is constructed to illustrate the complex folding surface. PMID:14704266

The human peripheral subunit-binding domain folds rapidly while overcoming repulsive Coulomb forces

PubMed Central

Arbely, Eyal; Neuweiler, Hannes; Sharpe, Timothy D; Johnson, Christopher M; Fersht, Alan R

2010-01-01

Peripheral subunit binding domains (PSBDs) are integral parts of large multienzyme complexes involved in carbohydrate metabolism. PSBDs facilitate shuttling of prosthetic groups between different catalytic subunits. Their protein surface is characterized by a high density of positive charges required for binding to subunits within the complex. Here, we investigated folding thermodynamics and kinetics of the human PSBD (HSBD) using circular dichroism and tryptophan fluorescence experiments. HSBD was only marginally stable under physiological solvent conditions but folded within microseconds via a barrier-limited apparent two-state transition, analogous to its bacterial homologues. The high positive surface-charge density of HSBD leads to repulsive Coulomb forces that modulate protein stability and folding kinetics, and appear to even induce native-state movement. The electrostatic strain was alleviated at high solution-ionic-strength by Debye-Hückel screening. Differences in ionic-strength dependent characteristics among PSBD homologues could be explained by differences in their surface charge distributions. The findings highlight the trade-off between protein function and stability during protein evolution. PMID:20662005

Discrete kinetic models from funneled energy landscape simulations.

PubMed

Schafer, Nicholas P; Hoffman, Ryan M B; Burger, Anat; Craig, Patricio O; Komives, Elizabeth A; Wolynes, Peter G

2012-01-01

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an "inside-out", nucleation-propagation like character.

Physical parameter estimation from porcine ex vivo vocal fold dynamics in an inverse problem framework.

PubMed

Gómez, Pablo; Schützenberger, Anne; Kniesburges, Stefan; Bohr, Christopher; Döllinger, Michael

2018-06-01

This study presents a framework for a direct comparison of experimental vocal fold dynamics data to a numerical two-mass-model (2MM) by solving the corresponding inverse problem of which parameters lead to similar model behavior. The introduced 2MM features improvements such as a variable stiffness and a modified collision force. A set of physiologically sensible degrees of freedom is presented, and three optimization algorithms are compared on synthetic vocal fold trajectories. Finally, a total of 288 high-speed video recordings of six excised porcine larynges were optimized to validate the proposed framework. Particular focus lay on the subglottal pressure, as the experimental subglottal pressure is directly comparable to the model subglottal pressure. Fundamental frequency, amplitude and objective function values were also investigated. The employed 2MM is able to replicate the behavior of the porcine vocal folds very well. The model trajectories' fundamental frequency matches the one of the experimental trajectories in [Formula: see text] of the recordings. The relative error of the model trajectory amplitudes is on average [Formula: see text]. The experiments feature a mean subglottal pressure of 10.16 (SD [Formula: see text]) [Formula: see text]; in the model, it was on average 7.61 (SD [Formula: see text]) [Formula: see text]. A tendency of the model to underestimate the subglottal pressure is found, but the model is capable of inferring trends in the subglottal pressure. The average absolute error between the subglottal pressure in the model and the experiment is 2.90 (SD [Formula: see text]) [Formula: see text] or [Formula: see text]. A detailed analysis of the factors affecting the accuracy in matching the subglottal pressure is presented.

Folding of apomyoglobin: Analysis of transient intermediate structure during refolding using quick hydrogen deuterium exchange and NMR

PubMed Central

NISHIMURA, Chiaki

2017-01-01

The structures of apomyoglobin folding intermediates have been widely analyzed using physical chemistry methods including fluorescence, circular dichroism, small angle X-ray scattering, NMR, mass spectrometry, and rapid mixing. So far, at least two intermediates (on sub-millisecond- and millisecond-scales) have been demonstrated for apomyoglobin folding. The combination of pH-pulse labeling and NMR is a useful tool for analyzing the kinetic intermediates at the atomic level. Its use has revealed that the latter-phase kinetic intermediate of apomyoglobin (6 ms) was composed of helices A, B, G and H, whereas the equilibrium intermediate, called the pH 4 molten-globule intermediate, was composed mainly of helices A, G and H. The improved strategy for the analysis of the kinetic intermediate was developed to include (1) the dimethyl sulfoxide method, (2) data processing with the various labeling times, and (3) a new in-house mixer. Particularly, the rapid mixing revealed that helices A and G were significantly more protected at the earlier stage (400 µs) of the intermediate (former-phase intermediate) than the other helices. Mutation studies, where each hydrophobic residue was replaced with an alanine in helices A, B, E, F, G and H, indicated that both non-native and native-like structures exist in the latter-phase folding intermediate. The N-terminal part of helix B is a weak point in the intermediate, and the docking of helix E residues to the core of the A, B, G and H helices was interrupted by a premature helix B, resulting in the accumulation of the intermediate composed of helices A, B, G and H. The prediction-based protein engineering produced important mutants: Helix F in a P88K/A90L/S92K/A94L mutant folded in the latter-phase intermediate, although helix F in the wild type does not fold even at the native state. Furthermore, in the L11G/W14G/A70L/G73W mutant, helix A did not fold but helix E did, which is similar to what was observed in the kinetic

Folding of apomyoglobin: Analysis of transient intermediate structure during refolding using quick hydrogen deuterium exchange and NMR.

PubMed

Nishimura, Chiaki

2017-01-01

The structures of apomyoglobin folding intermediates have been widely analyzed using physical chemistry methods including fluorescence, circular dichroism, small angle X-ray scattering, NMR, mass spectrometry, and rapid mixing. So far, at least two intermediates (on sub-millisecond- and millisecond-scales) have been demonstrated for apomyoglobin folding. The combination of pH-pulse labeling and NMR is a useful tool for analyzing the kinetic intermediates at the atomic level. Its use has revealed that the latter-phase kinetic intermediate of apomyoglobin (6 ms) was composed of helices A, B, G and H, whereas the equilibrium intermediate, called the pH 4 molten-globule intermediate, was composed mainly of helices A, G and H. The improved strategy for the analysis of the kinetic intermediate was developed to include (1) the dimethyl sulfoxide method, (2) data processing with the various labeling times, and (3) a new in-house mixer. Particularly, the rapid mixing revealed that helices A and G were significantly more protected at the earlier stage (400 µs) of the intermediate (former-phase intermediate) than the other helices. Mutation studies, where each hydrophobic residue was replaced with an alanine in helices A, B, E, F, G and H, indicated that both non-native and native-like structures exist in the latter-phase folding intermediate. The N-terminal part of helix B is a weak point in the intermediate, and the docking of helix E residues to the core of the A, B, G and H helices was interrupted by a premature helix B, resulting in the accumulation of the intermediate composed of helices A, B, G and H. The prediction-based protein engineering produced important mutants: Helix F in a P88K/A90L/S92K/A94L mutant folded in the latter-phase intermediate, although helix F in the wild type does not fold even at the native state. Furthermore, in the L11G/W14G/A70L/G73W mutant, helix A did not fold but helix E did, which is similar to what was observed in the kinetic

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches.

PubMed

Muñoz, Victor; Cerminara, Michele

2016-09-01

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats. © 2016 The Author(s).

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches

PubMed Central

Muñoz, Victor; Cerminara, Michele

2016-01-01

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico. All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats. PMID:27574021

Hydrogen-Bond Driven Loop-Closure Kinetics in Unfolded Polypeptide Chains

PubMed Central

Daidone, Isabella; Neuweiler, Hannes; Doose, Sören; Sauer, Markus; Smith, Jeremy C.

2010-01-01

Characterization of the length dependence of end-to-end loop-closure kinetics in unfolded polypeptide chains provides an understanding of early steps in protein folding. Here, loop-closure in poly-glycine-serine peptides is investigated by combining single-molecule fluorescence spectroscopy with molecular dynamics simulation. For chains containing more than 10 peptide bonds loop-closing rate constants on the 20–100 nanosecond time range exhibit a power-law length dependence. However, this scaling breaks down for shorter peptides, which exhibit slower kinetics arising from a perturbation induced by the dye reporter system used in the experimental setup. The loop-closure kinetics in the longer peptides is found to be determined by the formation of intra-peptide hydrogen bonds and transient β-sheet structure, that accelerate the search for contacts among residues distant in sequence relative to the case of a polypeptide chain in which hydrogen bonds cannot form. Hydrogen-bond-driven polypeptide-chain collapse in unfolded peptides under physiological conditions found here is not only consistent with hierarchical models of protein folding, that highlights the importance of secondary structure formation early in the folding process, but is also shown to speed up the search for productive folding events. PMID:20098498

Flexibility damps macromolecular crowding effects on protein folding dynamics: Application to the murine prion protein (121-231)

NASA Astrophysics Data System (ADS)

Bergasa-Caceres, Fernando; Rabitz, Herschel A.

2014-01-01

A model of protein folding kinetics is applied to study the combined effects of protein flexibility and macromolecular crowding on protein folding rate and stability. It is found that the increase in stability and folding rate promoted by macromolecular crowding is damped for proteins with highly flexible native structures. The model is applied to the folding dynamics of the murine prion protein (121-231). It is found that the high flexibility of the native isoform of the murine prion protein (121-231) reduces the effects of macromolecular crowding on its folding dynamics. The relevance of these findings for the pathogenic mechanism are discussed.

Analyzing the effect of homogeneous frustration in protein folding.

PubMed

Contessoto, Vinícius G; Lima, Debora T; Oliveira, Ronaldo J; Bruni, Aline T; Chahine, Jorge; Leite, Vitor B P

2013-10-01

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a Cα structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free-energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins. Copyright © 2013 Wiley Periodicals, Inc.

RNAiFold: a web server for RNA inverse folding and molecular design.

PubMed

Garcia-Martin, Juan Antonio; Clote, Peter; Dotu, Ivan

2013-07-01

Synthetic biology and nanotechnology are poised to make revolutionary contributions to the 21st century. In this article, we describe a new web server to support in silico RNA molecular design. Given an input target RNA secondary structure, together with optional constraints, such as requiring GC-content to lie within a certain range, requiring the number of strong (GC), weak (AU) and wobble (GU) base pairs to lie in a certain range, the RNAiFold web server determines one or more RNA sequences, whose minimum free-energy secondary structure is the target structure. RNAiFold provides access to two servers: RNA-CPdesign, which applies constraint programming, and RNA-LNSdesign, which applies the large neighborhood search heuristic; hence, it is suitable for larger input structures. Both servers can also solve the RNA inverse hybridization problem, i.e. given a representation of the desired hybridization structure, RNAiFold returns two sequences, whose minimum free-energy hybridization is the input target structure. The web server is publicly accessible at http://bioinformatics.bc.edu/clotelab/RNAiFold, which provides access to two specialized servers: RNA-CPdesign and RNA-LNSdesign. Source code for the underlying algorithms, implemented in COMET and supported on linux, can be downloaded at the server website.

Approaching the thermodynamic view of protein folding through the reproduction of Anfinsen's experiment by undergraduate physical biochemistry students.

PubMed

Fernandez-Reche, Andres; Cobos, Eva S; Luque, Irene; Ruiz-Sanz, Javier; Martinez, Jose C

2018-01-04

In 1972 Christian B. Anfinsen received the Nobel Prize in Chemistry for "…his work on ribonuclease, especially concerning the connection between the amino acid sequence and the biologically active conformation." The understanding of this principle is crucial for physical biochemistry students, since protein folding studies, bio-computing sciences and protein design approaches are founded on such a well-demonstrated connection. Herein, we describe a detailed and easy-to-follow experiment to reproduce the most relevant assays carried out at Anfinsen's laboratory in the 60s. This experiment provides students with a platform to interpret by themselves the structural and kinetic experiments conceived to understand the protein folding problem. In addition, this three-day experiment brings students a nice opportunity for protein manipulation as well as for the setting up of spectroscopic and chromatographic techniques. © 2018 by The International Union of Biochemistry and Molecular Biology, 2018. © 2018 The International Union of Biochemistry and Molecular Biology.

Modelling of lateral fold growth and fold linkage: Applications to fold-and-thrust belt tectonics

NASA Astrophysics Data System (ADS)

Grasemann, Bernhard; Schmalholz, Stefan

2013-04-01

We use a finite element model to investigate the three-dimensional fold growth and interference of two initially isolated fold segments. The most critical parameter, which controls the fold linkage mode, is the phase difference between the laterally growing fold hinge lines: 1) "Linear-linkage" yields a sub-cylindrical fold with a saddle at the location where the two initial folds linked. 2) "Oblique-linkage" produces a curved fold resembling a Type II refold structure. 3) "Oblique-no-linkage" results in two curved folds with fold axes plunging in opposite directions. 4) "Linear-no-linkage" yields a fold train of two separate sub-cylindrical folds with fold axes plunging in opposite directions. The transition from linkage to no-linkage occurs when the fold separation between the initially isolated folds is slightly larger than one half of the low-amplitude fold wavelength. The model results compare well with previously published plasticine analogue models and can be directly applied to the investigation of fold growth history in fold-and-thust belts. An excellent natural example of lateral fold linkage is described from the Zagros fold-and-thrust belt in the Kurdistan Region of Iraq. The fold growth in this region is not controlled by major thrust faults but the shortening of the Paleozoic to Cenozoic passive margin sediments of the Arabian plate occurred mainly by detachment folding. The sub-cylindrical anticlines with hinge-parallel lengths of more than 50 km have not developed from single sub-cylindrical embryonic folds but they have merged from different fold segments that joined laterally during fold amplification and lateral fold growth. Linkage points are marked by geomorphological saddle points which are structurally the lowermost points of antiforms and points of principal curvatures with opposite sign. Linkage points can significantly influence the migration of mineral-rich fluids and hydrocarbons and are therefore of great economic importance.

Modulation of frustration in folding by sequence permutation.

PubMed

Nobrega, R Paul; Arora, Karunesh; Kathuria, Sagar V; Graceffa, Rita; Barrea, Raul A; Guo, Liang; Chakravarthy, Srinivas; Bilsel, Osman; Irving, Thomas C; Brooks, Charles L; Matthews, C Robert

2014-07-22

Folding of globular proteins can be envisioned as the contraction of a random coil unfolded state toward the native state on an energy surface rough with local minima trapping frustrated species. These substructures impede productive folding and can serve as nucleation sites for aggregation reactions. However, little is known about the relationship between frustration and its underlying sequence determinants. Chemotaxis response regulator Y (CheY), a 129-amino acid bacterial protein, has been shown previously to populate an off-pathway kinetic trap in the microsecond time range. The frustration has been ascribed to premature docking of the N- and C-terminal subdomains or, alternatively, to the formation of an unproductive local-in-sequence cluster of branched aliphatic side chains, isoleucine, leucine, and valine (ILV). The roles of the subdomains and ILV clusters in frustration were tested by altering the sequence connectivity using circular permutations. Surprisingly, the stability and buried surface area of the intermediate could be increased or decreased depending on the location of the termini. Comparison with the results of small-angle X-ray-scattering experiments and simulations points to the accelerated formation of a more compact, on-pathway species for the more stable intermediate. The effect of chain connectivity in modulating the structures and stabilities of the early kinetic traps in CheY is better understood in terms of the ILV cluster model. However, the subdomain model captures the requirement for an intact N-terminal domain to access the native conformation. Chain entropy and aliphatic-rich sequences play crucial roles in biasing the early events leading to frustration in the folding of CheY.

Tracking polypeptide folds on the free energy surface: effects of the chain length and sequence.

PubMed

Brukhno, Andrey V; Ricchiuto, Piero; Auer, Stefan

2012-07-26

Characterization of the folding transition in polypeptides and assessing the thermodynamic stability of their structured folds are of primary importance for approaching the problem of protein folding. We use molecular dynamics simulations for a coarse grained polypeptide model in order to (1) obtain the equilibrium conformation diagram of homopolypeptides in a broad range of the chain lengths, N = 10, ..., 100, and temperatures, T (in a multicanonical ensemble), and (2) determine free energy profiles (FEPs) projected onto an optimal, so-called "natural", reaction coordinate that preserves the height of barriers and the diffusion coefficients on the underlying free energy hyper-surface. We then address the following fundamental questions. (i) How well does a kinetically determined free energy landscape of a single chain represent the polypeptide equilibrium (ensemble) behavior? In particular, under which conditions might the correspondence be lost, and what are the possible implications for the folding processes? (ii) How does the free energy landscape depend on the chain length (homopolypeptides) and the monomer interaction sequence (heteropolypeptides)? Our data reveal that at low T values equilibrium structures adopted by relatively short homopolypeptides (N < 60) are dominated by α-helical folds which correspond to the primary and secondary minima of the FEP. In contrast, longer homopolypeptides (N > 70), upon quasi-equilibrium cooling, fold preferentially in β-bundles with small helical portions, while the FEPs exhibit no distinct global minima. Moreover, subject to the choice of the initial configuration, at sufficiently low T, essentially metastable structures can be found and prevail far from the true thermodynamic equilibrium. We also show that, by sequence-enabling the polypeptide model, it is possible to restrict the chain to a very specific part of the configuration space, which results in substantial simplification and smoothing of the free energy

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Slow Proton Transfer Coupled to Unfolding Explains the Puzzling Results of Single-Molecule Experiments on BBL, a Paradigmatic Downhill Folding Protein

PubMed Central

Cerminara, Michele; Campos, Luis A.; Ramanathan, Ravishankar; Muñoz, Victor

2013-01-01

A battery of thermodynamic, kinetic, and structural approaches has indicated that the small α-helical protein BBL folds-unfolds via the one-state downhill scenario. Yet, single-molecule fluorescence spectroscopy offers a more conflicting view. Single-molecule experiments at pH 6 show a unique half-unfolded conformational ensemble at mid denaturation, whereas other experiments performed at higher pH show a bimodal distribution, as expected for two-state folding. Here we use thermodynamic and laser T-jump kinetic experiments combined with theoretical modeling to investigate the pH dependence of BBL stability, folding kinetics and mechanism within the pH 6–11 range. We find that BBL unfolding is tightly coupled to the protonation of one of its residues with an apparent pKa of ∼7. Therefore, in chemical denaturation experiments around neutral pH BBL unfolds gradually, and also converts in binary fashion to the protonated species. Moreover, under the single-molecule experimental conditions (denaturant midpoint and 279 K), we observe that proton transfer is much slower than the ∼15 microseconds folding-unfolding kinetics of BBL. The relaxation kinetics is distinctly biphasic, and the overall relaxation time (i.e. 0.2–0.5 ms) becomes controlled by the proton transfer step. We then show that a simple theoretical model of protein folding coupled to proton transfer explains quantitatively all these results as well as the two sets of single-molecule experiments, including their more puzzling features. Interestingly, this analysis suggests that BBL unfolds following a one-state downhill folding mechanism at all conditions. Accordingly, the source of the bimodal distributions observed during denaturation at pH 7–8 is the splitting of the unique conformational ensemble of BBL onto two slowly inter-converting protonation species. Both, the unprotonated and protonated species unfold gradually (one-state downhill), but they exhibit different degree of unfolding at any

Application of Time-Resolved Tryptophan Phosphorescence Spectroscopy to Protein Folding Studies.

NASA Astrophysics Data System (ADS)

Subramaniam, Vinod

This thesis presents studies of the protein folding problem, one of the most significant questions in contemporary biophysics. Sensitive biophysical techniques, including room temperature tryptophan phosphorescence, which reports on the local environment of the residue, and the lability of proteins to denaturation, a global parameter, were used to assess the validity of the traditional assumption that the biologically active state of a protein is the 'native' state, and to determine whether the pathways of folding in vitro lead to the folded state achieved in vivo. Phosphorescence techniques have also been extended to study, for the first time, emission from tryptophan residues engineered into specific positions as reporters of protein structure. During in vitro refolding of E. coli alkaline phosphatase and bovine 13-lactoglobulin, significant differences were found between the refolded proteins and the native conformations, which have no apparent effect on the biological functions. Slow conformational transitions, termed 'annealing,' that occur long after the return of enzyme activity of alkaline phosphatase are manifested in the retarded recovery of phosphorescence intensity, lifetime, and protein lability. While 'annealing' is not observed for beta -lactoglobulin, both phosphorescence and lability experiments reveal changes in the structure of the refolded protein, even though its biological activity, retinol binding, is fully recovered. This result suggests that the pathways of folding in vitro need not lead to the structure formed in vivo. We have used phosphorescence techniques to study the refolding of ribonuclease T1, which exhibits slow kinetics characteristic of proline isomerization. Furthermore, the ability to extract structural information from phosphorescent tryptophan probes engineered into selected regions represents an important advance in studying protein structure; we have reported the first such results from a mutant staphylococcal nuclease. The

Interactions of non-detergent sulfobetaines with early folding intermediates facilitate in vitro protein renaturation.

PubMed

Vuillard, L; Rabilloud, T; Goldberg, M E

1998-08-15

Non-detergent sulfobetaines (NDSB) are a family of solubilizing and stabilizing agents for proteins. In a previous study [Goldberg, M. E., Expert-Bezancon, N., Vuillard, L. & Rabilloud, T. (1996) Folding & Design 1, 21-27] we showed that the amount of active protein recovered in in vitro folding experiments could be significantly increased by some NDSBS. In this work we investigated the mechanisms by which these molecules facilitate protein renaturation. Stopped-flow and manual-mixing fluorescence and enzyme activity measurements were used to compare the kinetics of protein folding in the presence and absence of N-phenyl-methyl-N,N-dimethylammonium-propane-sulfonate (NDSB 256). Hen lysozyme and the beta2 subunit of Escherichia coli tryptophan synthase were chosen as model systems since their folding pathways had been previously investigated in detail. It is shown that, massive aggregation of tryptophan synthase occurs within less than 2.5 s after dilution in the renaturation buffer, but can be prevented by NDSB 256; only very early folding phases (such as the formation of a loosely packed hydrophobic core able to bind 8-anilino-1-naphthalenesulphonic acid, and the initial burying of tryptophan 177) are significantly altered by NDSB 256; none of the later phases is affected. Furthermore, NDSB 256 did not significantly affect any of the kinetic phases observed during the refolding of denatured lysozyme retaining intact disulphide bonds. This shows that NDSB 256 only interferes with very early steps in the folding process and acts by limiting the abortive interactions that could lead to the formation of inactive aggregates.

Course 12: Proteins: Structural, Thermodynamic and Kinetic Aspects

NASA Astrophysics Data System (ADS)

Finkelstein, A. V.

1 Introduction 2 Overview of protein architectures and discussion of physical background of their natural selection 2.1 Protein structures 2.2 Physical selection of protein structures 3 Thermodynamic aspects of protein folding 3.1 Reversible denaturation of protein structures 3.2 What do denatured proteins look like? 3.3 Why denaturation of a globular protein is the first-order phase transition 3.4 "Gap" in energy spectrum: The main characteristic that distinguishes protein chains from random polymers 4 Kinetic aspects of protein folding 4.1 Protein folding in vivo 4.2 Protein folding in vitro (in the test-tube) 4.3 Theory of protein folding rates and solution of the Levinthal paradox

Probing fast ribozyme reactions under biological conditions with rapid quench-flow kinetics

PubMed Central

Bingaman, Jamie L.; Messina, Kyle J.; Bevilacqua, Philip C.

2017-01-01

Reaction kinetics on the millisecond timescale pervade the protein and RNA fields. To study such reactions, investigators often perturb the system with abiological solution conditions or substrates in order to slow the rate to timescales accessible by hand-mixing; however, such perturbations can change the rate-limiting step and obscure key folding and chemical steps that are found under biological conditions. Mechanical methods for collecting data on the millisecond timescale, which allow these perturbations to be avoided, have been developed over the last few decades. These methods are relatively simple and can be conducted on affordable and commercially available instruments. Here, we focus on using the rapid quench-flow technique to study the fast reaction kinetics of RNA enzymes, or ribozymes, which often react on the millisecond timescale under biological conditions. Rapid quench of ribozymes is completely parallel to the familiar hand-mixing approach, including the use of radiolabeled RNAs and fractionation of reactions on polyacrylamide gels. We provide tips on addressing and preventing common problems that can arise with the rapid-quench technique. Guidance is also offered on ensuring the ribozyme is properly folded and fast-reacting. We hope that this article will facilitate the broader use of rapid-quench instrumentation to study fast-reacting ribozymes under biological reaction conditions. PMID:28315484

Probing the Non-Native H Helix Translocation in Apomyoglobin Folding Intermediates

PubMed Central

2015-01-01

Apomyoglobin folds via sequential helical intermediates that are formed by rapid collapse of the A, B, G, and H helix regions. An equilibrium molten globule with a similar structure is formed near pH 4. Previous studies suggested that the folding intermediates are kinetically trapped states in which folding is impeded by non-native packing of the G and H helices. Fluorescence spectra of mutant proteins in which cysteine residues were introduced at several positions in the G and H helices show differential quenching of W14 fluorescence, providing direct evidence of translocation of the H helix relative to helices A and G in both the kinetic and equilibrium intermediates. Förster resonance energy transfer measurements show that a 5-({2-[(acetyl)amino]ethyl}amino)naphthalene-1-sulfonic acid acceptor coupled to K140C (helix H) is closer to Trp14 (helix A) in the equilibrium molten globule than in the native state, by a distance that is consistent with sliding of the H helix in an N-terminal direction by approximately one helical turn. Formation of an S108C–L135C disulfide prevents H helix translocation in the equilibrium molten globule by locking the G and H helices into their native register. By enforcing nativelike packing of the A, G, and H helices, the disulfide resolves local energetic frustration and facilitates transient docking of the E helix region onto the hydrophobic core but has only a small effect on the refolding rate. The apomyoglobin folding landscape is highly rugged, with several energetic bottlenecks that frustrate folding; relief of any one of the major identified bottlenecks is insufficient to speed progression to the transition state. PMID:24857522

Determining the folding and unfolding rate constants of nucleic acids by biosensor. Application to telomere G-quadruplex.

PubMed

Zhao, Yong; Kan, Zhong-yuan; Zeng, Zhi-xiong; Hao, Yu-hua; Chen, Hua; Tan, Zheng

2004-10-20

Nucleic acid molecules may fold into secondary structures, and the formation of such structures is involved in many biological processes and technical applications. The folding and unfolding rate constants define the kinetics of conformation interconversion and the stability of these structures and is important in realizing their functions. We developed a method to determine these kinetic parameters using an optical biosensor based on surface plasmon resonance. The folding and unfolding of a nucleic acid is coupled with a hybridization reaction by immobilization of the target nucleic acid on a sensor chip surface and injection of a complementary probe nucleic acid over the sensor chip surface. By monitoring the time course of duplex formation, both the folding and unfolding rate constants for the target nucleic acid and the association and dissociation rate constants for the target-probe duplex can all be derived from the same measurement. We applied this method to determine the folding and unfolding rate constants of the G-quadruplex of human telomere sequence (TTAGGG)(4) and its association and dissociation rate constants with the complementary strand (CCCTAA)(4). The results show that both the folding and unfolding occur on the time scale of minutes at physiological concentration of K(+). We speculate that this property might be important for telomere elongation. A complete set of the kinetic parameters for both of the structures allows us to study the competition between the formation of the quadruplex and the duplex. Calculations indicate that the formation of both the quadruplex and the duplex is strand concentration-dependent, and the quadruplex can be efficiently formed at low strand concentration. This property may provide the basis for the formation of the quadruplex in vivo in the presence of a complementary strand.

Improving Protein Fold Recognition by Deep Learning Networks

NASA Astrophysics Data System (ADS)

Jo, Taeho; Hou, Jie; Eickholt, Jesse; Cheng, Jianlin

2015-12-01

For accurate recognition of protein folds, a deep learning network method (DN-Fold) was developed to predict if a given query-template protein pair belongs to the same structural fold. The input used stemmed from the protein sequence and structural features extracted from the protein pair. We evaluated the performance of DN-Fold along with 18 different methods on Lindahl’s benchmark dataset and on a large benchmark set extracted from SCOP 1.75 consisting of about one million protein pairs, at three different levels of fold recognition (i.e., protein family, superfamily, and fold) depending on the evolutionary distance between protein sequences. The correct recognition rate of ensembled DN-Fold for Top 1 predictions is 84.5%, 61.5%, and 33.6% and for Top 5 is 91.2%, 76.5%, and 60.7% at family, superfamily, and fold levels, respectively. We also evaluated the performance of single DN-Fold (DN-FoldS), which showed the comparable results at the level of family and superfamily, compared to ensemble DN-Fold. Finally, we extended the binary classification problem of fold recognition to real-value regression task, which also show a promising performance. DN-Fold is freely available through a web server at http://iris.rnet.missouri.edu/dnfold.

Improving Protein Fold Recognition by Deep Learning Networks.

PubMed

Jo, Taeho; Hou, Jie; Eickholt, Jesse; Cheng, Jianlin

2015-12-04

For accurate recognition of protein folds, a deep learning network method (DN-Fold) was developed to predict if a given query-template protein pair belongs to the same structural fold. The input used stemmed from the protein sequence and structural features extracted from the protein pair. We evaluated the performance of DN-Fold along with 18 different methods on Lindahl's benchmark dataset and on a large benchmark set extracted from SCOP 1.75 consisting of about one million protein pairs, at three different levels of fold recognition (i.e., protein family, superfamily, and fold) depending on the evolutionary distance between protein sequences. The correct recognition rate of ensembled DN-Fold for Top 1 predictions is 84.5%, 61.5%, and 33.6% and for Top 5 is 91.2%, 76.5%, and 60.7% at family, superfamily, and fold levels, respectively. We also evaluated the performance of single DN-Fold (DN-FoldS), which showed the comparable results at the level of family and superfamily, compared to ensemble DN-Fold. Finally, we extended the binary classification problem of fold recognition to real-value regression task, which also show a promising performance. DN-Fold is freely available through a web server at http://iris.rnet.missouri.edu/dnfold.

A simple quantitative model of macromolecular crowding effects on protein folding: Application to the murine prion protein(121-231)

NASA Astrophysics Data System (ADS)

Bergasa-Caceres, Fernando; Rabitz, Herschel A.

2013-06-01

A model of protein folding kinetics is applied to study the effects of macromolecular crowding on protein folding rate and stability. Macromolecular crowding is found to promote a decrease of the entropic cost of folding of proteins that produces an increase of both the stability and the folding rate. The acceleration of the folding rate due to macromolecular crowding is shown to be a topology-dependent effect. The model is applied to the folding dynamics of the murine prion protein (121-231). The differential effect of macromolecular crowding as a function of protein topology suffices to make non-native configurations relatively more accessible.

Chemical kinetics as a contract sport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolb, C.E.

1990-01-01

Earlier in this century chemical kinetics was a basic physical chemistry research topic widely pursued in leading academic chemistry departments. Chemical kinetics now appears to be a discipline practiced chiefly for its applications to societal problems. The chemical kinetics activities directed by D.M. Golden at SRI International are strikingly successful in generating data for key applied problems while at the same time advancing our understanding of chemical kinetics as a scientific discipline. In this talk, the author will contrast the chemical kinetics activities in two contract R D laboratories, one on the right side of the U.S. (ARI) and themore » other on the left (SRI). Their approach to common applied problems ranging from stratospheric heterogeneous kinetics to plasma etching systems for semiconductor processing will be compared and contrasted. Empirically discovered Golden Rules for the pursuit of quality chemical kinetics research in a contract R D environment will be presented and discussed.« less

Acceleration through passive destabilization: protein folding in a weak hydrophobic environment

NASA Astrophysics Data System (ADS)

Jewett, Andrew; Baumketner, Andrij; Shea, Joan-Emma

2004-03-01

The GroEL chaperonin is a biomolecule which assists the folding of an extremely diverse range of proteins in Eubacteria. Some proteins undergo many rounds of ATP-regulated binding and dissociation from GroEL/ES before folding. It has been proposed that transient stress from ATP-regulated binding and release from GroEL/ES frees frustrated proteins from misfolded conformations. However recent evidence suggests that chaperonin-accelerated protein folding can take place entirely within a mutated GroEL+ES cavity that is unable to open and release the protein. Using molecular dynamics, we demonstrate that static confinement within a weakly hydrophobic (attractive) cavity (similar to the interior of the cavity formed by the GroEL+ES complex) is sufficient to significantly accelerate the folding of a highly frustrated protein-like heteropolymer. Our frustrated molecule benifits kinetically from a static hydrophobic environment that destabilizes misfolded conformations. This may shed light on the mechanisms used by other chaperones which do not depend on ATP.

Folding and Stabilization of Native-Sequence-Reversed Proteins

PubMed Central

Zhang, Yuanzhao; Weber, Jeffrey K; Zhou, Ruhong

2016-01-01

Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we investigate how the reverse-sequences of native proteins might fold by examining a series of small proteins of increasing structural complexity (α-helix, β-hairpin, α-helix bundle, and α/β-protein). Employing a tandem protein structure prediction algorithmic and molecular dynamics simulation approach, we find that the ability of reverse sequences to adopt native-like folds is strongly influenced by protein size and the flexibility of the native hydrophobic core. For β-hairpins with reverse-sequences that fail to fold, we employ a simple mutational strategy for guiding stable hairpin formation that involves the insertion of amino acids into the β-turn region. This systematic look at reverse sequence duality sheds new light on the problem of protein sequence-structure mapping and may serve to inspire new protein design and protein structure prediction protocols. PMID:27113844

Folding and Stabilization of Native-Sequence-Reversed Proteins

NASA Astrophysics Data System (ADS)

Zhang, Yuanzhao; Weber, Jeffrey K.; Zhou, Ruhong

2016-04-01

Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we investigate how the reverse-sequences of native proteins might fold by examining a series of small proteins of increasing structural complexity (α-helix, β-hairpin, α-helix bundle, and α/β-protein). Employing a tandem protein structure prediction algorithmic and molecular dynamics simulation approach, we find that the ability of reverse sequences to adopt native-like folds is strongly influenced by protein size and the flexibility of the native hydrophobic core. For β-hairpins with reverse-sequences that fail to fold, we employ a simple mutational strategy for guiding stable hairpin formation that involves the insertion of amino acids into the β-turn region. This systematic look at reverse sequence duality sheds new light on the problem of protein sequence-structure mapping and may serve to inspire new protein design and protein structure prediction protocols.

Revealing the global map of protein folding space by large-scale simulations

NASA Astrophysics Data System (ADS)

Sinner, Claude; Lutz, Benjamin; Verma, Abhinav; Schug, Alexander

2015-12-01

The full characterization of protein folding is a remarkable long-standing challenge both for experiment and simulation. Working towards a complete understanding of this process, one needs to cover the full diversity of existing folds and identify the general principles driving the process. Here, we want to understand and quantify the diversity in folding routes for a large and representative set of protein topologies covering the full range from all alpha helical topologies towards beta barrels guided by the key question: Does the majority of the observed routes contribute to the folding process or only a particular route? We identified a set of two-state folders among non-homologous proteins with a sequence length of 40-120 residues. For each of these proteins, we ran native-structure based simulations both with homogeneous and heterogeneous contact potentials. For each protein, we simulated dozens of folding transitions in continuous uninterrupted simulations and constructed a large database of kinetic parameters. We investigate folding routes by tracking the formation of tertiary structure interfaces and discuss whether a single specific route exists for a topology or if all routes are equiprobable. These results permit us to characterize the complete folding space for small proteins in terms of folding barrier ΔG‡, number of routes, and the route specificity RT.

Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate.

PubMed

Krivov, Sergei V

2018-06-06

Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for

Fold pattern formation in 3D

NASA Astrophysics Data System (ADS)

Schmid, Daniel W.; Dabrowski, Marcin; Krotkiewski, Marcin

2010-05-01

The vast majority of studies concerned with folding focus on 2D and assume that the resulting fold structures are cylindrically extended in the out of place direction. This simplification is often justified as fold aspect ratios, length/width, are quite large. However, folds always exhibit finite aspect ratios and it is unclear what controls this (cf. Fletcher 1995). Surprisingly little is known about the fold pattern formation in 3D for different in-plane loading conditions. Even more complicated is the pattern formation when several folding events are superposed. Let us take the example of a plane strain pure shear superposed by the same kind of deformation but rotated by 90 degrees. The text book prediction for this event is the formation of an egg carton structure; relevant analogue models either agree and produce type 1 interference patterns or contradict and produce type 2. In order to map out 3D fold pattern formation we have performed a systematic parameter space investigation using BILAMIN, our efficient unstructured mesh finite element Stokes solver. BILAMIN is capable of solving problems with more than half a billion unknowns. This allows us to study fold patterns that emerge in randomly (red noise) perturbed layers. We classify the resulting structures with differential geometry tools. Our results show that there is a relationship between fold aspect ratio and in-plane loading conditions. We propose that this finding can be used to determine the complete parameter set potentially contained in the geometry of three dimensional folds: mechanical properties of natural rocks, maximum strain, and relative strength of the in-plane far-field load components. Furthermore, we show how folds in 3D amplify and that there is a second deformation mode, besides continuous amplification, where compression leads to a lateral rearrangement of blocks of folds. Finally, we demonstrate that the textbook prediction of egg carton shaped dome and basin structures resulting

A prospectus on kinetic heliophysics

NASA Astrophysics Data System (ADS)

Howes, Gregory G.

2017-05-01

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future.

A prospectus on kinetic heliophysics

PubMed Central

2017-01-01

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future. PMID:29104421

Comparison of detailed and reduced kinetics mechanisms of silane oxidation in the basis of detonation wave structure problem

NASA Astrophysics Data System (ADS)

Fedorov, A. V.; Tropin, D. A.; Fomin, P. A.

2018-03-01

The paper deals with the problem of the structure of detonation waves in the silane-air mixture within the framework of mathematical model of a nonequilibrium gas dynamics. Detailed kinetic scheme of silane oxidation as well as the newly developed reduced kinetic model of detonation combustion of silane are used. On its basis the detonation wave (DW) structure in stoichiometric silane - air mixture and dependences of Chapman-Jouguet parameters of mixture on stoichiometric ratio between the fuel (silane) and an oxidizer (air) were obtained.

A hybrid computer program for rapidly solving flowing or static chemical kinetic problems involving many chemical species

NASA Technical Reports Server (NTRS)

Mclain, A. G.; Rao, C. S. R.

1976-01-01

A hybrid chemical kinetic computer program was assembled which provides a rapid solution to problems involving flowing or static, chemically reacting, gas mixtures. The computer program uses existing subroutines for problem setup, initialization, and preliminary calculations and incorporates a stiff ordinary differential equation solution technique. A number of check cases were recomputed with the hybrid program and the results were almost identical to those previously obtained. The computational time saving was demonstrated with a propane-oxygen-argon shock tube combustion problem involving 31 chemical species and 64 reactions. Information is presented to enable potential users to prepare an input data deck for the calculation of a problem.

Reversible Aggregation Plays a Crucial Role on the Folding Landscape of p53 Core Domain

PubMed Central

Ishimaru, Daniella; Lima, Luis M. T. R.; Maia, Lenize F.; Lopez, Priscila M.; Ano Bom, Ana P.; Valente, Ana P.; Silva, Jerson L.

2004-01-01

The role of tumor suppressor protein p53 in cell cycle control depends on its flexible and partially unstructured conformation, which makes it crucial to understand its folding landscape. Here we report an intermediate structure of the core domain of the tumor suppressor protein p53 (p53C) during equilibrium and kinetic folding/unfolding transitions induced by guanidinium chloride. This partially folded structure was undetectable when investigated by intrinsic fluorescence. Indeed, the fluorescence data showed a simple two-state transition. On the other hand, analysis of far ultraviolet circular dichroism in 1.0 M guanidinium chloride demonstrated a high content of secondary structure, and the use of an extrinsic fluorescent probe, 4,4′-dianilino-1,1′ binaphthyl-5,5′-disulfonic acid, indicated an increase in exposure of the hydrophobic core at 1 M guanidinium chloride. This partially folded conformation of p53C was plagued by aggregation, as suggested by one-dimensional NMR and demonstrated by light-scattering and gel-filtration chromatography. Dissociation by high pressure of these aggregates reveals the reversibility of the process and that the aggregates have water-excluded cavities. Kinetic measurements show that the intermediate formed in a parallel reaction between unfolded and folded structures and that it is under fine energetic control. They are not only crucial to the folding pathway of p53C but may explain as well the vulnerability of p53C to undergo departure of the native to an inactive state, which makes the cell susceptible to malignant transformation. PMID:15298872

Solvent viscosity and friction in protein folding dynamics.

PubMed

Hagen, Stephen J

2010-08-01

The famous Kramers rate theory for diffusion-controlled reactions has been extended in numerous ways and successfully applied to many types of reactions. Its application to protein folding reactions has been of particular interest in recent years, as many researchers have performed experiments and simulations to test whether folding reactions are diffusion-controlled, whether the solvent is the source of the reaction friction, and whether the friction-dependence of folding rates generally can provide insight into folding dynamics. These experiments involve many practical difficulties, however. They have also produced some unexpected results. Here we briefly review the Kramers theory for reactions in the presence of strong friction and summarize some of the subtle problems that arise in the application of the theory to protein folding. We discuss how the results of these experiments ultimately point to a significant role for internal friction in protein folding dynamics. Studies of friction in protein folding, far from revealing any weakness in Kramers theory, may actually lead to new approaches for probing diffusional dynamics and energy landscapes in protein folding.

Measuring internal friction of an ultrafast-folding protein.

PubMed

Cellmer, Troy; Henry, Eric R; Hofrichter, James; Eaton, William A

2008-11-25

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

Functional analysis of propeptide as an intramolecular chaperone for in vivo folding of subtilisin nattokinase.

PubMed

Jia, Yan; Liu, Hui; Bao, Wei; Weng, Meizhi; Chen, Wei; Cai, Yongjun; Zheng, Zhongliang; Zou, Guolin

2010-12-01

Here, we show that during in vivo folding of the precursor, the propeptide of subtilisin nattokinase functions as an intramolecular chaperone (IMC) that organises the in vivo folding of the subtilisin domain. Two residues belonging to β-strands formed by conserved regions of the IMC are crucial for the folding of the subtilisin domain through direct interactions. An identical protease can fold into different conformations in vivo due to the action of a mutated IMC, resulting in different kinetic parameters. Some interfacial changes involving conserved regions, even those induced by the subtilisin domain, blocked subtilisin folding and altered its conformation. Insight into the interaction between the subtilisin and IMC domains is provided by a three-dimensional structural model. Copyright © 2010 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Evolutionary conservation of codon optimality reveals hidden signatures of cotranslational folding.

PubMed

Pechmann, Sebastian; Frydman, Judith

2013-02-01

The choice of codons can influence local translation kinetics during protein synthesis. Whether codon preference is linked to cotranslational regulation of polypeptide folding remains unclear. Here, we derive a revised translational efficiency scale that incorporates the competition between tRNA supply and demand. Applying this scale to ten closely related yeast species, we uncover the evolutionary conservation of codon optimality in eukaryotes. This analysis reveals universal patterns of conserved optimal and nonoptimal codons, often in clusters, which associate with the secondary structure of the translated polypeptides independent of the levels of expression. Our analysis suggests an evolved function for codon optimality in regulating the rhythm of elongation to facilitate cotranslational polypeptide folding, beyond its previously proposed role of adapting to the cost of expression. These findings establish how mRNA sequences are generally under selection to optimize the cotranslational folding of corresponding polypeptides.

Predicting protein folding rate change upon point mutation using residue-level coevolutionary information.

PubMed

Mallik, Saurav; Das, Smita; Kundu, Sudip

2016-01-01

Change in folding kinetics of globular proteins upon point mutation is crucial to a wide spectrum of biological research, such as protein misfolding, toxicity, and aggregations. Here we seek to address whether residue-level coevolutionary information of globular proteins can be informative to folding rate changes upon point mutations. Generating residue-level coevolutionary networks of globular proteins, we analyze three parameters: relative coevolution order (rCEO), network density (ND), and characteristic path length (CPL). A point mutation is considered to be equivalent to a node deletion of this network and respective percentage changes in rCEO, ND, CPL are found linearly correlated (0.84, 0.73, and -0.61, respectively) with experimental folding rate changes. The three parameters predict the folding rate change upon a point mutation with 0.031, 0.045, and 0.059 standard errors, respectively. © 2015 Wiley Periodicals, Inc.

Universality and diversity of folding mechanics for three-helix bundle proteins.

PubMed

Yang, Jae Shick; Wallin, Stefan; Shakhnovich, Eugene I

2008-01-22

In this study we evaluate, at full atomic detail, the folding processes of two small helical proteins, the B domain of protein A and the Villin headpiece. Folding kinetics are studied by performing a large number of ab initio Monte Carlo folding simulations using a single transferable all-atom potential. Using these trajectories, we examine the relaxation behavior, secondary structure formation, and transition-state ensembles (TSEs) of the two proteins and compare our results with experimental data and previous computational studies. To obtain a detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Moreover, rigorous p(fold) analysis is used to obtain representative samples of the TSEs and a good quantitative agreement between experimental and simulated Phi values is obtained for protein A. Phi values for Villin also are obtained and left as predictions to be tested by future experiments. Our analysis shows that the two-helix hairpin is a common partially stable structural motif that gets formed before entering the TSE in the studied proteins. These results together with our earlier study of Engrailed Homeodomain and recent experimental studies provide a comprehensive, atomic-level picture of folding mechanics of three-helix bundle proteins.

Four residues of propeptide are essential for precursor folding of nattokinase.

PubMed

Jia, Yan; Cao, Xinhua; Deng, Yu; Bao, Wei; Tang, Changyan; Ding, Hanjing; Zheng, Zhongliang; Zou, Guolin

2014-11-01

Subtilisin propeptide functions as an intramolecular chaperone that guides precursor folding. Nattokinase, a member of subtilisin family, is synthesized as a precursor consisting of a signal peptide, a propeptide, and a subtilisin domain, and the mechanism of its folding remains to be understood. In this study, the essential residues of nattokinase propeptide which contribute to precursor folding were determined. Deletion analysis showed that the conserved regions in propeptide were important for precursor folding. Single-site and multi-site mutagenesis studies confirmed the role of Tyr10, Gly13, Gly34, and Gly35. During stage (i) and (ii) of precursor folding, Tyr10 and Gly13 would form the part of interface with subtilisin domain. While Gly34 and Gly35 connected with an α-helix that would stabilize the structure of propeptide. The quadruple Ala mutation, Y10A/G13A/G34A/G35A, resulted in a loss of the chaperone function for the propeptide. This work showed the essential residues of propeptide for precursor folding via secondary structure and kinetic parameter analyses. © The Author 2014. Published by ABBS Editorial Office in association with Oxford University Press on behalf of the Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences.

Folding free-energy landscape of villin headpiece subdomain from molecular dynamics simulations.

PubMed

Lei, Hongxing; Wu, Chun; Liu, Haiguang; Duan, Yong

2007-03-20

High-accuracy ab initio folding has remained an elusive objective despite decades of effort. To explore the folding landscape of villin headpiece subdomain HP35, we conducted two sets of replica exchange molecular dynamics for 200 ns each and three sets of conventional microsecond-long molecular dynamics simulations, using AMBER FF03 force field and a generalized-Born solvation model. The protein folded consistently to the native state; the lowest C(alpha)-rmsd from the x-ray structure was 0.46 A, and the C(alpha)- rmsd of the center of the most populated cluster was 1.78 A at 300 K. ab initio simulations have previously not reached this level. The folding landscape of HP35 can be partitioned into the native, denatured, and two intermediate-state regions. The native state is separated from the major folding intermediate state by a small barrier, whereas a large barrier exists between the major folding intermediate and the denatured states. The melting temperature T(m) = 339 K extracted from the heat-capacity profile was in close agreement with the experimentally derived T(m) = 342 K. A comprehensive picture of the kinetics and thermodynamics of HP35 folding emerges when the results from replica exchange and conventional molecular dynamics simulations are combined.

Inflation Rates, Car Devaluation, and Chemical Kinetics.

ERIC Educational Resources Information Center

Pogliani, Lionello; Berberan-Santos, Mario N.

1996-01-01

Describes the inflation rate problem and offers an interesting analogy with chemical kinetics. Presents and solves the car devaluation problem as a normal chemical kinetic problem where the order of the rate law and the value of the rate constant are derived. (JRH)

The force-dependent mechanism of DnaK-mediated mechanical folding

PubMed Central

Perales-Calvo, Judit; Giganti, David; Stirnemann, Guillaume; Garcia-Manyes, Sergi

2018-01-01

It is well established that chaperones modulate the protein folding free-energy landscape. However, the molecular determinants underlying chaperone-mediated mechanical folding remain largely elusive, primarily because the force-extended unfolded conformation fundamentally differs from that characterized in biochemistry experiments. We use single-molecule force-clamp spectroscopy, combined with molecular dynamics simulations, to study the effect that the Hsp70 system has on the mechanical folding of three mechanically stiff model proteins. Our results demonstrate that, when working independently, DnaJ (Hsp40) and DnaK (Hsp70) work as holdases, blocking refolding by binding to distinct substrate conformations. Whereas DnaK binds to molten globule–like forms, DnaJ recognizes a cryptic sequence in the extended state in an unanticipated force-dependent manner. By contrast, the synergetic coupling of the Hsp70 system exhibits a marked foldase behavior. Our results offer unprecedented molecular and kinetic insights into the mechanisms by which mechanical force finely regulates chaperone binding, directly affecting protein elasticity. PMID:29487911

Chevron Behavior and Isostable Enthalpic Barriers in Protein Folding: Successes and Limitations of Simple Gō-like Modeling

PubMed Central

Kaya, Hüseyin; Liu, Zhirong; Chan, Hue Sun

2005-01-01

It has been demonstrated that a “near-Levinthal” cooperative mechanism, whereby the common Gō interaction scheme is augmented by an extra favorability for the native state as a whole, can lead to apparent two-state folding/unfolding kinetics over a broad range of native stabilities in lattice models of proteins. Here such a mechanism is shown to be generalizable to a simplified continuum (off-lattice) Langevin dynamics model with a Cα protein chain representation, with the resulting chevron plots exhibiting an extended quasilinear regime reminiscent of that of apparent two-state real proteins. Similarly high degrees of cooperativity are possible in Gō-like continuum models with rudimentary pairwise desolvation barriers as well. In these models, cooperativity increases with increasing desolvation barrier height, suggesting strongly that two-state-like folding/unfolding kinetics would be achievable when the pairwise desolvation barrier becomes sufficiently high. Besides cooperativity, another generic folding property of interest that has emerged from published experiments on several apparent two-state proteins is that their folding relaxation under constant native stability (isostability) conditions is essentially Arrhenius, entailing high intrinsic enthalpic folding barriers of ∼17–30 kcal/mol. Based on a new analysis of published data on barnase, here we propose that a similar property should also apply to a certain class of non-two-state proteins that fold with chevron rollovers. However, several continuum Gō-like constructs considered here fail to predict any significant intrinsic enthalpic folding barrier under isostability conditions; thus the physical origin of such barriers in real proteins remains to be elucidated. PMID:15863486

Coarse-grained sequences for protein folding and design

PubMed Central

Brown, Scott; Fawzi, Nicolas J.; Head-Gordon, Teresa

2003-01-01

We present the results of sequence design on our off-lattice minimalist model in which no specification of native-state tertiary contacts is needed. We start with a sequence that adopts a target topology and build on it through sequence mutation to produce new sequences that comprise distinct members within a target fold class. In this work, we use the α/β ubiquitin fold class and design two new sequences that, when characterized through folding simulations, reproduce the differences in folding mechanism seen experimentally for proteins L and G. The primary implication of this work is that patterning of hydrophobic and hydrophilic residues is the physical origin for the success of relative contact-order descriptions of folding, and that these physics-based potentials provide a predictive connection between free energy landscapes and amino acid sequence (the original protein folding problem). We present results of the sequence mapping from a 20- to the three-letter code for determining a sequence that folds into the WW domain topology to illustrate future extensions to protein design. PMID:12963815

Coarse-grained sequences for protein folding and design.

PubMed

Brown, Scott; Fawzi, Nicolas J; Head-Gordon, Teresa

2003-09-16

We present the results of sequence design on our off-lattice minimalist model in which no specification of native-state tertiary contacts is needed. We start with a sequence that adopts a target topology and build on it through sequence mutation to produce new sequences that comprise distinct members within a target fold class. In this work, we use the alpha/beta ubiquitin fold class and design two new sequences that, when characterized through folding simulations, reproduce the differences in folding mechanism seen experimentally for proteins L and G. The primary implication of this work is that patterning of hydrophobic and hydrophilic residues is the physical origin for the success of relative contact-order descriptions of folding, and that these physics-based potentials provide a predictive connection between free energy landscapes and amino acid sequence (the original protein folding problem). We present results of the sequence mapping from a 20- to the three-letter code for determining a sequence that folds into the WW domain topology to illustrate future extensions to protein design.

Probing fast ribozyme reactions under biological conditions with rapid quench-flow kinetics.

PubMed

Bingaman, Jamie L; Messina, Kyle J; Bevilacqua, Philip C

2017-05-01

Reaction kinetics on the millisecond timescale pervade the protein and RNA fields. To study such reactions, investigators often perturb the system with abiological solution conditions or substrates in order to slow the rate to timescales accessible by hand mixing; however, such perturbations can change the rate-limiting step and obscure key folding and chemical steps that are found under biological conditions. Mechanical methods for collecting data on the millisecond timescale, which allow these perturbations to be avoided, have been developed over the last few decades. These methods are relatively simple and can be conducted on affordable and commercially available instruments. Here, we focus on using the rapid quench-flow technique to study the fast reaction kinetics of RNA enzymes, or ribozymes, which often react on the millisecond timescale under biological conditions. Rapid quench of ribozymes is completely parallel to the familiar hand-mixing approach, including the use of radiolabeled RNAs and fractionation of reactions on polyacrylamide gels. We provide tips on addressing and preventing common problems that can arise with the rapid-quench technique. Guidance is also offered on ensuring the ribozyme is properly folded and fast-reacting. We hope that this article will facilitate the broader use of rapid-quench instrumentation to study fast-reacting ribozymes under biological reaction conditions. Copyright © 2017 Elsevier Inc. All rights reserved.

New approach to the study of transient protein conformations: the formation of a semiburied salt link in the folding pathway of barnase.

PubMed

Oliveberg, M; Fersht, A R

1996-05-28

We use in this study a novel kinetic approach to determine the H+ titration properties of a semiburied salt link in the transition state for unfolding of barnase. The approach is based on changes in the pH dependence of the kinetics upon mutation of a target residue. This makes it relatively insensitive to the absolute value of the stability and, thereby, to artifacts caused by structural rearrangements around the site of mutation. The semiburied salt bridge studied here is between Asp93 and Arg69. Mutation of either residue significantly destabilized the protein, and the pKa value of Asp93 is severely lowered in the native state to below 1 because of the ionic interaction with Arg69. The Asp93-Arg69 salt link appears to be formed early in the folding process; the pKa value of Asp93 in the transition state (approximately 1) is similar to that in the native state, and deletion of the ionic interaction with Arg69 substantially destabilizes the folding intermediate and changes the kinetic behavior from multistate to two-state or close to two-state, depending on the conditions. The results suggest that the formation of ionic interactions within clusters of hydrophobic residues can be important for early folding events and can control kinetically the folding pathway. This is not because of the inherent stability of the salt link but because the presence of two unpaired charges is very unfavorable. The data reveal also that fractional phi values are consistent with a uniformly expanded transition state or one with closely spaced energy levels and not with parallel folding pathways.

The Multiple-Minima Problem in Protein Folding

NASA Astrophysics Data System (ADS)

Scheraga, Harold A.

1991-10-01

The conformational energy surface of a polypeptide or protein has many local minima, and conventional energy minimization procedures reach only a local minimum (near the starting point of the optimization algorithm) instead of the global minimum (the multiple-minima problem). Several procedures have been developed to surmount this problem, the most promising of which are: (a) build up procedure, (b) optimization of electrostatics, (c) Monte Carlo-plus-energy minimization, (d) electrostatically-driven Monte Carlo, (e) inclusion of distance restraints, (f) adaptive importance-sampling Monte Carlo, (g) relaxation of dimensionality, (h) pattern-recognition, and (i) diffusion equation method. These procedures have been applied to a variety of polypeptide structural problems, and the results of such computations are presented. These include the computation of the structures of open-chain and cyclic peptides, fibrous proteins and globular proteins. Present efforts are being devoted to scaling up these procedures from small polypeptides to proteins, to try to compute the three-dimensional structure of a protein from its amino sequence.

Competition between protein folding and aggregation: A three-dimensional lattice-model simulation

NASA Astrophysics Data System (ADS)

Bratko, D.; Blanch, H. W.

2001-01-01

Aggregation of protein molecules resulting in the loss of biological activity and the formation of insoluble deposits represents a serious problem for the biotechnology and pharmaceutical industries and in medicine. Considerable experimental and theoretical efforts are being made in order to improve our understanding of, and ability to control, the process. In the present work, we describe a Monte Carlo study of a multichain system of coarse-grained model proteins akin to lattice models developed for simulations of protein folding. The model is designed to examine the competition between intramolecular interactions leading to the native protein structure, and intermolecular association, resulting in the formation of aggregates of misfolded chains. Interactions between the segments are described by a variation of the Go potential [N. Go and H. Abe, Biopolymers 20, 1013 (1981)] that extends the recognition between attracting types of segments to pairs on distinct chains. For the particular model we adopt, the global free energy minimum of a pair of protein molecules corresponds to a dimer of native proteins. When three or more molecules interact, clusters of misfolded chains can be more stable than aggregates of native folds. A considerable fraction of native structure, however, is preserved in these cases. Rates of conformational changes rapidly decrease with the size of the protein cluster. Within the timescale accessible to computer simulations, the folding-aggregation balance is strongly affected by kinetic considerations. Both the native form and aggregates can persist in metastable states, even if conditions such as temperature or concentration favor a transition to an alternative form. Refolding yield can be affected by the presence of an additional polymer species mimicking the function of a molecular chaperone.

Selected mode of dendritic growth with n-fold symmetry in the presence of a forced flow

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.; Galenko, P. K.

2017-07-01

The effect of n-fold crystal symmetry is investigated for a two-dimensional stable dendritic growth in the presence of a forced convective flow. We consider dendritic growth in a one-component undercooled liquid. The theory is developed for the parabolic solid-liquid surface of dendrite growing at arbitrary growth Péclet numbers keeping in mind small anisotropies of surface energy and growth kinetics. The selection criterion determining the stable growth velocity of the dendritic tip and its stable tip diameter is found on the basis of solvability analysis. The obtained criterion includes previously developed theories of thermally and kinetically controlled dendritic growth with convection for the case of four-fold crystal symmetry. The obtained nonlinear system of equations (representing the selection criterion and undercooling balance) for the determination of dendrite tip velocity and dendrite tip diameter is analytically solved in a parametric form. These exact solutions clearly demonstrate a transition between thermally and kinetically controlled growth regimes. In addition, we show that the dendrites with larger crystal symmetry grow faster than those with smaller symmetry.

Genetic Algorithms and Their Application to the Protein Folding Problem

DTIC Science & Technology

1993-12-01

and symbolic methods, random methods such as Monte Carlo simulation and simulated annealing, distance geometry, and molecular dynamics. Many of these...calculated energies with those obtained using the molecular simulation software package called CHARMm. 10 9) Test both the simple and parallel simpie genetic...homology-based, and simplification techniques. 3.21 Molecular Dynamics. Perhaps the most natural approach is to actually simulate the folding process. This

Solitons and protein folding: An In Silico experiment

NASA Astrophysics Data System (ADS)

Ilieva, N.; Dai, J.; Sieradzan, A.; Niemi, A.

2015-10-01

Protein folding [1] is the process of formation of a functional 3D structure from a random coil — the shape in which amino-acid chains leave the ribosome. Anfinsen's dogma states that the native 3D shape of a protein is completely determined by protein's amino acid sequence. Despite the progress in understanding the process rate and the success in folding prediction for some small proteins, with presently available physics-based methods it is not yet possible to reliably deduce the shape of a biologically active protein from its amino acid sequence. The protein-folding problem endures as one of the most important unresolved problems in science; it addresses the origin of life itself. Furthermore, a wrong fold is a common cause for a protein to lose its function or even endanger the living organism. Soliton solutions of a generalized discrete non-linear Schrödinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles κ and τ provide a constructive theoretical framework for describing protein folds and folding patterns [2]. Here we study the dynamics of this process by means of molecular-dynamics simulations. The soliton manifestation is the pattern helix-loop-helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins. We performed in silico experiments for unfolding one subunit of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK [3]) by molecular-dynamics simulations with the MD package GROMACS. We analyzed 80 ns trajectories, obtained with one united-atom and two different all-atom force fields, to justify the side-chain orientation quantification scheme adopted in the studies and to eliminate force-field based artifacts. Our results are compatible with the soliton model of protein folding and provide first insight into soliton-formation dynamics.

Evidence for a Shared Mechanism in the Formation of Urea-Induced Kinetic and Equilibrium Intermediates of Horse Apomyoglobin from Ultrarapid Mixing Experiments

PubMed Central

Mizukami, Takuya; Abe, Yukiko; Maki, Kosuke

2015-01-01

In this study, the equivalence of the kinetic mechanisms of the formation of urea-induced kinetic folding intermediates and non-native equilibrium states was investigated in apomyoglobin. Despite having similar structural properties, equilibrium and kinetic intermediates accumulate under different conditions and via different mechanisms, and it remains unknown whether their formation involves shared or distinct kinetic mechanisms. To investigate the potential mechanisms of formation, the refolding and unfolding kinetics of horse apomyoglobin were measured by continuous- and stopped-flow fluorescence over a time range from approximately 100 μs to 10 s, along with equilibrium unfolding transitions, as a function of urea concentration at pH 6.0 and 8°C. The formation of a kinetic intermediate was observed over a wider range of urea concentrations (0–2.2 M) than the formation of the native state (0–1.6 M). Additionally, the kinetic intermediate remained populated as the predominant equilibrium state under conditions where the native and unfolded states were unstable (at ~0.7–2 M urea). A continuous shift from the kinetic to the equilibrium intermediate was observed as urea concentrations increased from 0 M to ~2 M, which indicates that these states share a common kinetic folding mechanism. This finding supports the conclusion that these intermediates are equivalent. Our results in turn suggest that the regions of the protein that resist denaturant perturbations form during the earlier stages of folding, which further supports the structural equivalence of transient and equilibrium intermediates. An additional folding intermediate accumulated within ~140 μs of refolding and an unfolding intermediate accumulated in <1 ms of unfolding. Finally, by using quantitative modeling, we showed that a five-state sequential scheme appropriately describes the folding mechanism of horse apomyoglobin. PMID:26244984

Evidence for a Shared Mechanism in the Formation of Urea-Induced Kinetic and Equilibrium Intermediates of Horse Apomyoglobin from Ultrarapid Mixing Experiments.

PubMed

Mizukami, Takuya; Abe, Yukiko; Maki, Kosuke

2015-01-01

In this study, the equivalence of the kinetic mechanisms of the formation of urea-induced kinetic folding intermediates and non-native equilibrium states was investigated in apomyoglobin. Despite having similar structural properties, equilibrium and kinetic intermediates accumulate under different conditions and via different mechanisms, and it remains unknown whether their formation involves shared or distinct kinetic mechanisms. To investigate the potential mechanisms of formation, the refolding and unfolding kinetics of horse apomyoglobin were measured by continuous- and stopped-flow fluorescence over a time range from approximately 100 μs to 10 s, along with equilibrium unfolding transitions, as a function of urea concentration at pH 6.0 and 8°C. The formation of a kinetic intermediate was observed over a wider range of urea concentrations (0-2.2 M) than the formation of the native state (0-1.6 M). Additionally, the kinetic intermediate remained populated as the predominant equilibrium state under conditions where the native and unfolded states were unstable (at ~0.7-2 M urea). A continuous shift from the kinetic to the equilibrium intermediate was observed as urea concentrations increased from 0 M to ~2 M, which indicates that these states share a common kinetic folding mechanism. This finding supports the conclusion that these intermediates are equivalent. Our results in turn suggest that the regions of the protein that resist denaturant perturbations form during the earlier stages of folding, which further supports the structural equivalence of transient and equilibrium intermediates. An additional folding intermediate accumulated within ~140 μs of refolding and an unfolding intermediate accumulated in <1 ms of unfolding. Finally, by using quantitative modeling, we showed that a five-state sequential scheme appropriately describes the folding mechanism of horse apomyoglobin.

RNAiFOLD: a constraint programming algorithm for RNA inverse folding and molecular design.

PubMed

Garcia-Martin, Juan Antonio; Clote, Peter; Dotu, Ivan

2013-04-01

Synthetic biology is a rapidly emerging discipline with long-term ramifications that range from single-molecule detection within cells to the creation of synthetic genomes and novel life forms. Truly phenomenal results have been obtained by pioneering groups--for instance, the combinatorial synthesis of genetic networks, genome synthesis using BioBricks, and hybridization chain reaction (HCR), in which stable DNA monomers assemble only upon exposure to a target DNA fragment, biomolecular self-assembly pathways, etc. Such work strongly suggests that nanotechnology and synthetic biology together seem poised to constitute the most transformative development of the 21st century. In this paper, we present a Constraint Programming (CP) approach to solve the RNA inverse folding problem. Given a target RNA secondary structure, we determine an RNA sequence which folds into the target structure; i.e. whose minimum free energy structure is the target structure. Our approach represents a step forward in RNA design--we produce the first complete RNA inverse folding approach which allows for the specification of a wide range of design constraints. We also introduce a Large Neighborhood Search approach which allows us to tackle larger instances at the cost of losing completeness, while retaining the advantages of meeting design constraints (motif, GC-content, etc.). Results demonstrate that our software, RNAiFold, performs as well or better than all state-of-the-art approaches; nevertheless, our approach is unique in terms of completeness, flexibility, and the support of various design constraints. The algorithms presented in this paper are publicly available via the interactive webserver http://bioinformatics.bc.edu/clotelab/RNAiFold; additionally, the source code can be downloaded from that site.

Design and simulation of origami structures with smooth folds

PubMed Central

Peraza Hernandez, E. A.; Lagoudas, D. C.

2017-01-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds. This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh. PMID:28484322

Design and simulation of origami structures with smooth folds.

PubMed

Peraza Hernandez, E A; Hartl, D J; Lagoudas, D C

2017-04-01

Origami has enabled new approaches to the fabrication and functionality of multiple structures. Current methods for origami design are restricted to the idealization of folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures of non-negligible fold thickness or maximum curvature at the folds restricted by material limitations. For such structures, folds are not properly represented as creases but rather as bent regions of higher-order geometric continuity. Such fold regions of arbitrary order of continuity are termed as smooth folds . This paper presents a method for solving the following origami design problem: given a goal shape represented as a polygonal mesh (termed as the goal mesh ), find the geometry of a single planar sheet, its pattern of smooth folds, and the history of folding motion allowing the sheet to approximate the goal mesh. The parametrization of the planar sheet and the constraints that allow for a valid pattern of smooth folds are presented. The method is tested against various goal meshes having diverse geometries. The results show that every determined sheet approximates its corresponding goal mesh in a known folded configuration having fold angles obtained from the geometry of the goal mesh.

Predicting Electrostatic Forces in RNA Folding

PubMed Central

Tan, Zhi-Jie; Chen, Shi-Jie

2016-01-01

Metal ion-mediated electrostatic interactions are critical to RNA folding. Although considerable progress has been made in mechanistic studies, the problem of accurate predictions for the ion effects in RNA folding remains unsolved, mainly due to the complexity of several potentially important issues such as ion correlation and dehydration effects. In this chapter, after giving a brief overview of the experimental findings and theoretical approaches, we focus on a recently developed new model, the tightly bound ion (TBI) model, for ion electrostatics in RNA folding. The model is unique because it can treat ion correlation and fluctuation effects for realistic RNA 3D structures. For monovalent ion (such as Na+) solutions, where ion correlation is weak, TBI and the Poisson–Boltzmann (PB) theory give the same results and the results agree with the experimental data. For multivalent ion (such as Mg2+) solutions, where ion correlation can be strong, however, TBI gives much improved predictions than the PB. Moreover, the model suggests an ion correlation- induced mechanism for the unusual efficiency of Mg2+ ions in the stabilization of RNA tertiary folds. In this chapter, after introducing the theoretical framework of the TBI model, we will describe how to apply the model to predict ion-binding properties and ion-dependent folding stabilities. PMID:20946803

Cause of vocal fold scar.

PubMed

Allen, Jacqui

2010-12-01

The prolonged debilitation, loss of income, and decrement in quality of life caused by vocal fold scar is exacerbated by our inability to successfully treat this difficult problem. As technology focuses on developing innovative treatments, we need to fully appreciate and understand the mechanisms giving rise to glottal scar, on both a macroscopic and microscopic level. This review examines recent literature pertaining to the gross and molecular mechanisms which give rise to vocal fold scar. Mechanisms of vocal fold scar production have been examined in both macroscopic and microscopic detail. Trauma and injury involving any aspect of the lamina propria, particularly the deeper layers, may result in epithelial tethering and scar formation. At the molecular level, early inflammatory cytokines activate and recruit fibroblasts which then drive the fibrotic cascade. Transforming growth factor-β enhances fibrosis and is balanced by tissue matrix metalloproteinases and hepatocyte growth factor activity. Molecular signaling offers novel opportunities to intervene in scar formation. New work investigating the cause of vocal fold scar identifies complex molecular processes leading to fibrosis in the lamina propria. Improved mechanistic understanding offers insight into prevention strategies and possible targets for antifibrotic therapies that may help prevent or treat this debilitating condition.

Conserved nucleation sites reinforce the significance of Phi value analysis in protein-folding studies.

PubMed

Gianni, Stefano; Jemth, Per

2014-07-01

The only experimental strategy to address the structure of folding transition states, the so-called Φ value analysis, relies on the synergy between site directed mutagenesis and the measurement of reaction kinetics. Despite its importance, the Φ value analysis has been often criticized and its power to pinpoint structural information has been questioned. In this hypothesis, we demonstrate that comparing the Φ values between proteins not only allows highlighting the robustness of folding pathways but also provides per se a strong validation of the method. © 2014 International Union of Biochemistry and Molecular Biology.

Deterministic folding: The role of entropic forces and steric specificities

NASA Astrophysics Data System (ADS)

da Silva, Roosevelt A.; da Silva, M. A. A.; Caliri, A.

2001-03-01

The inverse folding problem of proteinlike macromolecules is studied by using a lattice Monte Carlo (MC) model in which steric specificities (nearest-neighbors constraints) are included and the hydrophobic effect is treated explicitly by considering interactions between the chain and solvent molecules. Chemical attributes and steric peculiarities of the residues are encoded in a 10-letter alphabet and a correspondent "syntax" is provided in order to write suitable sequences for the specified target structures; twenty-four target configurations, chosen in order to cover all possible values of the average contact order χ (0.2381⩽χ⩽0.4947 for this system), were encoded and analyzed. The results, obtained by MC simulations, are strongly influenced by geometrical properties of the native configuration, namely χ and the relative number φ of crankshafts-type structures: For χ<0.35 the folding is deterministic, that is, the syntax is able to encode successful sequences: The system presents larger encodability, minimum sequence-target degeneracies and smaller characteristic folding time τf. For χ⩾0.35 the above results are not reproduced any more: The folding success is severely reduced, showing strong correlation with φ. Additionally, the existence of distinct characteristic folding times suggests that different mechanisms are acting at the same time in the folding process. The results (all obtained from the same single model, under the same "physiological conditions") resemble some general features of the folding problem, supporting the premise that the steric specificities, in association with the entropic forces (hydrophobic effect), are basic ingredients in the protein folding process.

New insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: application to a hydrodynamic analysis of the folding flow.

PubMed

Kalgin, Igor V; Caflisch, Amedeo; Chekmarev, Sergei F; Karplus, Martin

2013-05-23

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance

New Insights into the Folding of a β-Sheet Miniprotein in a Reduced Space of Collective Hydrogen Bond Variables: Application to a Hydrodynamic Analysis of the Folding Flow

PubMed Central

Kalgin, Igor V.; Caflisch, Amedeo; Chekmarev, Sergei F.; Karplus, Martin

2013-01-01

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted Principal Component Analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed and it is complemented by a hydrodynamic analysis. The latter, making use of “passive tracers” in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface, but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with

Mining sequential patterns for protein fold recognition.

PubMed

Exarchos, Themis P; Papaloukas, Costas; Lampros, Christos; Fotiadis, Dimitrios I

2008-02-01

Protein data contain discriminative patterns that can be used in many beneficial applications if they are defined correctly. In this work sequential pattern mining (SPM) is utilized for sequence-based fold recognition. Protein classification in terms of fold recognition plays an important role in computational protein analysis, since it can contribute to the determination of the function of a protein whose structure is unknown. Specifically, one of the most efficient SPM algorithms, cSPADE, is employed for the analysis of protein sequence. A classifier uses the extracted sequential patterns to classify proteins in the appropriate fold category. For training and evaluating the proposed method we used the protein sequences from the Protein Data Bank and the annotation of the SCOP database. The method exhibited an overall accuracy of 25% in a classification problem with 36 candidate categories. The classification performance reaches up to 56% when the five most probable protein folds are considered.

The Folding of de Novo Designed Protein DS119 via Molecular Dynamics Simulations.

PubMed

Wang, Moye; Hu, Jie; Zhang, Zhuqing

2016-04-26

As they are not subjected to natural selection process, de novo designed proteins usually fold in a manner different from natural proteins. Recently, a de novo designed mini-protein DS119, with a βαβ motif and 36 amino acids, has folded unusually slowly in experiments, and transient dimers have been detected in the folding process. Here, by means of all-atom replica exchange molecular dynamics (REMD) simulations, several comparably stable intermediate states were observed on the folding free-energy landscape of DS119. Conventional molecular dynamics (CMD) simulations showed that when two unfolded DS119 proteins bound together, most binding sites of dimeric aggregates were located at the N-terminal segment, especially residues 5-10, which were supposed to form β-sheet with its own C-terminal segment. Furthermore, a large percentage of individual proteins in the dimeric aggregates adopted conformations similar to those in the intermediate states observed in REMD simulations. These results indicate that, during the folding process, DS119 can easily become trapped in intermediate states. Then, with diffusion, a transient dimer would be formed and stabilized with the binding interface located at N-terminals. This means that it could not quickly fold to the native structure. The complicated folding manner of DS119 implies the important influence of natural selection on protein-folding kinetics, and more improvement should be achieved in rational protein design.

Protein folding, protein structure and the origin of life: Theoretical methods and solutions of dynamical problems

NASA Technical Reports Server (NTRS)

Weaver, D. L.

1982-01-01

Theoretical methods and solutions of the dynamics of protein folding, protein aggregation, protein structure, and the origin of life are discussed. The elements of a dynamic model representing the initial stages of protein folding are presented. The calculation and experimental determination of the model parameters are discussed. The use of computer simulation for modeling protein folding is considered.

Enhanced picture of protein-folding intermediates using organic solvents in H/D exchange and quench-flow experiments

PubMed Central

Nishimura, Chiaki; Dyson, H. Jane; Wright, Peter E.

2005-01-01

Hydrogen/deuterium exchange followed by trapping of the labeled species in the aprotic solvent DMSO has been used to elucidate structure in both the burst-phase molten globule-folding intermediate of apomyoglobin and in an equilibrium intermediate that models the kinetic intermediate. Precise estimates can be made of exchange times in an interrupted exchange-out experiment at pH 4 followed by analysis in DMSO solution, giving extensive sequence-specific information about the structure of the equilibrium intermediate. In addition, the use of DMSO as a solvent for NMR measurements after quench-flow pH-pulse labeling experiments gives a greatly increased data set for the elucidation of the kinetic folding pathway. Interestingly, differences are observed in some regions of apomyoglobin between the equilibrium and kinetic intermediates. These differences are quantitative rather than qualitative; that is, the overall patterns of labeling and secondary structure formation remain similar between the two species. However, local differences are observed, which probably reflect the difference in the solution conditions for the equilibrium experiment (pH 4) vs. the kinetic experiment (pH 6) and the change in the status of the stabilizing hydrogen bond between the side chains of His-24 and His-119. PMID:15769860

UFO (UnFold Operator) computer program abstract

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kissel, L.; Biggs, F.

UFO (UnFold Operator) is an interactive user-oriented computer program designed to solve a wide range of problems commonly encountered in physical measurements. This document provides a summary of the capabilities of version 3A of UFO.

Interferences of Silica Nanoparticles in Green Fluorescent Protein Folding Processes.

PubMed

Klein, Géraldine; Devineau, Stéphanie; Aude, Jean Christophe; Boulard, Yves; Pasquier, Hélène; Labarre, Jean; Pin, Serge; Renault, Jean Philippe

2016-01-12

We investigated the relationship between unfolded proteins, silica nanoparticles and chaperonin to determine whether unfolded proteins could stick to silica surfaces and how this process could impair heat shock protein activity. The HSP60 catalyzed green fluorescent protein (GFP) folding was used as a model system. The adsorption isotherms and adsorption kinetics of denatured GFP were measured, showing that denaturation increases GFP affinity for silica surfaces. This affinity is maintained even if the surfaces are covered by a protein corona and allows silica NPs to interfere directly with GFP folding by trapping it in its unstructured state. We determined also the adsorption isotherms of HSP60 and its chaperonin activity once adsorbed, showing that SiO2 NP can interfere also indirectly with protein folding through chaperonin trapping and inhibition. This inhibition is specifically efficient when NPs are covered first with a layer of unfolded proteins. These results highlight for the first time the antichaperonin activity of silica NPs and ask new questions about the toxicity of such misfolded proteins/nanoparticles assembly toward cells.

A novel microfluidic mixer based on dual-hydrodynamic focusing for interrogating the kinetics of DNA-protein interaction.

PubMed

Li, Ying; Xu, Fei; Liu, Chao; Xu, Youzhi; Feng, Xiaojun; Liu, Bi-Feng

2013-08-21

Kinetic measurement of biomacromolecular interaction plays a significant role in revealing the underlying mechanisms of cellular activities. Due to the small diffusion coefficient of biomacromolecules, it is difficult to resolve the rapid kinetic process with traditional analytical methods such as stopped-flow or laminar mixers. Here, we demonstrated a unique continuous-flow laminar mixer based on microfluidic dual-hydrodynamic focusing to characterize the kinetics of DNA-protein interactions. The time window of this mixer for kinetics observation could cover from sub-milliseconds to seconds, which made it possible to capture the folding process with a wide dynamic range. Moreover, the sample consumption was remarkably reduced to <0.55 μL min⁻¹, over 1000-fold saving in comparison to those reported previously. We further interrogated the interaction kinetics of G-quadruplex and the single-stranded DNA binding protein, indicating that this novel micromixer would be a useful approach for analyzing the interaction kinetics of biomacromolecules.

Navigating ligand protein binding free energy landscapes: universality and diversity of protein folding and molecular recognition mechanisms

NASA Astrophysics Data System (ADS)

Verkhivker, Gennady M.; Rejto, Paul A.; Bouzida, Djamal; Arthurs, Sandra; Colson, Anthony B.; Freer, Stephan T.; Gehlhaar, Daniel K.; Larson, Veda; Luty, Brock A.; Marrone, Tami; Rose, Peter W.

2001-03-01

Thermodynamic and kinetic aspects of ligand-protein binding are studied for the methotrexate-dihydrofolate reductase system from the binding free energy profile constructed as a function of the order parameter. Thermodynamic stability of the native complex and a cooperative transition to the unique native structure suggest the nucleation kinetic mechanism at the equilibrium transition temperature. Structural properties of the transition state ensemble and the ensemble of nucleation conformations are determined by kinetic simulations of the transmission coefficient and ligand-protein association pathways. Structural analysis of the transition states and the nucleation conformations reconciles different views on the nucleation mechanism in protein folding.

Statistical mechanics of simple models of protein folding and design.

PubMed Central

Pande, V S; Grosberg, A Y; Tanaka, T

1997-01-01

It is now believed that the primary equilibrium aspects of simple models of protein folding are understood theoretically. However, current theories often resort to rather heavy mathematics to overcome some technical difficulties inherent in the problem or start from a phenomenological model. To this end, we take a new approach in this pedagogical review of the statistical mechanics of protein folding. The benefit of our approach is a drastic mathematical simplification of the theory, without resort to any new approximations or phenomenological prescriptions. Indeed, the results we obtain agree precisely with previous calculations. Because of this simplification, we are able to present here a thorough and self contained treatment of the problem. Topics discussed include the statistical mechanics of the random energy model (REM), tests of the validity of REM as a model for heteropolymer freezing, freezing transition of random sequences, phase diagram of designed ("minimally frustrated") sequences, and the degree to which errors in the interactions employed in simulations of either folding and design can still lead to correct folding behavior. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 6 PMID:9414231

Folding superfunnel to describe cooperative folding of interacting proteins.

PubMed

Smeller, László

2016-07-01

This paper proposes a generalization of the well-known folding funnel concept of proteins. In the funnel model the polypeptide chain is treated as an individual object not interacting with other proteins. Since biological systems are considerably crowded, protein-protein interaction is a fundamental feature during the life cycle of proteins. The folding superfunnel proposed here describes the folding process of interacting proteins in various situations. The first example discussed is the folding of the freshly synthesized protein with the aid of chaperones. Another important aspect of protein-protein interactions is the folding of the recently characterized intrinsically disordered proteins, where binding to target proteins plays a crucial role in the completion of the folding process. The third scenario where the folding superfunnel is used is the formation of aggregates from destabilized proteins, which is an important factor in case of several conformational diseases. The folding superfunnel constructed here with the minimal assumption about the interaction potential explains all three cases mentioned above. Proteins 2016; 84:1009-1016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Folding and Hydrodynamics of a DNA i-Motif from the c-MYC Promoter Determined by Fluorescent Cytidine Analogs

PubMed Central

Reilly, Samantha M.; Lyons, Daniel F.; Wingate, Sara E.; Wright, Robert T.; Correia, John J.; Jameson, David M.; Wadkins, Randy M.

2014-01-01

The four-stranded i-motif (iM) conformation of cytosine-rich DNA has importance to a wide variety of biochemical systems that range from their use in nanomaterials to potential roles in oncogene regulation. The iM structure is formed at slightly acidic pH, where hemiprotonation of cytosine results in a stable C-C+ basepair. Here, we performed fundamental studies to examine iM formation from a C-rich strand from the promoter of the human c-MYC gene. We used a number of biophysical techniques to characterize both the hydrodynamic properties and folding kinetics of a folded iM. Our hydrodynamic studies using fluorescence anisotropy decay and analytical ultracentrifugation show that the iM structure has a compact size in solution and displays the rigidity of a double strand. By studying the rates of circular dichroism spectral changes and quenching of fluorescent cytidine analogs, we also established a mechanism for the folding of a random coil oligo into the iM. In the course of determining this folding pathway, we established that the fluorescent dC analogs tC° and PdC can be used to monitor individual residues of an iM structure and to determine the pKa of an iM. We established that the C-C+ hydrogen bonding of certain bases initiates the folding of the iM structure. We also showed that substitutions in the loop regions of iMs give a distinctly different kinetic signature during folding compared with bases that are intercalated. Our data reveal that the iM passes through a distinct intermediate form between the unfolded and folded forms. Taken together, our results lay the foundation for using fluorescent dC analogs to follow structural changes during iM formation. Our technique may also be useful for examining folding and structural changes in more complex iMs. PMID:25296324

Direct Observation of Parallel Folding Pathways Revealed Using a Symmetric Repeat Protein System

PubMed Central

Aksel, Tural; Barrick, Doug

2014-01-01

Although progress has been made to determine the native fold of a polypeptide from its primary structure, the diversity of pathways that connect the unfolded and folded states has not been adequately explored. Theoretical and computational studies predict that proteins fold through parallel pathways on funneled energy landscapes, although experimental detection of pathway diversity has been challenging. Here, we exploit the high translational symmetry and the direct length variation afforded by linear repeat proteins to directly detect folding through parallel pathways. By comparing folding rates of consensus ankyrin repeat proteins (CARPs), we find a clear increase in folding rates with increasing size and repeat number, although the size of the transition states (estimated from denaturant sensitivity) remains unchanged. The increase in folding rate with chain length, as opposed to a decrease expected from typical models for globular proteins, is a clear demonstration of parallel pathways. This conclusion is not dependent on extensive curve-fitting or structural perturbation of protein structure. By globally fitting a simple parallel-Ising pathway model, we have directly measured nucleation and propagation rates in protein folding, and have quantified the fluxes along each path, providing a detailed energy landscape for folding. This finding of parallel pathways differs from results from kinetic studies of repeat-proteins composed of sequence-variable repeats, where modest repeat-to-repeat energy variation coalesces folding into a single, dominant channel. Thus, for globular proteins, which have much higher variation in local structure and topology, parallel pathways are expected to be the exception rather than the rule. PMID:24988356

High Pressure ZZ-Exchange NMR Reveals Key Features of Protein Folding Transition States.

PubMed

Zhang, Yi; Kitazawa, Soichiro; Peran, Ivan; Stenzoski, Natalie; McCallum, Scott A; Raleigh, Daniel P; Royer, Catherine A

2016-11-23

Understanding protein folding mechanisms and their sequence dependence requires the determination of residue-specific apparent kinetic rate constants for the folding and unfolding reactions. Conventional two-dimensional NMR, such as HSQC experiments, can provide residue-specific information for proteins. However, folding is generally too fast for such experiments. ZZ-exchange NMR spectroscopy allows determination of folding and unfolding rates on much faster time scales, yet even this regime is not fast enough for many protein folding reactions. The application of high hydrostatic pressure slows folding by orders of magnitude due to positive activation volumes for the folding reaction. We combined high pressure perturbation with ZZ-exchange spectroscopy on two autonomously folding protein domains derived from the ribosomal protein, L9. We obtained residue-specific apparent rates at 2500 bar for the N-terminal domain of L9 (NTL9), and rates at atmospheric pressure for a mutant of the C-terminal domain (CTL9) from pressure dependent ZZ-exchange measurements. Our results revealed that NTL9 folding is almost perfectly two-state, while small deviations from two-state behavior were observed for CTL9. Both domains exhibited large positive activation volumes for folding. The volumetric properties of these domains reveal that their transition states contain most of the internal solvent excluded voids that are found in the hydrophobic cores of the respective native states. These results demonstrate that by coupling it with high pressure, ZZ-exchange can be extended to investigate a large number of protein conformational transitions.

Multiple-probe analysis of folding and unfolding pathways of human serum albumin. Evidence for a framework mechanism of folding.

PubMed

Santra, Manas Kumar; Banerjee, Abhijit; Krishnakumar, Shyam Sundar; Rahaman, Obaidur; Panda, Dulal

2004-05-01

The changes in the far-UV CD signal, intrinsic tryptophan fluorescence and bilirubin absorbance showed that the guanidine hydrochloride (GdnHCl)-induced unfolding of a multidomain protein, human serum albumin (HSA), followed a two-state process. However, using environment sensitive Nile red fluorescence, the unfolding and folding pathways of HSA were found to follow a three-state process and an intermediate was detected in the range 0.25-1.5 m GdnHCl. The intermediate state displayed 45% higher fluorescence intensity than that of the native state. The increase in the Nile red fluorescence was found to be due to an increase in the quantum yield of the HSA-bound Nile red. Low concentrations of GdnHCl neither altered the binding affinity of Nile red to HSA nor induced the aggregation of HSA. In addition, the secondary structure of HSA was not perturbed during the first unfolding transition (<1.5 m GdnHCl); however, the secondary structure was completely lost during the second transition. The data together showed that the half maximal loss of the tertiary structure occurred at a lower GdnHCl concentration than the loss of the secondary structure. Further kinetic studies of the refolding process of HSA using multiple spectroscopic techniques showed that the folding occurred in two phases, a burst phase followed by a slow phase. An intermediate with native-like secondary structure but only a partial tertiary structure was found to form in the burst phase of refolding. Then, the intermediate slowly folded into the native state. An analysis of the refolding data suggested that the folding of HSA could be best explained by the framework model.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model.

PubMed

Wako, Hiroshi; Abe, Haruo

2016-01-01

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model

PubMed Central

Wako, Hiroshi; Abe, Haruo

2016-01-01

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding. PMID:28409079

Mechanical development of folded chert beds in Monterey Formation, California

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crowther, D.; Snyder, W.S.

1988-03-01

Small-scale folds in the upper siliceous facies of the Miocene Monterey Formation, at Lions Head, California (Santa Maria basin) are of tectonic origin. Folding is well developed in the chert-dominated zones and dies out rapidly in the adjacent siliceous mudstones. A tectonic origin is evidenced by the dominantly brittle deformation of the competent chert layers. Mechanically, the folds formed through a complex interrelationship between fracture and flexural slip. Opal-CT and quartz-chert layers display brittle fractures and rotated fracture blocks that responded to shortening. Thrusting of the chert layers is common in folds where fold propagation was impeded. Dilation breccia andmore » void space occur in the hinges and reflect room problems during development of these disharmonic folds. Subsequent diagenesis has partially healed the fractures and slip surfaces, creating the erroneous appearance that ductile deformation was an important factor in the formation of the folds.« less

Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem.

PubMed

Frausto-Solis, Juan; Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J Javier; González-Flores, Carlos; Castilla-Valdez, Guadalupe

2016-01-01

A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

The Folding of de Novo Designed Protein DS119 via Molecular Dynamics Simulations

PubMed Central

Wang, Moye; Hu, Jie; Zhang, Zhuqing

2016-01-01

As they are not subjected to natural selection process, de novo designed proteins usually fold in a manner different from natural proteins. Recently, a de novo designed mini-protein DS119, with a βαβ motif and 36 amino acids, has folded unusually slowly in experiments, and transient dimers have been detected in the folding process. Here, by means of all-atom replica exchange molecular dynamics (REMD) simulations, several comparably stable intermediate states were observed on the folding free-energy landscape of DS119. Conventional molecular dynamics (CMD) simulations showed that when two unfolded DS119 proteins bound together, most binding sites of dimeric aggregates were located at the N-terminal segment, especially residues 5–10, which were supposed to form β-sheet with its own C-terminal segment. Furthermore, a large percentage of individual proteins in the dimeric aggregates adopted conformations similar to those in the intermediate states observed in REMD simulations. These results indicate that, during the folding process, DS119 can easily become trapped in intermediate states. Then, with diffusion, a transient dimer would be formed and stabilized with the binding interface located at N-terminals. This means that it could not quickly fold to the native structure. The complicated folding manner of DS119 implies the important influence of natural selection on protein-folding kinetics, and more improvement should be achieved in rational protein design. PMID:27128902

Conceptual Transformation and Cognitive Processes in Origami Paper Folding

ERIC Educational Resources Information Center

Tenbrink, Thora; Taylor, Holly A.

2015-01-01

Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. Such tasks are not seen as cognitively challenging problems to be solved. In this paper, we challenge this assumption by analyzing verbal protocols collected during an Origami folding task. Participants…

Method-Unifying View of Loop-Formation Kinetics in Peptide and Protein Folding.

PubMed

Jacob, Maik H; D'Souza, Roy N; Schwarzlose, Thomas; Wang, Xiaojuan; Huang, Fang; Haas, Elisha; Nau, Werner M

2018-04-26

Protein folding can be described as a probabilistic succession of events in which the peptide chain forms loops closed by specific amino acid residue contacts, herein referred to as loop nodes. To measure loop rates, several photophysical methods have been introduced where a pair of optically active probes is incorporated at selected chain positions and the excited probe undergoes contact quenching (CQ) upon collision with the second probe. The quenching mechanisms involved triplet-triplet energy transfer, photoinduced electron transfer, and collision-induced fluorescence quenching, where the fluorescence of Dbo, an asparagine residue conjugated to 2,3-diazabicyclo[2.2.2]octane, is quenched by tryptophan. The discrepancy between the loop rates afforded from these three CQ techniques has, however, remained unresolved. In analyzing this discrepancy, we now report two short-distance FRET methods where Dbo acts as an energy acceptor in combination with tryptophan and naphtylalanine, two donors with largely different fluorescence lifetimes of 1.3 and 33 ns, respectively. Despite the different quenching mechanisms, the rates from FRET and CQ methods were, surprisingly, of comparable magnitude. This combination of FRET and CQ data led to a unifying physical model and to the conclusion that the rate of loop formation in folding reactions varies not only with the kind and number of residues that constitute the chain but also in particular with the size and properties of the residues that constitute the loop node.

Further optimization of a hybrid united-atom and coarse-grained force field for folding simulations: Improved backbone hydration and interactions between charged side chains

PubMed Central

Han, Wei; Schulten, Klaus

2012-01-01

PACE, a hybrid force field which couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve itse ciency for folding simulations. Backbone hydration parameters have been re-optimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE in order to provide a more realistic description of interactions between charged groups. Using replica exchange molecular dynamics (REMD), ab initio folding using the new PACE has been achieved for seven small proteins (16 – 23 residues) with different structural motifs. Experimental data about folded states, such as their stability at room temperature, melting point and NMR NOE constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temperature has been made with experiments, through standard MD simulations, showing that the new PACE may speed up the actual folding kinetics 5-10 times. Together with the computational speedup benefited from coarse-graining, the force field provides opportunities to study folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, 3D, in multiple 10 – 30 μs simulations, to its native states (Cα RMSD ~ 0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins. PMID:23204949

INFO-RNA--a fast approach to inverse RNA folding.

PubMed

Busch, Anke; Backofen, Rolf

2006-08-01

The structure of RNA molecules is often crucial for their function. Therefore, secondary structure prediction has gained much interest. Here, we consider the inverse RNA folding problem, which means designing RNA sequences that fold into a given structure. We introduce a new algorithm for the inverse folding problem (INFO-RNA) that consists of two parts; a dynamic programming method for good initial sequences and a following improved stochastic local search that uses an effective neighbor selection method. During the initialization, we design a sequence that among all sequences adopts the given structure with the lowest possible energy. For the selection of neighbors during the search, we use a kind of look-ahead of one selection step applying an additional energy-based criterion. Afterwards, the pre-ordered neighbors are tested using the actual optimization criterion of minimizing the structure distance between the target structure and the mfe structure of the considered neighbor. We compared our algorithm to RNAinverse and RNA-SSD for artificial and biological test sets. Using INFO-RNA, we performed better than RNAinverse and in most cases, we gained better results than RNA-SSD, the probably best inverse RNA folding tool on the market. www.bioinf.uni-freiburg.de?Subpages/software.html.

Alpha-glucosidase folding during urea denaturation: enzyme kinetics and computational prediction.

PubMed

Wu, Xue-Qiang; Wang, Jun; Lü, Zhi-Rong; Tang, Hong-Min; Park, Daeui; Oh, Sang-Ho; Bhak, Jong; Shi, Long; Park, Yong-Doo; Zou, Fei

2010-03-01

In this study, we investigated structural changes in alpha-glucosidase during urea denaturation. Alpha-glucosidase was inactivated by urea in a dose-dependent manner. The inactivation was a first-order reaction with a monophase process. Urea inhibited alpha-glucosidase in a mixed-type reaction. We found that an increase in the hydrophobic surface of this enzyme induced by urea resulted in aggregation caused by unstable folding intermediates. We also simulated the docking between alpha-glucosidase and urea. The docking simulation suggested that several residues, namely THR9, TRP14, LYS15, THR287, ALA289, ASP338, SER339, and TRP340, interact with urea. Our study provides insights into the alpha-glucosidase unfolding pathway and 3D structure of alpha-glucosidase.

Designing cooperatively folded abiotic uni- and multimolecular helix bundles

NASA Astrophysics Data System (ADS)

de, Soumen; Chi, Bo; Granier, Thierry; Qi, Ting; Maurizot, Victor; Huc, Ivan

2018-01-01

Abiotic foldamers, that is foldamers that have backbones chemically remote from peptidic and nucleotidic skeletons, may give access to shapes and functions different to those of peptides and nucleotides. However, design methodologies towards abiotic tertiary and quaternary structures are yet to be developed. Here we report rationally designed interactional patterns to guide the folding and assembly of abiotic helix bundles. Computational design facilitated the introduction of hydrogen-bonding functionalities at defined locations on the aromatic amide backbones that promote cooperative folding into helix-turn-helix motifs in organic solvents. The hydrogen-bond-directed aggregation of helices not linked by a turn unit produced several thermodynamically and kinetically stable homochiral dimeric and trimeric bundles with structures that are distinct from the designed helix-turn-helix. Relative helix orientation within the bundles may be changed from parallel to tilted on subtle solvent variations. Altogether, these results prefigure the richness and uniqueness of abiotic tertiary structure behaviour.

Pectin as an Extraordinary Natural Kinetic Hydrate Inhibitor

PubMed Central

Xu, Shurui; Fan, Shuanshi; Fang, Songtian; Lang, Xuemei; Wang, Yanhong; Chen, Jun

2016-01-01

Pectin as a novel natural kinetic hydrate inhibitor, expected to be eco-friendly and sufficiently biodegradable, was studied in this paper. The novel crystal growth inhibition (CGI) and standard induction time methods were used to evaluate its effect as hydrate inhibitor. It could successfully inhibit methane hydrate formation at subcooling temperature up to 12.5 °C and dramatically slowed the hydrate crystal growth. The dosage of pectin decreased by 66% and effective time extended 10 times than typical kinetic inhibitor. Besides, its maximum growth rate was no more than 2.0%/h, which was far less than 5.5%/h of growth rate for PVCap at the same dosage. The most prominent feature was that it totally inhibited methane hydrate crystal rapid growth when hydrate crystalline occurred. Moreover, in terms of typical natural inhibitors, the inhibition activity of pectin increased 10.0-fold in induction time and 2.5-fold in subcooling temperature. The extraordinary inhibition activity is closely related to its hydrogen bonding interaction with water molecules and the hydrophilic structure. Finally, the biodegradability and economical efficiency of pectin were also taken into consideration. The results showed the biodegradability improved 75.0% and the cost reduced by more than 73.3% compared to typical commercial kinetic inhibitors. PMID:26996773

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

PubMed Central

Strulson, Christopher A.; Boyer, Joshua A.; Whitman, Elisabeth E.; Bevilacqua, Philip C.

2014-01-01

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg2+ ion concentrations are low, K+ concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo–like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg2+ (0.5–2 mM) and K+ (140 mM) if the solution is supplemented with physiological amounts (∼20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution. PMID:24442612

Discovery and structural characterisation of new fold type IV-transaminases exemplify the diversity of this enzyme fold

PubMed Central

Pavkov-Keller, Tea; Strohmeier, Gernot A.; Diepold, Matthias; Peeters, Wilco; Smeets, Natascha; Schürmann, Martin; Gruber, Karl; Schwab, Helmut; Steiner, Kerstin

2016-01-01

Transaminases are useful biocatalysts for the production of amino acids and chiral amines as intermediates for a broad range of drugs and fine chemicals. Here, we describe the discovery and characterisation of new transaminases from microorganisms which were enriched in selective media containing (R)-amines as sole nitrogen source. While most of the candidate proteins were clearly assigned to known subgroups of the fold IV family of PLP-dependent enzymes by sequence analysis and characterisation of their substrate specificity, some of them did not fit to any of these groups. The structure of one of these enzymes from Curtobacterium pusillum, which can convert d-amino acids and various (R)-amines with high enantioselectivity, was solved at a resolution of 2.4 Å. It shows significant differences especially in the active site compared to other transaminases of the fold IV family and thus indicates the existence of a new subgroup within this family. Although the discovered transaminases were not able to convert ketones in a reasonable time frame, overall, the enrichment-based approach was successful, as we identified two amine transaminases, which convert (R)-amines with high enantioselectivity, and can be used for a kinetic resolution of 1-phenylethylamine and analogues to obtain the (S)-amines with e.e.s >99%. PMID:27905516

Coiling and Folding of Viscoelastic Jets

NASA Astrophysics Data System (ADS)

Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth

2007-11-01

The study of fluid jets impacting on a flat surface has industrial applications in many areas, including processing of foods and consumer goods, bottle filling, and polymer melt processing. Previous studies have focused primarily on purely viscous, Newtonian fluids, which exhibit a number of different dynamical regimes including dripping, steady jetting, folding, and steady coiling. Here we add another dimension to the problem by focusing on mobile (low viscosity) viscoelastic fluids, with the study of two wormlike-micellar fluids, a cetylpyridinum-salicylic acid salt (CPyCl/NaSal) solution, and an industrially relevant shampoo base. We investigate the effects of viscosity and elasticity on the dynamics of axi-symmetric jets. The viscoelasticity of the fluids is systematically controlled by varying the concentration of salt counterions. Experimental methods include shear and extensional rheology measurements to characterize the fluids, and high-speed digital video imaging. In addition to the regimes observed in purely viscous systems, we also find a novel regime in which the elastic jet buckles and folds on itself, and alternates between coiling and folding behavior. We suggest phase diagrams and scaling laws for the coiling and folding frequencies through a systematic exploration of the experimental parameter space (height of fall, imposed flow rate, elasticity of the solution).

Unique fluorophores in the dimeric archaeal histones hMfB and hPyA1 reveal the impact of nonnative structure in a monomeric kinetic intermediate

PubMed Central

Stump, Matthew R.; Gloss, Lisa M.

2008-01-01

Homodimeric archaeal histones and heterodimeric eukaryotic histones share a conserved structure but fold through different kinetic mechanisms, with a correlation between faster folding/association rates and the population of kinetic intermediates. Wild-type hMfB (from Methanothermus fervidus) has no intrinsic fluorophores; Met35, which is Tyr in hyperthermophilic archaeal histones such as hPyA1 (from Pyrococcus strain GB-3A), was mutated to Tyr and Trp. Two Tyr-to-Trp mutants of hPyA1 were also characterized. All fluorophores were introduced into the long, central α-helix of the histone fold. Far-UV circular dichroism (CD) indicated that the fluorophores did not significantly alter the helical content of the histones. The equilibrium unfolding transitions of the histone variants were two-state, reversible processes, with ΔG°(H2O) values within 1 kcal/mol of the wild-type dimers. The hPyA1 Trp variants fold by two-state kinetic mechanisms like wild-type hPyA1, but with increased folding and unfolding rates, suggesting that the mutated residues (Tyr-32 and Tyr-36) contribute to transition state structure. Like wild-type hMfB, M35Y and M35W hMfB fold by a three-state mechanism, with a stopped-flow CD burst-phase monomeric intermediate. The M35 mutants populate monomeric intermediates with increased secondary structure and stability but exhibit decreased folding rates; this suggests that nonnative interactions occur from burial of the hydrophobic Tyr and Trp residues in this kinetic intermediate. These results implicate the long central helix as a key component of the structure in the kinetic monomeric intermediates of hMfB as well as the dimerization transition state in the folding of hPyA1. PMID:18096639

Improved genetic algorithm for the protein folding problem by use of a Cartesian combination operator.

PubMed Central

Rabow, A. A.; Scheraga, H. A.

1996-01-01

We have devised a Cartesian combination operator and coding scheme for improving the performance of genetic algorithms applied to the protein folding problem. The genetic coding consists of the C alpha Cartesian coordinates of the protein chain. The recombination of the genes of the parents is accomplished by: (1) a rigid superposition of one parent chain on the other, to make the relation of Cartesian coordinates meaningful, then, (2) the chains of the children are formed through a linear combination of the coordinates of their parents. The children produced with this Cartesian combination operator scheme have similar topology and retain the long-range contacts of their parents. The new scheme is significantly more efficient than the standard genetic algorithm methods for locating low-energy conformations of proteins. The considerable superiority of genetic algorithms over Monte Carlo optimization methods is also demonstrated. We have also devised a new dynamic programming lattice fitting procedure for use with the Cartesian combination operator method. The procedure finds excellent fits of real-space chains to the lattice while satisfying bond-length, bond-angle, and overlap constraints. PMID:8880904

RNAiFold2T: Constraint Programming design of thermo-IRES switches.

PubMed

Garcia-Martin, Juan Antonio; Dotu, Ivan; Fernandez-Chamorro, Javier; Lozano, Gloria; Ramajo, Jorge; Martinez-Salas, Encarnacion; Clote, Peter

2016-06-15

RNA thermometers (RNATs) are cis-regulatory elements that change secondary structure upon temperature shift. Often involved in the regulation of heat shock, cold shock and virulence genes, RNATs constitute an interesting potential resource in synthetic biology, where engineered RNATs could prove to be useful tools in biosensors and conditional gene regulation. Solving the 2-temperature inverse folding problem is critical for RNAT engineering. Here we introduce RNAiFold2T, the first Constraint Programming (CP) and Large Neighborhood Search (LNS) algorithms to solve this problem. Benchmarking tests of RNAiFold2T against existent programs (adaptive walk and genetic algorithm) inverse folding show that our software generates two orders of magnitude more solutions, thus allowing ample exploration of the space of solutions. Subsequently, solutions can be prioritized by computing various measures, including probability of target structure in the ensemble, melting temperature, etc. Using this strategy, we rationally designed two thermosensor internal ribosome entry site (thermo-IRES) elements, whose normalized cap-independent translation efficiency is approximately 50% greater at 42 °C than 30 °C, when tested in reticulocyte lysates. Translation efficiency is lower than that of the wild-type IRES element, which on the other hand is fully resistant to temperature shift-up. This appears to be the first purely computational design of functional RNA thermoswitches, and certainly the first purely computational design of functional thermo-IRES elements. RNAiFold2T is publicly available as part of the new release RNAiFold3.0 at https://github.com/clotelab/RNAiFold and http://bioinformatics.bc.edu/clotelab/RNAiFold, which latter has a web server as well. The software is written in C ++ and uses OR-Tools CP search engine. clote@bc.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Equilibrium Ensembles for Insulin Folding from Bias-Exchange Metadynamics.

PubMed

Singh, Richa; Bansal, Rohit; Rathore, Anurag Singh; Goel, Gaurav

2017-04-25

Earliest events in the aggregation process, such as single molecule reconfiguration, are extremely important and the most difficult to characterize in experiments. To this end, we have used well-tempered bias exchange metadynamics simulations to determine the equilibrium ensembles of an insulin molecule under amyloidogenic conditions of low pH and high temperature. A bin-based clustering method that uses statistics accumulated in bias exchange metadynamics trajectories was employed to construct a detailed thermodynamic and kinetic model of insulin folding. The highest lifetime, lowest free-energy ensemble identified consisted of native conformations adopted by a folded insulin monomer in solution, namely, the R-, the R f -, and the T-states of insulin. The lowest free-energy structure had a root mean square deviation of only 0.15 nm from native x-ray structure. The second longest-lived metastable state was an unfolded, compact monomer with little similarity to the native structure. We have identified three additional long-lived, metastable states from the bin-based model. We then carried out an exhaustive structural characterization of metastable states on the basis of tertiary contact maps and per-residue accessible surface areas. We have also determined the lowest free-energy path between two longest-lived metastable states and confirm earlier findings of non-two-state folding for insulin through a folding intermediate. The ensemble containing the monomeric intermediate retained 58% of native hydrophobic contacts, however, accompanied by a complete loss of native secondary structure. We have discussed the relative importance of nativelike versus nonnative tertiary contacts for the folding transition. We also provide a simple measure to determine the importance of an individual residue for folding transition. Finally, we have compared and contrasted this intermediate with experimental data obtained in spectroscopic, crystallographic, and calorimetric measurements

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.

PubMed

Madain, Alia; Abu Dalhoum, Abdel Latif; Sleit, Azzam

2018-06-01

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.

The Effect of Surface Electrical Stimulation on Vocal Fold Position

PubMed Central

Humbert, Ianessa A.; Poletto, Christopher J.; Saxon, Keith G.; Kearney, Pamela R.; Ludlow, Christy L.

2008-01-01

Objectives/Hypothesis Closure of the true and false vocal folds is a normal part of airway protection during swallowing. Individuals with reduced or delayed true vocal fold closure can be at risk for aspiration and benefit from intervention to ameliorate the problem. Surface electrical stimulation is currently used during therapy for dysphagia, despite limited knowledge of its physiological effects. Design Prospective single effects study. Methods The immediate physiological effect of surface stimulation on true vocal fold angle was examined at rest in 27 healthy adults using ten different electrode placements on the submental and neck regions. Fiberoptic nasolaryngoscopic recordings during passive inspiration were used to measure change in true vocal fold angle with stimulation. Results Vocal fold angles changed only to a small extent during two electrode placements (p ≤ 0.05). When two sets of electrodes were placed vertically on the neck the mean true vocal fold abduction was 2.4 degrees; while horizontal placements of electrodes in the submental region produced a mean adduction of 2.8 degrees (p=0.03). Conclusions Surface electrical stimulation to the submental and neck regions does not produce immediate true vocal fold adduction adequate for airway protection during swallowing and one position may produce a slight increase in true vocal fold opening. PMID:18043496

The E. coli thioredoxin folding mechanism: the key role of the C-terminal helix.

PubMed

Vazquez, Diego S; Sánchez, Ignacio E; Garrote, Ana; Sica, Mauricio P; Santos, Javier

2015-02-01

In this work, the unfolding mechanism of oxidized Escherichia coli thioredoxin (EcTRX) was investigated experimentally and computationally. We characterized seven point mutants distributed along the C-terminal α-helix (CTH) and the preceding loop. The mutations destabilized the protein against global unfolding while leaving the native structure unchanged. Global analysis of the unfolding kinetics of all variants revealed a linear unfolding route with a high-energy on-pathway intermediate state flanked by two transition state ensembles TSE1 and TSE2. The experiments show that CTH is mainly unfolded in TSE1 and the intermediate and becomes structured in TSE2. Structure-based molecular dynamics are in agreement with these experiments and provide protein-wide structural information on transient states. In our model, EcTRX folding starts with structure formation in the β-sheet, while the protein helices coalesce later. As a whole, our results indicate that the CTH is a critical module in the folding process, restraining a heterogeneous intermediate ensemble into a biologically active native state and providing the native protein with thermodynamic and kinetic stability. Copyright © 2014 Elsevier B.V. All rights reserved.

Mechanisms of protein-folding diseases at a glance.

PubMed

Valastyan, Julie S; Lindquist, Susan

2014-01-01

For a protein to function appropriately, it must first achieve its proper conformation and location within the crowded environment inside the cell. Multiple chaperone systems are required to fold proteins correctly. In addition, degradation pathways participate by destroying improperly folded proteins. The intricacy of this multisystem process provides many opportunities for error. Furthermore, mutations cause misfolded, nonfunctional forms of proteins to accumulate. As a result, many pathological conditions are fundamentally rooted in the protein-folding problem that all cells must solve to maintain their function and integrity. Here, to illustrate the breadth of this phenomenon, we describe five examples of protein-misfolding events that can lead to disease: improper degradation, mislocalization, dominant-negative mutations, structural alterations that establish novel toxic functions, and amyloid accumulation. In each case, we will highlight current therapeutic options for battling such diseases.

Plasticity in the Oxidative Folding Pathway of the High Affinity Nerita Versicolor Carboxypeptidase Inhibitor (NvCI).

PubMed

Esperante, Sebastián A; Covaleda, Giovanni; Trejo, Sebastián A; Bronsoms, Sílvia; Aviles, Francesc X; Ventura, Salvador

2017-07-14

Nerita Versicolor carboxypeptidase inhibitor (NvCI) is the strongest inhibitor reported so far for the M14A subfamily of carboxypeptidases. It comprises 53 residues and a protein fold composed of a two-stranded antiparallel β sheet connected by three loops and stabilized by three disulfide bridges. Here we report the oxidative folding and reductive unfolding pathways of NvCI. Much debate has gone on whether protein conformational folding guides disulfide bond formation or instead they are disulfide bonds that favour the arrangement of local or global structural elements. We show here that for NvCI both possibilities apply. Under physiological conditions, this protein folds trough a funnelled pathway involving a network of kinetically connected native-like intermediates, all sharing the disulfide bond connecting the two β-strands. In contrast, under denaturing conditions, the folding of NvCI is under thermodynamic control and follows a "trial and error" mechanism, in which an initial quasi-stochastic population of intermediates rearrange their disulfide bonds to attain the stable native topology. Despite their striking mechanistic differences, the efficiency of both folding routes is similar. The present study illustrates thus a surprising plasticity in the folding of this extremely stable small disulfide-rich inhibitor and provides the basis for its redesign for biomedical applications.

Single-molecule investigation of G-quadruplex folds of the human telomere sequence in a protein nanocavity

PubMed Central

An, Na; Fleming, Aaron M.; Middleton, Eric G.; Burrows, Cynthia J.

2014-01-01

Human telomeric DNA consists of tandem repeats of the sequence 5′-TTAGGG-3′ that can fold into various G-quadruplexes, including the hybrid, basket, and propeller folds. In this report, we demonstrate use of the α-hemolysin ion channel to analyze these subtle topological changes at a nanometer scale by providing structure-dependent electrical signatures through DNA–protein interactions. Whereas the dimensions of hybrid and basket folds allowed them to enter the protein vestibule, the propeller fold exceeds the size of the latch region, producing only brief collisions. After attaching a 25-mer poly-2′-deoxyadenosine extension to these structures, unraveling kinetics also were evaluated. Both the locations where the unfolding processes occur and the molecular shapes of the G-quadruplexes play important roles in determining their unfolding profiles. These results provide insights into the application of α-hemolysin as a molecular sieve to differentiate nanostructures as well as the potential technical hurdles DNA secondary structures may present to nanopore technology. PMID:25225404

Basin Hopping Graph: a computational framework to characterize RNA folding landscapes

PubMed Central

Kucharík, Marcel; Hofacker, Ivo L.; Stadler, Peter F.; Qin, Jing

2014-01-01

Motivation: RNA folding is a complicated kinetic process. The minimum free energy structure provides only a static view of the most stable conformational state of the system. It is insufficient to give detailed insights into the dynamic behavior of RNAs. A sufficiently sophisticated analysis of the folding free energy landscape, however, can provide the relevant information. Results: We introduce the Basin Hopping Graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect basins when the direct transitions between them are ‘energetically favorable’. Edge weights endcode the corresponding saddle heights and thus measure the difficulties of these favorable transitions. BHGs can be approximated accurately and efficiently for RNA molecules well beyond the length range accessible to enumerative algorithms. Availability and implementation: The algorithms described here are implemented in C++ as standalone programs. Its source code and supplemental material can be freely downloaded from http://www.tbi.univie.ac.at/bhg.html. Contact: qin@bioinf.uni-leipzig.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:24648041

Biphasic Kinetic Behavior of Nitrate Reductase from Heterocystous, Nitrogen-Fixing Cyanobacteria 1

PubMed Central

Martin-Nieto, José; Flores, Enrique; Herrero, Antonia

1992-01-01

Nitrate reductase activity from filamentous, heterocyst-forming cyanobacteria showed a biphasic kinetic behavior with respect to nitrate as the variable substrate. Two kinetic components were detected, the first showing a higher affinity for nitrate (Km, 0.05-0.25 mm) and a lower catalytic activity and the second showing a lower affinity for nitrate (Km, 5-25 mm) and a higher (3- to 5-fold) catalytic activity. In contrast, among unicellular cyanobacteria, most representatives studied exhibited a monophasic, Michaelis-Menten kinetic pattern for nitrate reductase activity. Biphasic kinetics remained unchanged with the use of different assay conditions (i.e. cell disruption or permeabilization, two different electron donors) or throughout partial purification of the enzyme. PMID:16652939

WeFold: A Coopetition for Protein Structure Prediction

PubMed Central

Khoury, George A.; Liwo, Adam; Khatib, Firas; Zhou, Hongyi; Chopra, Gaurav; Bacardit, Jaume; Bortot, Leandro O.; Faccioli, Rodrigo A.; Deng, Xin; He, Yi; Krupa, Pawel; Li, Jilong; Mozolewska, Magdalena A.; Sieradzan, Adam K.; Smadbeck, James; Wirecki, Tomasz; Cooper, Seth; Flatten, Jeff; Xu, Kefan; Baker, David; Cheng, Jianlin; Delbem, Alexandre C. B.; Floudas, Christodoulos A.; Keasar, Chen; Levitt, Michael; Popović, Zoran; Scheraga, Harold A.; Skolnick, Jeffrey; Crivelli, Silvia N.; Players, Foldit

2014-01-01

The protein structure prediction problem continues to elude scientists. Despite the introduction of many methods, only modest gains were made over the last decade for certain classes of prediction targets. To address this challenge, a social-media based worldwide collaborative effort, named WeFold, was undertaken by thirteen labs. During the collaboration, the labs were simultaneously competing with each other. Here, we present the first attempt at “coopetition” in scientific research applied to the protein structure prediction and refinement problems. The coopetition was possible by allowing the participating labs to contribute different components of their protein structure prediction pipelines and create new hybrid pipelines that they tested during CASP10. This manuscript describes both successes and areas needing improvement as identified throughout the first WeFold experiment and discusses the efforts that are underway to advance this initiative. A footprint of all contributions and structures are publicly accessible at http://www.wefold.org. PMID:24677212

GLOBAL SOLUTIONS TO FOLDED CONCAVE PENALIZED NONCONVEX LEARNING

PubMed Central

Liu, Hongcheng; Yao, Tao; Li, Runze

2015-01-01

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms that find a provably global optimal solution. We refer to this reformulation-based technique as the mixed integer programming-based global optimization (MIPGO). To our knowledge, this is the first global optimization scheme with a theoretical guarantee for folded concave penalized nonconvex learning with the SCAD penalty (Fan and Li, 2001) and the MCP penalty (Zhang, 2010). Numerical results indicate a significant outperformance of MIPGO over the state-of-the-art solution scheme, local linear approximation, and other alternative solution techniques in literature in terms of solution quality. PMID:27141126

Generation of buckle folds in Naga fold thrust belt, north-east India

NASA Astrophysics Data System (ADS)

Saha, B.; Dietl, C.

2009-04-01

Naga fold thrust belt (NFTB), India, formed as a result of northward migration of the Indian plate initiated in Eocene and its subsequent collision with the Burmese plate during Oligocene. The NW-SE oriented compression generated a spectrum of structures; among them, we intend to focus on the folds- varying from gentle to tight asymmetric in geometry. Large recumbent folds are often associated with thrusting. Buckle folds forming under shallow crustal conditions are frequently reported from NFTB. Buckle folding occurs mainly within sandstones with intercalated shale layers which are in the study area typical for the Barail, Surma and Tipam Groups. We have tried to explain the controlling factors behind the variation of the buckle fold shapes and their varying wavelengths throughout the fold thrust belt with the aid of analogue (sand box) modelling. It is undoubted that competence contrast along with the layer parallel compressive stress are the major influencing factors in generation of buckle folds. Schmalholz and Podladchikov (1999) and Jeng et al. (2002) have shown that when low strain rate and low temperature are applicable, not only the viscosity contrast, but also the elasticity contrast govern the geometry of the developing buckle folds. Rocks deforming under high temperature and high pressure deform in pure viscous manner, whereas, rocks undergoing less confining stress and less temperature, are subjected to pure elastic deformation. However, they are the end members, and most of the deformations are a combination of these two end members, i.e. of viscoelastic nature. Our models are made up of sieved sand (0.5 mm grain size) and mica layers (1-5 mm) This interlayering imparts a mechanical anisotropy in the model. Mica is not a pure viscous material, rather it displays more elastic behaviour. The mica layers in the model produce bedding parallel slip during shortening through internal reorganization of the individual mica crystals leading to the thickening

Protein import and oxidative folding in the mitochondrial intermembrane space of intact mammalian cells

PubMed Central

Fischer, Manuel; Horn, Sebastian; Belkacemi, Anouar; Kojer, Kerstin; Petrungaro, Carmelina; Habich, Markus; Ali, Muna; Küttner, Victoria; Bien, Melanie; Kauff, Frank; Dengjel, Jörn; Herrmann, Johannes M.; Riemer, Jan

2013-01-01

Oxidation of cysteine residues to disulfides drives import of many proteins into the intermembrane space of mitochondria. Recent studies in yeast unraveled the basic principles of mitochondrial protein oxidation, but the kinetics under physiological conditions is unknown. We developed assays to follow protein oxidation in living mammalian cells, which reveal that import and oxidative folding of proteins are kinetically and functionally coupled and depend on the oxidoreductase Mia40, the sulfhydryl oxidase augmenter of liver regeneration (ALR), and the intracellular glutathione pool. Kinetics of substrate oxidation depends on the amount of Mia40 and requires tightly balanced amounts of ALR. Mia40-dependent import of Cox19 in human cells depends on the inner membrane potential. Our observations reveal considerable differences in the velocities of mitochondrial import pathways: whereas preproteins with bipartite targeting sequences are imported within seconds, substrates of Mia40 remain in the cytosol for several minutes and apparently escape premature degradation and oxidation. PMID:23676665

Folding Beauties

ERIC Educational Resources Information Center

Berman, Leah Wrenn

2006-01-01

This article has its genesis in an MAA mini-course on origami, where a way to get a parabola by folding paper was presented. This article discusses the methods and mathematics of other curves obtained by paper-folding.

Communication: Role of explicit water models in the helix folding/unfolding processes

NASA Astrophysics Data System (ADS)

Palazzesi, Ferruccio; Salvalaglio, Matteo; Barducci, Alessandro; Parrinello, Michele

2016-09-01

In the last years, it has become evident that computer simulations can assume a relevant role in modelling protein dynamical motions for their ability to provide a full atomistic image of the processes under investigation. The ability of the current protein force-fields in reproducing the correct thermodynamics and kinetics systems behaviour is thus an essential ingredient to improve our understanding of many relevant biological functionalities. In this work, employing the last developments of the metadynamics framework, we compare the ability of state-of-the-art all-atom empirical functions and water models to consistently reproduce the folding and unfolding of a helix turn motif in a model peptide. This theoretical study puts in evidence that the choice of the water models can influence the thermodynamic and the kinetics of the system under investigation, and for this reason cannot be considered trivial.

Unstirred Water Layers and the Kinetics of Organic Cation Transport

PubMed Central

Shibayama, Takahiro; Morales, Mark; Zhang, Xiaohong; Martinez, Lucy; Berteloot, Alfred; Secomb, Timothy W.; Wright, Stephen H.

2015-01-01

Purpose Unstirred water layers (UWLs) present an unavoidable complication in the measurement of transport kinetics in cultured cells and the high rates of transport achieved by overexpressing heterologous transporters exacerbate the UWL effect. This study examined the correlation between measured Jmax and Kt values and the effect of manipulating UWL thickness or transport Jmax on the accuracy of experimentally determined kinetics of the multidrug transporters, OCT2 and MATE1. Methods Transport of TEA and MPP was measured in CHO cells that stably expressed human OCT2 or MATE1. UWL thickness was manipulated by vigorous reciprocal shaking. Several methods were used to manipulate maximal transport rates. Results Vigorous stirring stimulated uptake of OCT2-mediated transport by decreasing apparent Kt (Ktapp) values. Systematic reduction in transport rates was correlated with reduction in Ktapp values. The slope of these relationships indicated a 1500 µm UWL in multiwell plates. Reducing the influence of UWLs (by decreasing either their thickness or the Jmax of substrate transport) reduced Ktapp by 2-fold to >10-fold. Conclusions Failure to take into account the presence of UWLs in experiments using cultured cells to measure transport kinetics can result in significant underestimates of the affinity of multidrug transporters for substrates. PMID:25791216

Topology-based modeling of intrinsically disordered proteins: balancing intrinsic folding and intermolecular interactions.

PubMed

Ganguly, Debabani; Chen, Jianhan

2011-04-01

Coupled binding and folding is frequently involved in specific recognition of so-called intrinsically disordered proteins (IDPs), a newly recognized class of proteins that rely on a lack of stable tertiary fold for function. Here, we exploit topology-based Gō-like modeling as an effective tool for the mechanism of IDP recognition within the theoretical framework of minimally frustrated energy landscape. Importantly, substantial differences exist between IDPs and globular proteins in both amino acid sequence and binding interface characteristics. We demonstrate that established Gō-like models designed for folded proteins tend to over-estimate the level of residual structures in unbound IDPs, whereas under-estimating the strength of intermolecular interactions. Such systematic biases have important consequences in the predicted mechanism of interaction. A strategy is proposed to recalibrate topology-derived models to balance intrinsic folding propensities and intermolecular interactions, based on experimental knowledge of the overall residual structure level and binding affinity. Applied to pKID/KIX, the calibrated Gō-like model predicts a dominant multistep sequential pathway for binding-induced folding of pKID that is initiated by KIX binding via the C-terminus in disordered conformations, followed by binding and folding of the rest of C-terminal helix and finally the N-terminal helix. This novel mechanism is consistent with key observations derived from a recent NMR titration and relaxation dispersion study and provides a molecular-level interpretation of kinetic rates derived from dispersion curve analysis. These case studies provide important insight into the applicability and potential pitfalls of topology-based modeling for studying IDP folding and interaction in general. Copyright © 2011 Wiley-Liss, Inc.

Mechanical restoration of large-scale folded multilayers using the finite element method: Application to the Zagros Simply Folded Belt, N-Iraq

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Reif, Daniel; Grasemann, Bernhard

2010-05-01

and digital elevation models using the dip-domain method for balancing the cross-section. The lithology consists of Cretaceous to Cenozoic sediments. Massive carbonate rock units act as the competent layers compared to the incompetent behavior of siltstone, claystone and marl layers. We show the first results of the mechanical restoration of the Zagros cross-section and we discuss advantages and disadvantages, as well as some technical aspects of the applied method. First results indicate that a shortening of at least 50% was necessary to create the present-day folded cross-section. This value is higher than estimates of the amount of shortening solely based on kinematic or geometric restoration. One particular problem that is discussed is the presence of (unnaturally) sharp edges in a balanced cross-section produced using the dip-domain method, which need to be eliminated for mechanical restoration calculations to get reasonable results.

What amyloidoses may tell us about normal protein folding: The Alzheimer's disease story

NASA Astrophysics Data System (ADS)

Teplow, David B.

2002-03-01

Alzheimer's disease (AD) is a progressive, neurodegenerative disorder characterized by severe neuronal injury and death. A prominent histopathologic feature of AD is disseminated parenchymal and vascular amyloid deposition. The fibrils in these deposits are composed of the amyloid β-protein (Aβ), a peptide of 4 kDa mass. In vitro and in vivo studies of Aβ fibril formation have shown that both oligomeric and polymeric Aβ assemblies have neurotoxic activity. Understanding how these assemblies form thus could be of direct therapeutic relevance. However, the aggregation and fibril-forming propensities of Aβ have complicated structure determination. Nevertheless, careful morphologic, spectroscopic, protein chemical, and physiologic analyses of the time-dependent changes in Aβ conformation, assembly state, and biological activity which occur during fibrillogenesis have significantly advanced our understanding of this clinically important process. Here, I will discuss recent findings about the pathway(s) of Aβ folding and assembly and about key structural features of Aβ which control the associated kinetics. Interestingly, the amyloidogenic folding pathway of Aβ is in some respects the mirror image of that through which natively folded amyloidogenic proteins proceed.

A New Folding Kinetic Mechanism for Human Transthyretin and the Influence of the Amyloidogenic V30M Mutation.

PubMed

Jesus, Catarina S H; Almeida, Zaida L; Vaz, Daniela C; Faria, Tiago Q; Brito, Rui M M

2016-08-31

Protein aggregation into insoluble amyloid fibrils is the hallmark of several neurodegenerative diseases, chief among them Alzheimer's and Parkinson's. Although caused by different proteins, these pathologies share some basic molecular mechanisms with familial amyloidotic polyneuropathy (FAP), a rare hereditary neuropathy caused by amyloid formation and deposition by transthyretin (TTR) in the peripheral and autonomic nervous systems. Among the amyloidogenic TTR mutations known, V30M-TTR is the most common in FAP. TTR amyloidogenesis (ATTR) is triggered by tetramer dissociation, followed by partial unfolding and aggregation of the low conformational stability monomers formed. Thus, tetramer dissociation kinetics, monomer conformational stability and competition between refolding and aggregation pathways do play a critical role in ATTR. Here, we propose a new model to analyze the refolding kinetics of WT-TTR and V30M-TTR, showing that at pH and protein concentrations close to physiological, a two-step mechanism with a unimolecular first step followed by a second-order second step adjusts well to the experimental data. Interestingly, although sharing the same kinetic mechanism, V30M-TTR refolds at a much slower rate than WT-TTR, a feature that may favor the formation of transient species leading to kinetic partition into amyloidogenic pathways and, thus, significantly increasing the probability of amyloid formation in vivo.

Two states or not two states: Single-molecule folding studies of protein L

NASA Astrophysics Data System (ADS)

Aviram, Haim Yuval; Pirchi, Menahem; Barak, Yoav; Riven, Inbal; Haran, Gilad

2018-03-01

Experimental tools of increasing sophistication have been employed in recent years to study protein folding and misfolding. Folding is considered a complex process, and one way to address it is by studying small proteins, which seemingly possess a simple energy landscape with essentially only two stable states, either folded or unfolded. The B1-IgG binding domain of protein L (PL) is considered a model two-state folder, based on measurements using a wide range of experimental techniques. We applied single-molecule fluorescence resonance energy transfer (FRET) spectroscopy in conjunction with a hidden Markov model analysis to fully characterize the energy landscape of PL and to extract the kinetic properties of individual molecules of the protein. Surprisingly, our studies revealed the existence of a third state, hidden under the two-state behavior of PL due to its small population, ˜7%. We propose that this minority intermediate involves partial unfolding of the two C-terminal β strands of PL. Our work demonstrates that single-molecule FRET spectroscopy can be a powerful tool for a comprehensive description of the folding dynamics of proteins, capable of detecting and characterizing relatively rare metastable states that are difficult to observe in ensemble studies.

Kinematic analysis of asymmetric folds in competent layers using mathematical modelling

NASA Astrophysics Data System (ADS)

Aller, J.; Bobillo-Ares, N. C.; Bastida, F.; Lisle, R. J.; Menéndez, C. O.

2010-08-01

Mathematical 2D modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms: tangential longitudinal strain, flexural flow and homogeneous deformation. The main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point. Forward modelling is performed mathematically using the software 'FoldModeler', by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds. The resulting folds are Ramsay class 1C folds, comparable to those formed by symmetric flattening, but with different length of limbs and layer thickness asymmetry. Inverse modelling is made by fitting the natural fold to a computer-simulated fold. A problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold. A comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds. Modelling of recumbent folds suggests that optimal conditions for their development are: a) buckling in a simple shear regime with a sub-horizontal shear direction and layering gently dipping towards this direction; b) kinematic amplification due to superimposition of a combination of simple shear and irrotational strain with a sub-vertical maximum shortening direction for the latter component. The modelling shows that the amount of homogeneous strain necessary for the development of recumbent folds is much less when an irrotational strain component is superimposed at this stage that when the superimposed strain is only simple shear. In nature, the amount of the irrotational strain component probably increases during the development of the fold as a consequence of the increasing influence of the gravity due to the tectonic

Linear Classifier with Reject Option for the Detection of Vocal Fold Paralysis and Vocal Fold Edema

NASA Astrophysics Data System (ADS)

Kotropoulos, Constantine; Arce, Gonzalo R.

2009-12-01

Two distinct two-class pattern recognition problems are studied, namely, the detection of male subjects who are diagnosed with vocal fold paralysis against male subjects who are diagnosed as normal and the detection of female subjects who are suffering from vocal fold edema against female subjects who do not suffer from any voice pathology. To do so, utterances of the sustained vowel "ah" are employed from the Massachusetts Eye and Ear Infirmary database of disordered speech. Linear prediction coefficients extracted from the aforementioned utterances are used as features. The receiver operating characteristic curve of the linear classifier, that stems from the Bayes classifier when Gaussian class conditional probability density functions with equal covariance matrices are assumed, is derived. The optimal operating point of the linear classifier is specified with and without reject option. First results using utterances of the "rainbow passage" are also reported for completeness. The reject option is shown to yield statistically significant improvements in the accuracy of detecting the voice pathologies under study.

Alternative kinetic energy metrics for Lagrangian systems

NASA Astrophysics Data System (ADS)

Sarlet, W.; Prince, G.

2010-11-01

We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.

Paper Folding Fractions

ERIC Educational Resources Information Center

Pagni, David

2007-01-01

In this article, the author presents a paper folding activity that can be used for teaching fractions. This activity can be used to describe areas of folded polygons in terms of a standard unit of measure. A paper folding fractions worksheet and its corresponding solutions are also presented in this article. (Contains 2 figures.)

Evidence for the principle of minimal frustration in the evolution of protein folding landscapes.

PubMed

Tzul, Franco O; Vasilchuk, Daniel; Makhatadze, George I

2017-02-28

Theoretical and experimental studies have firmly established that protein folding can be described by a funneled energy landscape. This funneled energy landscape is the result of foldable protein sequences evolving following the principle of minimal frustration, which allows proteins to rapidly fold to their native biologically functional conformations. For a protein family with a given functional fold, the principle of minimal frustration suggests that, independent of sequence, all proteins within this family should fold with similar rates. However, depending on the optimal living temperature of the organism, proteins also need to modulate their thermodynamic stability. Consequently, the difference in thermodynamic stability should be primarily caused by differences in the unfolding rates. To test this hypothesis experimentally, we performed comprehensive thermodynamic and kinetic analyses of 15 different proteins from the thioredoxin family. Eight of these thioredoxins were extant proteins from psychrophilic, mesophilic, or thermophilic organisms. The other seven protein sequences were obtained using ancestral sequence reconstruction and can be dated back over 4 billion years. We found that all studied proteins fold with very similar rates but unfold with rates that differ up to three orders of magnitude. The unfolding rates correlate well with the thermodynamic stability of the proteins. Moreover, proteins that unfold slower are more resistant to proteolysis. These results provide direct experimental support to the principle of minimal frustration hypothesis.

A New Folding Kinetic Mechanism for Human Transthyretin and the Influence of the Amyloidogenic V30M Mutation

PubMed Central

Jesus, Catarina S. H.; Almeida, Zaida L.; Vaz, Daniela C.; Faria, Tiago Q.; Brito, Rui M. M.

2016-01-01

Protein aggregation into insoluble amyloid fibrils is the hallmark of several neurodegenerative diseases, chief among them Alzheimer’s and Parkinson’s. Although caused by different proteins, these pathologies share some basic molecular mechanisms with familial amyloidotic polyneuropathy (FAP), a rare hereditary neuropathy caused by amyloid formation and deposition by transthyretin (TTR) in the peripheral and autonomic nervous systems. Among the amyloidogenic TTR mutations known, V30M-TTR is the most common in FAP. TTR amyloidogenesis (ATTR) is triggered by tetramer dissociation, followed by partial unfolding and aggregation of the low conformational stability monomers formed. Thus, tetramer dissociation kinetics, monomer conformational stability and competition between refolding and aggregation pathways do play a critical role in ATTR. Here, we propose a new model to analyze the refolding kinetics of WT-TTR and V30M-TTR, showing that at pH and protein concentrations close to physiological, a two-step mechanism with a unimolecular first step followed by a second-order second step adjusts well to the experimental data. Interestingly, although sharing the same kinetic mechanism, V30M-TTR refolds at a much slower rate than WT-TTR, a feature that may favor the formation of transient species leading to kinetic partition into amyloidogenic pathways and, thus, significantly increasing the probability of amyloid formation in vivo. PMID:27589730

A minimalist model protein with multiple folding funnels

PubMed Central

Locker, C. Rebecca; Hernandez, Rigoberto

2001-01-01

Kinetic and structural studies of wild-type proteins such as prions and amyloidogenic proteins provide suggestive evidence that proteins may adopt multiple long-lived states in addition to the native state. All of these states differ structurally because they lie far apart in configuration space, but their stability is not necessarily caused by cooperative (nucleation) effects. In this study, a minimalist model protein is designed to exhibit multiple long-lived states to explore the dynamics of the corresponding wild-type proteins. The minimalist protein is modeled as a 27-monomer sequence confined to a cubic lattice with three different monomer types. An order parameter—the winding index—is introduced to characterize the extent of folding. The winding index has several advantages over other commonly used order parameters like the number of native contacts. It can distinguish between enantiomers, its calculation requires less computational time than the number of native contacts, and reduced-dimensional landscapes can be developed when the native state structure is not known a priori. The results for the designed model protein prove by existence that the rugged energy landscape picture of protein folding can be generalized to include protein “misfolding” into long-lived states. PMID:11470921

The Role of High-Dimensional Diffusive Search, Stabilization, and Frustration in Protein Folding

PubMed Central

Rimratchada, Supreecha; McLeish, Tom C.B.; Radford, Sheena E.; Paci, Emanuele

2014-01-01

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold. PMID:24739172

Sparse RNA folding revisited: space-efficient minimum free energy structure prediction.

PubMed

Will, Sebastian; Jabbari, Hosna

2016-01-01

RNA secondary structure prediction by energy minimization is the central computational tool for the analysis of structural non-coding RNAs and their interactions. Sparsification has been successfully applied to improve the time efficiency of various structure prediction algorithms while guaranteeing the same result; however, for many such folding problems, space efficiency is of even greater concern, particularly for long RNA sequences. So far, space-efficient sparsified RNA folding with fold reconstruction was solved only for simple base-pair-based pseudo-energy models. Here, we revisit the problem of space-efficient free energy minimization. Whereas the space-efficient minimization of the free energy has been sketched before, the reconstruction of the optimum structure has not even been discussed. We show that this reconstruction is not possible in trivial extension of the method for simple energy models. Then, we present the time- and space-efficient sparsified free energy minimization algorithm SparseMFEFold that guarantees MFE structure prediction. In particular, this novel algorithm provides efficient fold reconstruction based on dynamically garbage-collected trace arrows. The complexity of our algorithm depends on two parameters, the number of candidates Z and the number of trace arrows T; both are bounded by [Formula: see text], but are typically much smaller. The time complexity of RNA folding is reduced from [Formula: see text] to [Formula: see text]; the space complexity, from [Formula: see text] to [Formula: see text]. Our empirical results show more than 80 % space savings over RNAfold [Vienna RNA package] on the long RNAs from the RNA STRAND database (≥2500 bases). The presented technique is intentionally generalizable to complex prediction algorithms; due to their high space demands, algorithms like pseudoknot prediction and RNA-RNA-interaction prediction are expected to profit even stronger than "standard" MFE folding. SparseMFEFold is free

Computer Folding of RNA Tetraloops: Identification of Key Force Field Deficiencies.

PubMed

Kührová, Petra; Best, Robert B; Bottaro, Sandro; Bussi, Giovanni; Šponer, Jiří; Otyepka, Michal; Banáš, Pavel

2016-09-13

The computer-aided folding of biomolecules, particularly RNAs, is one of the most difficult challenges in computational structural biology. RNA tetraloops are fundamental RNA motifs playing key roles in RNA folding and RNA-RNA and RNA-protein interactions. Although state-of-the-art Molecular Dynamics (MD) force fields correctly describe the native state of these tetraloops as a stable free-energy basin on the microsecond time scale, enhanced sampling techniques reveal that the native state is not the global free energy minimum, suggesting yet unidentified significant imbalances in the force fields. Here, we tested our ability to fold the RNA tetraloops in various force fields and simulation settings. We employed three different enhanced sampling techniques, namely, temperature replica exchange MD (T-REMD), replica exchange with solute tempering (REST2), and well-tempered metadynamics (WT-MetaD). We aimed to separate problems caused by limited sampling from those due to force-field inaccuracies. We found that none of the contemporary force fields is able to correctly describe folding of the 5'-GAGA-3' tetraloop over a range of simulation conditions. We thus aimed to identify which terms of the force field are responsible for this poor description of TL folding. We showed that at least two different imbalances contribute to this behavior, namely, overstabilization of base-phosphate and/or sugar-phosphate interactions and underestimated stability of the hydrogen bonding interaction in base pairing. The first artifact stabilizes the unfolded ensemble, while the second one destabilizes the folded state. The former problem might be partially alleviated by reparametrization of the van der Waals parameters of the phosphate oxygens suggested by Case et al., while in order to overcome the latter effect we suggest local potentials to better capture hydrogen bonding interactions.

Biosorption of landfill leachate by Phanerochaete sp. ISTL01: isotherms, kinetics and toxicological assessment.

PubMed

Ghosh, Pooja; Thakur, Indu Shekhar

2017-07-01

The study investigates the ability of fungus Phanerochaete sp. ISTL01 for biosorption of color from landfill leachate. Batch mode experiments were conducted to study the effects of pH, temperature, adsorbent dose, contact time and initial leachate concentration on biosorption. Maximum biosorption capacity was determined as 17.73 mg g -1 of biomass. Equilibrium isotherms and kinetics were further studied. The biosorption data were found to fit well to the Freundlich isotherm and pseudo-second-order kinetic model. The value of activation energy suggested that chemisorption mechanism was involved. Biosorption efficiency was also evaluated by the Methyltetrazolium (MTT) assay for cytotoxicity and alkaline comet assay in HepG2 human hepato-carcinoma cells. The fungus reduced toxicity as shown by 1.3-fold increase in MTT EC 50 and 1.5- and 1.1-fold reduction in Tail moment and Olive tail moment, respectively, after 12 h biosorption. The fungus showed good biosorption characteristics in terms of contaminant-level reduction per unit mass of adsorbent, process kinetics and toxicity reduction, envisaging its application in leachate treatment.

The H2A-H2B dimeric kinetic intermediate is stabilized by widespread hydrophobic burial with few fully native interactions.

PubMed

Guyett, Paul J; Gloss, Lisa M

2012-01-20

The H2A-H2B histone heterodimer folds via monomeric and dimeric kinetic intermediates. Within ∼5 ms, the H2A and H2B polypeptides associate in a nearly diffusion limited reaction to form a dimeric ensemble, denoted I₂ and I₂*, the latter being a subpopulation characterized by a higher content of nonnative structure (NNS). The I₂ ensemble folds to the native heterodimer, N₂, through an observable, first-order kinetic phase. To determine the regions of structure in the I₂ ensemble, we characterized 26 Ala mutants of buried hydrophobic residues, spanning the three helices of the canonical histone folds of H2A and H2B and the H2B C-terminal helix. All but one targeted residue contributed significantly to the stability of I₂, the transition state and N₂; however, only residues in the hydrophobic core of the dimer interface perturbed the I₂* population. Destabilization of I₂* correlated with slower folding rates, implying that NNS is not a kinetic trap but rather accelerates folding. The pattern of Φ values indicated that residues forming intramolecular interactions in the peripheral helices contributed similar stability to I₂ and N₂, but residues involved in intermolecular interactions in the hydrophobic core are only partially folded in I₂. These findings suggest a dimerize-then-rearrange model. Residues throughout the histone fold contribute to the stability of I₂, but after the rapid dimerization reaction, the hydrophobic core of the dimer interface has few fully native interactions. In the transition state leading to N₂, more native-like interactions are developed and nonnative interactions are rearranged. Copyright © 2011 Elsevier Ltd. All rights reserved.

Advances in electron kinetics and theory of gas discharges

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolobov, Vladimir I.; The University of Alabama in Huntsville, Huntsville, Alabama 35899

2013-10-15

“Electrons, like people, are fertile and infertile: high-energy electrons are fertile and able to reproduce.”—Lev TsendinModern physics of gas discharges increasingly uses physical kinetics for analysis of non-equilibrium plasmas. The description of underlying physics at the kinetic level appears to be important for plasma applications in modern technologies. In this paper, we attempt to grasp the legacy of Professor Lev Tsendin, who advocated the use of the kinetic approach for understanding fundamental problems of gas discharges. We outline the fundamentals of electron kinetics in low-temperature plasmas, describe elements of the modern kinetic theory of gas discharges, and show examples ofmore » the theoretical approach to gas discharge problems used by Lev Tsendin. Important connections between electron kinetics in gas discharges and semiconductors are also discussed. Using several examples, we illustrate how Tsendin's ideas and methods are currently being developed for the implementation of next generation computational tools for adaptive kinetic-fluid simulations of gas discharges used in modern technologies.« less

Kinetic: A system code for analyzing nuclear thermal propulsion rocket engine transients

NASA Astrophysics Data System (ADS)

Schmidt, Eldon; Lazareth, Otto; Ludewig, Hans

The topics are presented in viewgraph form and include the following: outline of kinetic code; a kinetic information flow diagram; kinetic neutronic equations; turbopump/nozzle algorithm; kinetic heat transfer equations per node; and test problem diagram.

Methods for the accurate estimation of confidence intervals on protein folding ϕ-values

PubMed Central

Ruczinski, Ingo; Sosnick, Tobin R.; Plaxco, Kevin W.

2006-01-01

ϕ-Values provide an important benchmark for the comparison of experimental protein folding studies to computer simulations and theories of the folding process. Despite the growing importance of ϕ measurements, however, formulas to quantify the precision with which ϕ is measured have seen little significant discussion. Moreover, a commonly employed method for the determination of standard errors on ϕ estimates assumes that estimates of the changes in free energy of the transition and folded states are independent. Here we demonstrate that this assumption is usually incorrect and that this typically leads to the underestimation of ϕ precision. We derive an analytical expression for the precision of ϕ estimates (assuming linear chevron behavior) that explicitly takes this dependence into account. We also describe an alternative method that implicitly corrects for the effect. By simulating experimental chevron data, we show that both methods accurately estimate ϕ confidence intervals. We also explore the effects of the commonly employed techniques of calculating ϕ from kinetics estimated at non-zero denaturant concentrations and via the assumption of parallel chevron arms. We find that these approaches can produce significantly different estimates for ϕ (again, even for truly linear chevron behavior), indicating that they are not equivalent, interchangeable measures of transition state structure. Lastly, we describe a Web-based implementation of the above algorithms for general use by the protein folding community. PMID:17008714

Assessment of local friction in protein folding dynamics using a helix cross-linker.

PubMed

Markiewicz, Beatrice N; Jo, Hyunil; Culik, Robert M; DeGrado, William F; Gai, Feng

2013-11-27

Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.

Kink detachment fold in the southwest Montana fold and thrust belt

NASA Astrophysics Data System (ADS)

Mitchell, Michael M.; Woodward, Nicholas B.

1988-02-01

The Hossfeldt anticline in the southwest Montana thrust belt is characterized by a kink geometry and probably overlies a thrust detachment at depth. The mesofabric distribution in the limbs documents that the eastern overturned limb has undergone most of the rotation and internal deformation during folding, leaving the gently dipping western limb virtually undeformed. The anticline exhibits unique mesofabrics in its hinge region that require a pinned anticlinal hinge during its evolution. The half-wavelength of the Hossfeldt anticline-Eustis syncline pair coincides with that predicted from buckling theory, if one considers the massive carbonates of the Paleozoic section as a competent beam. Although the geometry and mesofabric distribution of the Hossfeldt anticline satisfy the geometric requirements of either a fault-propagation fold or a detachment kink fold, the buckling wavelength strongly suggests that its origin was as a kink-buckle fold above a flat detachment rather than as a fault-propagation fold above a thrust ramp.

Enthalpy-Driven RNA Folding: Single-Molecule Thermodynamics of Tetraloop–Receptor Tertiary Interaction†

PubMed Central

Fiore, Julie L.; Kraemer, Benedikt; Koberling, Felix; Edmann, Rainer; Nesbitt, David J.

2010-01-01

RNA folding thermodynamics are crucial for structure prediction, which requires characterization of both enthalpic and entropic contributions of tertiary motifs to conformational stability. We explore the temperature dependence of RNA folding due to the ubiquitous GAAA tetraloop–receptor docking interaction, exploiting immobilized and freely diffusing single-molecule fluorescence resonance energy transfer (smFRET) methods. The equilibrium constant for intramolecular docking is obtained as a function of temperature (T = 21–47 °C), from which a van’t Hoff analysis yields the enthalpy (ΔH°) and entropy (ΔS°) of docking. Tetraloop–receptor docking is significantly exothermic and entropically unfavorable in 1 mM MgCl2 and 100 mM NaCl, with excellent agreement between immobilized (ΔH° = −17.4 ± 1.6 kcal/mol, and ΔS° = −56.2 ± 5.4 cal mol−1 K−1) and freely diffusing (ΔH° = −17.2 ± 1.6 kcal/mol, and ΔS° = −55.9 ± 5.2 cal mol−1 K−1) species. Kinetic heterogeneity in the tetraloop–receptor construct is unaffected over the temperature range investigated, indicating a large energy barrier for interconversion between the actively docking and nondocking subpopulations. Formation of the tetraloop–receptor interaction can account for ~60% of the ΔH° and ΔS° of P4–P6 domain folding in the Tetrahymena ribozyme, suggesting that it may act as a thermodynamic clamp for the domain. Comparison of the isolated tetraloop–receptor and other tertiary folding thermodynamics supports a theme that enthalpy- versus entropy-driven folding is determined by the number of hydrogen bonding and base stacking interactions. PMID:19186984

Microsecond Unfolding Kinetics of Sheep Prion Protein Reveals an Intermediate that Correlates with Susceptibility to Classical Scrapie

PubMed Central

Chen, Kai-Chun; Xu, Ming; Wedemeyer, William J.; Roder, Heinrich

2011-01-01

The microsecond folding and unfolding kinetics of ovine prion proteins (ovPrP) were measured under various solution conditions. A fragment comprising residues 94–233 of the full-length ovPrP was studied for four variants with differing susceptibilities to classical scrapie in sheep. The observed biexponential unfolding kinetics of ovPrP provides evidence for an intermediate species. However, in contrast to previous results for human PrP, there is no evidence for an intermediate under refolding conditions. Global analysis of the kinetic data, based on a sequential three-state mechanism, quantitatively accounts for all folding and unfolding data as a function of denaturant concentration. The simulations predict that an intermediate accumulates under both folding and unfolding conditions, but is observable only in unfolding experiments because the intermediate is optically indistinguishable from the native state. The relative population of intermediates in two ovPrP variants, both transiently and under destabilizing equilibrium conditions, correlates with their propensities for classical scrapie. The variant susceptible to classical scrapie has a larger population of the intermediate state than the resistant variant. Thus, the susceptible variant should be favored to undergo the PrPC to PrPSc conversion and oligomerization. PMID:21889460

Folding kinematics expressed in fracture patterns: An example from the Anti-Atlas fold belt, Morocco

NASA Astrophysics Data System (ADS)

Ismat, Zeshan

2008-11-01

The Anti-Atlas fold belt, Morocco, formed during the same Variscan collisional event that produced the Valley-and-Ridge fold-thrust belt of the Appalachian mountains. Both are external belts of the Appalachian-Ouachita-Mauritanides chain and at the map scale have very similar topographic expressions. The Anti-Atlas, however, consists of map-scale folds that are buckle-related, detachment folds, whereas the Valley-and-Ridge folds developed in response to imbricate thrusting. For this reason, the Anti-Atlas is referred to as a fold belt rather than a fold-thrust belt. This paper examines Variscan folding processes in the Anti-Atlas Mountains. Folding in some layers occurred by sliding along a penetrative network of mesoscale fractures, i.e. cataclastic flow, during buckling. Layer-parallel shortening fractures were reactivated in the later stages of folding to accommodate limb rotation. Although 'boutonnieres', i.e. basement uplifts, punctuate the fold belt, the fracture patterns indicate that the uplifts failed to provide any 'bending' component. Folding is also interpreted to occur under low to moderate confining pressures because the fracture network includes conjugate shear fractures with very small (˜20°) dihedral angles.

Molecular Simulations of Mutually Exclusive Folding in a Two-Domain Protein Switch

PubMed Central

Mills, Brandon M.; Chong, Lillian T.

2011-01-01

A major challenge with testing designs of protein conformational switches is the need for experimental probes that can independently monitor their individual protein domains. One way to circumvent this issue is to use a molecular simulation approach in which each domain can be directly observed. Here we report what we believe to be the first molecular simulations of mutually exclusive folding in an engineered two-domain protein switch, providing a direct view of how folding of one protein drives unfolding of the other in a barnase-ubiquitin fusion protein. These simulations successfully capture the experimental effects of interdomain linker length and ligand binding on the extent of unfolding in the less stable domain. In addition, the effect of linker length on the potential for oligomerization, which eliminates switch activity, is in qualitative agreement with analytical ultracentrifugation experiments. We also perform what we believe to be the first study of protein unfolding via progressive localized compression. Finally, we are able to explore the kinetics of mutually exclusive folding by determining the effect of linker length on rates of unfolding and refolding of each protein domain. Our results demonstrate that molecular simulations can provide seemingly novel biological insights on the behavior of individual protein domains, thereby aiding in the rational design of bifunctional switches. PMID:21281591

Improving protein fold recognition by extracting fold-specific features from predicted residue-residue contacts.

PubMed

Zhu, Jianwei; Zhang, Haicang; Li, Shuai Cheng; Wang, Chao; Kong, Lupeng; Sun, Shiwei; Zheng, Wei-Mou; Bu, Dongbo

2017-12-01

Accurate recognition of protein fold types is a key step for template-based prediction of protein structures. The existing approaches to fold recognition mainly exploit the features derived from alignments of query protein against templates. These approaches have been shown to be successful for fold recognition at family level, but usually failed at superfamily/fold levels. To overcome this limitation, one of the key points is to explore more structurally informative features of proteins. Although residue-residue contacts carry abundant structural information, how to thoroughly exploit these information for fold recognition still remains a challenge. In this study, we present an approach (called DeepFR) to improve fold recognition at superfamily/fold levels. The basic idea of our approach is to extract fold-specific features from predicted residue-residue contacts of proteins using deep convolutional neural network (DCNN) technique. Based on these fold-specific features, we calculated similarity between query protein and templates, and then assigned query protein with fold type of the most similar template. DCNN has showed excellent performance in image feature extraction and image recognition; the rational underlying the application of DCNN for fold recognition is that contact likelihood maps are essentially analogy to images, as they both display compositional hierarchy. Experimental results on the LINDAHL dataset suggest that even using the extracted fold-specific features alone, our approach achieved success rate comparable to the state-of-the-art approaches. When further combining these features with traditional alignment-related features, the success rate of our approach increased to 92.3%, 82.5% and 78.8% at family, superfamily and fold levels, respectively, which is about 18% higher than the state-of-the-art approach at fold level, 6% higher at superfamily level and 1% higher at family level. An independent assessment on SCOP_TEST dataset showed consistent

Improving strand pairing prediction through exploring folding cooperativity

PubMed Central

Jeong, Jieun; Berman, Piotr; Przytycka, Teresa M.

2008-01-01

The topology of β-sheets is defined by the pattern of hydrogen-bonded strand pairing. Therefore, predicting hydrogen bonded strand partners is a fundamental step towards predicting β-sheet topology. At the same time, finding the correct partners is very difficult due to long range interactions involved in strand pairing. Additionally, patterns of aminoacids observed in β-sheet formations are very general and therefore difficult to use for computational recognition of specific contacts between strands. In this work, we report a new strand pairing algorithm. To address above mentioned difficulties, our algorithm attempts to mimic elements of the folding process. Namely, in addition to ensuring that the predicted hydrogen bonded strand pairs satisfy basic global consistency constraints, it takes into account hypothetical folding pathways. Consistently with this view, introducing hydrogen bonds between a pair of strands changes the probabilities of forming hydrogen bonds between other pairs of strand. We demonstrate that this approach provides an improvement over previously proposed algorithms. We also compare the performance of this method to that of a global optimization algorithm that poses the problem as integer linear programming optimization problem and solves it using ILOG CPLEX™ package. PMID:18989036

Accurate template-based modeling in CASP12 using the IntFOLD4-TS, ModFOLD6, and ReFOLD methods.

PubMed

McGuffin, Liam J; Shuid, Ahmad N; Kempster, Robert; Maghrabi, Ali H A; Nealon, John O; Salehe, Bajuna R; Atkins, Jennifer D; Roche, Daniel B

2018-03-01

Our aim in CASP12 was to improve our Template-Based Modeling (TBM) methods through better model selection, accuracy self-estimate (ASE) scores and refinement. To meet this aim, we developed two new automated methods, which we used to score, rank, and improve upon the provided server models. Firstly, the ModFOLD6_rank method, for improved global Quality Assessment (QA), model ranking and the detection of local errors. Secondly, the ReFOLD method for fixing errors through iterative QA guided refinement. For our automated predictions we developed the IntFOLD4-TS protocol, which integrates the ModFOLD6_rank method for scoring the multiple-template models that were generated using a number of alternative sequence-structure alignments. Overall, our selection of top models and ASE scores using ModFOLD6_rank was an improvement on our previous approaches. In addition, it was worthwhile attempting to repair the detected errors in the top selected models using ReFOLD, which gave us an overall gain in performance. According to the assessors' formula, the IntFOLD4 server ranked 3rd/5th (average Z-score > 0.0/-2.0) on the server only targets, and our manual predictions (McGuffin group) ranked 1st/2nd (average Z-score > -2.0/0.0) compared to all other groups. © 2017 Wiley Periodicals, Inc.

Characterization of Folding Mechanisms of Trp-cage and WW-domain by Network Analysis of Simulations with a Hybrid-resolution Model

PubMed Central

Han, Wei; Schulten, Klaus

2013-01-01

In this study, we apply a hybrid-resolution model, namely PACE, to characterize the free energy surfaces (FESs) of trp-cage and a WW domain variant along with the respective folding mechanisms. Unbiased, independent simulations with PACE are found to achieve together multiple folding and unfolding events for both proteins, allowing us to perform network analysis of the FESs to identify folding pathways. PACE reproduces for both proteins expected complexity hidden in the folding FESs, in particular, meta-stable non-native intermediates. Pathway analysis shows that some of these intermediates are, actually, on-pathway folding intermediates and that intermediates kinetically closest to the native states can be either critical on-pathway or off-pathway intermediates, depending on the protein. Apart from general insights into folding, specific folding mechanisms of the proteins are resolved. We find that trp-cage folds via a dominant pathway in which hydrophobic collapse occurs before the N-terminal helix forms; full incorporation of Trp6 into the hydrophobic core takes place as the last step of folding, which, however, may not be the rate-limiting step. For the WW domain variant studied we observe two main folding pathways with opposite orders of formation of the two hairpins involved in the structure; for either pathway, formation of hairpin 1 is more likely to be the rate-limiting step. Altogether, our results suggest that PACE combined with network analysis is a computationally efficient and valuable tool for the study of protein folding. PMID:23915394

Removal of Covalent Heterogeneity Reveals Simple Folding Behavior for P4-P6 RNA*

PubMed Central

Greenfeld, Max; Solomatin, Sergey V.; Herschlag, Daniel

2011-01-01

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior. PMID:21478155

Structural evolution of the J-fold; a multi-scalar approach to modeling kinematic fold evolution in the Cordilleran fold-thrust belt, southwestern Montana

NASA Astrophysics Data System (ADS)

Wallace, James W.

The Highway 2 structural complex (HW2SC) is part of the North American western Cordilleran fold-and-thrust belt that extends from northern Wyoming into northwestern Canada. More precisely, the HW2SC is located on the southeastern margin of the Helena salient in what is known as the southwest Montana transverse zone. Based on the location of the HW2SC it appears to have formed as footwall deformation associated with displacement along the southwestern Montana transverse zone. The most prominent structural feature in the HW2SC is the Late-Cretaceous "J-fold", a east-west trending, muliti-hinged, northeast plunging anticline with an associated northeast plunging syncline. The purpose of this study is to provide insight into whether the geometries of thrust-related folds correlate to particular mechanical responses taking place within the folded sedimentary sequences. This is accomplished by conducting a multifaceted examination of the J-fold using high-resolution terrestrial laser scanning combined with detailed field measurements of kinematic indicators, and petrographic analysis of microstructures in thin section. Based on the findings of this study four specific conclusions about the kinematic and mechanical evolution of the J-fold can be made: 1) the J-fold kinematically behaves as a fault-bend fold throughout its structural evolution; 2) the J-fold enjoyed two stages of fault-bend folding deformation that produced its present day geometry; 3) the J-fold has been tectonically thinned by >50% in the Permian Phosphoria and Jurassic Ellis-Rierdon formations located in the Overturned forelimb; and finally 4) the J-fold is mechanically accommodating the thinning in the Overturned forelimb by pressure solution and dissolution of chert grains in the Permian Phosphoria formation and by faulting and shearing in the Jurassic Ellis-Rierdon formation.

Slowest kinetic modes revealed by metabasin renormalization

NASA Astrophysics Data System (ADS)

Okushima, Teruaki; Niiyama, Tomoaki; Ikeda, Kensuke S.; Shimizu, Yasushi

2018-02-01

Understanding the slowest relaxations of complex systems, such as relaxation of glass-forming materials, diffusion in nanoclusters, and folding of biomolecules, is important for physics, chemistry, and biology. For a kinetic system, the relaxation modes are determined by diagonalizing its transition rate matrix. However, for realistic systems of interest, numerical diagonalization, as well as extracting physical understanding from the diagonalization results, is difficult due to the high dimensionality. Here, we develop an alternative and generally applicable method of extracting the long-time scale relaxation dynamics by combining the metabasin analysis of Okushima et al. [Phys. Rev. E 80, 036112 (2009), 10.1103/PhysRevE.80.036112] and a Jacobi method. We test the method on an illustrative model of a four-funnel model, for which we obtain a renormalized kinematic equation of much lower dimension sufficient for determining slow relaxation modes precisely. The method is successfully applied to the vacancy transport problem in ionic nanoparticles [Niiyama et al., Chem. Phys. Lett. 654, 52 (2016), 10.1016/j.cplett.2016.04.088], allowing a clear physical interpretation that the final relaxation consists of two successive, characteristic processes.

A galaxy of folds.

PubMed

Alva, Vikram; Remmert, Michael; Biegert, Andreas; Lupas, Andrei N; Söding, Johannes

2010-01-01

Many protein classification systems capture homologous relationships by grouping domains into families and superfamilies on the basis of sequence similarity. Superfamilies with similar 3D structures are further grouped into folds. In the absence of discernable sequence similarity, these structural similarities were long thought to have originated independently, by convergent evolution. However, the growth of databases and advances in sequence comparison methods have led to the discovery of many distant evolutionary relationships that transcend the boundaries of superfamilies and folds. To investigate the contributions of convergent versus divergent evolution in the origin of protein folds, we clustered representative domains of known structure by their sequence similarity, treating them as point masses in a virtual 2D space which attract or repel each other depending on their pairwise sequence similarities. As expected, families in the same superfamily form tight clusters. But often, superfamilies of the same fold are linked with each other, suggesting that the entire fold evolved from an ancient prototype. Strikingly, some links connect superfamilies with different folds. They arise from modular peptide fragments of between 20 and 40 residues that co-occur in the connected folds in disparate structural contexts. These may be descendants of an ancestral pool of peptide modules that evolved as cofactors in the RNA world and from which the first folded proteins arose by amplification and recombination. Our galaxy of folds summarizes, in a single image, most known and many yet undescribed homologous relationships between protein superfamilies, providing new insights into the evolution of protein domains.

Inverse problem analysis for identification of reaction kinetics constants in microreactors for biodiesel synthesis

NASA Astrophysics Data System (ADS)

Pontes, P. C.; Naveira-Cotta, C. P.

2016-09-01

The theoretical analysis for the design of microreactors in biodiesel production is a complicated task due to the complex liquid-liquid flow and mass transfer processes, and the transesterification reaction that takes place within these microsystems. Thus, computational simulation is an important tool that aids in understanding the physical-chemical phenomenon and, consequently, in determining the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. A diffusive-convective-reactive coupled nonlinear mathematical model, that governs the mass transfer process during the transesterification reaction in parallel plates microreactors, under isothermal conditions, is here described. A hybrid numerical-analytical solution via the Generalized Integral Transform Technique (GITT) for this partial differential system is developed and the eigenfunction expansions convergence rates are extensively analyzed and illustrated. The heuristic method of Particle Swarm Optimization (PSO) is applied in the inverse analysis of the proposed direct problem, to estimate the reaction kinetics constants, which is a critical step in the design of such microsystems. The results present a good agreement with the limited experimental data in the literature, but indicate that the GITT methodology combined with the PSO approach provide a reliable computational algorithm for direct-inverse analysis in such reactive mass transfer problems.

Study of protein folding under native conditions by rapidly switching the hydrostatic pressure inside an NMR sample cell

PubMed Central

Charlier, Cyril; Alderson, T. Reid; Courtney, Joseph M.; Ying, Jinfa; Anfinrud, Philip

2018-01-01

In general, small proteins rapidly fold on the timescale of milliseconds or less. For proteins with a substantial volume difference between the folded and unfolded states, their thermodynamic equilibrium can be altered by varying the hydrostatic pressure. Using a pressure-sensitized mutant of ubiquitin, we demonstrate that rapidly switching the pressure within an NMR sample cell enables study of the unfolded protein under native conditions and, vice versa, study of the native protein under denaturing conditions. This approach makes it possible to record 2D and 3D NMR spectra of the unfolded protein at atmospheric pressure, providing residue-specific information on the folding process. 15N and 13C chemical shifts measured immediately after dropping the pressure from 2.5 kbar (favoring unfolding) to 1 bar (native) are close to the random-coil chemical shifts observed for a large, disordered peptide fragment of the protein. However, 15N relaxation data show evidence for rapid exchange, on a ∼100-μs timescale, between the unfolded state and unstable, structured states that can be considered as failed folding events. The NMR data also provide direct evidence for parallel folding pathways, with approximately one-half of the protein molecules efficiently folding through an on-pathway kinetic intermediate, whereas the other half fold in a single step. At protein concentrations above ∼300 μM, oligomeric off-pathway intermediates compete with folding of the native state. PMID:29666248

A kMC-MD method with generalized move-sets for the simulation of folding of α-helical and β-stranded peptides.

PubMed

Peter, Emanuel K; Pivkin, Igor V; Shea, Joan-Emma

2015-04-14

In Monte-Carlo simulations of protein folding, pathways and folding times depend on the appropriate choice of the Monte-Carlo move or process path. We developed a generalized set of process paths for a hybrid kinetic Monte Carlo-Molecular dynamics algorithm, which makes use of a novel constant time-update and allows formation of α-helical and β-stranded secondary structures. We apply our new algorithm to the folding of 3 different proteins: TrpCage, GB1, and TrpZip4. All three systems are seen to fold within the range of the experimental folding times. For the β-hairpins, we observe that loop formation is the rate-determining process followed by collapse and formation of the native core. Cluster analysis of both peptides reveals that GB1 folds with equal likelihood along a zipper or a hydrophobic collapse mechanism, while TrpZip4 follows primarily a zipper pathway. The difference observed in the folding behavior of the two proteins can be attributed to the different arrangements of their hydrophobic core, strongly packed, and dry in case of TrpZip4, and partially hydrated in the case of GB1.

Non-cylindrical fold growth in the Zagros fold and thrust belt (Kurdistan, NE-Iraq)

NASA Astrophysics Data System (ADS)

Bartl, Nikolaus; Bretis, Bernhard; Grasemann, Bernhard; Lockhart, Duncan

2010-05-01

The Zagros mountains extends over 1800 km from Kurdistan in N-Iraq to the Strait of Hormuz in Iran and is one of the world most promising regions for the future hydrocarbon exploration. The Zagros Mountains started to form as a result of the collision between the Eurasian and Arabian Plates, whose convergence began in the Late Cretaceous as part of the Alpine-Himalayan orogenic system. Geodetic and seismological data document that both plates are still converging and that the fold and thrust belt of the Zagros is actively growing. Extensive hydrocarbon exploration mainly focuses on the antiforms of this fold and thrust belt and therefore the growth history of the folds is of great importance. This work investigates by means of structural field work and quantitative geomorphological techniques the progressive fold growth of the Permam, Bana Bawi- and Safeen- Anticlines located in the NE of the city of Erbil in the Kurdistan region of Northern Iraq. This part of the Zagros fold and thrust belt belongs to the so-called Simply Folded Belt, which is dominated by gentle to open folding. Faults or fault related folds have only minor importance. The mechanical anisotropy of the formations consisting of a succession of relatively competent (massive dolomite and limestone) and incompetent (claystone and siltstone) sediments essentially controls the deformation pattern with open to gentle parallel folding of the competent layers and flexural flow folding of the incompetent layers. The characteristic wavelength of the fold trains is around 10 km. Due to faster erosion of the softer rock layers in the folded sequence, the more competent lithologies form sharp ridges with steeply sloping sides along the eroded flanks of the anticlines. Using an ASTER digital elevation model in combination with geological field data we quantified 250 drainage basins along the different limbs of the subcylindrical Permam, Bana Bawi- and Safeen- Anticlines. Geomorphological indices of the drainage

Integrating Kinetic Model of E. coli with Genome Scale Metabolic Fluxes Overcomes Its Open System Problem and Reveals Bistability in Central Metabolism

PubMed Central

Mannan, Ahmad A.; Toya, Yoshihiro; Shimizu, Kazuyuki; McFadden, Johnjoe; Kierzek, Andrzej M.; Rocco, Andrea

2015-01-01

An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi-‘omics’ steady state data and a genome-scale metabolic network model. We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population. PMID:26469081

Problems in hard and soft matter: From brain folds and Levy localization to active elasticity

NASA Astrophysics Data System (ADS)

Mayett, David

This thesis presents a study of condensed matter systems at different length scales. The first part presents a study of elastic instabilities in biological systems ranging from the cerebral cortex in the brain to the lining of the intestines. Such instabilities lead to a zoo of morphologies ranging from primary folds to villi and crypts to secondary folds and are brought about by growth, mechanical stresses, or a combination of the two. We propose a novel model for the description of primary folds in the cerebral cortex. Motivated by the spatial structure of the cortex, we model its elasticity as a smectic liquid crystal. With this novel description we show that vertical pulling forces via axonal tension from the brain underlying white matter can lead to buckling, which initiates the primary folds. Moreover, we are able to obtain a reasonable estimate of the critical wavelength and strain for buckling. We also model the formation of secondary folds in the cortex to obtain a more comprehensive theory. We continue this study of elastic instabilities due to growth by studying a more general system comprised of two coupled elastic membranes, one of which undergoes growth and one that does not. We employ an active formulation of growth and compare it to the one due to Rodriguez (Rodriguez). We show that different morphologies corresponding to different systems, such as the cerebral cortex and the lining of the intestines, can be obtained from our model by choosing different active stress functional forms to begin to classify the zoo of morphologies observed in seemingly different biological systems. In the second part of this thesis, to work towards a more microscopic view of biological tissues such as the brain tissue, which is composed of neurons, glial cells, and progenitor cells, we model an experiment (Theveneau) studying the dynamic interaction between neural crest cells and placodal cells in which the placodal cells run away from the neural crest cells following

Dynamics of folding: Impact of fault bend folds on earthquake cycles

NASA Astrophysics Data System (ADS)

Sathiakumar, S.; Barbot, S.; Hubbard, J.

2017-12-01

Earthquakes in subduction zones and subaerial convergent margins are some of the largest in the world. So far, forecasts of future earthquakes have primarily relied on assessing past earthquakes to look for seismic gaps and slip deficits. However, the roles of fault geometry and off-fault plasticity are typically overlooked. We use structural geology (fault-bend folding theory) to inform fault modeling in order to better understand how deformation is accommodated on the geological time scale and through the earthquake cycle. Fault bends in megathrusts, like those proposed for the Nepal Himalaya, will induce folding of the upper plate. This introduces changes in the slip rate on different fault segments, and therefore on the loading rate at the plate interface, profoundly affecting the pattern of earthquake cycles. We develop numerical simulations of slip evolution under rate-and-state friction and show that this effect introduces segmentation of the earthquake cycle. In crustal dynamics, it is challenging to describe the dynamics of fault-bend folds, because the deformation is accommodated by small amounts of slip parallel to bedding planes ("flexural slip"), localized on axial surface, i.e. folding axes pinned to fault bends. We use dislocation theory to describe the dynamics of folding along these axial surfaces, using analytic solutions that provide displacement and stress kernels to simulate the temporal evolution of folding and assess the effects of folding on earthquake cycles. Studies of the 2015 Gorkha earthquake, Nepal, have shown that fault geometry can affect earthquake segmentation. Here, we show that in addition to the fault geometry, the actual geology of the rocks in the hanging wall of the fault also affect critical parameters, including the loading rate on parts of the fault, based on fault-bend folding theory. Because loading velocity controls the recurrence time of earthquakes, these two effects together are likely to have a strong impact on the

Proteopedia: Rossmann Fold: A Beta-Alpha-Beta Fold at Dinucleotide Binding Sites

ERIC Educational Resources Information Center

Hanukoglu, Israel

2015-01-01

The Rossmann fold is one of the most common and widely distributed super-secondary structures. It is composed of a series of alternating beta strand (ß) and alpha helical (a) segments wherein the ß-strands are hydrogen bonded forming a ß-sheet. The initial beta-alpha-beta (ßaß) fold is the most conserved segment of Rossmann folds. As this segment…

Improved method for predicting protein fold patterns with ensemble classifiers.

PubMed

Chen, W; Liu, X; Huang, Y; Jiang, Y; Zou, Q; Lin, C

2012-01-27

Protein folding is recognized as a critical problem in the field of biophysics in the 21st century. Predicting protein-folding patterns is challenging due to the complex structure of proteins. In an attempt to solve this problem, we employed ensemble classifiers to improve prediction accuracy. In our experiments, 188-dimensional features were extracted based on the composition and physical-chemical property of proteins and 20-dimensional features were selected using a coupled position-specific scoring matrix. Compared with traditional prediction methods, these methods were superior in terms of prediction accuracy. The 188-dimensional feature-based method achieved 71.2% accuracy in five cross-validations. The accuracy rose to 77% when we used a 20-dimensional feature vector. These methods were used on recent data, with 54.2% accuracy. Source codes and dataset, together with web server and software tools for prediction, are available at: http://datamining.xmu.edu.cn/main/~cwc/ProteinPredict.html.

Design Principles of DNA Enzyme-Based Walkers: Translocation Kinetics and Photoregulation.

PubMed

Cha, Tae-Gon; Pan, Jing; Chen, Haorong; Robinson, Heather N; Li, Xiang; Mao, Chengde; Choi, Jong Hyun

2015-07-29

Dynamic DNA enzyme-based walkers complete their stepwise movements along the prescribed track through a series of reactions, including hybridization, enzymatic cleavage, and strand displacement; however, their overall translocation kinetics is not well understood. Here, we perform mechanistic studies to elucidate several key parameters that govern the kinetics and processivity of DNA enzyme-based walkers. These parameters include DNA enzyme core type and structure, upper and lower recognition arm lengths, and divalent metal cation species and concentration. A theoretical model is developed within the framework of single-molecule kinetics to describe overall translocation kinetics as well as each reaction step. A better understanding of kinetics and design parameters enables us to demonstrate a walker movement near 5 μm at an average speed of ∼1 nm s(-1). We also show that the translocation kinetics of DNA walkers can be effectively controlled by external light stimuli using photoisomerizable azobenzene moieties. A 2-fold increase in the cleavage reaction is observed when the hairpin stems of enzyme catalytic cores are open under UV irradiation. This study provides general design guidelines to construct highly processive, autonomous DNA walker systems and to regulate their translocation kinetics, which would facilitate the development of functional DNA walkers.

Comparison of fault-related folding algorithms to restore a fold-and-thrust-belt

NASA Astrophysics Data System (ADS)

Brandes, Christian; Tanner, David

2017-04-01

Fault-related folding means the contemporaneous evolution of folds as a consequence of fault movement. It is a common deformation process in the upper crust that occurs worldwide in accretionary wedges, fold-and-thrust belts, and intra-plate settings, in either strike-slip, compressional, or extensional regimes. Over the last 30 years different algorithms have been developed to simulate the kinematic evolution of fault-related folds. All these models of fault-related folding include similar simplifications and limitations and use the same kinematic behaviour throughout the model (Brandes & Tanner, 2014). We used a natural example of fault-related folding from the Limón fold-and-thrust belt in eastern Costa Rica to test two different algorithms and to compare the resulting geometries. A thrust fault and its hanging-wall anticline were restored using both the trishear method (Allmendinger, 1998; Zehnder & Allmendinger, 2000) and the fault-parallel flow approach (Ziesch et al. 2014); both methods are widely used in academia and industry. The resulting hanging-wall folds above the thrust fault are restored in substantially different fashions. This is largely a function of the propagation-to-slip ratio of the thrust, which controls the geometry of the related anticline. Understanding the controlling factors for anticline evolution is important for the evaluation of potential hydrocarbon reservoirs and the characterization of fault processes. References: Allmendinger, R.W., 1998. Inverse and forward numerical modeling of trishear fault propagation folds. Tectonics, 17, 640-656. Brandes, C., Tanner, D.C. 2014. Fault-related folding: a review of kinematic models and their application. Earth Science Reviews, 138, 352-370. Zehnder, A.T., Allmendinger, R.W., 2000. Velocity field for the trishear model. Journal of Structural Geology, 22, 1009-1014. Ziesch, J., Tanner, D.C., Krawczyk, C.M. 2014. Strain associated with the fault-parallel flow algorithm during kinematic fault

Viscoelastic measurements after vocal fold scarring in rabbits--short-term results after hyaluronan injection.

PubMed

Hertegård, S; Dahlqvist, A; Goodyer, E

2006-07-01

The scarring model resulted in significant damage and elevated viscoelasticity of the lamina propria. Hyaluronan preparations may alter viscoelasticity in scarred rabbit vocal folds. Vocal fold scarring results in stiffness of the lamina propria and severe voice problems. The aims of this study were to examine the degree of scarring achieved in the experiment and to measure the viscoelastic properties after injection of hyaluronan in rabbit vocal folds. Twenty-two vocal folds from 15 New Zealand rabbits were scarred, 8 vocal folds were controls. After 8 weeks 12 of the scarred vocal folds received injections with 2 types of cross-linked hyaluronan products and 10 scarred folds were injected with saline. After 11 more weeks the animals were sacrificed. After dissection, 15 vocal folds were frozen for viscoelastic measurements, whereas 14 vocal folds were prepared and stained. Measurements were made of the lamina propria thickness. Viscoelasticity was measured on intact vocal folds with a linear skin rheometer (LSR) adapted to laryngeal measurements. Measurements on the digitized slides showed a thickened lamina propria in the scarred samples as compared with the normal vocal folds (p<0.05). The viscoelastic analysis showed a tendency to stiffening of the scarred vocal folds as compared with the normal controls (p=0.05). There was large variation in stiffness between the two injected hyaluronan products.

Influence of the ventricular folds on a voice source with specified vocal fold motion1

PubMed Central

McGowan, Richard S.; Howe, Michael S.

2010-01-01

The unsteady drag on the vocal folds is the major source of sound during voiced speech. The drag force is caused by vortex shedding from the vocal folds. The influence of the ventricular folds (i.e., the “false” vocal folds that protrude into the vocal tract a short distance downstream of the glottis) on the drag and the voice source are examined in this paper by means of a theoretical model involving vortex sheets in a two-dimensional geometry. The effect of the ventricular folds on the output acoustic pressure is found to be small when the movement of the vocal folds is prescribed. It is argued that the effect remains small when fluid-structure interactions account for vocal fold movement. These conclusions can be justified mathematically when the characteristic time scale for change in the velocity of the glottal jet is large compared to the time it takes for a vortex disturbance to be convected through the vocal fold and ventricular fold region. PMID:20329852

The Risk of Vocal Fold Atrophy after Serial Corticosteroid Injections of the Vocal Fold.

PubMed

Shi, Lucy L; Giraldez-Rodriguez, Laureano A; Johns, Michael M

2016-11-01

The aim of this study was to illustrate the risk of vocal fold atrophy in patients who receive serial subepithelial steroid injections for vocal fold scar. This study is a retrospective case report of two patients who underwent a series of weekly subepithelial infusions of 10 mg/mL dexamethasone for benign vocal fold lesion. Shortly after the procedures, both patients developed a weak and breathy voice. The first patient was a 53-year-old man with radiation-induced vocal fold stiffness. Six injections were performed unilaterally, and 1 week later, he developed unilateral vocal fold atrophy with new glottal insufficiency. The second patient was a 67-year-old woman with severe vocal fold inflammation related to laryngitis and calcinosis, Raynaud's phenomenon, esophagean dysmotility, sclerodactyly, and telangiectasia (CREST) syndrome. Five injections were performed bilaterally, and 1 week later, she developed bilateral vocal fold atrophy with a large midline glottal gap during phonation. In both cases, the steroid-induced vocal atrophy resolved spontaneously after 4 months. Serial subepithelial steroid infusions of the vocal folds, although safe in the majority of patients, carry the risk of causing temporary vocal fold atrophy when given at short intervals. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Determination of thermodynamics and kinetics of RNA reactions by force

PubMed Central

Tinoco, Ignacio; Li, Pan T. X.; Bustamante, Carlos

2008-01-01

Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force. PMID:17040613

A DEAD-box RNA helicase promotes thermodynamic equilibration of kinetically trapped RNA structures in vivo.

PubMed

Ruminski, Dana J; Watson, Peter Y; Mahen, Elisabeth M; Fedor, Martha J

2016-03-01

RNAs must assemble into specific structures in order to carry out their biological functions, but in vitro RNA folding reactions produce multiple misfolded structures that fail to exchange with functional structures on biological time scales. We used carefully designed self-cleaving mRNAs that assemble through well-defined folding pathways to identify factors that differentiate intracellular and in vitro folding reactions. Our previous work showed that simple base-paired RNA helices form and dissociate with the same rate and equilibrium constants in vivo and in vitro. However, exchange between adjacent secondary structures occurs much faster in vivo, enabling RNAs to quickly adopt structures with the lowest free energy. We have now used this approach to probe the effects of an extensively characterized DEAD-box RNA helicase, Mss116p, on a series of well-defined RNA folding steps in yeast. Mss116p overexpression had no detectable effect on helix formation or dissociation kinetics or on the stability of interdomain tertiary interactions, consistent with previous evidence that intracellular factors do not affect these folding parameters. However, Mss116p overexpression did accelerate exchange between adjacent helices. The nonprocessive nature of RNA duplex unwinding by DEAD-box RNA helicases is consistent with a branch migration mechanism in which Mss116p lowers barriers to exchange between otherwise stable helices by the melting and annealing of one or two base pairs at interhelical junctions. These results suggest that the helicase activity of DEAD-box proteins like Mss116p distinguish intracellular RNA folding pathways from nonproductive RNA folding reactions in vitro and allow RNA structures to overcome kinetic barriers to thermodynamic equilibration in vivo. © 2016 Ruminski et al.; Published by Cold Spring Harbor Laboratory Press for the RNA Society.

Estimating pseudocounts and fold changes for digital expression measurements.

PubMed

Erhard, Florian

2018-06-19

Fold changes from count based high-throughput experiments such as RNA-seq suffer from a zero-frequency problem. To circumvent division by zero, so-called pseudocounts are added to make all observed counts strictly positive. The magnitude of pseudocounts for digital expression measurements and on which stage of the analysis they are introduced remained an arbitrary choice. Moreover, in the strict sense, fold changes are not quantities that can be computed. Instead, due to the stochasticity involved in the experiments, they must be estimated by statistical inference. Here, we build on a statistical framework for fold changes, where pseudocounts correspond to the parameters of the prior distribution used for Bayesian inference of the fold change. We show that arbirary and widely used choices for applying pseudocounts can lead to biased results. As a statistical rigorous alternative, we propose and test an empirical Bayes procedure to choose appropriate pseudocounts. Moreover, we introduce the novel estimator Ψ LFC for fold changes showing favorable properties with small counts and smaller deviations from the truth in simulations and real data compared to existing methods. Our results have direct implications for entities with few reads in sequencing experiments, and indirectly also affect results for entities with many reads. Ψ LFC is available as an R package under https://github.com/erhard-lab/lfc (Apache 2.0 license); R scripts to generate all figures are available at zenodo (doi:10.5281/zenodo.1163029).

Human telomere sequence DNA in water-free and high-viscosity solvents: G-quadruplex folding governed by Kramers rate theory.

PubMed

Lannan, Ford M; Mamajanov, Irena; Hud, Nicholas V

2012-09-19

Structures formed by human telomere sequence (HTS) DNA are of interest due to the implication of telomeres in the aging process and cancer. We present studies of HTS DNA folding in an anhydrous, high viscosity deep eutectic solvent (DES) comprised of choline choride and urea. In this solvent, the HTS DNA forms a G-quadruplex with the parallel-stranded ("propeller") fold, consistent with observations that reduced water activity favors the parallel fold, whereas alternative folds are favored at high water activity. Surprisingly, adoption of the parallel structure by HTS DNA in the DES, after thermal denaturation and quick cooling to room temperature, requires several months, as opposed to less than 2 min in an aqueous solution. This extended folding time in the DES is, in part, due to HTS DNA becoming kinetically trapped in a folded state that is apparently not accessed in lower viscosity solvents. A comparison of times required for the G-quadruplex to convert from its aqueous-preferred folded state to its parallel fold also reveals a dependence on solvent viscosity that is consistent with Kramers rate theory, which predicts that diffusion-controlled transitions will slow proportionally with solvent friction. These results provide an enhanced view of a G-quadruplex folding funnel and highlight the necessity to consider solvent viscosity in studies of G-quadruplex formation in vitro and in vivo. Additionally, the solvents and analyses presented here should prove valuable for understanding the folding of many other nucleic acids and potentially have applications in DNA-based nanotechnology where time-dependent structures are desired.

Metal cofactor modulated folding and target recognition of HIV-1 NCp7.

PubMed

Ren, Weitong; Ji, Dongqing; Xu, Xiulian

2018-01-01

The HIV-1 nucleocapsid 7 (NCp7) plays crucial roles in multiple stages of HIV-1 life cycle, and its biological functions rely on the binding of zinc ions. Understanding the molecular mechanism of how the zinc ions modulate the conformational dynamics and functions of the NCp7 is essential for the drug development and HIV-1 treatment. In this work, using a structure-based coarse-grained model, we studied the effects of zinc cofactors on the folding and target RNA(SL3) recognition of the NCp7 by molecular dynamics simulations. After reproducing some key properties of the zinc binding and folding of the NCp7 observed in previous experiments, our simulations revealed several interesting features in the metal ion modulated folding and target recognition. Firstly, we showed that the zinc binding makes the folding transition states of the two zinc fingers less structured, which is in line with the Hammond effect observed typically in mutation, temperature or denaturant induced perturbations to protein structure and stability. Secondly, We showed that there exists mutual interplay between the zinc ion binding and NCp7-target recognition. Binding of zinc ions enhances the affinity between the NCp7 and the target RNA, whereas the formation of the NCp7-RNA complex reshapes the intrinsic energy landscape of the NCp7 and increases the stability and zinc affinity of the two zinc fingers. Thirdly, by characterizing the effects of salt concentrations on the target RNA recognition, we showed that the NCp7 achieves optimal balance between the affinity and binding kinetics near the physiologically relevant salt concentrations. In addition, the effects of zinc binding on the inter-domain conformational flexibility and folding cooperativity of the NCp7 were also discussed.

NoFold: RNA structure clustering without folding or alignment.

PubMed

Middleton, Sarah A; Kim, Junhyong

2014-11-01

Structures that recur across multiple different transcripts, called structure motifs, often perform a similar function-for example, recruiting a specific RNA-binding protein that then regulates translation, splicing, or subcellular localization. Identifying common motifs between coregulated transcripts may therefore yield significant insight into their binding partners and mechanism of regulation. However, as most methods for clustering structures are based on folding individual sequences or doing many pairwise alignments, this results in a tradeoff between speed and accuracy that can be problematic for large-scale data sets. Here we describe a novel method for comparing and characterizing RNA secondary structures that does not require folding or pairwise alignment of the input sequences. Our method uses the idea of constructing a distance function between two objects by their respective distances to a collection of empirical examples or models, which in our case consists of 1973 Rfam family covariance models. Using this as a basis for measuring structural similarity, we developed a clustering pipeline called NoFold to automatically identify and annotate structure motifs within large sequence data sets. We demonstrate that NoFold can simultaneously identify multiple structure motifs with an average sensitivity of 0.80 and precision of 0.98 and generally exceeds the performance of existing methods. We also perform a cross-validation analysis of the entire set of Rfam families, achieving an average sensitivity of 0.57. We apply NoFold to identify motifs enriched in dendritically localized transcripts and report 213 enriched motifs, including both known and novel structures. © 2014 Middleton and Kim; Published by Cold Spring Harbor Laboratory Press for the RNA Society.

New Protein Mimetics: The Zinc Finger Motif as a Locked-In Tertiary Fold.

PubMed

Tuchscherer, Gabriele; Lehmann, Christian; Mathieu, Marc

1998-11-16

The principle of a molecular kit is used for the covalent assembly of secondary structure forming peptide blocks to predetermined packing topologies. The resulting locked-in folds (LIFs; depicted schematically) are readily accessible and bypass the intriguing folding problem of linear peptide chains. This strategy allows, for example, mimicking of the essential structural and functional features of zinc finger proteins. © 1998 WILEY-VCH Verlag GmbH, Weinheim, Fed. Rep. of Germany.

Influence of thermodynamically unfavorable secondary structures on DNA hybridization kinetics

PubMed Central

Hata, Hiroaki; Kitajima, Tetsuro

2018-01-01

Abstract Nucleic acid secondary structure plays an important role in nucleic acid–nucleic acid recognition/hybridization processes, and is also a vital consideration in DNA nanotechnology. Although the influence of stable secondary structures on hybridization kinetics has been characterized, unstable secondary structures, which show positive ΔG° with self-folding, can also form, and their effects have not been systematically investigated. Such thermodynamically unfavorable secondary structures should not be ignored in DNA hybridization kinetics, especially under isothermal conditions. Here, we report that positive ΔG° secondary structures can change the hybridization rate by two-orders of magnitude, despite the fact that their hybridization obeyed second-order reaction kinetics. The temperature dependence of hybridization rates showed non-Arrhenius behavior; thus, their hybridization is considered to be nucleation limited. We derived a model describing how ΔG° positive secondary structures affect hybridization kinetics in stopped-flow experiments with 47 pairs of oligonucleotides. The calculated hybridization rates, which were based on the model, quantitatively agreed with the experimental rate constant. PMID:29220504

Models of fold-related hysteresis

NASA Astrophysics Data System (ADS)

Shtern, Vladimir

2018-05-01

Hysteresis is a strongly nonlinear physics phenomenon observed in many fluid mechanics flows. This paper composes evolution equations of the minimal nonlinearity and dimension which describe three hysteresis kinds related to a fold catastrophe formed by (i) two fold bifurcations, (ii) fold and transcritical bifurcations, and (iii) fold and subcritical bifurcations.

Kinematics, structural mechanics, and design of origami structures with smooth folds

NASA Astrophysics Data System (ADS)

Peraza Hernandez, Edwin Alexander

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a

Evidence for close side-chain packing in an early protein folding intermediate previously assumed to be a molten globule

PubMed Central

Rosen, Laura E.; Connell, Katelyn B.; Marqusee, Susan

2014-01-01

The molten globule, a conformational ensemble with significant secondary structure but only loosely packed tertiary structure, has been suggested to be a ubiquitous intermediate in protein folding. However, it is difficult to assess the tertiary packing of transiently populated species to evaluate this hypothesis. Escherichia coli RNase H is known to populate an intermediate before the rate-limiting barrier to folding that has long been thought to be a molten globule. We investigated this hypothesis by making mimics of the intermediate that are the ground-state conformation at equilibrium, using two approaches: a truncation to generate a fragment mimic of the intermediate, and selective destabilization of the native state using point mutations. Spectroscopic characterization and the response of the mimics to further mutation are consistent with studies on the transient kinetic intermediate, indicating that they model the early intermediate. Both mimics fold cooperatively and exhibit NMR spectra indicative of a closely packed conformation, in contrast to the hypothesis of molten tertiary packing. This result is important for understanding the nature of the subsequent rate-limiting barrier to folding and has implications for the assumption that many other proteins populate molten globule folding intermediates. PMID:25258414

Evidence for close side-chain packing in an early protein folding intermediate previously assumed to be a molten globule.

PubMed

Rosen, Laura E; Connell, Katelyn B; Marqusee, Susan

2014-10-14

The molten globule, a conformational ensemble with significant secondary structure but only loosely packed tertiary structure, has been suggested to be a ubiquitous intermediate in protein folding. However, it is difficult to assess the tertiary packing of transiently populated species to evaluate this hypothesis. Escherichia coli RNase H is known to populate an intermediate before the rate-limiting barrier to folding that has long been thought to be a molten globule. We investigated this hypothesis by making mimics of the intermediate that are the ground-state conformation at equilibrium, using two approaches: a truncation to generate a fragment mimic of the intermediate, and selective destabilization of the native state using point mutations. Spectroscopic characterization and the response of the mimics to further mutation are consistent with studies on the transient kinetic intermediate, indicating that they model the early intermediate. Both mimics fold cooperatively and exhibit NMR spectra indicative of a closely packed conformation, in contrast to the hypothesis of molten tertiary packing. This result is important for understanding the nature of the subsequent rate-limiting barrier to folding and has implications for the assumption that many other proteins populate molten globule folding intermediates.

Deciphering the mechanisms of binding induced folding at nearly atomic resolution: The Φ value analysis applied to IDPs.

PubMed

Gianni, Stefano; Dogan, Jakob; Jemth, Per

2014-01-01

The Φ value analysis is a method to analyze the structure of metastable states in reaction pathways. Such a methodology is based on the quantitative analysis of the effect of point mutations on the kinetics and thermodynamics of the probed reaction. The Φ value analysis is routinely used in protein folding studies and is potentially an extremely powerful tool to analyze the mechanism of binding induced folding of intrinsically disordered proteins. In this review we recapitulate the key equations and experimental advices to perform the Φ value analysis in the perspective of the possible caveats arising in intrinsically disordered systems. Finally, we briefly discuss some few examples already available in the literature.

Mechanisms of flexural flow folding of competent single-layers as evidenced by folded fibrous dolomite veins

NASA Astrophysics Data System (ADS)

Torremans, Koen; Muchez, Philippe; Sintubin, Manuel

2014-12-01

Flexural flow is thought unlikely to occur in naturally deformed, competent isotropic single-layers. In this study we discuss a particular case of folded bedding-parallel fibrous dolomite veins in shale, in which the internal strain pattern and microstructural deformation features provide new insights in the mechanisms enabling flexural flow folding. Strain in the pre-folding veins is accommodated by two main mechanisms: intracrystalline deformation by bending and intergranular deformation with bookshelf rotation of dolomite fibres. The initially orthogonal dolomite fibres allowed a reconstruction of the strain distribution across the folded veins. This analysis shows that the planar mechanical anisotropy created by the fibres causes the veins to approximate flexural flow. During folding, synkinematic veins overgrow the pre-folding fibrous dolomite veins. Microstructures and dolomite growth morphologies reflect growth during progressive fold evolution, with evidence for flexural slip at fold lock-up. Homogeneous flattening, as evidenced by disjunctive axial-planar cleavage, subsequently modified these folds from class 1B to 1C folds. Our study shows that the internal vein fabric has a first-order influence on folding kinematics. Moreover, the fibrous dolomite veins show high viscosity contrasts with the shale matrix, essential in creating transient permeability for subsequent mineralising stages in the later synkinematic veins during progressive folding.

Mutational Studies Uncover Non-Native Structure in the Dimeric Kinetic Intermediate of the H2A-H2B Heterodimer

PubMed Central

Stump, Matthew R.; Gloss, Lisa M.

2010-01-01

The folding pathway of the histone H2A-H2B heterodimer minimally includes an on-pathway, dimeric, burst-phase intermediate, I2. The partially folded H2A and H2B monomers populated at equilibrium were characterized as potential monomeric kinetic intermediates. Folding kinetics were compared for initiation from isolated, folded monomers and the heterodimer unfolded in 4 M urea. The observed rates were virtually identical above 0.4 M urea, exhibiting a log-linear relationship on the final denaturant concentration. Below ~0.4 M urea (concentrations inaccessible from the 4 M urea unfolded state), a roll-over in the rates was observed; this suggests that a component of the I2 ensemble contains non-native structure that rearranges/isomerizes to a more native-like species. The contribution of helix propensity to the stability of the I2 ensemble was assessed with a set of H2A-H2B mutants containing Ala and Gly replacements at nine sites, focusing mainly on the long, central α2 helix. Equilibrium and kinetic folding/unfolding data were collected to determine the effects of the mutations on the stability of I2 and the transition state between I2 and N2. This limited mutational study indicated that residues in the α2 helices of H2A and H2B, as well as α1 of H2B and both the C-terminus of α3 and the short αC helix of H2A contribute to the stability of the I2 burst phase species. Interestingly, at least eight of the nine targeted residues stabilize I2 by interactions that are non-native to some extent. Given that destabilizing I2 and these non-native interactions does not accelerate folding, it is concluded that the native and non-native structure present in the I2 ensemble enables efficient folding of H2A-H2B. PMID:20600120

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

Folding of polyglutamine chains

NASA Astrophysics Data System (ADS)

Chopra, Manan; Reddy, Allam S.; Abbott, N. L.; de Pablo, J. J.

2008-10-01

Long polyglutamine chains have been associated with a number of neurodegenerative diseases. These include Huntington's disease, where expanded polyglutamine (PolyQ) sequences longer than 36 residues are correlated with the onset of symptoms. In this paper we study the folding pathway of a 54-residue PolyQ chain into a β-helical structure. Transition path sampling Monte Carlo simulations are used to generate unbiased reactive pathways between unfolded configurations and the folded β-helical structure of the polyglutamine chain. The folding process is examined in both explicit water and an implicit solvent. Both models reveal that the formation of a few critical contacts is necessary and sufficient for the molecule to fold. Once the primary contacts are formed, the fate of the protein is sealed and it is largely committed to fold. We find that, consistent with emerging hypotheses about PolyQ aggregation, a stable β-helical structure could serve as the nucleus for subsequent polymerization of amyloid fibrils. Our results indicate that PolyQ sequences shorter than 36 residues cannot form that nucleus, and it is also shown that specific mutations inferred from an analysis of the simulated folding pathway exacerbate its stability.

Transient state kinetics tutorial using the kinetics simulation program, KINSIM.

PubMed Central

Wachsstock, D H; Pollard, T D

1994-01-01

This article provides an introduction to a computer tutorial on transient state kinetics. The tutorial uses our Macintosh version of the computer program, KINSIM, that calculates the time course of reactions. KINSIM is also available for other popular computers. This program allows even those investigators not mathematically inclined to evaluate the rate constants for the transitions between the intermediates in any reaction mechanism. These rate constants are one of the insights that are essential for understanding how biochemical processes work at the molecular level. The approach is applicable not only to enzyme reactions but also to any other type of process of interest to biophysicists, cell biologists, and molecular biologists in which concentrations change with time. In principle, the same methods could be used to characterize time-dependent, large-scale processes in ecology and evolution. Completion of the tutorial takes students 6-10 h. This investment is rewarded by a deep understanding of the principles of chemical kinetics and familiarity with the tools of kinetics simulation as an approach to solve everyday problems in the laboratory. PMID:7811941

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Effectiveness and Adoption of a Drawing-to-Learn Study Tool for Recall and Problem Solving: Minute Sketches with Folded Lists

PubMed Central

Heideman, Paul D.; Flores, K. Adryan; Sevier, Lu M.; Trouton, Kelsey E.

2017-01-01

Drawing by learners can be an effective way to develop memory and generate visual models for higher-order skills in biology, but students are often reluctant to adopt drawing as a study method. We designed a nonclassroom intervention that instructed introductory biology college students in a drawing method, minute sketches in folded lists (MSFL), and allowed them to self-assess their recall and problem solving, first in a simple recall task involving non-European alphabets and later using unfamiliar biology content. In two preliminary ex situ experiments, students had greater recall on the simple learning task, non-European alphabets with associated phonetic sounds, using MSFL in comparison with a preferred method, visual review (VR). In the intervention, students studying using MSFL and VR had ∼50–80% greater recall of content studied with MSFL and, in a subset of trials, better performance on problem-solving tasks on biology content. Eight months after beginning the intervention, participants had shifted self-reported use of drawing from 2% to 20% of study time. For a small subset of participants, MSFL had become a preferred study method, and 70% of participants reported continued use of MSFL. This brief, low-cost intervention resulted in enduring changes in study behavior. PMID:28495932

Structural Bridges through Fold Space.

PubMed

Edwards, Hannah; Deane, Charlotte M

2015-09-01

Several protein structure classification schemes exist that partition the protein universe into structural units called folds. Yet these schemes do not discuss how these units sit relative to each other in a global structure space. In this paper we construct networks that describe such global relationships between folds in the form of structural bridges. We generate these networks using four different structural alignment methods across multiple score thresholds. The networks constructed using the different methods remain a similar distance apart regardless of the probability threshold defining a structural bridge. This suggests that at least some structural bridges are method specific and that any attempt to build a picture of structural space should not be reliant on a single structural superposition method. Despite these differences all representations agree on an organisation of fold space into five principal community structures: all-α, all-β sandwiches, all-β barrels, α/β and α + β. We project estimated fold ages onto the networks and find that not only are the pairings of unconnected folds associated with higher age differences than bridged folds, but this difference increases with the number of networks displaying an edge. We also examine different centrality measures for folds within the networks and how these relate to fold age. While these measures interpret the central core of fold space in varied ways they all identify the disposition of ancestral folds to fall within this core and that of the more recently evolved structures to provide the peripheral landscape. These findings suggest that evolutionary information is encoded along these structural bridges. Finally, we identify four highly central pivotal folds representing dominant topological features which act as key attractors within our landscapes.

Folding domain B of protein A on a dynamically partitioned free energy landscape.

PubMed

Nelson, Erik D; Grishin, Nick V

2008-02-05

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.

Accelerated Simulation of Kinetic Transport Using Variational Principles and Sparsity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caflisch, Russel

This project is centered on the development and application of techniques of sparsity and compressed sensing for variational principles, PDEs and physics problems, in particular for kinetic transport. This included derivation of sparse modes for elliptic and parabolic problems coming from variational principles. The research results of this project are on methods for sparsity in differential equations and their applications and on application of sparsity ideas to kinetic transport of plasmas.

Extracting rate coefficients from single-molecule photon trajectories and FRET efficiency histograms for a fast-folding protein.

PubMed

Chung, Hoi Sung; Gopich, Irina V; McHale, Kevin; Cellmer, Troy; Louis, John M; Eaton, William A

2011-04-28

Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, α(3)D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross-correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin

Exploring the Energy Landscapes of Protein Folding Simulations with Bayesian Computation

PubMed Central

Burkoff, Nikolas S.; Várnai, Csilla; Wells, Stephen A.; Wild, David L.

2012-01-01

Nested sampling is a Bayesian sampling technique developed to explore probability distributions localized in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algorithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering. In this article, we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Gō-like force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins that are commonly used for testing protein-folding procedures. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high-level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used. PMID:22385859

Structural Characteristic of the Initial Unfolded State on Refolding Determines Catalytic Efficiency of the Folded Protein in Presence of Osmolytes

PubMed Central

Warepam, Marina; Sharma, Gurumayum Suraj; Dar, Tanveer Ali; Khan, Md. Khurshid Alam; Singh, Laishram Rajendrakumar

2014-01-01

Osmolytes are low molecular weight organic molecules accumulated by organisms to assist proper protein folding, and to provide protection to the structural integrity of proteins under denaturing stress conditions. It is known that osmolyte-induced protein folding is brought by unfavorable interaction of osmolytes with the denatured/unfolded states. The interaction of osmolyte with the native state does not significantly contribute to the osmolyte-induced protein folding. We have therefore investigated if different denatured states of a protein (generated by different denaturing agents) interact differently with the osmolytes to induce protein folding. We observed that osmolyte-assisted refolding of protein obtained from heat-induced denatured state produces native molecules with higher enzyme activity than those initiated from GdmCl- or urea-induced denatured state indicating that the structural property of the initial denatured state during refolding by osmolytes determines the catalytic efficiency of the folded protein molecule. These conclusions have been reached from the systematic measurements of enzymatic kinetic parameters (K m and k cat), thermodynamic stability (T m and ΔH m) and secondary and tertiary structures of the folded native proteins obtained from refolding of various denatured states (due to heat-, urea- and GdmCl-induced denaturation) of RNase-A in the presence of various osmolytes. PMID:25313668

Stabilization of a protein conferred by an increase in folded state entropy.

PubMed

Dagan, Shlomi; Hagai, Tzachi; Gavrilov, Yulian; Kapon, Ruti; Levy, Yaakov; Reich, Ziv

2013-06-25

Entropic stabilization of native protein structures typically relies on strategies that serve to decrease the entropy of the unfolded state. Here we report, using a combination of experimental and computational approaches, on enhanced thermodynamic stability conferred by an increase in the configurational entropy of the folded state. The enhanced stability is observed upon modifications of a loop region in the enzyme acylphosphatase and is achieved despite significant enthalpy losses. The modifications that lead to increased stability, as well as those that result in destabilization, however, strongly compromise enzymatic activity, rationalizing the preservation of the native loop structure even though it does not provide the protein with maximal stability or kinetic foldability.

Structural and kinetic mapping of side-chain exposure onto the protein energy landscape.

PubMed

Bernstein, Rachel; Schmidt, Kierstin L; Harbury, Pehr B; Marqusee, Susan

2011-06-28

Identification and characterization of structural fluctuations that occur under native conditions is crucial for understanding protein folding and function, but such fluctuations are often rare and transient, making them difficult to study. Native-state hydrogen exchange (NSHX) has been a powerful tool for identifying such rarely populated conformations, but it generally reveals no information about the placement of these species along the folding reaction coordinate or the barriers separating them from the folded state and provides little insight into side-chain packing. To complement such studies, we have performed native-state alkyl-proton exchange, a method analogous to NSHX that monitors cysteine modification rather than backbone amide exchange, to examine the folding landscape of Escherichia coli ribonuclease H, a protein well characterized by hydrogen exchange. We have chosen experimental conditions such that the rate-limiting barrier acts as a kinetic partition: residues that become exposed only upon crossing the unfolding barrier are modified in the EX1 regime (alkylation rates report on the rate of unfolding), while those exposed on the native side of the barrier are modified predominantly in the EX2 regime (alkylation rates report on equilibrium populations). This kinetic partitioning allows for identification and placement of partially unfolded forms along the reaction coordinate. Using this approach we detect previously unidentified, rarely populated conformations residing on the native side of the barrier and identify side chains that are modified only upon crossing the unfolding barrier. Thus, in a single experiment under native conditions, both sides of the rate-limiting barrier are investigated.

Structural and kinetic mapping of side-chain exposure onto the protein energy landscape

PubMed Central

Bernstein, Rachel; Schmidt, Kierstin L.; Harbury, Pehr B.; Marqusee, Susan

2011-01-01

Identification and characterization of structural fluctuations that occur under native conditions is crucial for understanding protein folding and function, but such fluctuations are often rare and transient, making them difficult to study. Native-state hydrogen exchange (NSHX) has been a powerful tool for identifying such rarely populated conformations, but it generally reveals no information about the placement of these species along the folding reaction coordinate or the barriers separating them from the folded state and provides little insight into side-chain packing. To complement such studies, we have performed native-state alkyl-proton exchange, a method analogous to NSHX that monitors cysteine modification rather than backbone amide exchange, to examine the folding landscape of Escherichia coli ribonuclease H, a protein well characterized by hydrogen exchange. We have chosen experimental conditions such that the rate-limiting barrier acts as a kinetic partition: residues that become exposed only upon crossing the unfolding barrier are modified in the EX1 regime (alkylation rates report on the rate of unfolding), while those exposed on the native side of the barrier are modified predominantly in the EX2 regime (alkylation rates report on equilibrium populations). This kinetic partitioning allows for identification and placement of partially unfolded forms along the reaction coordinate. Using this approach we detect previously unidentified, rarely populated conformations residing on the native side of the barrier and identify side chains that are modified only upon crossing the unfolding barrier. Thus, in a single experiment under native conditions, both sides of the rate-limiting barrier are investigated. PMID:21670244

The fast-folding HP35 double mutant has a substantially reduced primary folding free energy barrier

NASA Astrophysics Data System (ADS)

Lei, Hongxing; Deng, Xiaojian; Wang, Zhixiang; Duan, Yong

2008-10-01

The LYS24/29NLE double mutant of villin headpiece subdomain (HP35) is the fastest folding protein known so far with a folding time constant of 0.6μs. In this work, the folding mechanism of the mutant has been investigated by both conventional and replica exchange molecular dynamics (CMD and REMD) simulations with AMBER FF03 force field and a generalized-Born solvation model. Direct comparison to the ab initio folding of the wild type HP35 enabled a close examination on the mutational effect on the folding process. The mutant folded to the native state, as demonstrated by the 0.50Å Cα-root mean square deviation (RMSD) sampled in both CMD and REMD simulations and the high population of the folded conformation compared with the denatured conformations. Consistent with experiments, the significantly reduced primary folding free energy barrier makes the mutant closer to a downhill folder than the wild type HP35 that directly leads to the faster transition and higher melting temperature. However, unlike the proposed downhill folding which envisages a smooth shift between unfolded and folded states without transition barrier, we observed a well-defined folding transition that was consistent with experiments. Further examination of the secondary structures revealed that the two mutated residues have higher intrinsic helical preference that facilitated the formation of both helix III and the intermediate state which contains the folded segment helix II/III. Other factors contributing to the faster folding include the more favorable electrostatic interactions in the transition state with the removal of the charged NH3+ groups from LYS. In addition, both transition state ensemble and denatured state ensemble are shifted in the mutant.

Congenital hypothyroidism mutations affect common folding and trafficking in the α/β-hydrolase fold proteins

PubMed Central

De Jaco, Antonella; Dubi, Noga; Camp, Shelley; Taylor, Palmer

2017-01-01

The α/β-hydrolase fold superfamily of proteins is composed of structurally related members that, despite great diversity in their catalytic, recognition, adhesion and chaperone functions, share a common fold governed by homologous residues and conserved disulfide bridges. Non-synonymous single nucleotide polymorphisms within the α/β-hydrolase fold domain in various family members have been found for congenital endocrine, metabolic and nervous system disorders. By examining the amino acid sequence from the various proteins, mutations were found to be prevalent in conserved residues within the α/β-hydrolase fold of the homologous proteins. This is the case for the thyroglobulin mutations linked to congenital hypothyroidism. To address whether correct folding of the common domain is required for protein export, we inserted the thyroglobulin mutations at homologous positions in two correlated but simpler α/β-hydrolase fold proteins known to be exported to the cell surface: neuroligin3 and acetylcholinesterase. Here we show that these mutations in the cholinesterase homologous region alter the folding properties of the α/β-hydrolase fold domain, which are reflected in defects in protein trafficking, folding and function, and ultimately result in retention of the partially processed proteins in the endoplasmic reticulum. Accordingly, mutations at conserved residues may be transferred amongst homologous proteins to produce common processing defects despite disparate functions, protein complexity and tissue-specific expression of the homologous proteins. More importantly, a similar assembly of the α/β-hydrolase fold domain tertiary structure among homologous members of the superfamily is required for correct trafficking of the proteins to their final destination. PMID:23035660

Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study.

PubMed

Chikenji, George; Fujitsuka, Yoshimi; Takada, Shoji

2006-02-28

Predicting protein tertiary structure by folding-like simulations is one of the most stringent tests of how much we understand the principle of protein folding. Currently, the most successful method for folding-based structure prediction is the fragment assembly (FA) method. Here, we address why the FA method is so successful and its lesson for the folding problem. To do so, using the FA method, we designed a structure prediction test of "chimera proteins." In the chimera proteins, local structural preference is specific to the target sequences, whereas nonlocal interactions are only sequence-independent compaction forces. We find that these chimera proteins can find the native folds of the intact sequences with high probability indicating dominant roles of the local interactions. We further explore roles of local structural preference by exact calculation of the HP lattice model of proteins. From these results, we suggest principles of protein folding: For small proteins, compact structures that are fully compatible with local structural preference are few, one of which is the native fold. These local biases shape up the funnel-like energy landscape.

Structure of human POFUT2: insights into thrombospondin type 1 repeat fold and O-fucosylation

PubMed Central

Chen, Chun-I; Keusch, Jeremy J; Klein, Dominique; Hess, Daniel; Hofsteenge, Jan; Gut, Heinz

2012-01-01

Protein O-fucosylation is a post-translational modification found on serine/threonine residues of thrombospondin type 1 repeats (TSR). The fucose transfer is catalysed by the enzyme protein O-fucosyltransferase 2 (POFUT2) and >40 human proteins contain the TSR consensus sequence for POFUT2-dependent fucosylation. To better understand O-fucosylation on TSR, we carried out a structural and functional analysis of human POFUT2 and its TSR substrate. Crystal structures of POFUT2 reveal a variation of the classical GT-B fold and identify sugar donor and TSR acceptor binding sites. Structural findings are correlated with steady-state kinetic measurements of wild-type and mutant POFUT2 and TSR and give insight into the catalytic mechanism and substrate specificity. By using an artificial mini-TSR substrate, we show that specificity is not primarily encoded in the TSR protein sequence but rather in the unusual 3D structure of a small part of the TSR. Our findings uncover that recognition of distinct conserved 3D fold motifs can be used as a mechanism to achieve substrate specificity by enzymes modifying completely folded proteins of very wide sequence diversity and biological function. PMID:22588082

Shear properties of vocal fold mucosal tissues and their effect on vocal fold oscillation

NASA Astrophysics Data System (ADS)

Chan, Roger Wai Kai

Viscoelastic shear properties of vocal fold mucosal tissues and phonosurgical biomaterials were measured with a parallel-plate rotational rheometer. Elastic, viscous and damping properties were quantified as a function of frequency (0.01 Hz to 15 Hz) for human vocal fold mucosal tissues (N = 15), implantable biomaterials commonly used in the treatment of vocal fold paralysis (Teflon, gelatin, and collagen) (the non-mucosal group), and biomaterials currently or potentially useful in the treatment of vocal fold mucosal defects (adipose tissue or fat, hyaluronic acid, and fibronectin) (the mucosal group). It was found that intersubject differences as large as an order of magnitude were often observed for the shear properties of vocal fold mucosal tissues, part of which may be age- and gender-related. Shear properties of the non-mucosal group biomaterials were often much higher than those of the mucosal group biomaterials, which were relatively close to the shear properties of mucosal tissues. Viscoelastic and rheological modeling showed that shear properties of human vocal fold mucosa may be described by a quasi-linear viscoelastic theory and a statistical network theory, based upon which extrapolations to audio frequencies were possible. A theory of small-amplitude vocal fold oscillation was revisited to describe the effects of tissue shear properties on vocal fold oscillation and phonation threshold pressure, a measure of the 'ease' of phonation and an objective indication of vocal function. It was found that phonation threshold pressure is directly related to the viscous shear modulus or the 'effective damping modulus', a concept proposed to quantify the effective amount of damping in vocal fold oscillation. The mucosal group biomaterials were incorporated into the artificial vocal fold mucosa of a physical model in order to empirically assess their effects on phonation threshold pressure. Results showed that higher threshold pressures were consistently observed

Entropic formulation for the protein folding process: Hydrophobic stability correlates with folding rates

NASA Astrophysics Data System (ADS)

Dal Molin, J. P.; Caliri, A.

2018-01-01

Here we focus on the conformational search for the native structure when it is ruled by the hydrophobic effect and steric specificities coming from amino acids. Our main tool of investigation is a 3D lattice model provided by a ten-letter alphabet, the stereochemical model. This minimalist model was conceived for Monte Carlo (MC) simulations when one keeps in mind the kinetic behavior of protein-like chains in solution. We have three central goals here. The first one is to characterize the folding time (τ) by two distinct sampling methods, so we present two sets of 103 MC simulations for a fast protein-like sequence. The resulting sets of characteristic folding times, τ and τq were obtained by the application of the standard Metropolis algorithm (MA), as well as by an enhanced algorithm (Mq A). The finding for τq shows two things: (i) the chain-solvent hydrophobic interactions {hk } plus a set of inter-residues steric constraints {ci,j } are able to emulate the conformational search for the native structure. For each one of the 103MC performed simulations, the target is always found within a finite time window; (ii) the ratio τq / τ ≅ 1 / 10 suggests that the effect of local thermal fluctuations, encompassed by the Tsallis weight, provides to the chain an innate efficiency to escape from energetic and steric traps. We performed additional MC simulations with variations of our design rule to attest this first result, both algorithms the MA and the Mq A were applied to a restricted set of targets, a physical insight is provided. Our second finding was obtained by a set of 600 independent MC simulations, only performed with the Mq A applied to an extended set of 200 representative targets, our native structures. The results show how structural patterns should modulate τq, which cover four orders of magnitude; this finding is our second goal. The third, and last result, was obtained with a special kind of simulation performed with the purpose to explore a

First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach?

PubMed

Kalgin, Igor V; Chekmarev, Sergei F; Karplus, Martin

2014-04-24

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed "streamlines", the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.

First Passage Analysis of the Folding of a β-Sheet Miniprotein: Is it More Realistic Than the Standard Equilibrium Approach?

PubMed Central

2015-01-01

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations. PMID:24669953

Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

PubMed Central

Wensley, Beth G.; Kwa, Lee Gyan; Shammas, Sarah L.; Rogers, Joseph M.; Browning, Stuart; Yang, Ziqi; Clarke, Jane

2012-01-01

The elongated three-helix bundle domains spectrin R16 and R17 fold some two to three orders of magnitude more slowly than their homologue R15. We have shown that this slow folding is due, at least in part, to roughness in the free-energy landscape of R16 and R17. We have proposed that this roughness is due to a frustrated search for the correct docking of partly preformed helices. However, this accounts for only a small part of the slowing of folding and unfolding. Five residues on the A helix of R15, when inserted together into R16 or R17, increase the folding rate constants, reduce landscape roughness, and alter the folding mechanism to one resembling R15. The effect of each of these mutations individually is investigated here. No one mutation causes the behavior seen for the five in combination. However, two mutations, E18F and K25V, significantly increase the folding and unfolding rates of both R16 and R17 but without a concomitant loss in landscape roughness. E18F has the greatest effect on the kinetics, and a Φ-value analysis of the C helix reveals that the folding mechanism is unchanged. For both E18F and K25V the removal of the charge and resultant transition state stabilization is the main origin of the faster folding. Consequently, the major cause of the unusually slow folding of R16 and R17 is the non-native burial of the two charged residues in the transition state. The slowing due to landscape roughness is only about fivefold. PMID:22711800

Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains.

PubMed

Wensley, Beth G; Kwa, Lee Gyan; Shammas, Sarah L; Rogers, Joseph M; Browning, Stuart; Yang, Ziqi; Clarke, Jane

2012-10-30

The elongated three-helix bundle domains spectrin R16 and R17 fold some two to three orders of magnitude more slowly than their homologue R15. We have shown that this slow folding is due, at least in part, to roughness in the free-energy landscape of R16 and R17. We have proposed that this roughness is due to a frustrated search for the correct docking of partly preformed helices. However, this accounts for only a small part of the slowing of folding and unfolding. Five residues on the A helix of R15, when inserted together into R16 or R17, increase the folding rate constants, reduce landscape roughness, and alter the folding mechanism to one resembling R15. The effect of each of these mutations individually is investigated here. No one mutation causes the behavior seen for the five in combination. However, two mutations, E18F and K25V, significantly increase the folding and unfolding rates of both R16 and R17 but without a concomitant loss in landscape roughness. E18F has the greatest effect on the kinetics, and a Φ-value analysis of the C helix reveals that the folding mechanism is unchanged. For both E18F and K25V the removal of the charge and resultant transition state stabilization is the main origin of the faster folding. Consequently, the major cause of the unusually slow folding of R16 and R17 is the non-native burial of the two charged residues in the transition state. The slowing due to landscape roughness is only about fivefold.

Protein Quality Control Acts on Folding Intermediates to Shape the Effects of Mutations on Organismal Fitness

PubMed Central

Bershtein, Shimon; Mu, Wanmeng; Serohijos, Adrian W. R.; Zhou, Jingwen; Shakhnovich, Eugene I.

2012-01-01

Summary What are the molecular properties of proteins that fall on the radar of protein quality control (PQC)? Here we mutate the E. coli’s gene encoding dihydrofolate reductase (DHFR), and replace it with bacterial orthologous genes to determine how components of PQC modulate fitness effects of these genetic changes. We find that chaperonins GroEL/ES and protease Lon compete for binding to molten globule intermediate of DHFR, resulting in a peculiar symmetry in their action: Over-expression of GroEL/ES and deletion of Lon both restore growth of deleterious DHFR mutants and most of the slow-growing orthologous DHFR strains. Kinetic steady-state modeling predicts and experimentation verifies that mutations affect fitness by shifting the flux balance in cellular milieu between protein production, folding and degradation orchestrated by PQC through the interaction with folding intermediates. PMID:23219534

Proline 54 trans-cis isomerization is responsible for the kinetic partitioning at the last-step photocycle of photoactive yellow protein

PubMed Central

Lee, Byoung-Chul; Hoff, Wouter D.

2008-01-01

Photoactive yellow protein (PYP), a blue-light photoreceptor for Ectothiorhodospira halophila, has provided a unique system for studying protein folding that is coupled with a photocycle. Upon receptor activation by blue light, PYP proceeds through a photocycle that includes a partially folded signaling state. The last-step photocycle is a thermal recovery reaction from the signaling state to the native state. Bi-exponential kinetics had been observed for the last-step photocycle; however, the slow phase of the bi-exponential kinetics has not been extensively studied. Here we analyzed both fast and slow phases of the last-step photocycle in PYP. From the analysis of the denaturant dependence of the fast and slow phases, we found that the last-step photocycle proceeds through parallel channels of the folding pathway. The burial of the solvent-accessible area was responsible for the transition state of the fast phase, while structural rearrangement from the compact state to the native state was responsible for the transition state of the slow phase. The photocycle of PYP was linked to the thermodynamic cycle that includes both unfolding and refolding of the fast- and slow-phase intermediates. In order to test the hypothesis of proline-limited folding for the slow phase, we constructed two proline mutants: P54A and P68A. We found that only a single phase of the last-step photocycle was observed in P54A. This suggests that there is a low energy barrier between trans to cis conformation in P54 in the light-induced state of PYP, and the resulting cis conformation of P54 generates a slow-phase kinetic trap during the photocycle-coupled folding pathway of PYP. PMID:18794212

Nonminimal kinetic coupled gravity: Inflation on the warped DGP brane

NASA Astrophysics Data System (ADS)

Darabi, F.; Parsiya, A.; Atazadeh, K.

2016-03-01

We consider the nonminimally kinetic coupled version of DGP brane model, where the kinetic term of the scalar field is coupled to the metric and Einstein tensor on the brane by a coupling constant ζ. We obtain the corresponding field equations, using the Friedmann-Robertson-Walker metric and the perfect fluid, and study the inflationary scenario to confront the numerical analysis of six typical scalar field potentials with the current observational results. We find that among the suggested potentials and coupling constants, subject to the e-folding N = 60, the potentials V (ϕ) = σϕ, V (ϕ) = σϕ2 and V (ϕ) = σϕ3 provide the best fits with both Planck+WP+highL data and Planck+WP+highL+BICEP2 data.

Periodic folding of viscous sheets

NASA Astrophysics Data System (ADS)

Ribe, Neil M.

2003-09-01

The periodic folding of a sheet of viscous fluid falling upon a rigid surface is a common fluid mechanical instability that occurs in contexts ranging from food processing to geophysics. Asymptotic thin-layer equations for the combined stretching-bending deformation of a two-dimensional sheet are solved numerically to determine the folding frequency as a function of the sheet’s initial thickness, the pouring speed, the height of fall, and the fluid properties. As the buoyancy increases, the system bifurcates from “forced” folding driven kinematically by fluid extrusion to “free” folding in which viscous resistance to bending is balanced by buoyancy. The systematics of the numerically predicted folding frequency are in good agreement with laboratory experiments.

Fan-fold shielded electrical leads

DOEpatents

Rohatgi, R.R.; Cowan, T.E.

1996-06-11

Disclosed are fan-folded electrical leads made from copper cladded Kapton, for example, with the copper cladding on one side serving as a ground plane and the copper cladding on the other side being etched to form the leads. The Kapton is fan folded with the leads located at the bottom of the fan-folds. Electrical connections are made by partially opening the folds of the fan and soldering, for example, the connections directly to the ground plane and/or the lead. The fan folded arrangement produces a number of advantages, such as electrically shielding the leads from the environment, is totally non-magnetic, and has a very low thermal conductivity, while being easy to fabricate. 3 figs.

Fan-fold shielded electrical leads

DOEpatents

Rohatgi, Rajeev R.; Cowan, Thomas E.

1996-01-01

Fan-folded electrical leads made from copper cladded Kapton, for example, with the copper cladding on one side serving as a ground plane and the copper cladding on the other side being etched to form the leads. The Kapton is fan folded with the leads located at the bottom of the fan-folds. Electrical connections are made by partially opening the folds of the fan and soldering, for example, the connections directly to the ground plane and/or the lead. The fan folded arrangement produces a number of advantages, such as electrically shielding the leads from the environment, is totally non-magnetic, and has a very low thermal conductivity, while being easy to fabricate.

Explaining the discrepancy between forced fold amplitude and sill thickness.

NASA Astrophysics Data System (ADS)

Hoggett, Murray; Jones, Stephen M.; Reston, Timothy; Magee, Craig; Jackson, Christopher AL

2017-04-01

Understanding the behaviour of Earth's surface in response to movement and emplacement of magma underground is important because it assists calculation of subsurface magma volumes, and could feed into eruption forecasting. Studies of seismic reflection data have observed that the amplitude of a forced fold above an igneous sill is usually smaller than the thickness of the sill itself. This observation implies that fold amplitude alone provides only a lower bound for magma volume, and an understanding of the mechanism(s) behind the fold amplitude/sill thickness discrepancy is also required to obtain a true estimate of magma volume. Mechanisms suggested to explain the discrepancy include problems with seismic imaging and varying strain behaviour of the host rock. Here we examine the extent to which host-rock compaction can explain the fold amplitude/sill thickness discrepancy. This mechanism operates in cases where a sill is injected into the upper few kilometres of sedimentary rock that contain significant porosity. Accumulation of sediment after sill intrusion reduces the amplitude of the forced fold by compaction, but the sill itself undergoes little compaction since its starting porosity is almost zero. We compiled a database of good-quality 2D and 3D seismic observations where sill thickness has been measured independently of forced fold geometry. We then backstripped the post-intrusion sedimentary section to reconstruct the amplitude of the forced fold at the time of intrusion. We used the standard compaction model in which porosity decays exponentially below the sediment surface. In all examples we studied, post-sill-emplacement compaction can explain all of the fold amplitude/sill thickness discrepancy, subject to uncertainty in compaction model parameters. This result leads directly to an improved method of predicting magma volume from fold amplitude, including how uncertainty in compaction parameters maps onto uncertainty in magma volume. Our work implies

ALCHEMIC: Advanced time-dependent chemical kinetics

NASA Astrophysics Data System (ADS)

Semenov, Dmitry A.

2017-08-01

ALCHEMIC solves chemical kinetics problems, including gas-grain interactions, surface reactions, deuterium fractionization, and transport phenomena and can model the time-dependent chemical evolution of molecular clouds, hot cores, corinos, and protoplanetary disks.

Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent.

PubMed

Peter, Emanuel K; Shea, Joan-Emma; Pivkin, Igor V

2016-05-14

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC). The new development significantly can reduce the amount of replicas and the computational cost needed to enhance sampling in protein simulations. We introduce 2 different methods which primarily differ in the exchange scheme between the parallel ensembles. We apply this approach on folding of 2 different β-stranded peptides: the C-terminal β-hairpin fragment of GB1 and TrpZip4. Additionally, we use the new simulation technique to study the folding of TrpCage, a small fast folding α-helical peptide. Subsequently, we apply the new methodology on conformation changes in signaling of the light-oxygen voltage (LOV) sensitive domain from Avena sativa (AsLOV2). Our results agree well with data reported in the literature. In simulations of dialanine, we compare the statistical sampling of the 2 techniques with conventional REMD and analyze their performance. The new techniques can reduce the computational cost of REMD significantly and can be used in enhanced sampling simulations of biomolecules.

Kinetics of Photoelectrochemical Oxidation of Methanol on Hematite Photoanodes

PubMed Central

2017-01-01

The kinetics of photoelectrochemical (PEC) oxidation of methanol, as a model organic substrate, on α-Fe2O3 photoanodes are studied using photoinduced absorption spectroscopy and transient photocurrent measurements. Methanol is oxidized on α-Fe2O3 to formaldehyde with near unity Faradaic efficiency. A rate law analysis under quasi-steady-state conditions of PEC methanol oxidation indicates that rate of reaction is second order in the density of surface holes on hematite and independent of the applied potential. Analogous data on anatase TiO2 photoanodes indicate similar second-order kinetics for methanol oxidation with a second-order rate constant 2 orders of magnitude higher than that on α-Fe2O3. Kinetic isotope effect studies determine that the rate constant for methanol oxidation on α-Fe2O3 is retarded ∼20-fold by H/D substitution. Employing these data, we propose a mechanism for methanol oxidation under 1 sun irradiation on these metal oxide surfaces and discuss the implications for the efficient PEC methanol oxidation to formaldehyde and concomitant hydrogen evolution. PMID:28735533

Single-Molecule Imaging of an in Vitro-Evolved RNA Aptamer Reveals Homogeneous Ligand Binding Kinetics

PubMed Central

2009-01-01

Many studies of RNA folding and catalysis have revealed conformational heterogeneity, metastable folding intermediates, and long-lived states with distinct catalytic activities. We have developed a single-molecule imaging approach for investigating the functional heterogeneity of in vitro-evolved RNA aptamers. Monitoring the association of fluorescently labeled ligands with individual RNA aptamer molecules has allowed us to record binding events over the course of multiple days, thus providing sufficient statistics to quantitatively define the kinetic properties at the single-molecule level. The ligand binding kinetics of the highly optimized RNA aptamer studied here displays a remarkable degree of uniformity and lack of memory. Such homogeneous behavior is quite different from the heterogeneity seen in previous single-molecule studies of naturally derived RNA and protein enzymes. The single-molecule methods we describe may be of use in analyzing the distribution of functional molecules in heterogeneous evolving populations or even in unselected samples of random sequences. PMID:19572753

Exploring the energy landscapes of protein folding simulations with Bayesian computation.