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Sample records for folding problem kinetics

  1. 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

  2. Problem Solving through Paper Folding

    ERIC Educational Resources Information Center

    Wares, Arsalan

    2014-01-01

    The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

  3. Kinetic partitioning mechanism of HDV ribozyme folding

    NASA Astrophysics Data System (ADS)

    Chen, Jiawen; Gong, Sha; Wang, Yujie; Zhang, Wenbing

    2014-01-01

    RNA folding kinetics is directly tied to RNA biological functions. We introduce here a new approach for predicting the folding kinetics of RNA secondary structure with pseudoknots. This approach is based on our previous established helix-based method for predicting the folding kinetics of RNA secondary structure. In this approach, the transition rates for an elementary step: (1) formation, (2) disruption of a helix stem, and (3) helix formation with concomitant partial melting of an incompatible helix, are calculated with the free energy landscape. The folding kinetics of the Hepatitis delta virus (HDV) ribozyme and the mutated sequences are studied with this method. The folding pathways are identified by recursive searching the states with high net flux-in(out) population starting from the native state. The theory results are in good agreement with that of the experiments. The results indicate that the bi-phasic folding kinetics for the wt HDV sequence is ascribed to the kinetic partitioning mechanism: Part of the population will quickly fold to the native state along the fast pathway, while another part of the population will fold along the slow pathway, in which the population is trapped in a non-native state. Single mutation not only changes the folding rate but also the folding pathway.

  4. Kinetic partitioning mechanism of HDV ribozyme folding

    SciTech Connect

    Chen, Jiawen; Gong, Sha; Wang, Yujie; Zhang, Wenbing

    2014-01-14

    RNA folding kinetics is directly tied to RNA biological functions. We introduce here a new approach for predicting the folding kinetics of RNA secondary structure with pseudoknots. This approach is based on our previous established helix-based method for predicting the folding kinetics of RNA secondary structure. In this approach, the transition rates for an elementary step: (1) formation, (2) disruption of a helix stem, and (3) helix formation with concomitant partial melting of an incompatible helix, are calculated with the free energy landscape. The folding kinetics of the Hepatitis delta virus (HDV) ribozyme and the mutated sequences are studied with this method. The folding pathways are identified by recursive searching the states with high net flux-in(out) population starting from the native state. The theory results are in good agreement with that of the experiments. The results indicate that the bi-phasic folding kinetics for the wt HDV sequence is ascribed to the kinetic partitioning mechanism: Part of the population will quickly fold to the native state along the fast pathway, while another part of the population will fold along the slow pathway, in which the population is trapped in a non-native state. Single mutation not only changes the folding rate but also the folding pathway.

  5. Energy Landscapes and Solved Protein Folding Problems

    NASA Astrophysics Data System (ADS)

    Wolynes, Peter

    2004-03-01

    Peter G. Wolynes Center for Theoretical Biological Physics Department of Chemistry and Biochemistry and Physics University of California, San Diego La Jolla, CA 92093-0371 Fifteen years ago, how proteins folded into organized structures on the basis of their sequence was a great mystery. By characterizing the energy landscapes of proteins with tools from the statistical mechanics of disordered systems like spin glasses, a "new view' of the folding process became possible. Energy landscape theory provided an incentive to pursue heroic new experiments and to carry out difficult computer simulations addressing protein folding mechanisms. Many aspects of folding kinetics revealed by these studies can be quantitatively understood using the simple idea that the topography of the energy landscape is that of a "rugged funnel". Energy landscape theory provided a quantitative means of characterizing which amino acid sequences can rapidly fold. Algorithms based on energy landscape theory have been used to successfully design novel sequences that fold to a given structure in the laboratory. Energy landscape ideas have begun to transform the prediction of protein structure from sequence data from being an art to being a science. The success of energy landscape- based algorithms in predicting protein structure from sequence will be highlighted. While there is still much to learn about folding mechanisms and much work to do achieving universally reliable structure prediction, many parts of what used to be called "the protein folding problem" can now be considered solved.

  6. Kinetic Analysis of Protein Folding Lattice Models

    NASA Astrophysics Data System (ADS)

    Chen, Hu; Zhou, Xin; Liaw, Chih Young; Koh, Chan Ghee

    Based on two-dimensional square lattice models of proteins, the relation between folding time and temperature is studied by Monte Carlo simulation. The results can be represented by a kinetic model with three states — random coil, molten globule, and native state. The folding process is composed of nonspecific collapse and final searching for the native state. At high temperature, it is easy to escape from local traps in the folding process. With decreasing temperature, because of the trapping in local traps, the final searching speed decreases. Then the folding shows chevron rollover. Through the analysis of the fitted parameters of the kinetic model, it is found that the main difference between the energy landscapes of the HP model and the Go model is that the number of local minima of the Go model is less than that of the HP model.

  7. The primary dynamics in protein folding: the earliest kinetic steps.

    NASA Astrophysics Data System (ADS)

    Callender, Robert

    1996-03-01

    A novel laser-induced temperature jump (T-jump) of 20 C or more is used to initiate the unfolding process of peptides and proteins on the picosecond time scale, and amide I time-resolved infrared absorbance transients are used to characterize the resulting kinetics. We have used this method to study the kinetics of folding and unfolding of a small 21 residue alanine based peptide and molten globule and native states of apomyoglobin, models for the helix which is an basic motif found in proteins. An essential result of our study is that the folding kinetics of a short length of peptide can occur within a few tens of nanoseconds which is much shorter than the time scale of the formation of intramolecular tertiary contacts from one point of a polypeptide chain to another. Furthermore, we observed that helices stabilized by tertiary contact formation unfold slower than helices surrounded by solvent by three orders of magnitude. These results bear directly on the protein folding problem, that is how do proteins fold from a large number of heterogeneous unfolded states to find the specific biologically active folded state on biologically relevent time scales, by suggesting that secondary structure forms first followed by tertiary structure. This work is a collaborative effort with R. GILMANSHIN at City College and S. WILLIAMS, R. B. DYER, and W. H. WOODRUFF at CST-4, Los Alamos National Laboratory, Los Alamos, NM 87545.

  8. Length dependent folding kinetics of phenylacetylene oligomers: Structural characterization of a kinetic trap

    NASA Astrophysics Data System (ADS)

    Elmer, Sidney P.; Pande, Vijay S.

    2005-03-01

    Using simulation to study the folding kinetics of 20-mer poly-phenylacetylene (pPA) oligomers, we find a long time scale trapped kinetic phase in the cumulative folding time distribution. This is demonstrated using molecular dynamics to simulate an ensemble of over 100 folding trajectories. The simulation data are fit to a four-state kinetic model which includes the typical folded and unfolded states, along with an intermediate state, and most surprisingly, a kinetically trapped state. Topologically diverse conformations reminiscent of α helices, β turns, and sheets in proteins are observed, along with unique structures in the form of knots. The nonhelical conformations are implicated, on the basis of structural correlations to kinetic parameters, to contribute to the trapped kinetic behavior. The strong solvophobic forces which mediate the folding process and produce a stable helical folded state also serve to overstabilize the nonhelical conformations, ultimately trapping them. From our simulations, the folding time is predicted to be on the order of 2.5-12.5 μs in the presence of the trapped kinetic phase. The folding mechanism for these 20-mer chains is compared with the previously reported folding mechanism for the pPA 12-mer chains. A linear scaling relationship between the chain length and the mean first passage time is predicted in the absence of the trapped kinetic phase. We discuss the major implications of this discovery in the design of self-assembling nanostructures.

  9. Simulating replica exchange simulations of protein folding with a kinetic network model

    PubMed Central

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

    2007-01-01

    Replica exchange (RE) is a generalized ensemble simulation method for accelerating the exploration of free-energy landscapes, which define many challenging problems in computational biophysics, including protein folding and binding. Although temperature RE (T-RE) is a parallel simulation technique whose implementation is relatively straightforward, kinetics and the approach to equilibrium in the T-RE ensemble are very complicated; there is much to learn about how to best employ T-RE to protein folding and binding problems. We have constructed a kinetic network model for RE studies of protein folding and used this reduced model to carry out “simulations of simulations” to analyze how the underlying temperature dependence of the conformational kinetics and the basic parameters of RE (e.g., the number of replicas, the RE rate, and the temperature spacing) all interact to affect the number of folding transitions observed. When protein folding follows anti-Arrhenius kinetics, we observe a speed limit for the number of folding transitions observed at the low temperature of interest, which depends on the maximum of the harmonic mean of the folding and unfolding transition rates at high temperature. The results shown here for the network RE model suggest ways to improve atomic-level RE simulations such as the use of “training” simulations to explore some aspects of the temperature dependence for folding of the atomic-level models before performing RE studies. PMID:17878309

  10. Chemical, physical, and theoretical kinetics of an ultrafast folding protein

    PubMed Central

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

    2008-01-01

    An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein—the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models—a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 105 possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 105 microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models. PMID:19033473

  11. Folding and unfolding kinetics of a single semiflexible polymer.

    PubMed

    Yoshinaga, Natsuhiko

    2008-06-01

    We investigate theoretically the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decreases with an increase in the number of monomers in the collapsed domain, suggesting that the main contribution to dissipation is from the motion of the domain. In the unfolding transition, the dynamic scaling exponents 1/8 and 1/4 were determined for the disentanglement and relaxation steps, respectively. We performed Langevin dynamics simulations to test our theory. It is found that our theory is in good agreement with simulations. We also propose the kinetics of the transitions in the presence of a hydrodynamic interaction. PMID:18643293

  12. Proteome folding kinetics is limited by protein halflife.

    PubMed

    Zou, Taisong; Williams, Nickolas; Ozkan, S Banu; Ghosh, Kingshuk

    2014-01-01

    How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution - using the native topology - for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds ([Formula: see text]8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures - to make proteins fold faster - other than the primary requirement to "sufficiently beat the clock" against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife. PMID:25393560

  13. Oxidative folding of peptides with cystine-knot architectures: kinetic studies and optimization of folding conditions.

    PubMed

    Reinwarth, Michael; Glotzbach, Bernhard; Tomaszowski, Michael; Fabritz, Sebastian; Avrutina, Olga; Kolmar, Harald

    2013-01-01

    Bioactive peptides often contain several disulfide bonds that provide the main contribution to conformational rigidity and structural, thermal, or biological stability. Among them, cystine-knot peptides-commonly named "knottins"-make up a subclass with several thousand natural members. Hence, they are considered promising frameworks for peptide-based pharmaceuticals. Although cystine-knot peptides are available through chemical and recombinant synthetic routes, oxidative folding to afford the bioactive isomers still remains a crucial step. We therefore investigated the oxidative folding of ten protease-inhibiting peptides from two knottin families, as well as that of an HIV entry inhibitor and of aprotinin, under two conventional sets of folding conditions and by a newly developed procedure. Kinetic studies identified folding conditions that resulted in correctly folded miniproteins with high rates of conversion even for highly hydrophobic and aggregation-prone peptides in concentrated solutions. PMID:23229141

  14. Insights into Coupled Folding and Binding Mechanisms from Kinetic Studies.

    PubMed

    Shammas, Sarah L; Crabtree, Michael D; Dahal, Liza; Wicky, Basile I M; Clarke, Jane

    2016-03-25

    Intrinsically disordered proteins (IDPs) are characterized by a lack of persistent structure. Since their identification more than a decade ago, many questions regarding their functional relevance and interaction mechanisms remain unanswered. Although most experiments have taken equilibrium and structural perspectives, fewer studies have investigated the kinetics of their interactions. Here we review and highlight the type of information that can be gained from kinetic studies. In particular, we show how kinetic studies of coupled folding and binding reactions, an important class of signaling event, are needed to determine mechanisms. PMID:26851275

  15. Periodic and stochastic thermal modulation of protein folding kinetics

    SciTech Connect

    Platkov, Max; Gruebele, Martin

    2014-07-21

    Chemical reactions are usually observed either by relaxation of a bulk sample after applying a sudden external perturbation, or by intrinsic fluctuations of a few molecules. Here we show that the two ideas can be combined to measure protein folding kinetics, either by periodic thermal modulation, or by creating artificial thermal noise that greatly exceeds natural thermal fluctuations. We study the folding reaction of the enzyme phosphoglycerate kinase driven by periodic temperature waveforms. As the temperature waveform unfolds and refolds the protein, its fluorescence color changes due to FRET (Förster resonant Energy Transfer) of two donor/acceptor fluorophores labeling the protein. We adapt a simple model of periodically driven kinetics that nicely fits the data at all temperatures and driving frequencies: The phase shifts of the periodic donor and acceptor fluorescence signals as a function of driving frequency reveal reaction rates. We also drive the reaction with stochastic temperature waveforms that produce thermal fluctuations much greater than natural fluctuations in the bulk. Such artificial thermal noise allows the recovery of weak underlying signals due to protein folding kinetics. This opens up the possibility for future detection of a stochastic resonance for protein folding subject to noise with controllable amplitude.

  16. Periodic and stochastic thermal modulation of protein folding kinetics.

    PubMed

    Platkov, Max; Gruebele, Martin

    2014-07-21

    Chemical reactions are usually observed either by relaxation of a bulk sample after applying a sudden external perturbation, or by intrinsic fluctuations of a few molecules. Here we show that the two ideas can be combined to measure protein folding kinetics, either by periodic thermal modulation, or by creating artificial thermal noise that greatly exceeds natural thermal fluctuations. We study the folding reaction of the enzyme phosphoglycerate kinase driven by periodic temperature waveforms. As the temperature waveform unfolds and refolds the protein, its fluorescence color changes due to FRET (Förster resonant Energy Transfer) of two donor/acceptor fluorophores labeling the protein. We adapt a simple model of periodically driven kinetics that nicely fits the data at all temperatures and driving frequencies: The phase shifts of the periodic donor and acceptor fluorescence signals as a function of driving frequency reveal reaction rates. We also drive the reaction with stochastic temperature waveforms that produce thermal fluctuations much greater than natural fluctuations in the bulk. Such artificial thermal noise allows the recovery of weak underlying signals due to protein folding kinetics. This opens up the possibility for future detection of a stochastic resonance for protein folding subject to noise with controllable amplitude. PMID:25053342

  17. Periodic and stochastic thermal modulation of protein folding kinetics

    PubMed Central

    Platkov, Max; Gruebele, Martin

    2014-01-01

    Chemical reactions are usually observed either by relaxation of a bulk sample after applying a sudden external perturbation, or by intrinsic fluctuations of a few molecules. Here we show that the two ideas can be combined to measure protein folding kinetics, either by periodic thermal modulation, or by creating artificial thermal noise that greatly exceeds natural thermal fluctuations. We study the folding reaction of the enzyme phosphoglycerate kinase driven by periodic temperature waveforms. As the temperature waveform unfolds and refolds the protein, its fluorescence color changes due to FRET (Förster resonant Energy Transfer) of two donor/acceptor fluorophores labeling the protein. We adapt a simple model of periodically driven kinetics that nicely fits the data at all temperatures and driving frequencies: The phase shifts of the periodic donor and acceptor fluorescence signals as a function of driving frequency reveal reaction rates. We also drive the reaction with stochastic temperature waveforms that produce thermal fluctuations much greater than natural fluctuations in the bulk. Such artificial thermal noise allows the recovery of weak underlying signals due to protein folding kinetics. This opens up the possibility for future detection of a stochastic resonance for protein folding subject to noise with controllable amplitude. PMID:25053342

  18. Periodic and stochastic thermal modulation of protein folding kinetics

    NASA Astrophysics Data System (ADS)

    Platkov, Max; Gruebele, Martin

    2014-07-01

    Chemical reactions are usually observed either by relaxation of a bulk sample after applying a sudden external perturbation, or by intrinsic fluctuations of a few molecules. Here we show that the two ideas can be combined to measure protein folding kinetics, either by periodic thermal modulation, or by creating artificial thermal noise that greatly exceeds natural thermal fluctuations. We study the folding reaction of the enzyme phosphoglycerate kinase driven by periodic temperature waveforms. As the temperature waveform unfolds and refolds the protein, its fluorescence color changes due to FRET (Förster resonant Energy Transfer) of two donor/acceptor fluorophores labeling the protein. We adapt a simple model of periodically driven kinetics that nicely fits the data at all temperatures and driving frequencies: The phase shifts of the periodic donor and acceptor fluorescence signals as a function of driving frequency reveal reaction rates. We also drive the reaction with stochastic temperature waveforms that produce thermal fluctuations much greater than natural fluctuations in the bulk. Such artificial thermal noise allows the recovery of weak underlying signals due to protein folding kinetics. This opens up the possibility for future detection of a stochastic resonance for protein folding subject to noise with controllable amplitude.

  19. Temperature dependence of protein folding kinetics in living cells

    PubMed Central

    Guo, Minghao; Xu, Yangfan; Gruebele, Martin

    2012-01-01

    We measure the stability and folding rate of a mutant of the enzyme phosphoglycerate kinase (PGK) inside bone tissue cells as a function of temperature from 38 to 48 °C. To facilitate measurement in individual living cells, we developed a rapid laser temperature stepping method capable of measuring complete thermal melts and kinetic traces in about two min. We find that this method yields improved thermal melts compared to heating a sample chamber or microscope stage. By comparing results for six cells with in vitro data, we show that the protein is stabilized by about 6 kJ/mole in the cytoplasm, but the temperature dependence of folding kinetics is similar to in vitro. The main difference is a slightly steeper temperature dependence of the folding rate in some cells that can be rationalized in terms of temperature-dependent crowding, local viscosity, or hydrophobicity. The observed rate coefficients can be fitted within measurement uncertainty by an effective two-state model, even though PGK folds by a multistate mechanism. We validate the effective two-state model with a three-state free energy landscape of PGK to illustrate that the effective fitting parameters can represent a more complex underlying free energy landscape. PMID:22665776

  20. Microsecond Microfluidic Mixing for Investigation of Protein Folding Kinetics

    SciTech Connect

    Hertzog, D E; Santiago, J G; Bakajin, O

    2003-06-25

    We have developed and characterized a mixer to study the reaction kinetics of protein folding on a microsecond timescale. The mixer uses hydrodynamic focusing of pressure-driven flow in a microfluidic channel to reduce diffusion times as first demonstrated by Knight et al.[1]. Features of the mixer include 1 {micro}s mixing times, sample consumptions of order 1 nl/s, loading sample volumes on the order of microliters, and the ability to manufacture in fused silica for compatibility with most spectroscopic methods.

  1. Microsecond Microfluidic Mixing for Investigation of Protein Folding Kinetics

    SciTech Connect

    Hertzog, D E; Santiago, J G; Bakajin, O

    2005-02-10

    We have developed and characterized a mixer to study the reaction kinetics of protein folding on a microsecond timescale. The mixer uses hydrodynamic focusing of pressure-driven flow in a microfluidic channel to reduce diffusion times as first demonstrated by Knight et al.[1]. Features of the mixer include 1 {micro}s mixing times, sample consumptions of order 1 nl/s, loading sample volumes on the order of microliters, and the ability to manufacture in fused silica for compatibility with most spectroscopic methods.

  2. Protein folding: Vexing debates on a fundamental problem.

    PubMed

    Gianni, Stefano; Jemth, Per

    2016-05-01

    The folding of proteins has been at the heart of protein chemistry and biophysics ever since the pioneering experiments by the labs of Fred Richards and Christian Anfinsen. But, despite nearly 60years of intense research, there are unresolved issues and a lively debate regarding some aspects of this fundamental problem. In this review we give a personal account on some key topics in the field: (i) the nature of the denatured state of a protein, (ii) nucleation sites in the folding reaction, and (iii) the time it takes for individual molecules to traverse the transition state. PMID:27018826

  3. Reducing the dimensionality of the protein-folding search problem.

    PubMed

    Chellapa, George D; Rose, George D

    2012-08-01

    How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string. PMID:22692765

  4. Reducing the dimensionality of the protein-folding search problem

    PubMed Central

    Chellapa, George D; Rose, George D

    2012-01-01

    How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string. PMID:22692765

  5. Combined approach to the inverse protein folding problem. Final report

    SciTech Connect

    Ruben A. Abagyan

    2000-06-01

    The main scientific contribution of the project ''Combined approach to the inverse protein folding problem'' submitted in 1996 and funded by the Department of Energy in 1997 is the formulation and development of the idea of the multilink recognition method for identification of functional and structural homologues of newly discovered genes. This idea became very popular after they first announced it and used it in prediction of the threading targets for the CASP2 competition (Critical Assessment of Structure Prediction).

  6. Scaling approach to the folding kinetics of large proteins.

    PubMed

    Nelson, Erik D; Grishin, Nick V

    2006-01-01

    We study a nucleation-growth model of protein folding and extend it to describe larger proteins with multiple folding units. The model is of one of an extremely simple type in which amino acids are allowed just two states--either folded (frozen) or unfolded. Its energetics are heterogeneous and Gō-like, the energy being defined in terms of the number of atom-to-atom contacts that would occur between frozen amino acids in the native crystal structure of the protein. Each collective state of the amino acids is intended to represent a small free energy microensemble consisting of the possible configurations of unfolded loops, open segments, and free ends constrained by the cross-links that form between folded parts of the molecule. We approximate protein free energy landscapes by an infinite subset of these microensemble topologies in which loops and open unfolded segments can be viewed roughly as independent objects for the purpose of calculating their entropy, and we develop a means to implement this approximation in Monte Carlo simulations. We show that this approach describes transition state structures (phi values) more accurately and identifies folding intermediates that were unavailable to previous versions of the model that restricted the number of loops and nuclei. PMID:16486182

  7. Translation Initiation is Controlled by RNA Folding Kinetics via a Ribosome Drafting Mechanism.

    PubMed

    Espah Borujeni, Amin; Salis, Howard M

    2016-06-01

    RNA folding plays an important role in controlling protein synthesis as well as other cellular processes. Existing models have focused on how RNA folding energetics control translation initiation rate under equilibrium conditions but have largely ignored the effects of nonequilibrium RNA folding. We introduce a new mechanism, called "ribosome drafting", that explains how a mRNA's folding kinetics and the ribosome's binding rate collectively control its translation initiation rate. During cycles of translation, ribosome drafting emerges whenever successive ribosomes bind to a mRNA faster than the mRNA can refold, maintaining it in a nonequilibrium state with an acceleration of protein synthesis. Using computational design, time-correlated single photon counting, and expression measurements, we demonstrate that slow-folding and fast-folding RNA structures with equivalent folding energetics can vary protein synthesis rates by 1000-fold. We determine the necessary conditions for ribosome drafting by characterizing mRNAs with rationally designed ribosome binding rates, folding kinetics, and folding energetics, confirming the predictions of a nonequilibrium Markov model of translation. Our results have widespread implications, illustrating how competitive folding and assembly kinetics can shape the gene expression machinery's sequence-structure-function relationship inside cells. PMID:27199273

  8. Ultrafast Absorption Kinetics of NADH in Folded and Unfolded Conformations

    NASA Astrophysics Data System (ADS)

    Heiner, Z.; Roland, T.; Léonard, J.; Haacke, S.; Groma, G. I.

    2013-03-01

    The non-radiative energy transfer is shown to occur on a ˜3ps time scale for NADH in the folded form in H2O. Addition of methanol thermodynamically favours the open form, for which energy transfer does not occur.

  9. Monitoring the folding kinetics of a β-hairpin by time-resolved IR spectroscopy in silico.

    PubMed

    Daidone, Isabella; Thukral, Lipi; Smith, Jeremy C; Amadei, Andrea

    2015-04-01

    Protein folding is one of the most fundamental problems in modern biochemistry. Time-resolved infrared (IR) spectroscopy in the amide I region is commonly used to monitor folding kinetics. However, associated atomic detail information on the folding mechanism requires simulations. In atomistic simulations structural order parameters are typically used to follow the folding process along the simulated trajectories. However, a rigorous test of the reliability of the mechanisms found in the simulations requires calculation of the time-dependent experimental observable, i.e., in the present case the IR signal in the amide I region. Here, we combine molecular dynamics simulation with a mixed quantum mechanics/molecular mechanics theoretical methodology, the Perturbed Matrix Method, in order to characterize the folding of a β-hairpin peptide, through modeling the time-dependence of the amide I IR signal. The kinetic and thermodynamic data (folding and unfolding rate constants, and equilibrium folded- and unfolded-state probabilities) obtained from the fit of the calculated signal are in good agreement with the available experimental data [Xu et al. J. Am. Chem. Soc. 2003, 125, 15388-15394]. To the best of our knowledge, this is the first report of the simulation of the time-resolved IR signal of a complex process occurring on a long (microsecond) time scale. PMID:25777154

  10. Negative activation enthalpies in the kinetics of protein folding.

    PubMed

    Oliveberg, M; Tan, Y J; Fersht, A R

    1995-09-12

    Although the rates of chemical reactions become faster with increasing temperature, the converse may be observed with protein-folding reactions. The rate constant for folding initially increases with temperature, goes through a maximum, and then decreases. The activation enthalpy is thus highly temperature dependent because of a large change in specific heat (delta Cp). Such a delta Cp term is usually presumed to be a consequence of a large decrease in exposure of hydrophobic surfaces to water as the reaction proceeds from the denatured state to the transition state for folding: the hydrophobic side chains are surrounded by "icebergs" of water that melt with increasing temperature, thus making a large contribution to the Cp of the denatured state and a smaller one to the more compact transition state. The rate could also be affected by temperature-induced changes in the conformational population of the ground state: the heat required for the progressive melting of residual structure in the denatured state will contribute to delta Cp. By examining two proteins with different refolding mechanisms, we are able to find both of these two processes; barley chymotrypsin inhibitor 2, which refolds from a highly unfolded state, fits well to a hydrophobic interaction model with a constant delta Cp of activation, whereas barnase, which refolds from a more structured denatured state, deviates from this ideal behavior. PMID:7568045

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

    PubMed

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

    2012-07-20

    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 of molecular-dynamics-generated folding trajectories of the triple β-strand WW domain from formin binding protein 28 (FBP28) (Protein Data Bank ID: 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 the 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 the FBP28 WW domain and its full-size and truncated mutants explore their conformational space is examined in terms of the mean-square displacement and principal component analysis eigenvalue spectrum analyses. Subdiffusive behavior is observed for all studied systems. PMID:22560992

  12. Thermodynamics and kinetics of apoazurin folding under macromolecular crowding effect and chemical interference

    NASA Astrophysics Data System (ADS)

    Zegarra, Fabio; Cheung, Margaret

    2013-03-01

    Proteins fold in a cellular milieu crowded by different kinds of macromolecules. They exert volume exclusion impacting protein folding processes in vivo. Folding processes, however, has been studied by chemical denaturation under in vitro conditions. The impact of the two factors as an attempt to advance the understanding of folding mechanism in vivo is not understood. Here, we investigate the folding mechanisms of apoazurin affected by the macromolecular crowding and chemical interference by using coarse-grained molecular simulations. Crowding agents are modeled as hard-spheres and the chemical denaturation effects are implemented into an energy function of the side chain and backbone interactions. Protein folding stability, mechanism, and kinetics rates of apoazurin under chemical interference and macromolecular crowding conditions are being investigated. Supported by NSF, Molecular & Cellular Biosciences (MCB0919974).

  13. Cooperative folding kinetics of BBL protein and peripheral subunit-binding domain homologues

    PubMed Central

    Yu, Wookyung; Chung, Kwanghoon; Cheon, Mookyung; Heo, Muyoung; Han, Kyou-Hoon; Ham, Sihyun; Chang, Iksoo

    2008-01-01

    Recent experiments claiming that Naf-BBL protein follows a global downhill folding raised an important controversy as to the folding mechanism of fast-folding proteins. Under the global downhill folding scenario, not only do proteins undergo a gradual folding, but folding events along the continuous folding pathway also could be mapped out from the equilibrium denaturation experiment. Based on the exact calculation using a free energy landscape, relaxation eigenmodes from a master equation, and Monte Carlo simulation of an extended Muñoz–Eaton model that incorporates multiscale-heterogeneous pairwise interactions between amino acids, here we show that the very nature of a two-state cooperative transition such as a bimodal distribution from an exact free energy landscape and biphasic relaxation kinetics manifest in the thermodynamics and folding–unfolding kinetics of BBL and peripheral subunit-binding domain homologues. Our results provide an unequivocal resolution to the fundamental controversy related to the global downhill folding scheme, whose applicability to other proteins should be critically reexamined. PMID:18272497

  14. Kinetics methods for clinical epidemiology problems.

    PubMed

    Corlan, Alexandru Dan; Ross, John

    2015-11-17

    Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality. PMID:26578757

  15. Kinetics methods for clinical epidemiology problems

    PubMed Central

    Corlan, Alexandru Dan; Ross, John

    2015-01-01

    Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality. PMID:26578757

  16. Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

    PubMed Central

    2015-01-01

    Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides. PMID:25136267

  17. 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

  18. Highly anomalous energetics of protein cold denaturation linked to folding-unfolding kinetics.

    PubMed

    Romero-Romero, M Luisa; Inglés-Prieto, Alvaro; Ibarra-Molero, Beatriz; Sanchez-Ruiz, Jose M

    2011-01-01

    Despite several careful experimental analyses, it is not yet clear whether protein cold-denaturation is just a "mirror image" of heat denaturation or whether it shows unique structural and energetic features. Here we report that, for a well-characterized small protein, heat denaturation and cold denaturation show dramatically different experimental energetic patterns. Specifically, while heat denaturation is endothermic, the cold transition (studied in the folding direction) occurs with negligible heat effect, in a manner seemingly akin to a gradual, second-order-like transition. We show that this highly anomalous energetics is actually an apparent effect associated to a large folding/unfolding free energy barrier and that it ultimately reflects kinetic stability, a naturally-selected trait in many protein systems. Kinetics thus emerges as an important factor linked to differential features of cold denaturation. We speculate that kinetic stabilization against cold denaturation may play a role in cold adaptation of psychrophilic organisms. Furthermore, we suggest that folding-unfolding kinetics should be taken into account when analyzing in vitro cold-denaturation experiments, in particular those carried out in the absence of destabilizing conditions. PMID:21829584

  19. A simple model for calculating the kinetics of protein folding from three-dimensional structures.

    PubMed

    Muñoz, V; Eaton, W A

    1999-09-28

    An elementary statistical mechanical model was used to calculate the folding rates for 22 proteins from their known three-dimensional structures. In this model, residues come into contact only after all of the intervening chain is in the native conformation. An additional simplifying assumption is that native structure grows from localized regions that then fuse to form the complete native molecule. The free energy function for this model contains just two contributions-conformational entropy of the backbone and the energy of the inter-residue contacts. The matrix of inter-residue interactions is obtained from the atomic coordinates of the three-dimensional structure. For the 18 proteins that exhibit two-state equilibrium and kinetic behavior, profiles of the free energy versus the number of native peptide bonds show two deep minima, corresponding to the native and denatured states. For four proteins known to exhibit intermediates in folding, the free energy profiles show additional deep minima. The calculated rates of folding the two-state proteins, obtained by solving a diffusion equation for motion on the free energy profiles, reproduce the experimentally determined values surprisingly well. The success of these calculations suggests that folding speed is largely determined by the distribution and strength of contacts in the native structure. We also calculated the effect of mutations on the folding kinetics of chymotrypsin inhibitor 2, the most intensively studied two-state protein, with some success. PMID:10500173

  20. Kinetically coupled folding of a single HIV-1 glycoprotein 41 complex in viral membrane fusion and inhibition

    PubMed Central

    Jiao, Junyi; Rebane, Aleksander A.; Ma, Lu; Gao, Ying; Zhang, Yongli

    2015-01-01

    HIV-1 glycoprotein 41 (gp41) mediates viral entry into host cells by coupling its folding energy to membrane fusion. Gp41 folding is blocked by fusion inhibitors, including the commercial drug T20, to treat HIV/AIDS. However, gp41 folding intermediates, energy, and kinetics are poorly understood. Here, we identified the folding intermediates of a single gp41 trimer-of-hairpins and measured their associated energy and kinetics using high-resolution optical tweezers. We found that folding of gp41 hairpins was energetically independent but kinetically coupled: Each hairpin contributed a folding energy of ∼−23 kBT, but folding of one hairpin successively accelerated the folding rate of the next one by ∼20-fold. Membrane-mimicking micelles slowed down gp41 folding and reduced the stability of the six-helix bundle. However, the stability was restored by cooperative folding of the membrane-proximal external region. Surprisingly, T20 strongly inhibited gp41 folding by actively displacing the C-terminal hairpin strand in a force-dependent manner. The inhibition was abolished by a T20-resistant gp41 mutation. The energetics and kinetics of gp41 folding established by us provides a basis to understand viral membrane fusion, infection, and therapeutic intervention. PMID:26038562

  1. Subcellular modulation of protein VlsE stability and folding kinetics.

    PubMed

    Tai, Jonathan; Dave, Kapil; Hahn, Vincent; Guzman, Irisbel; Gruebele, Martin

    2016-05-01

    The interior of a cell interacts differently with proteins than a dilute buffer because of a wide variety of macromolecules, chaperones, and osmolytes that crowd and interact with polypeptide chains. We compare folding of fluorescent constructs of protein VlsE among three environments inside cells. The nucleus increases the stability of VlsE relative to the cytoplasm, but slows down folding kinetics. VlsE is also more stable in the endoplasmic reticulum, but unlike PGK, tends to aggregate there. Although fluorescent-tagged VlsE and PGK show opposite stability trends from in vitro to the cytoplasm, their trends from cytoplasm to nucleus are similar. PMID:27129718

  2. Deconstructing time-resolved optical rotatory dispersion kinetic measurements of cytochrome c folding: from molten globule to the native state.

    PubMed

    Chen, Eefei; Kliger, David S

    2012-01-01

    The far-UV time-resolved optical rotatory dispersion (TRORD) technique has contributed significantly to our understanding of nanosecond secondary structure kinetics in protein folding and function reactions. For reduced cytochrome c, protein folding kinetics have been probed largely from the unfolded to the native state. Here we provide details about sample preparation and the TRORD apparatus and measurements for studying folding from a partly unfolded state to the native secondary structure conformation of reduced cytochrome c. PMID:22760330

  3. The initial step of DNA hairpin folding: a kinetic analysis using fluorescence correlation spectroscopy

    PubMed Central

    Kim, Jiho; Doose, Sören; Neuweiler, Hannes; Sauer, Markus

    2006-01-01

    Conformational fluctuations of single-stranded DNA (ssDNA) oligonucleotides were studied in aqueous solution by monitoring contact-induced fluorescence quenching of the oxazine fluorophore MR121 by intrinsic guanosine residues (dG). We applied fluorescence correlation spectroscopy as well as steady-state and time-resolved fluorescence spectroscopy to analyze kinetics of DNA hairpin folding. We first characterized the reporter system by investigating bimolecular quenching interactions between MR121 and guanosine monophosphate in aqueous solution estimating rate constants, efficiency and stability for formation of quenched complexes. We then studied the kinetics of complex formation between MR121 and dG residues site-specifically incorporated in DNA hairpins. To uncover the initial steps of DNA hairpin folding we investigated complex formation in ssDNA carrying one or two complementary base pairs (dC–dG pairs) that could hybridize to form a short stem. Our data show that incorporation of a single dC–dG pair leads to non-exponential decays for opening and closing kinetics and reduces rate constants by one to two orders of magnitude. We found positive activation enthalpies independent of the number of dC–dG pairs. These results imply that the rate limiting step of DNA hairpin folding is not determined by loop dynamics, or by mismatches in the stem, but rather by interactions between stem and loop nucleotides. PMID:16687657

  4. Quantifying Instrumental Artifacts in Folding Kinetics Measured by Single-Molecule Force Spectroscopy.

    PubMed

    Neupane, Krishna; Woodside, Michael T

    2016-07-26

    Force spectroscopy is commonly used to measure the kinetics of processes occurring in single biological molecules. These measurements involve attaching the molecule of interest to micron-sized or larger force probes via compliant linkers. Recent theoretical work has described how the properties of the probes and linkers can alter the observed kinetics from the intrinsic behavior of the molecule in isolation. We applied this theory to estimate the errors in measurements of folding made using optical tweezers. Errors in the folding rates arising from instrument artifacts were only ∼20% for constant-force measurements of DNA hairpins with typical choices of linker length and probe size. Measurements of transition paths using a constant trap position at high trap stiffness were also found to be in the low-artifact limit. These results indicate that typical optical trap measurements of kinetics reflect the dynamics of the molecule fairly well, and suggest practical limitations on experimental design to ensure reliable kinetic measurements. PMID:27369870

  5. Kinetics and energetics of the translocation of maltose binding protein folding mutants.

    PubMed

    Tomkiewicz, Danuta; Nouwen, Nico; Driessen, Arnold J M

    2008-03-14

    Protein translocation in Escherichia coli is mediated by the translocase that, in its minimal form, comprises a protein-conducting pore (SecYEG) and a motor protein (SecA). The SecYEG complex forms a narrow channel in the membrane that allows passage of secretory proteins (preproteins) in an unfolded state only. It has been suggested that the SecA requirement for translocation depends on the folding stability of the mature preprotein domain. Here we studied the effects of the signal sequence and SecB on the folding and translocation of folding stabilizing and destabilizing mutants of the mature maltose binding protein (MBP). Although the mutations affect the folding of the precursor form of MBP, these are drastically overruled by the combined unfolding stabilization of the signal sequence and SecB. Consequently, the translocation kinetics, the energetics and the SecA and SecB dependence of the folding mutants are indistinguishable from those of wild-type preMBP. These data indicate that unfolding of the mature domain of preMBP is likely not a rate-determining step in translocation when the protein is targeted to the translocase via SecB. PMID:18241889

  6. Ultrafast folding kinetics and cooperativity of villin headpiece in single-molecule force spectroscopy.

    PubMed

    Žoldák, Gabriel; Stigler, Johannes; Pelz, Benjamin; Li, Hongbin; Rief, Matthias

    2013-11-01

    In this study we expand the accessible dynamic range of single-molecule force spectroscopy by optical tweezers to the microsecond range by fast sampling. We are able to investigate a single molecule for up to 15 min and with 300-kHz bandwidth as the protein undergoes tens of millions of folding/unfolding transitions. Using equilibrium analysis and autocorrelation analysis of the time traces, the full energetics as well as real-time kinetics of the ultrafast folding of villin headpiece 35 and a stable asparagine 68 alanine/lysine 70 methionine variant can be measured directly. We also performed Brownian dynamics simulations of the response of the bead-DNA system to protein-folding fluctuations. All key features of the force-dependent deflection fluctuations could be reproduced: SD, skewness, and autocorrelation function. Our measurements reveal a difference in folding pathway and cooperativity between wild-type and stable variant of headpiece 35. Autocorrelation force spectroscopy pushes the time resolution of single-molecule force spectroscopy to ∼10 µs thus approaching the timescales accessible for all atom molecular dynamics simulations. PMID:24145407

  7. Complex RNA Folding Kinetics Revealed by Single-Molecule FRET and Hidden Markov Models

    PubMed Central

    2014-01-01

    We have developed a hidden Markov model and optimization procedure for photon-based single-molecule FRET data, which takes into account the trace-dependent background intensities. This analysis technique reveals an unprecedented amount of detail in the folding kinetics of the Diels–Alderase ribozyme. We find a multitude of extended (low-FRET) and compact (high-FRET) states. Five states were consistently and independently identified in two FRET constructs and at three Mg2+ concentrations. Structures generally tend to become more compact upon addition of Mg2+. Some compact structures are observed to significantly depend on Mg2+ concentration, suggesting a tertiary fold stabilized by Mg2+ ions. One compact structure was observed to be Mg2+-independent, consistent with stabilization by tertiary Watson–Crick base pairing found in the folded Diels–Alderase structure. A hierarchy of time scales was discovered, including dynamics of 10 ms or faster, likely due to tertiary structure fluctuations, and slow dynamics on the seconds time scale, presumably associated with significant changes in secondary structure. The folding pathways proceed through a series of intermediate secondary structures. There exist both compact pathways and more complex ones, which display tertiary unfolding, then secondary refolding, and, subsequently, again tertiary refolding. PMID:24568646

  8. Local Kinetic Measures of Macromolecular Structure Reveal Partitioning Among Multiple Parallel Pathways from the Earliest Steps in the Folding of a Large RNA Molecule

    SciTech Connect

    Laederach,A.; Shcherbakova, I.; Liang, M.; Brenowitz, M.; Altman, R.

    2006-01-01

    At the heart of the RNA folding problem is the number, structures, and relationships among the intermediates that populate the folding pathways of most large RNA molecules. Unique insight into the structural dynamics of these intermediates can be gleaned from the time-dependent changes in local probes of macromolecular conformation (e.g. reports on individual nucleotide solvent accessibility offered by hydroxyl radical ({center_dot}OH) footprinting). Local measures distributed around a macromolecule individually illuminate the ensemble of separate changes that constitute a folding reaction. Folding pathway reconstruction from a multitude of these individual measures is daunting due to the combinatorial explosion of possible kinetic models as the number of independent local measures increases. Fortunately, clustering of time progress curves sufficiently reduces the dimensionality of the data so as to make reconstruction computationally tractable. The most likely folding topology and intermediates can then be identified by exhaustively enumerating all possible kinetic models on a super-computer grid. The folding pathways and measures of the relative flux through them were determined for Mg{sup 2+} and Na{sup +}-mediated folding of the Tetrahymena thermophila group I intron using this combined experimental and computational approach. The flux during Mg{sup 2+}-mediated folding is divided among numerous parallel pathways. In contrast, the flux during the Na{sup +}-mediated reaction is predominantly restricted through three pathways, one of which is without detectable passage through intermediates. Under both conditions, the folding reaction is highly parallel with no single pathway accounting for more than 50% of the molecular flux. This suggests that RNA folding is non-sequential under a variety of different experimental conditions even at the earliest stages of folding. This study provides a template for the systematic analysis of the time-evolution of RNA structure

  9. Single-molecule kinetics under force: probing protein folding and enzymatic activity with optical tweezers

    NASA Astrophysics Data System (ADS)

    Wong, Wesley

    2010-03-01

    Weak non-covalent bonds between and within single molecules govern many aspects of biological structure and function (e.g. DNA base-paring, receptor-ligand binding, protein folding, etc.) In living systems, these interactions are often subject to mechanical forces, which can greatly alter their kinetics and activity. My group develops and applies novel single-molecule manipulation techniques to explore and quantify these force-dependent kinetics. Using optical tweezers, we have quantified the force-dependent unfolding and refolding kinetics of different proteins, including the cytoskeletal protein spectrin in collaboration with E. Evans's group [1], and the A2 domain of the von Willebrand factor blood clotting protein in collaboration with T. Springer's group [2]. Furthermore, we have studied the kinetics of the ADAMTS13 enzyme acting on a single A2 domain, and have shown that physiolgical forces in the circulation can act as a cofactor for enzymatic cleavage, regulating hemostatic activity [2]. References: 1. E. Evans, K. Halvorsen, K. Kinoshita, and W.P. Wong, Handbook of Single Molecule Biophysics, P. Hinterdorfer, ed., Springer (2009). 2. X. Zhang, K. Halvorsen, C.-Z. Zhang, W.P. Wong, and T.A. Springer, Science 324 (5932), 1330-1334 (2009).

  10. Kinetic folding mechanism of an integral membrane protein examined by pulsed oxidative labeling and mass spectrometry.

    PubMed

    Pan, Yan; Brown, Leonid; Konermann, Lars

    2011-07-01

    We report the application of pulsed oxidative labeling for deciphering the folding mechanism of a membrane protein. SDS-denatured bacteriorhodopsin (BR) was refolded by mixing with bicelles in the presence of free retinal. At various time points (20 ms to 1 day), the protein was exposed to a microsecond ·OH pulse that induces oxidative modifications at solvent-accessible methionine side chains. The extent of labeling was determined by mass spectrometry. These measurements were complemented by stopped-flow spectroscopy. Major time-dependent changes in solvent accessibility were detected for M20 (helix A) and M118 (helix D). Our kinetic data indicate a sequential folding mechanism, consistent with models previously suggested by others on the basis of optical data. Yet, ·OH labeling provides additional structural insights. An initial folding intermediate I(1) gets populated within 20 ms, concomitantly with formation of helix A. Subsequent structural consolidation leads to a transient species I(2). Noncovalent retinal binding to I(2) induces folding of helix D, thereby generating an intermediate I(R). In the absence of retinal, the latter transition does not take place. Hence, formation of helix D depends on retinal binding, whereas this is not the case for helix A. As the cofactor settles deeper into its binding pocket, a final transient species I(R) is generated. This intermediate converts into native BR within minutes by formation of the retinal-K216 Schiff base linkage. The combination of pulsed covalent labeling and optical spectroscopy employed here should also be suitable for exploring the folding mechanisms of other membrane proteins. PMID:21570983

  11. Integral and differential form of the protein folding problem

    NASA Astrophysics Data System (ADS)

    Tramontano, Anna

    2004-07-01

    The availability of the complete genomic sequences of many species, including human, has raised enormous expectations in medicine, pharmacology, ecology, biotechnology and forensic sciences. However, knowledge is only a first step toward understanding, and we are only at the early stage of a scientific process that might lead us to satisfy all the expectations raised by the genomic projects. In this review I will discuss the present status of computational methods that attempt to infer the unique three-dimensional structure of proteins from their amino acid sequences. Although this problem has been defined as the “holy grail” of biology, it represents only one of the many hurdles in our path towards the understanding of life at a molecular level.

  12. Theoretical volume profiles as a tool for probing transition states: folding kinetics.

    PubMed

    Wiebe, H; Weinberg, N

    2014-03-28

    The mechanism by which conformational changes, particularly folding and unfolding, occur in proteins and other biopolymers has been widely discussed in the literature. Molecular dynamics (MD) simulations of protein folding present a formidable challenge since these conformational changes occur on a time scale much longer than what can be afforded at the current level of computational technology. Transition state (TS) theory offers a more economic description of kinetic properties of a reaction system by relating them to the properties of the TS, or for flexible systems, the TS ensemble (TSE). The application of TS theory to protein folding is limited by ambiguity in the definition of the TSE for this process. We propose to identify the TSE for conformational changes in flexible systems by comparison of its experimentally determined volumetric property, known as the volume of activation, to the structure-specific volume profile of the process calculated using MD. We illustrate this approach by its successful application to unfolding of a model chain system. PMID:24697422

  13. Kinetic Definition of Protein Folding Transition State Ensembles and Reaction Coordinates

    PubMed Central

    Snow, Christopher D.; Rhee, Young Min; Pande, Vijay S.

    2006-01-01

    Using distributed molecular dynamics simulations we located four distinct folding transitions for a 39-residue ββαβ protein fold. To characterize the nature of each room temperature transition, we calculated the probability of transmission for 500 points along each free energy barrier. We introduced a method for determining transition states by employing the transmission probability, Ptrans, and determined which conformations were transition state ensemble members (Ptrans ≈ 0.5). The transmission probability may be used to characterize the barrier in several ways. For example, we ran simulations at 82°C, determined the change in Ptrans with temperature for all 2,000 conformations, and quantified Hammond behavior directly using Ptrans correlation. Additionally, we propose that diffusion along Ptrans may provide the configurational diffusion rate at the top of the barrier. Specifically, given a transition state conformation x0 with estimated Ptrans = 0.5, we selected a large set of subsequent conformations from independent trajectories, each exactly a small time δt after x0 (250 ps). Calculating Ptrans for the new trial conformations, we generated the P(Ptrans|δt = 250 ps) distribution that reflected diffusion. This approach provides a novel perspective on the diffusive nature of a protein folding transition and provides a framework for a quantitative study of activated relaxation kinetics. PMID:16617068

  14. Structure-approximating inverse protein folding problem in the 2D HP model.

    PubMed

    Gupta, Arvind; Manuch, Ján; Stacho, Ladislav

    2005-12-01

    The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper, we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein (in drug design) is its stability--the aptitude not to fold simultaneously into other structures. We show that for a number of basic structures, our sequences have a unique fold. PMID:16379538

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

    SciTech Connect

    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. 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.

  16. Entanglement in correlated random spin chains, RNA folding and kinetic roughening

    NASA Astrophysics Data System (ADS)

    Rodríguez-Laguna, Javier; Santalla, Silvia N.; Ramírez, Giovanni; Sierra, Germán

    2016-07-01

    Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long range correlations, generated as gaussian fields with a power-law spectral function. Ground states are always planar valence bond states, and their statistical ensembles are characterized in terms of their block entropy and their bond-length distribution, which follow power-laws. We conjecture the existence of a critical value for the spectral exponent, below which the system behavior is identical to the case of uncorrelated couplings. Above that critical value, the entanglement entropy violates the area law and grows as a power law of the block size, with an exponent which increases from zero to one. Interestingly, we show that XXZ models with positive anisotropy present the opposite behavior, and strong correlations in the couplings lead to lower entropies. Similar planar bond structures are also found in statistical models of RNA folding and kinetic roughening, and we trace an analogy between them and quantum valence bond states. Using an inverse renormalization procedure we determine the optimal spin-chain couplings which give rise to a given planar bond structure, and study the statistical properties of the couplings whose bond structures mimic those found in RNA folding.

  17. Acid stability of the kinetically stable alkaline serine protease possessing polyproline II fold.

    PubMed

    Rohamare, Sonali; Javdekar, Vaishali; Dalal, Sayli; Nareddy, Pavan Kumar; Swamy, Musti J; Gaikwad, Sushama M

    2015-02-01

    The kinetically stable alkaline serine protease from Nocardiopsis sp.; NprotI, possessing polyproline II fold (PPII) was characterized for its pH stability using proteolytic assay, fluorescence and Circular Dichroism (CD) spectroscopy, and Differential Scanning Calorimetry (DSC). NprotI was found to be functionally stable when incubated at pH 1.0, even after 24 h, while after incubation at pH 10.0, drastic loss in the activity was observed. The enzyme showed enhanced activity after incubation at pH 1.0 and 3.0, at higher temperature (50-60 °C). NprotI maintained the overall PPII fold in broad pH range as seen using far UV CD spectroscopy. The PPII fold of NprotI incubated at pH 1.0 remained fairly intact up to 70 °C. Based on the isodichroic point and Tm values revealed by secondary structural transitions, different modes of thermal denaturation at pH 1.0, 5.0 and 10.0 were observed. DSC studies of NprotI incubated at acidic pH (pH 1.0-5.0) showed Tm values in the range of 74-76 °C while significant decrease in Tm (63.8 °C) was observed at pH 10.0. NprotI could be chemically denatured at pH 5.0 (stability pH) only with guanidine thiocynate. NprotI can be classified as type III protein among the three acid denatured states. Acid tolerant and thermostable NprotI can serve as a potential candidate for biotechnological applications. PMID:25576306

  18. 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

  19. A quantitative treatment of the kinetics of the folding transition of ribonuclease A.

    PubMed

    Hagerman, P J; Baldwin, R L

    1976-04-01

    New experimental data and a quantitative theoretical treatment are given for the kinetics of the thermal folding transition of ribonuclease A at pH 3.0. A three-species mechanism is used as a starting point for the analysis: U1 (slow) in equilibrium U2(fast) in equilibrium N, where U1 and U2 are two forms of the unfolded enzyme with markedly different rates of refolding and N is the native enzyme. This mechanism is based on certain facts established in previous studies of refolding. The kinetics of unfolding and refolding show two phases a fast phase and a slow phase, over a range of temperatures extending above the transition midpoint, Tm. The three-species mechanism can be used in this range. At higher temperatures a new much faster kinetic phase is also observed corresponding to the transient formation of a new intermediate (I). Although the general solution for a four-species mechanism is complex it is not difficult to extend the three-species analysis for the special case found here, in which the fast reaction (I in equilibrium N) is well separated from the other two reactions. At temperatures below the transition zone the slow phase of refolding becomes kinetically complex. No attempt has been made to extend the analysis to include this effect. The basic test of the three-state analysis is the prediction as a function of temperature of alpha2, the relative amplitude of the fast phase, both for unfolding and refolding. At temperatures above Tm for which the three-state analysis must be extended to include the new intermediate I, a crresponding quanitity alpha2(cor) is predicted and compared with measured values. Data used in the three-state prediction are values of tau2 and tau1, the time constants of the fast and slow kinetic phases, plus a single value of alpha2 measured when tau2 and tau1 are well separated. The observed and predicted values of alpha2 agree within experimental error. The analysis predicts correctly that, for these experiments, alpha2 should

  20. Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes

    SciTech Connect

    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 carbon 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.

  1. Folding mechanism of reduced cytochrome c: Equilibrium and kinetic properties in the presence of carbon monoxide

    PubMed Central

    Latypov, Ramil F.; Maki, Kosuke; Cheng, Hong; Luck, Stanley D.; Roder, Heinrich

    2008-01-01

    Despite close structural similarity, the ferric and ferrous forms of cytochrome c (cyt c) differ greatly in terms of their ligand binding properties, stability, folding and dynamics. The reduced heme iron binds diatomic ligands such as CO only under destabilizing conditions that promote weakening or disruption of the native methionine-iron linkage. This makes CO a useful conformational probe for detecting partially structured states that cannot be observed in the absence of endogenous ligands. Heme absorbance, circular dichroism and NMR were used to characterize the denaturant-induced unfolding equilibrium of Fe2+ cyt c in the presence and absence of CO. In addition to the native state (N), which does not bind CO, and the unfolded CO-complex (U-CO), a structurally distinct CO-bound form (M-CO) accumulates to high levels (~75% of the population) at intermediate guanidine hydrochloride concentrations. Comparison of the unfolding transition for different conformational probes reveals that M-CO is a compact state containing a native-like helical core and regions of local disorder in the segment containing the native Met80 ligand and adjacent loops. Kinetic measurements of CO binding and dissociation under native, partially denaturing and fully unfolded conditions indicate that a state, M, that is structurally analogous to M-CO is populated even in the absence of CO. The binding energy of the CO ligand lowers the free energy of this high-energy state to such an extent that it accumulates even under mildly denaturing equilibrium conditions. The thermodynamic and kinetic parameters obtained in this study provide a fully self-consistent description of the linked unfolding/CO-binding equilibria of reduced cyt c. PMID:18761351

  2. Kinetic model solves visbreaker constraint control problem

    SciTech Connect

    Iscovici, R.S. )

    1994-05-01

    A kinetic model of the visbreaking process was developed and used in an advanced control algorithm implemented in a distributed control system (DCS). During development, model predictions were checked against unit history data and compared to the actual unit performance with respect to fuel oil stability vs. cracking conversion. In the first stage, the algorithm was used in open-loop supervisory control. In the second stage the advanced control loop was closed and the visbreaking units was run automatically. The visbreaker control, based on process kinetics, is simple enough to be developed and implemented in a DCS, eliminating need for higher-power computers at the information system (IS) level, and reducing to a minimum data transfer from them to the process regulatory control level based on the DCS. The advanced control application led to profits estimated at $4.5 million annually, more than expected. The visbreaker advanced control showed how process engineering knowledge used in powerful and versatile DCSs could increase profit, shorten pay-out time and ease the workload on unit operators.

  3. Kinetic folding design of aptazyme-regulated expression devices as riboswitches for metabolic engineering.

    PubMed

    Sparkman-Yager, David; Correa-Rojas, Rodrigo A; Carothers, James M

    2015-01-01

    Recent developments in the fields of synthetic biology and metabolic engineering have opened the doors for the microbial production of biofuels and other valuable organic compounds. There remain, however, significant metabolic hurdles to the production of these compounds in cost-effective quantities. This is due, in part, to mismatches between the metabolic engineer's desire for high yields and the microbe's desire to survive. Many valuable compounds, or the intermediates necessary for their biosynthesis, prove deleterious at the desired production concentrations. One potential solution to these toxicity-related issues is the implementation of nonnative dynamic genetic control mechanisms that sense excessively high concentrations of metabolic intermediates and respond accordingly to alleviate their impact. One potential class of dynamic regulator is the riboswitch: cis-acting RNA elements that regulate the expression of downstream genes based on the presence of an effector molecule. Here, we present combined methods for constructing aptazyme-regulated expression devices (aREDs) through computational cotranscriptional kinetic folding design and experimental validation. These approaches can be used to engineer aREDs within novel genetic contexts for the predictable, dynamic regulation of gene expression in vivo. PMID:25605393

  4. 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.

  5. 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.

  6. Analysis of the pH-dependent thermodynamic stability, local motions, and microsecond folding kinetics of carbonmonoxycytochrome c.

    PubMed

    Kumar, Rajesh

    2016-09-15

    This paper analyzes the effect of pH on thermodynamic stability, low-frequency local motions and microsecond folding kinetics of carbonmonoxycytochrome c (Cyt-CO) all across the alkaline pH-unfolding transition of protein. Thermodynamic analysis of urea-induced unfolding transitions of Cyt-CO measured between pH 6 and pH 11.9 reveals that Cyt-CO is maximally stable at pH∼9.5. Dilution of unfolded Cyt-CO into refolding medium forms a native-like compact state (NCO-state), where Fe(2+)-CO interaction persists. Kinetic and thermodynamic parameters measured for slow thermally-driven CO dissociation (NCO→N+CO) and association (N+CO→NCO) reactions between pH 6.5 and pH 13 reveal that the thermal-motions of M80-containing Ω-loop are decreased in subdenaturing limit of alkaline pH. Laser photolysis of Fe(2+)-CO bond in NCO-state triggers the microsecond folding (NCO→N). The microsecond kinetics measured all across the alkaline pH-unfolding transition of Cyt-CO produce rate rollover in the refolding limb of chevron plot, which suggests a glass transition of NCO en route to N. Between pH 7 and pH 11.9, the natural logarithm of the microsecond folding rate varies by < 1.5 units while the natural logarithm of apparent equilibrium constant varies by 11.8 units. This finding indicates that the pH-dependent ionic-interactions greatly affect the global stability of protein but have very small effect on folding kinetics. PMID:27424489

  7. Probing Protein Folding Kinetics with High-resolution, Stabilized Optical Tweezers

    NASA Astrophysics Data System (ADS)

    Wong, Wesley; Halvorsen, Ken

    2009-03-01

    Single-molecule techniques provide a powerful means of exploring molecular transitions such as the unfolding and refolding of a protein. However, the quantification of bi-directional transitions and near-equilibrium phenomena poses unique challenges, and is often limited by the detection resolution and long-term stability of the instrument. We have developed unique optical tweezers methods that address these problems, including an interference-based method for high-resolution 3D bead tracking (˜1 nm laterally, ˜0.3 nm vertically, at > 100 Hz), and a continuous autofocus system that stabilizes the trap height to within 1-2 nm longterm [1,2]. We have used our instruments to quantify the force-dependent unfolding and refolding kinetics of single protein domains (e.g. spectrin in collaboration with E. Evans). These single-molecule studies are presented, together with the accompanying probabilistic analysis that we have developed. References: 1. W.P. Wong, V. Heinrich, E. Evans, Mat. Res. Soc. Symp. Proc., 790, P5.1-P5.10 (2004). 2. V. Heinrich, W.P. Wong, K. Halvorsen, E. Evans, Langmuir, 24, 1194-1203 (2008).

  8. Solvation and desolvation effects in protein folding: native flexibility, kinetic cooperativity and enthalpic barriers under isostability conditions.

    PubMed

    Liu, Zhirong; Chan, Hue Sun

    2005-11-01

    As different parts of a protein chain approach one another during folding, they are expected to encounter desolvation barriers before optimal packing is achieved. This impediment originates from the water molecule's finite size, which entails a net energetic cost for water exclusion when the formation of compensating close intraprotein contacts is not yet complete. Based on recent advances, we extend our exploration of these microscopic elementary desolvation barriers' roles in the emergence of generic properties of protein folding. Using continuum Gō-like C(alpha) chain models of chymotrypsin inhibitor 2 (CI2) and barnase as examples, we underscore that elementary desolvation barriers between a protein's constituent groups can significantly reduce native conformational fluctuations relative to model predictions that neglected these barriers. An increasing height of elementary desolvation barriers leads to thermodynamically more cooperative folding/unfolding transitions (i.e., higher overall empirical folding barriers) and higher degrees of kinetic cooperativity as manifested by more linear rate-stability relationships under constant temperature. Applying a spatially non-uniform thermodynamic parametrization we recently introduced for the pairwise C(alpha) potentials of mean force, the present barnase model further illustrates that desolvation is a probable physical underpinning for the experimentally observed high intrinsic enthalpic folding barrier under isostability conditions. PMID:16280624

  9. Thermodynamics, kinetics, and salt-dependence of folding of YopM, a large leucine-rich repeat protein

    PubMed Central

    Kloss, Ellen; Barrick, Doug

    2011-01-01

    Small globular proteins have many contacts between residues that are distant in primary sequence. These contacts create a complex network between sequence-distant segments of secondary structure, which may be expected to promote the cooperative folding of globular proteins. Although repeat proteins, which are made up of tandem modular units, lack sequence-distant contacts, several of considerable length have been shown to undergo cooperative two-state folding. To explore the limits of cooperativity in repeat proteins, we have studied the unfolding of YopM, a leucine-rich repeat (LRR) protein of over 400 residues. Despite its large size and modular architecture (15 repeats), YopM equilibrium unfolding is highly cooperative, and shows a very strong dependence on urea concentration. In contrast, kinetic studies of YopM folding indicate a mechanism that includes one or more transient intermediates. The urea dependence of the folding and unfolding rates suggests a relatively small transition state ensemble. As with the urea dependence, we have found an extreme dependence of the free energy of unfolding on salt concentration. This salt dependence likely results from general screening of a large number of unfavorable columbic interactions in the folded state, rather than from specific cation binding. PMID:18793647

  10. Sequence and solvent effects on telomeric DNA bimolecular G-quadruplex folding kinetics.

    PubMed

    Marchand, Adrien; Ferreira, Rubén; Tateishi-Karimata, Hisae; Miyoshi, Daisuke; Sugimoto, Naoki; Gabelica, Valérie

    2013-10-17

    Telomeric DNA sequences are particularly polymorphic: the adopted structure is exquisitely sensitive to the sequence and to the chemical environment, for example, solvation. Dehydrating conditions are known to stabilize G-quadruplex structures, but information on how solvation influences the individual rates of folding and unfolding of G-quadruplexes remains scarce. Here, we used electrospray mass spectrometry for the first time to monitor bimolecular G-quadruplex formation from 12-mer telomeric strands, in the presence of common organic cosolvents (methanol, ethanol, isopropanol, and acetonitrile). Based on the ammonium ion distribution, the total dimer signal was decomposed into contributions from the parallel and antiparallel structures to obtain individual reaction rates, and the antiparallel G-quadruplex structure was found to form faster than the parallel one. A dimeric reaction intermediate, in rapid equilibrium with the single strands, was also identified. Organic cosolvents increase the stability of the final structures mainly by increasing the folding rates. Our quantitative analysis of reaction rate dependence on cosolvent percentage shows that organic cosolvent molecules can be captured or released upon G-quadruplex formation, highlighting that they are not inert with DNA. In contrast to the folding rates, the G-quadruplex unfolding rates are almost insensitive to solvation effects, but are instead governed by the sequence and by the final structure: parallel dimers dissociate slower than antiparallel dimers only when thymine bases are present at the 5'-end. These results contribute unraveling the folding pathways of telomeric G-quadruplexes. The solvent effects revealed here enlighten that G-quadruplex structure in dehydrated, and molecularly crowded environments are modulated by the nature of cosolvent (e.g., methanol favors antiparallel structures) due to direct interactions, and by the time scale of the reaction, with >200-fold acceleration of

  11. RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity.

    PubMed

    Lin, Jong-Chin; Hyeon, Changbong; Thirumalai, D

    2012-11-19

    Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules. PMID:23336034

  12. 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.

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

    PubMed Central

    Liñán-García, Ernesto; Sánchez-Hernández, Juan Paulo; González-Barbosa, J. Javier; González-Flores, Carlos

    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. PMID:27413369

  14. Molecular Dynamics Simulation for the Dynamics and Kinetics of Folding Peptides in the Gas Phase.

    PubMed

    Litinas, Iraklis; Koutselos, Andreas D

    2015-12-31

    The conformations of flexible molecular species, such as oligomers and oligopeptides, and their interconversion in the gas phase have been probed by ion mobility spectrometry measurements. The ion motion is interpreted through the calculation of effective cross sections in the case of stable conformations of the macromolecules. However, when the molecular structures transform to each other as the ions collide with gas atoms during their flight through the drift tube, the introduction of an average cross section is required. To provide a direct way for the reproduction of the ion motion, we employ a nonequilibrium molecular dynamics simulation method and consider a molecular model that consists of two connected stiff cylindrical bodies interacting through an intramolecular model potential. With this procedure we have calculated the ion mobility as a function of temperature for a prototype peptide that converts between a helical and an extended globular form. The results are in good agreement with ion mobility spectrometry data confirming that an angular vibration coordinate can be used for the interpretation of the shifting of the drift-time distributions at high temperatures. The approach produces mean kinetic energies as well as various combined distributions of the ion degrees of freedom. It is easily applied to flexible macromolecular ions and can be extended to include additional degrees of freedom. PMID:26641107

  15. A 3-fold "butterfly valve" in command of the encapsulation's kinetic stability. Molecular baskets at work.

    PubMed

    Wang, Bao-Yu; Bao, Xiaoguang; Yan, Zhiqing; Maslak, Veselin; Hadad, Christopher M; Badjić, Jovica D

    2008-11-12

    Molecular basket 1, composed of a semirigid tris-norbornadiene framework and three revolving pyridine-based gates at the rim, has been built to "dynamically" enclose space and as such regulate molecular encapsulation. The gates were shown to fold via intramolecular hydrogen bonding and thereby form a C3nu symmetrical receptor: the 1H NMR resonance for the amide N-H protons of the pyridine gates appeared downfield (delta= 10.98 ppm), and the N-H vibrational stretch (IR) was observed at 3176 cm(-1). Accordingly, density functional theory (DFT, B3LYP) investigations revealed for the closed conformers of 1 to be energetically the most stable and dominant. The gearing of the pyridine "gates", about their axis, led to the interconversion of two dynamic enantiomers 1A and 1B comprising the clockwise and counterclockwise seam of intramolecular hydrogen bonds. Dynamic 1H NMR spectroscopic measurements and line-shape simulations suggested that the energy barrier of 10.0 kcal/mol (DeltaG++(A/B), 298 K) is required for the 1A/B interconversion, when CCl4 occupies the cavity of 1. Likewise, the activation free energy for CCl4 departing the basket was found to be 13.1 kcal/mol (DeltaG++, 298 K), whereas the thermodynamic stability of 1:CCl4 complex was -2.7 kcal/mol (DeltaGdegrees, 298 K). In view of that, CCl4 (but also (CH3)3CBr) was proposed to escape from, and a molecule of solvent to enter, the basket when the gates rotate about their axis: the exit of CCl4 requires the activation energy of 12.7 kcal/mol (DeltaG++(A/B) + DeltaGdegrees), similar to the experimentally found 13.1 kcal/mol (DeltaG++). PMID:18937455

  16. Protein folds and protein folding

    PubMed Central

    Schaeffer, R. Dustin; Daggett, Valerie

    2011-01-01

    The classification of protein folds is necessarily based on the structural elements that distinguish domains. Classification of protein domains consists of two problems: the partition of structures into domains and the classification of domains into sets of similar structures (or folds). Although similar topologies may arise by convergent evolution, the similarity of their respective folding pathways is unknown. The discovery and the characterization of the majority of protein folds will be followed by a similar enumeration of available protein folding pathways. Consequently, understanding the intricacies of structural domains is necessary to understanding their collective folding pathways. We review the current state of the art in the field of protein domain classification and discuss methods for the systematic and comprehensive study of protein folding across protein fold space via atomistic molecular dynamics simulation. Finally, we discuss our large-scale Dynameomics project, which includes simulations of representatives of all autonomous protein folds. PMID:21051320

  17. 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

  18. Kinetics of α-Globin Binding to α-Hemoglobin Stabilizing Protein (AHSP) Indicate Preferential Stabilization of Hemichrome Folding Intermediate*

    PubMed Central

    Mollan, Todd L.; Khandros, Eugene; Weiss, Mitchell J.; Olson, John S.

    2012-01-01

    Human α-hemoglobin stabilizing protein (AHSP) is a conserved mammalian erythroid protein that facilitates the production of Hemoglobin A by stabilizing free α-globin. AHSP rapidly binds to ferrous α with association (k′AHSP) and dissociation (kAHSP) rate constants of ≈10 μm−1 s−1 and 0.2 s−1, respectively, at pH 7.4 at 22 °C. A small slow phase was observed when AHSP binds to excess ferrous αCO. This slow phase appears to be due to cis to trans prolyl isomerization of the Asp29-Pro30 peptide bond in wild-type AHSP because it was absent when αCO was mixed with P30A and P30W AHSP, which are fixed in the trans conformation. This slow phase was also absent when met(Fe3+)-α reacted with wild-type AHSP, suggesting that met-α is capable of rapidly binding to either Pro30 conformer. Both wild-type and Pro30-substituted AHSPs drive the formation of a met-α hemichrome conformation following binding to either met- or oxy(Fe2+)-α. The dissociation rate of the met-α·AHSP complex (kAHSP ≈ 0.002 s−1) is ∼100-fold slower than that for ferrous α·AHSP complexes, resulting in a much higher affinity of AHSP for met-α. Thus, in vivo, AHSP acts as a molecular chaperone by rapidly binding and stabilizing met-α hemichrome folding intermediates. The low rate of met-α dissociation also allows AHSP to have a quality control function by kinetically trapping ferric α and preventing its incorporation into less stable mixed valence Hemoglobin A tetramers. Reduction of AHSP-bound met-α allows more rapid release to β subunits to form stable fully, reduced hemoglobin dimers and tetramers. PMID:22298770

  19. 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

  20. Kinetic Transition Networks for the Thomson Problem and Smale's Seventh Problem

    NASA Astrophysics Data System (ADS)

    Mehta, Dhagash; Chen, Jianxu; Chen, Danny Z.; Kusumaatmaja, Halim; Wales, David J.

    2016-07-01

    The Thomson problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here, we show that the energy landscape of the Thomson problem for N particles with N =132 , 135, 138, 141, 144, 147, and 150 is single funneled, characteristic of a structure-seeking organization where the global minimum is easily accessible. Algorithmically, constructing starting points close to the global minimum of such a potential with spherical constraints is one of Smale's 18 unsolved problems in mathematics for the 21st century because it is important in the solution of univariate and bivariate random polynomial equations. By analyzing the kinetic transition networks, we show that a randomly chosen minimum is, in fact, always "close" to the global minimum in terms of the number of transition states that separate them, a characteristic of small world networks.

  1. Kinetic Transition Networks for the Thomson Problem and Smale's Seventh Problem.

    PubMed

    Mehta, Dhagash; Chen, Jianxu; Chen, Danny Z; Kusumaatmaja, Halim; Wales, David J

    2016-07-01

    The Thomson problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here, we show that the energy landscape of the Thomson problem for N particles with N=132, 135, 138, 141, 144, 147, and 150 is single funneled, characteristic of a structure-seeking organization where the global minimum is easily accessible. Algorithmically, constructing starting points close to the global minimum of such a potential with spherical constraints is one of Smale's 18 unsolved problems in mathematics for the 21st century because it is important in the solution of univariate and bivariate random polynomial equations. By analyzing the kinetic transition networks, we show that a randomly chosen minimum is, in fact, always "close" to the global minimum in terms of the number of transition states that separate them, a characteristic of small world networks. PMID:27447530

  2. 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.

  3. The Ensemble Folding Kinetics of the FBP28 WW Domain Revealed by an All-atom Monte Carlo Simulation in a Knowledge-based Potential

    PubMed Central

    Xu, Jiabin; Huang, Lei; Shakhnovich, Eugene I.

    2011-01-01

    In this work, we apply a detailed all-atom model with a transferable knowledge-based potential to study the folding kinetics of Formin-Binding protein, FBP28, which is a canonical three-stranded β-sheet WW domain. Replica exchange Monte Carlo (REMC) simulations starting from random coils find native-like (C α RMSD of 2.68Å) lowest energy structure. We also study the folding kinetics of FBP28 WW domain by performing a large number of ab initio Monte Carlo folding simulations. Using these trajectories, we examine the order of formation of two β –hairpins, the folding mechanism of each individual β– hairpin, and transition state ensemble (TSE) of FBP28 WW domain and compare our results with experimental data and previous computational studies. To obtain detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Further, a rigorous Pfold analysis is used to obtain representative samples of the TSEs showing good quantitative agreement between experimental and simulated Φ values. Our analysis shows that the turn structure between first and second β strands is a partially stable structural motif that gets formed before entering the TSE in FBP28 WW domain and there exist two major pathways for the folding of FBP28 WW domain, which differ in the order and mechanism of hairpin formation. PMID:21365688

  4. An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem

    PubMed Central

    Shmygelska, Alena; Hoos, Holger H

    2005-01-01

    Background The protein folding problem is a fundamental problems in computational molecular biology and biochemical physics. Various optimisation methods have been applied to formulations of the ab-initio folding problem that are based on reduced models of protein structure, including Monte Carlo methods, Evolutionary Algorithms, Tabu Search and hybrid approaches. In our work, we have introduced an ant colony optimisation (ACO) algorithm to address the non-deterministic polynomial-time hard (NP-hard) combinatorial problem of predicting a protein's conformation from its amino acid sequence under a widely studied, conceptually simple model – the 2-dimensional (2D) and 3-dimensional (3D) hydrophobic-polar (HP) model. Results We present an improvement of our previous ACO algorithm for the 2D HP model and its extension to the 3D HP model. We show that this new algorithm, dubbed ACO-HPPFP-3, performs better than previous state-of-the-art algorithms on sequences whose native conformations do not contain structural nuclei (parts of the native fold that predominantly consist of local interactions) at the ends, but rather in the middle of the sequence, and that it generally finds a more diverse set of native conformations. Conclusions The application of ACO to this bioinformatics problem compares favourably with specialised, state-of-the-art methods for the 2D and 3D HP protein folding problem; our empirical results indicate that our rather simple ACO algorithm scales worse with sequence length but usually finds a more diverse ensemble of native states. Therefore the development of ACO algorithms for more complex and realistic models of protein structure holds significant promise. PMID:15710037

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

    PubMed

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

    2016-08-23

    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

  6. Network measures for protein folding state discrimination

    PubMed Central

    Menichetti, Giulia; Fariselli, Piero; Remondini, Daniel

    2016-01-01

    Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there is not a first-principle model to explain this different behavior. We exploit the network properties of protein structures by introducing novel observables to address the problem of classifying the different types of folding kinetics. These observables display a plain physical meaning, in terms of vibrational modes, possible configurations compatible with the native protein structure, and folding cooperativity. The relevance of these observables is supported by a classification performance up to 90%, even with simple classifiers such as discriminant analysis. PMID:27464796

  7. The Knotted Protein UCH-L1 Exhibits Partially Unfolded Forms under Native Conditions that Share Common Structural Features with Its Kinetic Folding Intermediates.

    PubMed

    Lou, Shih-Chi; Wetzel, Svava; Zhang, Hongyu; Crone, Elizabeth W; Lee, Yun-Tzai; Jackson, Sophie E; Hsu, Shang-Te Danny

    2016-06-01

    The human ubiquitin C-terminal hydrolase, UCH-L1, is an abundant neuronal deubiquitinase that is associated with Parkinson's disease. It contains a complex Gordian knot topology formed by the polypeptide chain alone. Using a combination of fluorescence-based kinetic measurements, we show that UCH-L1 has two distinct kinetic folding intermediates that are transiently populated on parallel pathways between the denatured and native states. NMR hydrogen-deuterium exchange (HDX) experiments indicate the presence of partially unfolded forms (PUFs) of UCH-L1 under native conditions. HDX measurements as a function of urea concentration were used to establish the structure of the PUFs and pulse-labelled HDX NMR was used to show that the PUFs and the folding intermediates are likely the same species. In both cases, a similar stable core encompassing most of the central β-sheet is highly structured and α-helix 3, which is partially formed, packs against it. In contrast to the stable β-sheet core, the peripheral α-helices display significant local fluctuations leading to rapid exchange. The results also suggest that the main difference between the two kinetic intermediates is structure and packing of α-helices 3 and 7 and the degree of structure in β-strand 5. Together, the fluorescence and NMR results establish that UCH-L1 neither folds through a continuum of pathways nor by a single discrete pathway. Its folding is complex, the β-sheet core forms early and is present in both intermediate states, and the rate-limiting step which is likely to involve the threading of the chain to form the 52-knot occurs late on the folding pathway. PMID:27067109

  8. Solving the eigenvalue problem of the nuclear Yukawa-folded mean-field Hamiltonian

    NASA Astrophysics Data System (ADS)

    Dobrowolski, A.; Pomorski, K.; Bartel, J.

    2016-02-01

    The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by the equivalent sharp surface described either by the well known Funny-Hills or the Trentalange-Koonin-Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left-right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the z-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle π around the z-axis. On output, the computer code produces for a given nucleus with mass number A and charge number Z the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation.

  9. 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

    2016-03-01

    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. PMID:26717836

  10. 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

    2016-06-01

    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. PMID:27276251

  11. A Hooke׳s law-based approach to protein folding rate.

    PubMed

    Ruiz-Blanco, Yasser B; Marrero-Ponce, Yovani; Prieto, Pablo J; Salgado, Jesús; García, Yamila; Sotomayor-Torres, Clivia M

    2015-01-01

    Kinetics is a key aspect of the renowned protein folding problem. Here, we propose a comprehensive approach to folding kinetics where a polypeptide chain is assumed to behave as an elastic material described by the Hooke׳s law. A novel parameter called elastic-folding constant results from our model and is suggested to distinguish between protein with two-state and multi-state folding pathways. A contact-free descriptor, named folding degree, is introduced as a suitable structural feature to study protein-folding kinetics. This approach generalizes the observed correlations between varieties of structural descriptors with the folding rate constant. Additionally several comparisons among structural classes and folding mechanisms were carried out showing the good performance of our model with proteins of different types. The present model constitutes a simple rationale for the structural and energetic factors involved in protein folding kinetics. PMID:25245368

  12. Radiative Transfer Reconsidered as a Quantum Kinetic Theory Problem

    NASA Astrophysics Data System (ADS)

    Rosato, J.

    2015-12-01

    We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a balance relation in the phase space, which involves nonlocal terms owing to radiation coherence. In a perturbative framework, we focus on the lowest order term in ℏ-expansion and show that the radiation coherence results in an alteration of the photon group velocity. An application to the formation of hydrogen lines in stellar atmospheres is performed as an illustration.

  13. Scanning Single-Molecule Fluorescence Correlation Spectroscopy Enables Kinetics Study of DNA Hairpin Folding with a Time Window from Microseconds to Seconds.

    PubMed

    Bi, Huimin; Yin, Yandong; Pan, Bailong; Li, Geng; Zhao, Xin Sheng

    2016-05-19

    Single-molecule fluorescence measurements have been widely used to explore kinetics and dynamics of biological systems. Among them, single-molecule imaging (SMI) is good at tracking processes slower than tens of milliseconds, whereas fluorescence correlation spectroscopy (FCS) is good at probing processes faster than submilliseconds. However, there is still shortage of simple yet effective single-molecule fluorescence method to cover the time-scale between submilliseconds and tens of milliseconds. To effectively bridge this millisecond gap, we developed a single-molecule fluorescence correlation spectroscopy (smFCS) method that works on surface-immobilized single molecules through surface scanning. We validated it by monitoring the classical DNA hairpin folding process. With a wide time window from microseconds to seconds, the experimental data are well fitted to the two-state folding model. All relevant molecular parameters, including the relative fluorescence brightness, equilibrium constant, and reaction rate constants, were uniquely determined. PMID:27140004

  14. 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

    2016-01-01

    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

  15. Multipixel spectral imaging of green fluorescent protein (GFP) in COS-7 cells: folding kinetics and chromophore formation

    NASA Astrophysics Data System (ADS)

    Greenbaum, Lior; Rothmann, Chana; Hanania, Judith; Malik, Zvi

    2000-12-01

    Spectrally resolved imaging of Green fluorescent protein (GFP) expressed in living COS-7 kidney cells distinguished the subcellular localization and demarcated the processes of protein folding and chromophore formation. COS-7 kidney cells were transfected by a plasmid pEGFP-N1 plasmid followed by incubation for 15 hours for gen expression. At different intervals the cells were examined by fluorescence microscopy and analyzed by a spectral imaging system. After 7 hours, GFP was detected in the cytoplasm, concentrated in a localized form. Spectra of the initial GFP evinced several components that belong both tot he typical fluorescent signal as well as to unspecific fingerprints. At 10 and 15 hours, GFP was seen spread in the cytoplasm as well as in the nucleus, and the specific spectra of the GFP were dominant at the later time. The typical GFP spectral fingerprint is the result of protein folding and chromophore formation following internal oxidation reactions. This folding and chromophore formation process, up to final conformation, was detected by spectral imaging as localized in the nucleus rather than in the cytosol. Thus, the method of fluorescence microscopy combined with multiplex spectral imaging demonstrates distinct biochemical pathways leading to GFP conformation.

  16. The experimental folding landscape of monomeric lactose repressor, a large two-domain protein, involves two kinetic intermediates.

    PubMed

    Wilson, Corey J; Das, Payel; Clementi, Cecilia; Matthews, Kathleen S; Wittung-Stafshede, Pernilla

    2005-10-11

    To probe the experimental folding behavior of a large protein with complex topology, we created a monomeric variant of the lactose repressor protein (MLAc), a well characterized tetrameric protein that regulates transcription of the lac operon. Purified MLAc is folded, fully functional, and binds the inducer isopropyl beta-d-thiogalactoside with the same affinity as wild-type LacI. Equilibrium unfolding of MLAc induced by the chemical denaturant urea is a reversible, apparent two-state process (pH 7.5, 20 degrees C). However, time-resolved experiments demonstrate that unfolding is single-exponential, whereas refolding data indicate two transient intermediates. The data reveal the initial formation of a burst-phase (tau < ms) intermediate that corresponds to approximately 50% of the total secondary-structure content. This step is followed by a rearrangement reaction that is rate-limited by an unfolding process (tau approximately 3 s; pH 7.5, 20 degrees C) and results in a second intermediate. This MLAc intermediate converts to the native structure (tau approximately 30 s; pH 7.5, 20 degrees C). Remarkably, the experimental folding-energy landscape for MLAc is in excellent agreement with theoretical predictions using a simple topology-based C(alpha)-model as presented in a companion article in this issue. PMID:16203983

  17. 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

  18. Probing Kinetic Mechanisms of Protein Function and Folding with Time-Resolved Natural and Magnetic Chiroptical Spectroscopies

    PubMed Central

    Kliger, David S.; Chen, Eefei; Goldbeck, Robert A.

    2012-01-01

    Recent and ongoing developments in time-resolved spectroscopy have made it possible to monitor circular dichroism, magnetic circular dichroism, optical rotatory dispersion, and magnetic optical rotatory dispersion with nanosecond time resolution. These techniques have been applied to determine structural changes associated with the function of several proteins as well as to determine the nature of early events in protein folding. These studies have required new approaches in triggering protein reactions as well as the development of time-resolved techniques for polarization spectroscopies with sufficient time resolution and sensitivity to probe protein structural changes. PMID:22312279

  19. 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

  20. The unsolved chapter of vocal fold scars and how tissue engineering could help us solve the problem.

    PubMed

    Graupp, M; Bachna-Rotter, S; Gerstenberger, C; Friedrich, G; Fröhlich-Sorger, E; Kiesler, K; Gugatschka, M

    2016-09-01

    Vocal fold scarring is a relatively small field in scar research with prerequisites found nowhere else. The deterioration of the delicate tri-layered micro-structure of the epithelium of the vocal folds leads to impaired vibration characteristics resulting in a permanent hoarse and breathy voice. Tissue engineering approaches could help to restore the pre-injury status. Despite a considerable progress in this field during the last years, routine clinical applications are not available so far. One reason might be that vocal fold fibroblasts, as the responsible cell type for fibrogenesis, have very particular properties that are only poorly characterized. Moreover, in vivo trials are costly and time consuming and a representative in vitro model does not exist so far. These particular circumstances lead to innovative in vitro strategies and concepts such as macro-molecular crowding that can also be applied in adjacent fields. PMID:26108198

  1. The nature of protein folding pathways.

    PubMed

    Englander, S Walter; Mayne, Leland

    2014-11-11

    How do proteins fold, and why do they fold in that way? This Perspective integrates earlier and more recent advances over the 50-y history of the protein folding problem, emphasizing unambiguously clear structural information. Experimental results show that, contrary to prior belief, proteins are multistate rather than two-state objects. They are composed of separately cooperative foldon building blocks that can be seen to repeatedly unfold and refold as units even under native conditions. Similarly, foldons are lost as units when proteins are destabilized to produce partially unfolded equilibrium molten globules. In kinetic folding, the inherently cooperative nature of foldons predisposes the thermally driven amino acid-level search to form an initial foldon and subsequent foldons in later assisted searches. The small size of foldon units, ∼ 20 residues, resolves the Levinthal time-scale search problem. These microscopic-level search processes can be identified with the disordered multitrack search envisioned in the "new view" model for protein folding. Emergent macroscopic foldon-foldon interactions then collectively provide the structural guidance and free energy bias for the ordered addition of foldons in a stepwise pathway that sequentially builds the native protein. These conclusions reconcile the seemingly opposed new view and defined pathway models; the two models account for different stages of the protein folding process. Additionally, these observations answer the "how" and the "why" questions. The protein folding pathway depends on the same foldon units and foldon-foldon interactions that construct the native structure. PMID:25326421

  2. The energy landscape for folding and function

    NASA Astrophysics Data System (ADS)

    Onuchic, Jose

    2006-03-01

    Globally the energy landscape of a folding protein resembles a partially rough funnel. The local roughness of the funnel reflects transient trapping of the protein configurations in local free energy minima. The kinetics of folding is best considered as a progressive organization of an ensemble of partially folded structures through which the protein passes through on its way to the folded structure. The folding mechanisms for several fast-folding proteins can be described using an energy landscape theory to set up the correspondence with simulations of protein minimalist models. Using these simulations together with analytical theory, we can learn about good (minimally frustrated) folding sequences and non-folding (frustrated) sequences. An important idea that emerges from this theory is that subtle features of the protein landscape can profoundly affect the apparent mechanism of folding. Experiments on the dependence of the folding/unfolding times, and the stability of these proteins to denaturant concentration and site-directed mutagenesis, and on the early events of folding allow to infer the global characteristics of the landscape. In addition to need to minimize energetic frustration, the topology of the native fold also plays a major role in the folding mechanism. Some folding motifs are easier to design than others suggesting the possibility that evolution not only selected sequences with sufficiently small energetic frustration but also selected more easily designable native structures. Several proteins (such as CI2 and SH3) have sufficiently reduced energetic frustration) that much of the heterogeneity observed in their transition state ensemble (TSE) is determined by topology. Topological effects go beyond the structure of the TSE. The overall structure of the on-route and off-route (traps) intermediates for the folding of more complex proteins is also influenced by topology. Utilizing this theoretical framework, simulations of minimalist models and

  3. THE SOLAR ABUNDANCE PROBLEM: THE EFFECT OF THE TURBULENT KINETIC FLUX ON THE SOLAR ENVELOPE MODEL

    SciTech Connect

    Zhang, Q. S.

    2014-06-01

    Recent three-dimensional (3D) simulations have shown that the turbulent kinetic flux (TKF) is significant. We discuss the effects of TKF on the size of the convection zone and find that the TKF may help solve the solar abundance problem. The solar abundance problem is that, with new abundances, the solar convection zone depth, the sound speed in the radiative interior, the helium abundance, and the density in the convective envelope are not in agreement with helioseismic inversions. We have performed Monte Carlo simulations on solar convective envelope models with different profiles of TKF to test its effects. The solar abundance problem is revealed in the standard solar convective envelope model with AGSS09 composition, which shows significant differences (∼10)) in density from the helioseismic inversions, but the differences in the model with the old composition GN93 is small (∼0.5)). In the testing models with a different TKF imposed, it is found that the density profile is sensitive to the value of TKF at the base of the convective envelope and insensitive to the structure of TKF in the convection zone. The required value of turbulent kinetic luminosity at the base is about –13% to – 19% L {sub ☉}. Comparing with the 3D simulations, this value is plausible. This study is for the solar convective envelope only. Evolutionary solar models with TKF are required to investigat the effects of TKF on the solar interior structure below the convection zone and the whole solar abundance problem, but the profile of the TKF in the overshoot region is necessary.

  4. 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.

  5. Transtensional folding

    NASA Astrophysics Data System (ADS)

    Fossen, Haakon; Teyssier, Christian; Whitney, Donna L.

    2014-05-01

    For now three decades transpression has dominated the concepts that underlie oblique tectonics, but in more recent years transtension has garnered much interest as a simple model that can be applied to shallow and deep crustal tectonics. One fundamental aspect that distinguishes transtension from transpression is that material lines in transtension rotate toward the direction of oblique divergence. Another point that may be less intuitive when thinking of transtension is that while transtensional strain involves shortening in the vertical direction, one of the horizontal axes is also a shortening axis, whatever the angle of divergence. It is the combination of these two shortening axes that leads to constrictional finite strain in transtension. The existence of a horizontal shortening strain axis implies that transtension offers the potential for folds of horizontal layers to form and then rotate toward the direction of oblique divergence. An investigation of transtensional folding using 3D strain modeling reveals that folding is more likely for simple shear dominated transtension (large wrench component). Transtensional folds can only accumulate a fixed amount of horizontal shortening and tightness that are prescribed by the angle of oblique divergence, regardless of finite strain. Transtensional folds are characterized by hinge-parallel stretching that exceeds that expected from pure wrenching. In addition, the magnitude of hinge-parallel stretching always exceeds hinge-perpendicular shortening, causing constrictional fabrics and hinge-parallel boudinage to develop. Because the dominant vertical strain axis is shortening, transtensional fold growth is generally suppressed, but when folds do develop their limbs enter the field of shortening, resulting in possible fold interference patterns akin to cascading folds. Application of these transtensional folding principles to regions of oblique rifting (i.e. Gulf of California) or exhumation of deep crust (i.e. Western

  6. Protein folding in a force clamp

    NASA Astrophysics Data System (ADS)

    Cieplak, Marek; Szymczak, P.

    2006-05-01

    Kinetics of folding of a protein held in a force clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed variations in the end-to-end distance reflect microscopic events during folding. However, the folding scenarios in and out of the force clamp are distinct.

  7. Protein folding. Translational tuning optimizes nascent protein folding in cells.

    PubMed

    Kim, Soo Jung; Yoon, Jae Seok; Shishido, Hideki; Yang, Zhongying; Rooney, LeeAnn A; Barral, Jose M; Skach, William R

    2015-04-24

    In cells, biosynthetic machinery coordinates protein synthesis and folding to optimize efficiency and minimize off-pathway outcomes. However, it has been difficult to delineate experimentally the mechanisms responsible. Using fluorescence resonance energy transfer, we studied cotranslational folding of the first nucleotide-binding domain from the cystic fibrosis transmembrane conductance regulator. During synthesis, folding occurred discretely via sequential compaction of N-terminal, α-helical, and α/β-core subdomains. Moreover, the timing of these events was critical; premature α-subdomain folding prevented subsequent core formation. This process was facilitated by modulating intrinsic folding propensity in three distinct ways: delaying α-subdomain compaction, facilitating β-strand intercalation, and optimizing translation kinetics via codon usage. Thus, de novo folding is translationally tuned by an integrated cellular response that shapes the cotranslational folding landscape at critical stages of synthesis. PMID:25908822

  8. 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.

  9. Kinetics and motional dynamics of spin-labeled yeast iso-1-cytochrome c: 1. Stopped-flow electron paramagnetic resonance as a probe for protein folding/unfolding of the C-terminal helix spin-labeled at cysteine 102.

    PubMed

    Qu, K; Vaughn, J L; Sienkiewicz, A; Scholes, C P; Fetrow, J S

    1997-03-11

    The kinetics of chemically induced folding and unfolding processes in spin-labeled yeast iso-1-cytochrome c were measured by stopped-flow electron paramagnetic resonance (EPR). Stopped-flow EPR, based on a new dielectric resonator structure [Sienkiewicz, A., Qu, K., & Scholes, C. P. (1994) Rev. Sci. Instrum. 65, 68-74], gives a new temporal component to probing nanosecond molecular tumbling motions that are modulated by macromolecular processes requiring time resolution of milliseconds to seconds. The stopped-flow EPR technique presented in this work is a kinetic technique that has not been previously used with such a time resolution on spin-labeled systems, and it has the potential for application to numerous spin-labeled sites in this and other proteins. The cysteine-specific spin-label, methanethiosulfonate spin-label (MTSSL), was attached to yeast iso-1-cytochrome c at the single naturally occurring cysteine102, and the emphasis for this work was on this disulfide-attached spin-labeled prototype. This probe has the advantage of reflecting the protein tertiary fold, as shown by recent, systematic site-directed spin labeling of T4 lysozyme [Mchaourab, H. S. Lietzow, M. A., Hideg, K., & Hubbell, W. L. (1996) Biochemistry 35, 7692-7704], and protein backbone dynamics, as also shown by model peptide studies [Todd, A. P., & Millhauser, G. L. (1991) Biochemistry 30, 5515-5523]. The C-terminal cytochrome c helix where the label is attached is thought to be critical in the initial steps of protein folding and unfolding. Stopped-flow EPR resolved the monoexponential, guanidinium-induced unfolding process at pH 6.5 with an approximately 20 ms time constant; this experiment required less than 150 microL of 80 microM spin-labeled protein. We observed an approximately 50-fold decrease of this unfolding time from the 1 s range to the 20 ms time range as the guanidinium denaturant concentration was increased from 0.6 to 2.0 M. The more complex refolding kinetics of our labeled

  10. The nature of protein folding pathways

    PubMed Central

    Englander, S. Walter; Mayne, Leland

    2014-01-01

    How do proteins fold, and why do they fold in that way? This Perspective integrates earlier and more recent advances over the 50-y history of the protein folding problem, emphasizing unambiguously clear structural information. Experimental results show that, contrary to prior belief, proteins are multistate rather than two-state objects. They are composed of separately cooperative foldon building blocks that can be seen to repeatedly unfold and refold as units even under native conditions. Similarly, foldons are lost as units when proteins are destabilized to produce partially unfolded equilibrium molten globules. In kinetic folding, the inherently cooperative nature of foldons predisposes the thermally driven amino acid-level search to form an initial foldon and subsequent foldons in later assisted searches. The small size of foldon units, ∼20 residues, resolves the Levinthal time-scale search problem. These microscopic-level search processes can be identified with the disordered multitrack search envisioned in the “new view” model for protein folding. Emergent macroscopic foldon–foldon interactions then collectively provide the structural guidance and free energy bias for the ordered addition of foldons in a stepwise pathway that sequentially builds the native protein. These conclusions reconcile the seemingly opposed new view and defined pathway models; the two models account for different stages of the protein folding process. Additionally, these observations answer the “how” and the “why” questions. The protein folding pathway depends on the same foldon units and foldon–foldon interactions that construct the native structure. PMID:25326421

  11. Understanding the folding rates and folding nuclei of globular proteins.

    PubMed

    Finkelstein, Alexei V; Ivankov, Dmitry N; Garbuzynskiy, Sergiy O; Galzitskaya, Oxana V

    2007-12-01

    The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data. PMID:18220841

  12. Criteria for folding in structure-based models of proteins

    NASA Astrophysics Data System (ADS)

    Wołek, Karol; Cieplak, Marek

    2016-05-01

    In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very low thermodynamic stability, especially when the contact map used is too sparse. We consider six different structure-based models and show that allowing for a small, but model-dependent, percentage of the native contacts not being established boosts the folding temperature substantially while affecting the time scales of folding only in a minor way. We also compare other properties of the six models. We show that the choice of the description of the backbone stiffness has a substantial effect on the values of characteristic temperatures that relate both to equilibrium and kinetic properties. Models without any backbone stiffness (like the self-organized polymer) are found to perform similar to those with the stiffness, including in the studies of stretching.

  13. Criteria for folding in structure-based models of proteins.

    PubMed

    Wołek, Karol; Cieplak, Marek

    2016-05-14

    In structure-based models of proteins, one often assumes that folding is accomplished when all contacts are established. This assumption may frequently lead to a conceptual problem that folding takes place in a temperature region of very low thermodynamic stability, especially when the contact map used is too sparse. We consider six different structure-based models and show that allowing for a small, but model-dependent, percentage of the native contacts not being established boosts the folding temperature substantially while affecting the time scales of folding only in a minor way. We also compare other properties of the six models. We show that the choice of the description of the backbone stiffness has a substantial effect on the values of characteristic temperatures that relate both to equilibrium and kinetic properties. Models without any backbone stiffness (like the self-organized polymer) are found to perform similar to those with the stiffness, including in the studies of stretching. PMID:27179507

  14. Evolutionary optimization of protein folding.

    PubMed

    Debès, Cédric; Wang, Minglei; Caetano-Anollés, Gustavo; Gräter, Frauke

    2013-01-01

    Nature has shaped the make up of proteins since their appearance, [Formula: see text]3.8 billion years ago. However, the fundamental drivers of structural change responsible for the extraordinary diversity of proteins have yet to be elucidated. Here we explore if protein evolution affects folding speed. We estimated folding times for the present-day catalog of protein domains directly from their size-modified contact order. These values were mapped onto an evolutionary timeline of domain appearance derived from a phylogenomic analysis of protein domains in 989 fully-sequenced genomes. Our results show a clear overall increase of folding speed during evolution, with known ultra-fast downhill folders appearing rather late in the timeline. Remarkably, folding optimization depends on secondary structure. While alpha-folds showed a tendency to fold faster throughout evolution, beta-folds exhibited a trend of folding time increase during the last [Formula: see text]1.5 billion years that began during the "big bang" of domain combinations. As a consequence, these domain structures are on average slow folders today. Our results suggest that fast and efficient folding of domains shaped the universe of protein structure. This finding supports the hypothesis that optimization of the kinetic and thermodynamic accessibility of the native fold reduces protein aggregation propensities that hamper cellular functions. PMID:23341762

  15. Solvent–amino acid interaction energies in three-dimensional-lattice Monte Carlo simulations of a model 27-mer protein: Folding thermodynamics and kinetics

    PubMed Central

    Leonhard, Kai; Prausnitz, John M.; Radke, Clayton J.

    2004-01-01

    Amino acid residue–solvent interactions are required for lattice Monte Carlo simulations of model proteins in water. In this study, we propose an interaction-energy scale that is based on the interaction scale by Miyazawa and Jernigan. It permits systematic variation of the amino acid–solvent interactions by introducing a contrast parameter for the hydrophobicity, Cs, and a mean attraction parameter for the amino acids, ω. Changes in the interaction energies strongly affect many protein properties. We present an optimized energy parameter set for best representing realistic behavior typical for many proteins (fast folding and high cooperativity for single chains). Our optimal parameters feature a much weaker hydrophobicity contrast and mean attraction than does the original interaction scale. The proposed interaction scale is designed for calculating the behavior of proteins in bulk and at interfaces as a function of solvent characteristics, as well as protein size and sequence. PMID:14739322

  16. Peptide folding simulations.

    PubMed

    Gnanakaran, S; Nymeyer, Hugh; Portman, John; Sanbonmatsu, Kevin Y; García, Angel E

    2003-04-01

    Developments in the design of small peptides that mimic proteins in complexity, recent advances in nanosecond time-resolved spectroscopy methods to study peptides and the development of modern, highly parallel simulation algorithms have come together to give us a detailed picture of peptide folding dynamics. Two newly implemented simulation techniques, parallel replica dynamics and replica exchange molecular dynamics, can now describe directly from simulations the kinetics and thermodynamics of peptide formation, respectively. Given these developments, the simulation community now has the tools to verify and validate simulation protocols and models (forcefields). PMID:12727509

  17. 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

  18. Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry.

    PubMed

    Flyvbjerg, H; Jobs, E; Leibler, S

    1996-06-11

    Experimental time series for a nonequilibrium reaction may in some cases contain sufficient data to determine a unique kinetic model for the reaction by a systematic mathematical analysis. As an example, a kinetic model for the self-assembly of microtubules is derived here from turbidity time series for solutions in which microtubules assemble. The model may be seen as a generalization of Oosawa's classical nucleation-polymerization model. It reproduces the experimental data with a four-stage nucleation process and a critical nucleus of 15 monomers. PMID:8650204

  19. Protein folding in a force-clamp

    NASA Astrophysics Data System (ADS)

    Cieplak, Marek; Szymczak, Piotr

    2006-03-01

    Kinetics of folding of a protein held in a force-clamp are compared to an unconstrained folding. The comparison is made within a simple topology-based dynamical model of ubiquitin. We demonstrate that the experimentally observed rapid changes in the end-to-end distance mirror microscopic events during folding. However, the folding scenarios in and out of the force-clamp are distinct.

  20. Limited cooperativity in protein folding.

    PubMed

    Muñoz, Victor; Campos, Luis A; Sadqi, Mourad

    2016-02-01

    Theory and simulations predict that the structural concert of protein folding reactions is relatively low. Experimentally, folding cooperativity has been difficult to study, but in recent years we have witnessed major advances. New analytical procedures in terms of conformational ensembles rather than discrete states, experimental techniques with improved time, structural, or single-molecule resolution, and combined thermodynamic and kinetic analysis of fast folding have contributed to demonstrate a general scenario of limited cooperativity in folding. Gradual structural disorder is already apparent on the unfolded and native states of slow, two-state folding proteins, and it greatly increases in magnitude for fast folding domains. These results demonstrate a direct link between how fast a single-domain protein folds and unfolds, and how cooperative (or structurally diverse) is its equilibrium unfolding process. Reducing cooperativity also destabilizes the native structure because it affects unfolding more than folding. We can thus define a continuous cooperativity scale that goes from the 'pliable' two-state character of slow folders to the gradual unfolding of one-state downhill, and eventually to intrinsically disordered proteins. The connection between gradual unfolding and intrinsic disorder is appealing because it suggests a conformational rheostat mechanism to explain the allosteric effects of folding coupled to binding. PMID:26845039

  1. Protein folding guides disulfide bond formation

    PubMed Central

    Qin, Meng; Wang, Wei; Thirumalai, D.

    2015-01-01

    The Anfinsen principle that the protein sequence uniquely determines its structure is based on experiments on oxidative refolding of a protein with disulfide bonds. The problem of how protein folding drives disulfide bond formation is poorly understood. Here, we have solved this long-standing problem by creating a general method for implementing the chemistry of disulfide bond formation and rupture in coarse-grained molecular simulations. As a case study, we investigate the oxidative folding of bovine pancreatic trypsin inhibitor (BPTI). After confirming the experimental findings that the multiple routes to the folded state contain a network of states dominated by native disulfides, we show that the entropically unfavorable native single disulfide [14–38] between Cys14 and Cys38 forms only after polypeptide chain collapse and complete structuring of the central core of the protein containing an antiparallel β-sheet. Subsequent assembly, resulting in native two-disulfide bonds and the folded state, involves substantial unfolding of the protein and transient population of nonnative structures. The rate of [14–38] formation increases as the β-sheet stability increases. The flux to the native state, through a network of kinetically connected native-like intermediates, changes dramatically by altering the redox conditions. Disulfide bond formation between Cys residues not present in the native state are relevant only on the time scale of collapse of BPTI. The finding that formation of specific collapsed native-like structures guides efficient folding is applicable to a broad class of single-domain proteins, including enzyme-catalyzed disulfide proteins. PMID:26297249

  2. Suitable combination of promoter and micellar catalyst for kilo fold rate acceleration on benzaldehyde to benzoic acid conversion in aqueous media at room temperature: a kinetic approach.

    PubMed

    Ghosh, Aniruddha; Saha, Rumpa; Ghosh, Sumanta K; Mukherjee, Kakali; Saha, Bidyut

    2013-05-15

    The kinetics of oxidation of benzaldehyde by chromic acid in aqueous and aqueous surfactant (sodium dodecyl sulfate, SDS, alkyl phenyl polyethylene glycol, Triton X-100 and N-cetylpyridinium chloride, CPC) media have been investigated in the presence of promoter at 303 K. The pseudo-first-order rate constants (kobs) were determined from a logarithmic plot of absorbance as a function time. The rate constants were found to increase with introduction of heteroaromatic nitrogen base promoters such as Picolinic acid (PA), 2,2'-bipyridine (bipy) and 1,10-phenanthroline (phen). The product benzoic acid has been characterized by conventional melting point experiment, NMR, HRMS and FTIR spectral analysis. The mechanism of both unpromoted and promoted reaction path has been proposed for the reaction. In presence of the anionic surfactant SDS, cationic surfactant CPC and neutral surfactant TX-100 the reaction can undergo simultaneously in both aqueous and micellar phase with an enhanced rate of oxidation in the micellar phase. Both SDS and TX-100 produce normal micellar effect whereas CPC produce reverse micellar effect in the presence of benzaldehyde. The observed net enhancement of rate effects has been explained by considering the hydrophobic and electrostatic interaction between the surfactants and reactants. SDS and bipy combination is the suitable one for benzaldehyde oxidation. PMID:23501718

  3. Suitable combination of promoter and micellar catalyst for kilo fold rate acceleration on benzaldehyde to benzoic acid conversion in aqueous media at room temperature: A kinetic approach

    NASA Astrophysics Data System (ADS)

    Ghosh, Aniruddha; Saha, Rumpa; Ghosh, Sumanta K.; Mukherjee, Kakali; Saha, Bidyut

    2013-05-01

    The kinetics of oxidation of benzaldehyde by chromic acid in aqueous and aqueous surfactant (sodium dodecyl sulfate, SDS, alkyl phenyl polyethylene glycol, Triton X-100 and N-cetylpyridinium chloride, CPC) media have been investigated in the presence of promoter at 303 K. The pseudo-first-order rate constants (kobs) were determined from a logarithmic plot of absorbance as a function time. The rate constants were found to increase with introduction of heteroaromatic nitrogen base promoters such as Picolinic acid (PA), 2,2'-bipyridine (bipy) and 1,10-phenanthroline (phen). The product benzoic acid has been characterized by conventional melting point experiment, NMR, HRMS and FTIR spectral analysis. The mechanism of both unpromoted and promoted reaction path has been proposed for the reaction. In presence of the anionic surfactant SDS, cationic surfactant CPC and neutral surfactant TX-100 the reaction can undergo simultaneously in both aqueous and micellar phase with an enhanced rate of oxidation in the micellar phase. Both SDS and TX-100 produce normal micellar effect whereas CPC produce reverse micellar effect in the presence of benzaldehyde. The observed net enhancement of rate effects has been explained by considering the hydrophobic and electrostatic interaction between the surfactants and reactants. SDS and bipy combination is the suitable one for benzaldehyde oxidation.

  4. Problem with nonequilibrium boundary conditions in the kinetic theory of gases

    NASA Astrophysics Data System (ADS)

    Aristov, V. V.; Zabelok, S. A.; Fedosov, M. A.; Frolova, A. A.

    2016-05-01

    The Boltzmann kinetic equation is considered in a new formulation with nonequilibrium distribution functions on free boundaries, which makes it possible to simulate nonequilibrium superand subsonic flows. Transport processes for such flows are analyzed. The possibility of anomalous transport is determined, in which case the heat flux, temperature gradient, and the corresponding components of the nonequilibrium stress tensor and the velocity gradient have the same sign.

  5. Chirality and protein folding

    NASA Astrophysics Data System (ADS)

    Kwiecinska, Joanna I.; Cieplak, Marek

    2005-05-01

    There are several simple criteria of folding to a native state in model proteins. One of them involves crossing of a threshold value of the root mean square deviation distance away from the native state. Another checks whether all native contacts are established, i.e. whether the interacting amino acids come closer than some characteristic distance. We use Go-like models of proteins and show that such simple criteria may prompt one to declare folding even though fragments of the resulting conformations have a wrong sense of chirality. We propose that a better condition of folding should augment the simple criteria with the requirement that most of the local values of the chirality should be nearly native. The kinetic discrepancy between the simple and compound criteria can be substantially reduced in the Go-like models by providing the Hamiltonian with a term which favours native values of the local chirality. We study the effects of this term as a function of its amplitude and compare it to other models such as ones with side groups and ones with angle-dependent potentials.

  6. Quantifying Nonnative Interactions in the Protein-Folding Free-Energy Landscape.

    PubMed

    Mouro, Paulo Ricardo; de Godoi Contessoto, Vinícius; Chahine, Jorge; Junio de Oliveira, Ronaldo; Pereira Leite, Vitor Barbanti

    2016-07-26

    Protein folding is a central problem in biological physics. Energetic roughness is an important aspect that controls protein-folding stability and kinetics. The roughness is associated with conflicting interactions in the protein and is also known as frustration. Recent studies indicate that an addition of a small amount of energetic frustration may enhance folding speed for certain proteins. In this study, we have investigated the conditions under which frustration increases the folding rate. We used a Cα structure-based model to simulate a group of proteins. We found that the free-energy barrier at the transition state (ΔF) correlates with nonnative-contact variation (ΔA), and the simulated proteins are clustered according to their fold motifs. These findings are corroborated by the Clementi-Plotkin analytical model. As a consequence, the optimum frustration regime for protein folding can be predicted analytically. PMID:27463131

  7. Basic kinetic wealth-exchange models: common features and open problems

    NASA Astrophysics Data System (ADS)

    Patriarca, M.; Heinsalu, E.; Chakraborti, A.

    2010-01-01

    We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65, 293 (1986); J. Math. Sociol. 26, 217 (2002)], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35, 735 (1988)], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000)], and of Dragulescu and Yakovenko [A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 17, 723 (2000)]. Analytical fitting forms for the equilibrium wealth distributions are proposed. The influence of heterogeneity is investigated, the appearance of the fat tail in the wealth distribution and the relaxation to equilibrium are discussed. A unified reformulation of the models considered is suggested.

  8. Pseudoknots in RNA folding landscapes

    PubMed Central

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

    2016-01-01

    Motivation: The function of an RNA molecule is not only linked to its native structure, which is usually taken to be the ground state of its folding landscape, but also in many cases crucially depends on the details of the folding pathways such as stable folding intermediates or the timing of the folding process itself. To model and understand these processes, it is necessary to go beyond ground state structures. The study of rugged RNA folding landscapes holds the key to answer these questions. Efficient coarse-graining methods are required to reduce the intractably vast energy landscapes into condensed representations such as barrier trees or basin hopping graphs (BHG) that convey an approximate but comprehensive picture of the folding kinetics. So far, exact and heuristic coarse-graining methods have been mostly restricted to the pseudoknot-free secondary structures. Pseudoknots, which are common motifs and have been repeatedly hypothesized to play an important role in guiding folding trajectories, were usually excluded. Results: We generalize the BHG framework to include pseudoknotted RNA structures and systematically study the differences in predicted folding behavior depending on whether pseudoknotted structures are allowed to occur as folding intermediates or not. We observe that RNAs with pseudoknotted ground state structures tend to have more pseudoknotted folding intermediates than RNAs with pseudoknot-free ground state structures. The occurrence and influence of pseudoknotted intermediates on the folding pathway, however, appear to depend very strongly on the individual RNAs so that no general rule can be inferred. 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

  9. Kinetic and thermodynamic treatment for the Rayleigh flow problem of an inhomogeneous charged gas mixture

    NASA Astrophysics Data System (ADS)

    Abourabia, Aly Maher; Abdel Wahid, Taha Zakaraia

    2012-03-01

    The extension of our previous paper [Can. J. Phys., 88 (2010), 501-511] has been made for an inhomogeneous charged rarefied gas mixture (two components plasma) instead of a single electron gas. In the present work, the kinetic and the irreversible thermodynamic properties of the plasma are presented from the molecular point of view. Our study is based on the solution of the BGK (Bhatnager-Gross-Krook) model of the Boltzmann kinetic equation together with the Maxwell's equations for both positive ions and electrons in the vicinity of a moving rigid plane. The fundamental aim of this investigation is to illustrate the mutual effects caused by collisions on the distribution functions. The distinction and comparisons between the perturbed and the equilibrium velocity distribution functions are illustrated for both electrons and ions. The ratios between the different contributions of the internal energy changes are predicted via the Gibbs's equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory Argon plasma.

  10. Reaction kinetics in zeolites as a random walk problem: Theory versus experiment

    NASA Astrophysics Data System (ADS)

    Barzykin, A. V.; Hashimoto, S.

    2000-08-01

    We present a continuous time random walk (CTRW) model for the kinetics of pseudo-first-order long-range reactions in zeolites assisted by migration between the adsorption sites. Both Markovian and non-Markovian formulations admit a simple matrix solution in terms of the lattice Green's function. Diffuse-reflectance transient absorption study of triplet anthracene quenching by azulene in NaY zeolite is reported giving a direct visual indication of the long-range reaction between molecules residing in the neighboring cages, reflecting an open structure of the cage network. The Markovian model with unbiased nearest-neighbor CTRW on a diamond lattice of NaY supercages explains the experimental decay data. This practical example demonstrates a general possibility to consistently recover information about intercage transport in zeolites and related microporous materials by using an indicator reaction and an appropriate theoretical interpretation, complementary to conventional NMR techniques.

  11. Reduced alphabet for protein folding prediction.

    PubMed

    Huang, Jitao T; Wang, Titi; Huang, Shanran R; Li, Xin

    2015-04-01

    What are the key building blocks that would have been needed to construct complex protein folds? This is an important issue for understanding protein folding mechanism and guiding de novo protein design. Twenty naturally occurring amino acids and eight secondary structures consist of a 28-letter alphabet to determine folding kinetics and mechanism. Here we predict folding kinetic rates of proteins from many reduced alphabets. We find that a reduced alphabet of 10 letters achieves good correlation with folding rates, close to the one achieved by full 28-letter alphabet. Many other reduced alphabets are not significantly correlated to folding rates. The finding suggests that not all amino acids and secondary structures are equally important for protein folding. The foldable sequence of a protein could be designed using at least 10 folding units, which can either promote or inhibit protein folding. Reducing alphabet cardinality without losing key folding kinetic information opens the door to potentially faster machine learning and data mining applications in protein structure prediction, sequence alignment and protein design. PMID:25641420

  12. Application of a four-step HMX kinetic model to an impact-induced fraction ignition problems

    SciTech Connect

    Perry, William L; Gunderson, Jake A; Dickson, Peter M

    2010-01-01

    There has been a long history of interest in the decomposition kinetics of HMX and HMX-based formulations due to the widespread use of this explosive in high performance systems. The kinetics allow us to predict, or attempt to predict, the behavior of the explosive when subjected to thermal hazard scenarios that lead to ignition via impact, spark, friction or external heat. The latter, commonly referred to as 'cook off', has been widely studied and contemporary kinetic and transport models accurately predict time and location of ignition for simple geometries. However, there has been relatively little attention given to the problem of localized ignition that results from the first three ignition sources of impact, spark and friction. The use of a zero-order single-rate expression describing the exothermic decomposition of explosives dates to the early work of Frank-Kamanetskii in the late 1930s and continued through the 60's and 70's. This expression provides very general qualitative insight, but cannot provide accurate spatial or timing details of slow cook off ignition. In the 70s, Catalano, et al., noted that single step kinetics would not accurately predict time to ignition in the one-dimensional time to explosion apparatus (ODTX). In the early 80s, Tarver and McGuire published their well-known three step kinetic expression that included an endothermic decomposition step. This scheme significantly improved the accuracy of ignition time prediction for the ODTX. However, the Tarver/McGuire model could not produce the internal temperature profiles observed in the small-scale radial experiments nor could it accurately predict the location of ignition. Those factors are suspected to significantly affect the post-ignition behavior and better models were needed. Brill, et al. noted that the enthalpy change due to the beta-delta crystal phase transition was similar to the assumed endothermic decomposition step in the Tarver/McGuire model. Henson, et al., deduced the

  13. Unfolded protein ensembles, folding trajectories, and refolding rate prediction.

    PubMed

    Das, A; Sin, B K; Mohazab, A R; Plotkin, S S

    2013-09-28

    Computer simulations can provide critical information on the unfolded ensemble of proteins under physiological conditions, by explicitly characterizing the geometrical properties of the diverse conformations that are sampled in the unfolded state. A general computational analysis across many proteins has not been implemented however. Here, we develop a method for generating a diverse conformational ensemble, to characterize properties of the unfolded states of intrinsically disordered or intrinsically folded proteins. The method allows unfolded proteins to retain disulfide bonds. We examined physical properties of the unfolded ensembles of several proteins, including chemical shifts, clustering properties, and scaling exponents for the radius of gyration with polymer length. A problem relating simulated and experimental residual dipolar couplings is discussed. We apply our generated ensembles to the problem of folding kinetics, by examining whether the ensembles of some proteins are closer geometrically to their folded structures than others. We find that for a randomly selected dataset of 15 non-homologous 2- and 3-state proteins, quantities such as the average root mean squared deviation between the folded structure and unfolded ensemble correlate with folding rates as strongly as absolute contact order. We introduce a new order parameter that measures the distance travelled per residue, which naturally partitions into a smooth "laminar" and subsequent "turbulent" part of the trajectory. This latter conceptually simple measure with no fitting parameters predicts folding rates in 0 M denaturant with remarkable accuracy (r = -0.95, p = 1 × 10(-7)). The high correlation between folding times and sterically modulated, reconfigurational motion supports the rapid collapse of proteins prior to the transition state as a generic feature in the folding of both two-state and multi-state proteins. This method for generating unfolded ensembles provides a powerful approach to

  14. Unfolded protein ensembles, folding trajectories, and refolding rate prediction

    NASA Astrophysics Data System (ADS)

    Das, A.; Sin, B. K.; Mohazab, A. R.; Plotkin, S. S.

    2013-09-01

    Computer simulations can provide critical information on the unfolded ensemble of proteins under physiological conditions, by explicitly characterizing the geometrical properties of the diverse conformations that are sampled in the unfolded state. A general computational analysis across many proteins has not been implemented however. Here, we develop a method for generating a diverse conformational ensemble, to characterize properties of the unfolded states of intrinsically disordered or intrinsically folded proteins. The method allows unfolded proteins to retain disulfide bonds. We examined physical properties of the unfolded ensembles of several proteins, including chemical shifts, clustering properties, and scaling exponents for the radius of gyration with polymer length. A problem relating simulated and experimental residual dipolar couplings is discussed. We apply our generated ensembles to the problem of folding kinetics, by examining whether the ensembles of some proteins are closer geometrically to their folded structures than others. We find that for a randomly selected dataset of 15 non-homologous 2- and 3-state proteins, quantities such as the average root mean squared deviation between the folded structure and unfolded ensemble correlate with folding rates as strongly as absolute contact order. We introduce a new order parameter that measures the distance travelled per residue, which naturally partitions into a smooth "laminar" and subsequent "turbulent" part of the trajectory. This latter conceptually simple measure with no fitting parameters predicts folding rates in 0 M denaturant with remarkable accuracy (r = -0.95, p = 1 × 10-7). The high correlation between folding times and sterically modulated, reconfigurational motion supports the rapid collapse of proteins prior to the transition state as a generic feature in the folding of both two-state and multi-state proteins. This method for generating unfolded ensembles provides a powerful approach to

  15. In-Space Propulsion, Logistics Reduction, and Evaluation of Steam Reformer Kinetics: Problems and Prospects

    NASA Technical Reports Server (NTRS)

    Jaworske, D. A.; Palaszewski, B. A.; Kulis, M. J.; Gokoglu, S. A.

    2015-01-01

    Human space missions generate waste materials. A 70-kg crewmember creates a waste stream of 1 kg per day, and a four-person crew on a deep space habitat for a 400+ day mission would create over 1600 kg of waste. Converted into methane, the carbon could be used as a fuel for propulsion or power. The NASA Advanced Exploration Systems (AES) Logistics Reduction and Repurposing (LRR) project is investing in space resource utilization with an emphasis on repurposing logistics materials for useful purposes and has selected steam reforming among many different competitive processes as the preferred method for repurposing organic waste into methane. Already demonstrated at the relevant processing rate of 5.4 kg of waste per day, high temperature oxygenated steam consumes waste and produces carbon dioxide, carbon monoxide, and hydrogen which can then be converted into methane catalytically. However, the steam reforming process has not been studied in microgravity. Data are critically needed to understand the mechanisms that allow use of steam reforming in a reduced gravity environment. This paper reviews the relevant literature, identifies gravity-dependent mechanisms within the steam gasification process, and describes an innovative experiment to acquire the crucial kinetic information in a small-scale reactor specifically designed to operate within the requirements of a reduced gravity aircraft flight. The experiment will determine if the steam reformer process is mass-transport limited, and if so, what level of forced convection will be needed to obtain performance comparable to that in 1-g.

  16. Cooperativity in protein-folding kinetics.

    PubMed Central

    Dill, K A; Fiebig, K M; Chan, H S

    1993-01-01

    How does a protein find its native state without a globally exhaustive search? We propose the "HZ" (hydrophobic zipper) hypothesis: hydrophobic contacts act as constraints that bring other contacts into spatial proximity, which then further constrain and zip up the next contacts, etc. In contrast to helix-coil cooperativity, HZ-heteropolymer collapse cooperativity is driven by nonlocal interactions, causes sheet and irregular conformations in addition to helices, leads to secondary structures concurrently with early hydrophobic core formation, is much more sequence dependent than helix-coil processes, and involves compact intermediate states that have much secondary--but little tertiary--structure. Hydrophobic contacts in the 1992 Protein Data Bank have the type of "topological localness" predicted by the hypothesis. The HZ paths for amino acid sequences that mimic crambin and bovine pancreatic trypsin inhibitor are quickly found by computer; the best configurations thus reached have single hydrophobic cores that are within about 3 kcal/mol of the global minimum. This hypothesis shows how proteins could find globally optimal states without exhaustive search. Images Fig. 3 PMID:7680482

  17. Improving protein fold recognition by random forest

    PubMed Central

    2014-01-01

    Background Recognizing the correct structural fold among known template protein structures for a target protein (i.e. fold recognition) is essential for template-based protein structure modeling. Since the fold recognition problem can be defined as a binary classification problem of predicting whether or not the unknown fold of a target protein is similar to an already known template protein structure in a library, machine learning methods have been effectively applied to tackle this problem. In our work, we developed RF-Fold that uses random forest - one of the most powerful and scalable machine learning classification methods - to recognize protein folds. Results RF-Fold consists of hundreds of decision trees that can be trained efficiently on very large datasets to make accurate predictions on a highly imbalanced dataset. We evaluated RF-Fold on the standard Lindahl's benchmark dataset comprised of 976 × 975 target-template protein pairs through cross-validation. Compared with 17 different fold recognition methods, the performance of RF-Fold is generally comparable to the best performance in fold recognition of different difficulty ranging from the easiest family level, the medium-hard superfamily level, and to the hardest fold level. Based on the top-one template protein ranked by RF-Fold, the correct recognition rate is 84.5%, 63.4%, and 40.8% at family, superfamily, and fold levels, respectively. Based on the top-five template protein folds ranked by RF-Fold, the correct recognition rate increases to 91.5%, 79.3% and 58.3% at family, superfamily, and fold levels. Conclusions The good performance achieved by the RF-Fold demonstrates the random forest's effectiveness for protein fold recognition. PMID:25350499

  18. Folding of proteins with diverse folds.

    PubMed

    Mohanty, Sandipan; Hansmann, Ulrich H E

    2006-11-15

    Using parallel tempering simulations with high statistics, we investigate the folding and thermodynamic properties of three small proteins with distinct native folds: the all-helical 1RIJ, the all-sheet beta3s, and BBA5, which has a mixed helix-sheet fold. In all three cases, simulations with our energy function find the native structures as global minima in free energy at experimentally relevant temperatures. However, the folding process strongly differs for the three molecules, indicating that the folding mechanism is correlated with the form of the native structure. PMID:16950845

  19. Stochastic Resonance in Protein Folding Dynamics.

    PubMed

    Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A

    2016-05-01

    Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics. PMID:26992148

  20. 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

  1. 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.

  2. Polymer principles and protein folding.

    PubMed Central

    Dill, K. A.

    1999-01-01

    This paper surveys the emerging role of statistical mechanics and polymer theory in protein folding. In the polymer perspective, the folding code is more a solvation code than a code of local phipsi propensities. The polymer perspective resolves two classic puzzles: (1) the Blind Watchmaker's Paradox that biological proteins could not have originated from random sequences, and (2) Levinthal's Paradox that the folded state of a protein cannot be found by random search. Both paradoxes are traditionally framed in terms of random unguided searches through vast spaces, and vastness is equated with impossibility. But both processes are partly guided. The searches are more akin to balls rolling down funnels than balls rolling aimlessly on flat surfaces. In both cases, the vastness of the search is largely irrelevant to the search time and success. These ideas are captured by energy and fitness landscapes. Energy landscapes give a language for bridging between microscopics and macroscopics, for relating folding kinetics to equilibrium fluctuations, and for developing new and faster computational search strategies. PMID:10386867

  3. Let Them Fold

    ERIC Educational Resources Information Center

    Grant, Nicholas; Tobin, Alexander

    1972-01-01

    Directions are given for seven activities involving the folding of paper strips to illustrate geometric concepts. Properties of pentagons, triangles, hexagons, and Mobius bands resulting from the various foldings are discussed. (DT)

  4. Mechanics of Curved Folds

    NASA Astrophysics Data System (ADS)

    Dias, Marcelo A.; Santangelo, Christian D.

    2011-03-01

    Despite an almost two thousand year history, origami, the art of folding paper, remains a challenge both artistically and scientifically. Traditionally, origami is practiced by folding along straight creases. A whole new set of shapes can be explored, however, if, instead of straight creases, one folds along arbitrary curves. We present a mechanical model for curved fold origami in which the energy of a plastically-deformed crease is balanced by the bending energy of developable regions on either side of the crease. Though geometry requires that a sheet buckle when folded along a closed curve, its shape depends on the elasticity of the sheet. NSF DMR-0846582.

  5. Teaching polymers to fold

    SciTech Connect

    Judson, R.S. )

    1992-12-10

    A new method is presented for predicting folding pathways of polymers. The folding pathway is described as a generic program or sequence of logical steps of such a form that a computer can carry them out to produce a folded structure. A genetic (GA) is used to learn specific sequences or folding pathways that carry a denatured conformation into a target final conformation. The method is demonstrated on a model 2-dimensional polymer for which the global energy minimum is known. The GA learns a program that will fold a denatured polymer into its global energy minimum conformation. 27 refs., 4 figs.

  6. 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

  7. Single-molecule Studies of Riboswitch Folding

    PubMed Central

    Savinov, Andrew; Perez, Christian F.; Block, Steven M.

    2014-01-01

    The folding dynamics of riboswitches are central to their ability to modulate gene expression in response to environmental cues. In most cases, a structural competition between the formation of a ligand-binding aptamer and an expression platform (or some other competing off-state) determines the regulatory outcome. Here, we review single-molecule studies of riboswitch folding and function, predominantly carried out using single-molecule FRET or optical trapping approaches. Recent results have supplied new insights into riboswitch folding energy landscapes, the mechanisms of ligand binding, the roles played by divalent ions, the applicability of hierarchical folding models, and kinetic vs. thermodynamic control schemes. We anticipate that future work, based on improved data sets and potentially combining multiple experimental techniques, will enable the development of more complete models for complex RNA folding processes. PMID:24727093

  8. STIS MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2013-10-01

    The performance of MAMA microchannel plates can be monitored using a MAMA fold distribution procedure. The fold distribution provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of change in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the STIS MAMA Fold Distribution, Proposal 13149, as Cycle 20.

  9. STIS MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2012-10-01

    The performance of MAMA microchannel plates can be monitored using a MAMA fold distribution procedure. The fold distribution provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of change in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the STIS MAMA Fold Distribution, Proposal 12778, as Cycle 19.

  10. STIS MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2010-09-01

    The performance of MAMA microchannel plates can be monitored using a MAMA fold analysis procedure. The fold analysis provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of changes in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the STIS MAMA Fold Analysis {11863} during Cycle 17.

  11. STIS MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2011-10-01

    The performance of MAMA microchannel plates can be monitored using a MAMA fold analysis procedure. The fold analysis provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of changes in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the STIS MAMA Fold Analysis, Proposal 12416, as Cycle 18.

  12. 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. PMID:19937658

  13. Effects of Knots on Protein Folding Properties

    PubMed Central

    Soler, Miguel A.; Faísca, Patrícia F. N.

    2013-01-01

    This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation. PMID:24023962

  14. Who solved the protein folding problem?

    PubMed

    Sippl, M J

    1999-04-15

    For the third time, techniques for the prediction of three-dimensional structures of proteins were critically assessed in a worldwide blind test. Steady progress is undeniable. How did this happen and what are the implications? PMID:10196132

  15. Multiply folded graphene

    NASA Astrophysics Data System (ADS)

    Kim, Kwanpyo; Lee, Zonghoon; Malone, Brad D.; Chan, Kevin T.; Alemán, Benjamín; Regan, William; Gannett, Will; Crommie, M. F.; Cohen, Marvin L.; Zettl, A.

    2011-06-01

    The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material, folding may transform it to complex shapes with new and distinct properties. Here, we present experimental results that folded structures in graphene, termed grafold, exist, and their formations can be controlled by introducing anisotropic surface curvature during graphene synthesis or transfer processes. Using pseudopotential-density-functional-theory calculations, we also show that double folding modifies the electronic band structure of graphene. Furthermore, we demonstrate the intercalation of C60 into the grafolds. Intercalation or functionalization of the chemically reactive folds further expands grafold's mechanical, chemical, optical, and electronic diversity.

  16. Folding of a miniprotein with mixed fold.

    PubMed

    Mohanty, Sandipan; Hansmann, U H E

    2007-07-21

    Using the 28 residue betabetaalpha protein FSD-EY as a target system, we examine correction terms for the ECEPP/3 force field. We find an increased probability of formation of the native state at low temperatures resulting from a reduced propensity to form alpha helices and increased formation of beta sheets. Our analysis of the observed folding events suggests that the C-terminal helix of FSD-EY is much more stable than the N-terminal beta hairpin and forms first. The hydrophobic groups of the helix provide a template which promotes the formation of the beta hairpin that is never observed to form without the helix. PMID:17655464

  17. Protein folding and misfolding: mechanism and principles.

    PubMed

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

    2007-11-01

    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

  18. Learning Protein Folding Energy Functions

    PubMed Central

    Guan, Wei; Ozakin, Arkadas; Gray, Alexander; Borreguero, Jose; Pandit, Shashi; Jagielska, Anna; Wroblewska, Liliana; Skolnick, Jeffrey

    2014-01-01

    A critical open problem in ab initio protein folding is protein energy function design, which pertains to defining the energy of protein conformations in a way that makes folding most efficient and reliable. In this paper, we address this issue as a weight optimization problem and utilize a machine learning approach, learning-to-rank, to solve this problem. We investigate the ranking-via-classification approach, especially the RankingSVM method and compare it with the state-of-the-art approach to the problem using the MINUIT optimization package. To maintain the physicality of the results, we impose non-negativity constraints on the weights. For this we develop two efficient non-negative support vector machine (NNSVM) methods, derived from L2-norm SVM and L1-norm SVMs, respectively. We demonstrate an energy function which maintains the correct ordering with respect to structure dissimilarity to the native state more often, is more efficient and reliable for learning on large protein sets, and is qualitatively superior to the current state-of-the-art energy function. PMID:25311546

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    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.

  20. Folding pathways of the Tetrahymena ribozyme

    PubMed Central

    Mitchell, David; Russell, Rick

    2014-01-01

    Like many structured RNAs, the Tetrahymena group I intron ribozyme folds through multiple pathways and intermediates. Under standard conditions in vitro, a small fraction reaches the native state (N) with kobs ≈ 0.6 min–1, while the remainder forms a long-lived misfolded conformation (M) thought to differ in topology. These alternative outcomes reflect a pathway that branches late in folding, after disruption of a trapped intermediate (Itrap). Here, we use catalytic activity to probe the folding transitions from Itrap to the native and misfolded states. We show that mutations predicted to weaken the core helix P3 do not increase the rate of folding from Itrap but they increase the fraction that reaches the native state rather than forming the misfolded state. Thus, P3 is disrupted during folding to the native state but not to the misfolded state, and P3 disruption occurs after the rate-limiting step. Interestingly, P3-strengthening mutants also increase native folding. Additional experiments show that these mutants are rapidly committed to folding to the native state, although they reach the native state with approximately the same rate constant as the wild-type ribozyme (~1 min–1). Thus, the P3-strengthening mutants populate a distinct pathway that includes at least one intermediate but avoids the M state, most likely because P3 and the correct topology are formed early. Our results highlight multiple pathways in RNA folding and illustrate how kinetic competitions between rapid events can have long-lasting effects because the ‘choice’ is enforced by energy barriers that grow larger as folding progresses. PMID:24747051

  1. Programmable matter by folding

    PubMed Central

    Hawkes, E.; An, B.; Benbernou, N. M.; Tanaka, H.; Kim, S.; Demaine, E. D.; Rus, D.; Wood, R. J.

    2010-01-01

    Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. This concept requires constituent elements to interact and rearrange intelligently in order to meet the goal. This paper considers achieving programmable sheets that can form themselves in different shapes autonomously by folding. Past approaches to creating transforming machines have been limited by the small feature sizes, the large number of components, and the associated complexity of communication among the units. We seek to mitigate these difficulties through the unique concept of self-folding origami with universal crease patterns. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. To implement this self-folding origami concept, we have developed a scalable end-to-end planning and fabrication process. Given a set of desired objects, the system computes an optimized design for a single sheet and multiple controllers to achieve each of the desired objects. The material, called programmable matter by folding, is an example of a system capable of achieving multiple shapes for multiple functions. PMID:20616049

  2. Folding without charges

    PubMed Central

    Kurnik, Martin; Hedberg, Linda; Danielsson, Jens; Oliveberg, Mikael

    2012-01-01

    Surface charges of proteins have in several cases been found to function as “structural gatekeepers,” which avoid unwanted interactions by negative design, for example, in the control of protein aggregation and binding. The question is then if side-chain charges, due to their desolvation penalties, play a corresponding role in protein folding by avoiding competing, misfolded traps? To find out, we removed all 32 side-chain charges from the 101-residue protein S6 from Thermus thermophilus. The results show that the charge-depleted S6 variant not only retains its native structure and cooperative folding transition, but folds also faster than the wild-type protein. In addition, charge removal unleashes pronounced aggregation on longer timescales. S6 provides thus an example where the bias toward native contacts of a naturally evolved protein sequence is independent of charges, and point at a fundamental difference in the codes for folding and intermolecular interaction: specificity in folding is governed primarily by hydrophobic packing and hydrogen bonding, whereas solubility and binding relies critically on the interplay of side-chain charges. PMID:22454493

  3. Folding a protein by discretizing its backbone torsional dynamics

    NASA Astrophysics Data System (ADS)

    Fernández, Ariel

    1999-05-01

    The aim of this work is to provide a coarse codification of local conformational constraints associated with each folding motif of a peptide chain in order to obtain a rough solution to the protein folding problem. This is accomplished by implementing a discretized version of the soft-mode dynamics on a personal computer (PC). Our algorithm mimics a parallel process as it evaluates concurrent folding possibilities by pattern recognition. It may be implemented in a PC as a sequence of perturbation-translation-renormalization (p-t-r) cycles performed on a matrix of local topological constraints (LTM). This requires suitable representational tools and a periodic quenching of the dynamics required for renormalization. We introduce a description of the peptide chain based on a local discrete variable the values of which label the basins of attraction of the Ramachandran map for each residue. Thus, the local variable indicates the basin in which the torsional coordinates of each residue lie at a given time. In addition, a coding of local topological constraints associated with each secondary and tertiary structural motif is introduced. Our treatment enables us to adopt a computation time step of 81 ps, a value far larger than hydrodynamic drag time scales. Folding pathways are resolved as transitions between patterns of locally encoded structural signals that change within the 10 μs-100 ms time scale range. These coarse folding pathways are generated by the periodic search for structural patterns in the time-evolving LTM. Each pattern is recorded as a contact matrix, an operation subject to a renormalization feedback loop. The validity of our approach is tested vis-a-vis experimentally-probed folding pathways eventually generating tertiary interactions in proteins which recover their active structure under in vitro renaturation conditions. As an illustration, we focus on determining significant folding intermediates and late kinetic bottlenecks that occur within the

  4. Visualizing chaperone-assisted protein folding.

    PubMed

    Horowitz, Scott; Salmon, Loïc; Koldewey, Philipp; Ahlstrom, Logan S; Martin, Raoul; Quan, Shu; Afonine, Pavel V; van den Bedem, Henry; Wang, Lili; Xu, Qingping; Trievel, Raymond C; Brooks, Charles L; Bardwell, James C A

    2016-07-01

    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 chaperone 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. PMID:27239796

  5. Hydrogen Bonds in Polymer Folding

    NASA Astrophysics Data System (ADS)

    Borg, Jesper; Jensen, Mogens H.; Sneppen, Kim; Tiana, Guido

    2001-02-01

    We studied the thermodynamics of a homopolymeric chain with both van der Waals and directed hydrogen bond interaction. The effect of hydrogen bonds is to reduce dramatically the entropy of low-lying states and to give rise to long-range order and to conformations displaying secondary structures. For compact polymers a transition is found between helix-rich states and low-entropy sheet-dominated states. The consequences of this transition for protein folding and, in particular, for the problem of prions are discussed.

  6. Synthesizing folded band chaos.

    PubMed

    Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

    2007-04-01

    A randomly driven linear filter that synthesizes Lorenz-like, reverse-time chaos is shown also to produce Rössler-like folded band wave forms when driven using a different encoding of the random source. The relationship between the topological entropy of the random source, dissipation in the linear filter, and the positive Lyapunov exponent for the reverse-time wave form is exposed. The two drive encodings are viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing both the Lorenz butterfly and Rössler folded band paradigms of nonlinear dynamics. PMID:17500950

  7. Design principles for rapid folding of knotted DNA nanostructures.

    PubMed

    Kočar, Vid; Schreck, John S; Čeru, Slavko; Gradišar, Helena; Bašić, Nino; Pisanski, Tomaž; Doye, Jonathan P K; Jerala, Roman

    2016-01-01

    Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the 'free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. PMID:26887681

  8. Prediction of protein folding rates from simplified secondary structure alphabet.

    PubMed

    Huang, Jitao T; Wang, Titi; Huang, Shanran R; Li, Xin

    2015-10-21

    Protein folding is a very complicated and highly cooperative dynamic process. However, the folding kinetics is likely to depend more on a few key structural features. Here we find that secondary structures can determine folding rates of only large, multi-state folding proteins and fails to predict those for small, two-state proteins. The importance of secondary structures for protein folding is ordered as: extended β strand > α helix > bend > turn > undefined secondary structure>310 helix > isolated β strand > π helix. Only the first three secondary structures, extended β strand, α helix and bend, can achieve a good correlation with folding rates. This suggests that the rate-limiting step of protein folding would depend upon the formation of regular secondary structures and the buckling of chain. The reduced secondary structure alphabet provides a simplified description for the machine learning applications in protein design. PMID:26247139

  9. Design principles for rapid folding of knotted DNA nanostructures

    PubMed Central

    Kočar, Vid; Schreck, John S.; Čeru, Slavko; Gradišar, Helena; Bašić, Nino; Pisanski, Tomaž; Doye, Jonathan P. K.; Jerala, Roman

    2016-01-01

    Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. PMID:26887681

  10. Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part II. Computation problems and validation on INCONEL 718 superalloy castings

    NASA Astrophysics Data System (ADS)

    Nastac, L.; Stefanescu, D. M.

    1996-12-01

    In Part I of the article, a new analytical model that describes solidification of equiaxed dendrites was presented. In this part of the article, the model is used to simulate the solidification of INCONEL 718 superalloy castings. The model was incorporated into a commercial finite-element code, PROCAST. A special procedure called microlatent heat method (MLHM) was used for coupling between macroscopic heat flow and microscopic growth kinetics. A criterion for time-stepping selection in microscopic modeling has been derived in conjunction with MLHM. Reductions in computational (CPU) time up to 90 pct over the classic latent heat method were found by adopting this coupling. Validation of the model was performed against experimental data for an INCONEL 718 superalloy casting. In the present calculations, the model for globulitic dendrite was used. The evolution of fraction of solid calculated with the present model was compared with Scheil’s model and experiments. An important feature in solidification of INCONEL 718 is the detrimental Laves phase. Laves phase content is directly related to the intensity of microsegregation of niobium, which is very sensitive to the evolution of the fraction of solid. It was found that there is a critical cooling rate at which the amount of Laves phase is maximum. The critical cooling rate is not a function of material parameters (diffusivity, partition coefficient, etc.). It depends only on the grain size and solidification time. The predictions generated with the present model are shown to agree very well with experiments.

  11. Macrotransport-solidification kinetics modeling of equiaxed dendritic growth. Part 2: Computation problems and validation on INCONEL 718 superalloy castings

    SciTech Connect

    Nastac, L.; Stefanescu, D.M.

    1996-12-01

    In Part 1 of the article, a new analytical model that describes solidification of equiaxed dendrites was presented. In this part of the article, the model is used to simulate the solidification of INCONEL 718 superalloy castings. The model was incorporated into a commercial finite-element code, PROCAST. A special procedure called microlatent heat method (MLHM) was used for coupling between macroscopic heat flow and microscopic growth kinetics. A criterion for time-stepping selection in microscopic modeling has been derived in conjunction with MLHM. Reductions in computational (CPU) time up to 90 pct over the classic latent heat method were found by adopting this coupling. Validation of the model was performed against experimental data for an INCONEL 718 superalloy casting. In the present calculations, the model for globulitic dendrite was used. The evolution of fraction of solid calculated with the present model was compared with Scheil`s model and experiments. An important feature in solidification of INCONEL 718 is the detrimental Laves phase. Laves phase content is directly related to the intensity of microsegregation of niobium, which is very sensitive to the evolution of the fraction of solid. It was found that thee is a critical cooling rate at which the amount of Laves phase is maximum. The critical cooling rate is not a function of material parameters (diffusivity, partition coefficient, etc.). It depends only on the grain size and solidification time. The predictions generated with the present model are shown to agree very well with experiments.

  12. 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.

  13. The uteroglobin fold.

    PubMed

    Callebaut, I; Poupon, A; Bally, R; Demaret, J P; Housset, D; Delettré, J; Hossenlopp, P; Mornon, J P

    2000-01-01

    Uteroglobin (UTG) forms a fascinating homodimeric structure that binds small- to medium-sized ligands through an internal hydrophobic cavity, located at the interface between the two monomers. Previous studies have shown that UTG fold is not limited to the UTG/CC10 family, whose sequence/structure relationships are highlighted here, but can be extended to the cap domain of Xanthobacter autotrophicus haloalkane dehalogenase. We show here that UTG fold is adopted by several other cap domains within the alpha/beta hydrolase family, making it a well-suited "geode" structure allowing it to sequester various hydrophobic molecules. Additionally, some data about a new crystal form of oxidized rabbit UTG are presented, completing previous structural studies, as well as results from molecular dynamics, suggesting an alternative way for the ligand to reach the internal cavity. PMID:11193783

  14. Folding funnels, binding funnels, and protein function.

    PubMed Central

    Tsai, C. J.; Kumar, S.; Ma, B.; Nussinov, R.

    1999-01-01

    , with a range of complexed conformations. Hence, knowledge of the shape of the folding funnels is biologically very useful. The converse also holds: If kinetic and thermodynamic data are available, hints regarding the role of the protein and its binding selectivity may be obtained. Thus, the utility of the concept of the funnel carries over to the origin of the protein and to its function. PMID:10386868

  15. The protein folding network

    NASA Astrophysics Data System (ADS)

    Rao, Francesco; Caflisch, Amedeo

    2004-03-01

    Networks are everywhere. The conformation space of a 20-residue antiparallel beta-sheet peptide [1], sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. As previously found for the World-Wide Web as well as for social and biological networks , the conformation space contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the network shows a hierarchical modularity [2] which is consistent with the funnel mechanism of folding [3] and is not observed for a random heteropolymer lacking a native state. Here we show that the conformation space network describes the free energy landscape without requiring projections into arbitrarily chosen reaction coordinates. The network analysis provides a basis for understanding the heterogeneity of the folding transition state and the existence of multiple pathways. [1] P. Ferrara and A. Caflisch, Folding simulations of a three-stranded antiparallel beta-sheet peptide, PNAS 97, 10780-10785 (2000). [2] Ravasz, E. and Barabási, A. L. Hierarchical organization in complex networks. Phys. Rev. E 67, 026112 (2003). [3] Dill, K. and Chan, H From Levinthal to pathways to funnels. Nature Struct. Biol. 4, 10-19 (1997)

  16. Ab initio RNA folding

    NASA Astrophysics Data System (ADS)

    Cragnolini, Tristan; Derreumaux, Philippe; Pasquali, Samuela

    2015-06-01

    RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

  17. Ab initio RNA folding.

    PubMed

    Cragnolini, Tristan; Derreumaux, Philippe; Pasquali, Samuela

    2015-06-17

    RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding. PMID:25993396

  18. Folding within seconds

    NASA Astrophysics Data System (ADS)

    Kenkmann, Thomas

    2002-03-01

    Hypervelocity impacts of cosmic projectiles larger than ˜200 m diameter are capable of forming complex craters on Earth. At these craters, shock loading, shock damage, and excavation flow are followed by a gravity-driven collapse of the deep transient cavity. Such impact structures are characterized by a central uplift, a flat crater floor, and a terraced crater rim. Collapse-induced deformation features, like folds and brittle fault zones, have many similarities to tectonic structures. Typical deformation patterns of complex terrestrial impact craters of 5 15 km diameter are compiled and analyzed with respect to their kinematic development. Unlike their tectonic counterparts, deformation structures are always the result of non-plane-strain deformation and are formed in a single event that takes place in seconds to minutes. To understand the high-strain-rate processes, the microstructure of an impact-induced fold of the Crooked Creek impact crater (˜7 km diameter), Missouri, United States, is investigated in detail. A period of 20 30 s at the most is determined for the collapse phase of this crater. The gross plastic deformation behavior of the fold is achieved by localized brittle deformation along millimeter- to centimeter-spaced fault zones, forming a network of veins. Shock damage has fractured ˜40% of grain boundaries. The onset of collapse and associated deformation started in rocks with a reduced cohesion and is friction controlled.

  19. Folded waveguide coupler

    DOEpatents

    Owens, Thomas L.

    1988-03-01

    A resonant cavity waveguide coupler for ICRH of a magnetically confined plasma. The coupler consists of a series of inter-leaved metallic vanes disposed withn an enclosure analogous to a very wide, simple rectangular waveguide that has been "folded" several times. At the mouth of the coupler, a polarizing plate is provided which has coupling apertures aligned with selected folds of the waveguide through which rf waves are launched with magnetic fields of the waves aligned in parallel with the magnetic fields confining the plasma being heated to provide coupling to the fast magnetosonic wave within the plasma in the frequency usage of from about 50-200 mHz. A shorting plate terminates the back of the cavity at a distance approximately equal to one-half the guide wavelength from the mouth of the coupler to ensure that the electric field of the waves launched through the polarizing plate apertures are small while the magnetic field is near a maximum. Power is fed into the coupler folded cavity by means of an input coaxial line feed arrangement at a point which provides an impedance match between the cavity and the coaxial input line.

  20. 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.

  1. Kinematics of constant arc length folding for different fold shapes

    NASA Astrophysics Data System (ADS)

    Ghassemi, Mohammad R.; Schmalholz, Stefan M.; Ghassemi, Ali R.

    2010-06-01

    Basic mathematical functions are applied for the two-dimensional geometrical and kinematical analysis of different fold shapes. Relationships between different fold parameters are established and related to the bulk shortening taking place during folding under upper crustal conditions. The bulk shortening taking place during constant arc length folding is mathematically related to the bulk shortening during homogenous pure shear using a particular aspect ratio, which is for folding the ratio of amplitude to half wavelength and for pure shear the ratio of vertical to horizontal length of the deformed, initially square body. The evolution of the fold aspect ratio with bulk shortening is similar for a wide range of fold shapes and indicates that the fold aspect ratio allows a good estimate of the bulk shortening. The change of the geometry of individual layers across a multilayer sequence in disharmonic folding indicates a specific kinematics of multilayer folding, referred to here as "wrap folding", which does not require significant flexural slip nor flexural flow. The kinematic analysis indicates that there is a critical value for constant arc length folding between shortening values of 30-40% (depending on the fold geometry). For shortening values smaller than the critical value limb rotation and fold amplitude growth are dominating. For shortening larger than this value, faulting, boudinage and foliation development are likely the dominating deformation process during continued shortening. The kinematical analysis of constant arc length folding can be used for estimating the bulk shortening taking place during multilayer folding which is an important component of the deformation of crustal rocks during the early history of shortening. The bulk shortening is estimated for a natural, multilayer detachment fold and the shortening estimates based on the kinematic analysis are compared and supported by numerical finite element simulations of multilayer detachment

  2. Information from folds: A review

    NASA Astrophysics Data System (ADS)

    Hudleston, Peter J.; Treagus, Susan H.

    2010-12-01

    Folds are spectacular geological structures that are seen in layered rock on many different scales. To mark 30 years of the Journal of Structural Geology, we review the information that can be gained from studies of folds in theory, experiment and nature. We first review theoretical considerations and modeling, from classical approaches to current developments. The subject is dominated by single-layer fold theory, with the assumption of perfect layer-parallel shortening, but we also review multilayer fold theory and modeling, and folding of layers that are oblique to principal stresses and strains. This work demonstrates that viscosity ratio, degree of non-linearity of the flow law, anisotropy, and the thickness and spacing distribution of layers of different competence are all important in determining the nature and strength of the folding instability. Theory and modeling provide the basis for obtaining rheological information from natural folds, through analysis of wavelength/thickness ratios of single layer folds, and fold shapes. They also provide a basis for estimating the bulk strain from folded layers. Information about folding mechanisms can be obtained by analysis of cleavage and fabric patterns in folded rocks, and the history of deformation can be revealed by understanding how asymmetry can develop in folds, by how folds develop in shear zones, and how folds develop in more complex three-dimensional deformations.

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

    PubMed Central

    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

  4. Folds on Europa

    NASA Technical Reports Server (NTRS)

    2000-01-01

    This image, acquired by NASA's Galileo spacecraft on September 26, 1998, shows features on the surface of Jupiter's moon Europa that a scientific report published today interprets as signs of compressive folding.

    The imaged area is in the Astypalaea Linea region of Europa's southern hemisphere, seen with low-angle sunshine coming from the upper right. North is toward the top.

    Astypalaea Linea is the smooth, gray area that stretches from north to south across the image mosaic. It is thought to have formed by a combination of pulling apart and sliding of the icy surface. The telltale fold features are within the smoother portions of the surface between the more dominant ridges, which are attributed to upwelling of material through surface ice. In the smooth areas, the surface has gentle swells and dips, which show most clearly in the version on the right, processed to accentuate broader-scale shapes. For example, a dip about 15 kilometers (about 10 miles) wide cuts diagonally across the northern half of the largest smooth area, and a rise runs parallel to that in the southern half of the smooth area. closeup detail

    Louise M. Prockter, at Johns Hopkins University, and Robert T. Pappalardo, at Brown University, report in the journal Science today that those rises, or anticlines, and dips, or synclines, appear to be the result of compression causing the crust to fold.

    Additional evidence comes from smaller features more visible in the version on the left, covering the same area. At the crest of the gentle rise in the largest smooth area are small fractures that could be caused by the stretching stress of bending the surface layer upwards. Similarly, at the bottom of the adjacent dip are small, wrinkle-like ridges that could be caused by stress from bending the surface layer downwards.

    The Jet Propulsion Laboratory, Pasadena, Calif., manages the Galileo mission for NASA's Office of Space Science, Washington, D.C. JPL is a division of the California

  5. Protein folding and protein metallocluster studies using synchrotron small angler X-ray scattering

    SciTech Connect

    Eliezer, D.

    1994-06-01

    Proteins, biological macromolecules composed of amino-acid building blocks, possess unique three dimensional shapes or conformations which are intimately related to their biological function. All of the information necessary to determine this conformation is stored in a protein`s amino acid sequence. The problem of understanding the process by which nature maps protein amino-acid sequences to three-dimensional conformations is known as the protein folding problem, and is one of the central unsolved problems in biophysics today. The possible applications of a solution are broad, ranging from the elucidation of thousands of protein structures to the rational modification and design of protein-based drugs. The scattering of X-rays by matter has long been useful as a tool for the characterization of physical properties of materials, including biological samples. The high photon flux available at synchrotron X-ray sources allows for the measurement of scattering cross-sections of dilute and/or disordered samples. Such measurements do not yield the detailed geometrical information available from crystalline samples, but do allow for lower resolution studies of dynamical processes not observable in the crystalline state. The main focus of the work described here has been the study of the protein folding process using time-resolved small-angle x-ray scattering measurements. The original intention was to observe the decrease in overall size which must accompany the folding of a protein from an extended conformation to its compact native state. Although this process proved too fast for the current time-resolution of the technique, upper bounds were set on the probable compaction times of several small proteins. In addition, an interesting and unexpected process was detected, in which the folding protein passes through an intermediate state which shows a tendency to associate. This state is proposed to be a kinetic molten globule folding intermediate.

  6. Improving Protein Fold Recognition by Deep Learning Networks

    PubMed Central

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

    2015-01-01

    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. PMID:26634993

  7. Improving Protein Fold Recognition by Deep Learning Networks.

    PubMed

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

    2015-01-01

    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. PMID:26634993

  8. 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.

  9. Dynamic Coupling between Folding, Binding and Function

    NASA Astrophysics Data System (ADS)

    Wolynes, Peter G.

    2003-03-01

    Elementary presentations of biophysics suggest a clear separation between the events of protein folding and function. The situation is much more interesting and complex. Many proteins in the cell are unfolded until called upon to interact with targets. Why? Energy landscape theory suggest some interesting kinetic advantages and possible explanations concerning the promiscuity of protein-protein interactions. This will be discussed in the context of protein DNA recognition. The energy landscapes for binding surfaces show interesting systematic differences from those of protein interiors. Energy landscape ideas also raise the prospect that folded proteins partially unfold during their function. I will illustrate this with a specific example of large scale conformation change in a kinase.

  10. A Simple Model for Protein Folding

    NASA Astrophysics Data System (ADS)

    Henry, Eric R.; Eaton, William A.

    We describe a simple Ising-like statistical mechanical model for folding proteins based on the α-carbon contact map of the native structure. In this model residues can adopt two microscopic states corresponding to the native and non-native conformations. In order to exactly enumerate the large number of possible configurations, structure is considered to grow as continuous sequences of native residues, with no more than two sequences in each molecule. Inter-residue contacts can only form within each sequence and between residues of the two native sequences. As structure grows there is a tradeoff between the stabilizing effect of inter-residue contacts and the entropy losses from ordering residues in their native conformation and from forming a disordered loop to connect two continuous sequences. Folding kinetics are calculated from the dynamics on the free energy profile, as in Kramers' reaction rate theory. Although non-native interactions responsible for roughness in the energy landscape are not explicitly considered in the model, they are implicitly included by determining the absolute rates for motion on the free energy profile. With the exception of α-helical proteins, the kinetic progress curves exhibit single exponential time courses, consistent with two state behavior, as observed experimentally. The calculated folding rates are in remarkably good agreement with the measured values for the 25 two-state proteins investigated, with a correlation coefficient of 0.8. With its coarse-grained description of both the energy and entropy, and only three independently adjustable parameters, the model may be regarded as the simplest possible analytical model of protein folding capable of predicting experimental properties of specific proteins.

  11. Improved Method of Design for Folding Inflatable Shells

    NASA Technical Reports Server (NTRS)

    Johnson, Christopher J.

    2009-01-01

    An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One particularly difficult problem is that of mathematically defining fold lines on a gore pattern in a double- curvature region. Moreover, because the fold lines in a double-curvature region tend to be curved, there is a practical problem of how to implement the folds. Another problem is that of modifying the basic gore shapes and sizes for the various layers so that when they are folded as part of the integral structure, they do not mechanically interfere with each other at the fold lines. Heretofore, it has been a common practice to design an inflatable shell to be assembled in the deployed configuration, without regard for the need to fold it into compact form. Typically, the result has been that folding has been a difficult, time-consuming process resulting in a An improved method of designing complexly shaped inflatable shells to be assembled from gores was conceived for original application to the inflatable outer shell of a developmental habitable spacecraft module having a cylindrical mid-length section with toroidal end caps. The method is also applicable to inflatable shells of various shapes for terrestrial use. The method addresses problems associated with the assembly, folding, transport, and deployment of inflatable shells that may comprise multiple layers and have complex shapes that can include such doubly curved surfaces as toroids and spheres. One

  12. A hydrodynamic view of the first-passage folding of Trp-cage miniprotein.

    PubMed

    Andryushchenko, Vladimir A; Chekmarev, Sergei F

    2016-04-01

    We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential. PMID:26559408

  13. On the need to consider kinetic as well as thermodynamic consequences of the parking problem in quantitative studies of nonspecific binding between proteins and linear polymer chains.

    PubMed

    Munro, P D; Jackson, C M; Winzor, D J

    1998-04-20

    Attention is drawn to a need for caution in the thermodynamic characterization of nonspecific binding of a large ligand to a linear acceptor such as a polynucleotide or a polysaccharide-because of the potential for misidentification of a transient (pseudoequilibrium) state as true equilibrium. The time course of equilibrium attainment during the binding of a large ligand to nonspecific three-residue sequences of a linear acceptor lattice has been simulated, either by numerical integration of the system of ordinary differential equations or by a Monte Carlo procedure, to identify the circumstances under which the kinetics of elimination of suboptimal ligand attachment (called the parking problem) create such difficulties. These simulations have demonstrated that the potential for the existence of a transient plateau in the time course of equilibrium attainment increases greatly (i) with increasing extent of acceptor saturation (i.e., with increasing ligand concentration), (ii) with increasing magnitude of the binding constant, and (iii) with increasing length of the acceptor lattice. Because the capacity of the polymer lattice for ligand is most readily determined under conditions conducive to essentially stoichiometric interaction, the parameter so obtained is thus likely to reflect the transient (irreversible) rather than equilibrium binding capacity. A procedure is described for evaluating the equilibrium capacity from that irreversible parameter; and illustrated by application to published results [M. Nesheim, M.N. Blackburn, C.M. Lawler, K.G. Mann, J. Biol. Chem. 261 (1986) 3214-3221] for the stoichiometric titration of heparin with thrombin. PMID:17029698

  14. Protein folding: the stepwise assembly of foldon units.

    PubMed

    Maity, Haripada; Maity, Mita; Krishna, Mallela M G; Mayne, Leland; Englander, S Walter

    2005-03-29

    Equilibrium and kinetic hydrogen exchange experiments show that cytochrome c is composed of five foldon units that continually unfold and refold even under native conditions. Folding proceeds by the stepwise assembly of the foldon units rather than one amino acid at a time. The folding pathway is determined by a sequential stabilization process; previously formed foldons guide and stabilize subsequent foldons to progressively build the native protein. Four other proteins have been found to show similar behavior. These results support stepwise protein folding pathways through discrete intermediates. PMID:15774579

  15. How the genome folds

    NASA Astrophysics Data System (ADS)

    Lieberman Aiden, Erez

    2012-02-01

    I describe Hi-C, a novel technology for probing the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing. Working with collaborators at the Broad Institute and UMass Medical School, we used Hi-C to construct spatial proximity maps of the human genome at a resolution of 1Mb. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. We identified an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments. At the megabase scale, the chromatin conformation is consistent with a fractal globule, a knot-free conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi-C to map the dynamic conformations of whole genomes.

  16. Protein folding in the ER.

    SciTech Connect

    Stevens, F. J.; Argon, Y.; Biosciences Division; Univ. of Chicago

    1999-10-01

    The endoplasmic reticulum (ER) is a major protein folding compartment for secreted, plasma membrane and organelle proteins. Each of these newly-synthesized polypeptides folds in a deterministic process, affected by the unique conditions that exist in the ER. An understanding of protein folding in the ER is a fundamental biomolecular challenge at two levels. The first level addresses how the amino acid sequence programs that polypeptide to efficiently arrive at a particular fold out of a multitude of alternatives, and how different sequences obtain similar folds. At the second level are the issues introduced by folding not in the cytosol, but in the ER, including the risk of aggregation in a molecularly crowded environment, accommodation of post-translational modifications and the compatibility with subsequent intracellular trafficking. This review discusses both the physicochemical and cell biological constraints of folding, which are the challenges that the ER molecular chaperones help overcome.

  17. Structural origin of slow diffusion in protein folding.

    PubMed

    Chung, Hoi Sung; Piana-Agostinetti, Stefano; Shaw, David E; Eaton, William A

    2015-09-25

    Experimental, theoretical, and computational studies of small proteins suggest that interresidue contacts not present in the folded structure play little or no role in the self-assembly mechanism. Non-native contacts can, however, influence folding kinetics by introducing additional local minima that slow diffusion over the global free-energy barrier between folded and unfolded states. Here, we combine single-molecule fluorescence with all-atom molecular dynamics simulations to discover the structural origin for the slow diffusion that markedly decreases the folding rate for a designed α-helical protein. Our experimental determination of transition path times and our analysis of the simulations point to non-native salt bridges between helices as the source, which provides a quantitative glimpse of how specific intramolecular interactions influence protein folding rates by altering dynamics and not activation free energies. PMID:26404828

  18. Rise of the Helix from a Collapsed Globule during the Folding of Monellin.

    PubMed

    Goluguri, Rama Reddy; Udgaonkar, Jayant B

    2015-09-01

    Early kinetic intermediates observed during the folding of many proteins are invariably compact and appear to possess some secondary structure. Consequently, it has been difficult to understand whether compaction drives secondary structure formation or secondary structure formation facilitates compaction during folding. In this study of the folding of single-chain monellin, it is shown that a kinetic molten globule (MG) is populated at 2 ms of folding. Far-UV circular dichroism (CD) measurements show that the kinetic MG is devoid of any helical structure even under the most stabilizing folding conditions. Multisite fluorescence resonance energy transfer (FRET) measurements show that the kinetic MG is compact with different segments having contracted to different extents. It is shown that the sequence segment that goes on to form the sole helix in the native protein is fully collapsed in the kinetic MG. This segment expands to accommodate the helix as the kinetic MG folds further to the native state, while other segments of the protein contract. Helix formation starting from the kinetic MG is shown to occur in multiple kinetic steps, whether measured by far-UV CD or by FRET. PMID:26258844

  19. Alpha-Helix folding in the presence of structural constraints.

    PubMed

    Ihalainen, Janne A; Paoli, Beatrice; Muff, Stefanie; Backus, Ellen H G; Bredenbeck, Jens; Woolley, G Andrew; Caflisch, Amedeo; Hamm, Peter

    2008-07-15

    We have investigated the site-specific folding kinetics of a photoswitchable cross-linked alpha-helical peptide by using single (13)C = (18)O isotope labeling together with time-resolved IR spectroscopy. We observe that the folding times differ from site to site by a factor of eight at low temperatures (6 degrees C), whereas at high temperatures (45 degrees C), the spread is considerably smaller. The trivial sum of the site signals coincides with the overall folding signal of the unlabeled peptide, and different sites fold in a noncooperative manner. Moreover, one of the sites exhibits a decrease of hydrogen bonding upon folding, implying that the unfolded state at low temperature is not unstructured. Molecular dynamics simulations at low temperature reveal a stretched-exponential behavior which originates from parallel folding routes that start from a kinetically partitioned unfolded ensemble. Different metastable structures (i.e., traps) in the unfolded ensemble have a different ratio of loop and helical content. Control simulations of the peptide at high temperature, as well as without the cross-linker at low temperature, show faster and simpler (i.e., single-exponential) folding kinetics. The experimental and simulation results together provide strong evidence that the rate-limiting step in formation of a structurally constrained alpha-helix is the escape from heterogeneous traps rather than the nucleation rate. This conclusion has important implications for an alpha-helical segment within a protein, rather than an isolated alpha-helix, because the cross-linker is a structural constraint similar to those present during the folding of a globular protein. PMID:18621686

  20. WW domain folding complexity revealed by infrared spectroscopy.

    PubMed

    Davis, Caitlin M; Dyer, R Brian

    2014-09-01

    Although the intrinsic tryptophan fluorescence of proteins offers a convenient probe of protein folding, interpretation of the fluorescence spectrum is often difficult because it is sensitive to both global and local changes. Infrared (IR) spectroscopy offers a complementary measure of structural changes involved in protein folding, because it probes changes in the secondary structure of the protein backbone. Here we demonstrate the advantages of using multiple probes, infrared and fluorescence spectroscopy, to study the folding of the FBP28 WW domain. Laser-induced temperature jumps coupled with fluorescence or infrared spectroscopy have been used to probe changes in the peptide backbone on the submillisecond time scale. The relaxation dynamics of the β-sheets and β-turn were measured independently by probing the corresponding IR bands assigned in the amide I region. Using these wavelength-dependent measurements, we observe three kinetics phases, with the fastest process corresponding to the relaxation kinetics of the turns. In contrast, fluorescence measurements of the wild-type WW domain and tryptophan mutants exhibit single-exponential kinetics with a lifetime that corresponds to the slowest phase observed by infrared spectroscopy. Mutant sequences provide evidence of an intermediate dry molten globule state. The slowest step in the folding of this WW domain is the tight packing of the side chains in the transition from the dry molten globule intermediate to the native structure. This study demonstrates that using multiple complementary probes enhances the interpretation of protein folding dynamics. PMID:25121968

  1. Graphene folding on flat substrates

    SciTech Connect

    Chen, Xiaoming; Zhao, Yadong; Ke, Changhong; Zhang, Liuyang; Wang, Xianqiao

    2014-10-28

    We present a combined experimental-theoretical study of graphene folding on flat substrates. The structure and deformation of the folded graphene sheet are experimentally characterized by atomic force microscopy. The local graphene folding behaviors are interpreted based on nonlinear continuum mechanics modeling and molecular dynamics simulations. Our study on self-folding of a trilayer graphene sheet reports a bending stiffness of about 6.57 eV, which is about four times the reported values for monolayer graphene. Our results reveal that an intriguing free sliding phenomenon occurs at the interlayer van der Waals interfaces during the graphene folding process. This work demonstrates that it is a plausible venue to quantify the bending stiffness of graphene based on its self-folding conformation on flat substrates. The findings reported in this work are useful to a better understanding of the mechanical properties of graphene and in the pursuit of its applications.

  2. COS NUV MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2010-09-01

    The performance of the MAMA microchannel plate can be monitored using a MAMA fold analysis procedure. The fold analysis provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of changes in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the COS MAMA Fold Analysis {11891} during Cycle 17.

  3. COS NUV MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2012-10-01

    The performance of the MAMA microchannel plate can be monitored using a MAMA fold analysis procedure. The fold analysis provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of changes in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as the COS MAMA Fold Analysis {12723} during Cycle 19.

  4. Paradoxical Vocal Fold Movement (PVFM)

    MedlinePlus

    ... Careers Certification Publications Events Advocacy Continuing Education Practice Management Research Home / Information for the Public / Speech, Language and Swallowing / Disorders and Diseases Paradoxical Vocal Fold ...

  5. Compact intermediates in RNA folding

    SciTech Connect

    Woodson, S.A.

    2011-12-14

    Large noncoding RNAs fold into their biologically functional structures via compact yet disordered intermediates, which couple the stable secondary structure of the RNA with the emerging tertiary fold. The specificity of the collapse transition, which coincides with the assembly of helical domains, depends on RNA sequence and counterions. It determines the specificity of the folding pathways and the magnitude of the free energy barriers to the ensuing search for the native conformation. By coupling helix assembly with nascent tertiary interactions, compact folding intermediates in RNA also play a crucial role in ligand binding and RNA-protein recognition.

  6. 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. PMID:27090200

  7. 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

  8. Characterization of a folding intermediate from HIV-1 ribonuclease H.

    PubMed Central

    Kern, G.; Handel, T.; Marqusee, S.

    1998-01-01

    The RNase H domain from HIV-1 (HIV RNase H) encodes an essential retroviral activity. Refolding of the isolated HIV RNase H domain shows a kinetic intermediate detectable by stopped-flow far UV circular dichroism and pulse-labeling H/D exchange. In this intermediate, strands 1, 4, and 5 as well as helices A and D appear to be structured. Compared to its homolog from Escherichia coli, the rate limiting step in refolding of HIV RNase H appears closer to the native state. We have modeled this kinetic intermediate using a C-terminal deletion fragment lacking helix E. Like the kinetic intermediate, this variant folds rapidly and shows a decrease in stability. We propose that inhibition of the docking of helix E to this folding intermediate may present a novel strategy for anti HIV-1 therapy. PMID:9792104

  9. 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

  10. 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. PMID:27574021

  11. Structural Bridges through Fold Space

    PubMed Central

    Edwards, Hannah; Deane, Charlotte M.

    2015-01-01

    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. PMID:26372166

  12. Folding and escape of nascent proteins at ribosomal exit tunnel

    NASA Astrophysics Data System (ADS)

    Bui, Phuong Thuy; Hoang, Trinh Xuan

    2016-03-01

    We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein.

  13. Folding and escape of nascent proteins at ribosomal exit tunnel.

    PubMed

    Bui, Phuong Thuy; Hoang, Trinh Xuan

    2016-03-01

    We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein. PMID:26957181

  14. Maximum Probability Reaction Sequences in Stochastic Chemical Kinetic Systems

    PubMed Central

    Salehi, Maryam; Perkins, Theodore J.

    2010-01-01

    The detailed behavior of many molecular processes in the cell, such as protein folding, protein complex assembly, and gene regulation, transcription and translation, can often be accurately captured by stochastic chemical kinetic models. We investigate a novel computational problem involving these models – that of finding the most-probable sequence of reactions that connects two or more states of the system observed at different times. We describe an efficient method for computing the probability of a given reaction sequence, but argue that computing most-probable reaction sequences is EXPSPACE-hard. We develop exact (exhaustive) and approximate algorithms for finding most-probable reaction sequences. We evaluate these methods on test problems relating to a recently-proposed stochastic model of folding of the Trp-cage peptide. Our results provide new computational tools for analyzing stochastic chemical models, and demonstrate their utility in illuminating the behavior of real-world systems. PMID:21629860

  15. UFO (UnFold Operator) computer program abstract

    SciTech Connect

    Kissel, L.; Biggs, F.

    1982-11-01

    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.

  16. COS NUV MAMA Fold Distribution

    NASA Astrophysics Data System (ADS)

    Wheeler, Thomas

    2013-10-01

    The performance of the MAMA microchannel plate can be monitored using a MAMA fold analysis procedure. The fold analysis provides a measurement of the distribution of charge cloud sizes incident upon the anode giving some measure of changes in the pulse-height distribution of the MCP and, therefore, MCP gain. This proposal executes the same steps as Cycle 20 proposal 13128.

  17. 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

  18. How do chaperonins fold protein?

    PubMed Central

    Motojima, Fumihiro

    2015-01-01

    Protein folding is a biological process that is essential for the proper functioning of proteins in all living organisms. In cells, many proteins require the assistance of molecular chaperones for their folding. Chaperonins belong to a class of molecular chaperones that have been extensively studied. However, the mechanism by which a chaperonin mediates the folding of proteins is still controversial. Denatured proteins are folded in the closed chaperonin cage, leading to the assumption that denatured proteins are completely encapsulated inside the chaperonin cage. In contrast to the assumption, we recently found that denatured protein interacts with hydrophobic residues at the subunit interfaces of the chaperonin, and partially protrude out of the cage. In this review, we will explain our recent results and introduce our model for the mechanism by which chaperonins accelerate protein folding, in view of recent findings.

  19. 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

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

    PubMed

    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

  1. Microfluidic Mixers for Studying Protein Folding

    PubMed Central

    Waldauer, Steven A.; Wu, Ling; Yao, Shuhuai; Bakajin, Olgica; Lapidus, Lisa J.

    2012-01-01

    The process by which a protein folds into its native conformation is highly relevant to biology and human health yet still poorly understood. One reason for this is that folding takes place over a wide range of timescales, from nanoseconds to seconds or longer, depending on the protein1. Conventional stopped-flow mixers have allowed measurement of folding kinetics starting at about 1 ms. We have recently developed a microfluidic mixer that dilutes denaturant ~100-fold in ~8 μs2. Unlike a stopped-flow mixer, this mixer operates in the laminar flow regime in which turbulence does not occur. The absence of turbulence allows precise numeric simulation of all flows within the mixer with excellent agreement to experiment3-4. Laminar flow is achieved for Reynolds numbers Re ≤100. For aqueous solutions, this requires micron scale geometries. We use a hard substrate, such as silicon or fused silica, to make channels 5-10 μm wide and 10 μm deep (See Figure 1). The smallest dimensions, at the entrance to the mixing region, are on the order of 1 μm in size. The chip is sealed with a thin glass or fused silica coverslip for optical access. Typical total linear flow rates are ~1 m/s, yielding Re~10, but the protein consumption is only ~0.5 nL/s or 1.8 μL/hr. Protein concentration depends on the detection method: For tryptophan fluorescence the typical concentration is 100 μM (for 1 Trp/protein) and for FRET the typical concentration is ~100 nM. The folding process is initiated by rapid dilution of denaturant from 6 M to 0.06 M guanidine hydrochloride. The protein in high denaturant flows down a central channel and is met on either side at the mixing region by buffer without denaturant moving ~100 times faster (see Figure 2). This geometry causes rapid constriction of the protein flow into a narrow jet ~100 nm wide. Diffusion of the light denaturant molecules is very rapid, while diffusion of the heavy protein molecules is much slower, diffusing less than 1 μm in 1 ms

  2. Chemical chaperones assist intracellular folding to buffer mutational variations

    PubMed Central

    Bandyopadhyay, Anannya; Saxena, Kanika; Kasturia, Neha; Dalal, Vijit; Bhatt, Niraj; Rajkumar, Asher; Maity, Shuvadeep; Sengupta, Shantanu; Chakraborty, Kausik

    2012-01-01

    Hidden genetic variations harbor potential for the evolution of new traits. Molecular chaperones, that assist protein folding, may conceal genetic variations in protein coding regions. Here, we investigate if the chemical milieu of cells has the potential to alleviate intracellular protein folding; potentially implicating a role of osmolytes in concealing genetic variations. Using the model osmolyte TMAO, we uncover that it can buffer mutations that impose kinetic traps in the folding pathways of two model proteins. Using this information, we rationally designed TMAO-dependent mutants in vivo, starting from a TMAO-independent protein. Strikingly, we delineate different osmolytes to have a unique spectrum of buffered-mutations. Consequently, the chemical milieu of cells may alter the folding pathways of unique mutant variants in polymorphic populations and lead to unanticipated spectra of genetic buffering. PMID:22246401

  3. Impact of structure space continuity on protein fold classification

    PubMed Central

    Xu, Jinrui; Zhang, Jianzhi

    2016-01-01

    Protein structure classification hierarchically clusters domain structures based on structure and/or sequence similarities and plays important roles in the study of protein structure-function relationship and protein evolution. Among many classifications, SCOP and CATH are widely viewed as the gold standards. Fold classification is of special interest because this is the lowest level of classification that does not depend on protein sequence similarity. The current fold classifications such as those in SCOP and CATH are controversial because they implicitly assume that folds are discrete islands in the structure space, whereas increasing evidence suggests significant similarities among folds and supports a continuous fold space. Although this problem is widely recognized, its impact on fold classification has not been quantitatively evaluated. Here we develop a likelihood method to classify a domain into the existing folds of CATH or SCOP using both query-fold structure similarities and within-fold structure heterogeneities. The new classification differs from the original classification for 3.4–12% of domains, depending on factors such as the structure similarity score and original classification scheme used. Because these factors differ for different biological purposes, our results indicate that the importance of considering structure space continuity in fold classification depends on the specific question asked. PMID:27006112

  4. Exploring the protein funnel energy landscape for folding and function

    NASA Astrophysics Data System (ADS)

    Onuchic, Jose

    2005-03-01

    Globally the energy landscape of a folding protein resembles a partially rough funnel. Using minimalist model simulations together with analytical theory, we learn about good (minimally frustrated) folding sequences and non-folding (frustrated) sequences In addition to the need to minimize energetic frustration, the fold topology also plays a major role in the folding mechanism. Some folding motifs are easier to design than others, suggesting the possibility that evolution not only selected sequences with sufficiently small energetic frustration but also more easily designable native structures. We have demonstrated for several proteins (such as CI2 and SH3) that they are sufficiently well designed (i.e., reduced energetic frustration) that much of the heterogeneity observed in their transition state ensemble (TSE) is determined by topology. Topological effects go beyond the TSE. The overall structure of the on-route and off-route (traps) intermediates for the folding of more complex proteins and protein dimers is also strongly influenced by topology.this theoretical framework, simulations of minimalist models and their connections to more computationally-expensive all-atom simulations, we are now in the process of obtaining a quantitative understanding of the folding problem, which allows for a direct comparison to a new generation of folding experiments. Connections between the folding landscape and protein function will also be discussed.

  5. Complex Pathways in Folding of Protein G Explored by Simulation and Experiment

    PubMed Central

    Lapidus, Lisa J.; Acharya, Srabasti; Schwantes, Christian R.; Wu, Ling; Shukla, Diwakar; King, Michael; DeCamp, Stephen J.; Pande, Vijay S.

    2014-01-01

    The B1 domain of protein G has been a classic model system of folding for decades, the subject of numerous experimental and computational studies. Most of the experimental work has focused on whether the protein folds via an intermediate, but the evidence is mostly limited to relatively slow kinetic observations with a few structural probes. In this work we observe folding on the submillisecond timescale with microfluidic mixers using a variety of probes including tryptophan fluorescence, circular dichroism, and photochemical oxidation. We find that each probe yields different kinetics and compare these observations with a Markov State Model constructed from large-scale molecular dynamics simulations and find a complex network of states that yield different kinetics for different observables. We conclude that there are many folding pathways before the final folding step and that these paths do not have large free energy barriers. PMID:25140430

  6. 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).

  7. Fast events in protein folding

    SciTech Connect

    Woodruff, W.; Callender, R.; Causgrove, T.; Dyer, R.; Williams, S.

    1996-04-01

    The primary objective of this work was to develop a molecular understanding of how proteins achieve their native three-dimensional (folded) structures. This requires the identification and characterization of intermediates in the protein folding process on all relevant timescales, from picoseconds to seconds. The short timescale events in protein folding have been entirely unknown. Prior to this work, state-of-the-art experimental approaches were limited to milliseconds or longer, when much of the folding process is already over. The gap between theory and experiment is enormous: current theoretical and computational methods cannot realistically model folding processes with lifetimes longer than one nanosecond. This unique approach to employ laser pump-probe techniques that combine novel methods of laser flash photolysis with time-resolved vibrational spectroscopic probes of protein transients. In this scheme, a short (picosecond to nanosecond) laser photolysis pulse was used to produce an instantaneous pH or temperature jump, thereby initiating a protein folding or unfolding reaction. Structure-specific, time-resolved vibrational probes were then used to identify and characterize protein folding intermediates.

  8. 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

  9. Helical Folding Competing with Unfolded Aggregation in Phenylene Ethynylene Foldamers.

    PubMed

    Luo, Zhouyang; Zhu, Ningbo; Zhao, Dahui

    2016-07-25

    The folding and aggregation behavior of a pair of oligo(phenylene ethynylene) (OPE) foldamers are investigated by means of UV/Vis absorption and circular dichroism spectroscopy. With identical OPE backbones, two foldamers, 1 with alkyl side groups and 2 with triethylene glycol side chains, manifest similar helical conformations in solutions in n-hexane and methanol, respectively. However, disparate and competing folding and aggregation processes are observed in alternative solvents. In cyclohexane, oligomer 1 initially adopts the helical conformation, but the self-aggregation of unfolded chains, as a minor component, gradually drives the folding-unfolding transition eventually to the unfolded aggregate state completely. In contrast, in aqueous solution (CH3 OH/H2 O) both folded and unfolded oligomer 2 appear to undergo self-association; aggregates of the folded chains are thermodynamically more stable. In solutions with a high H2 O content, self-aggregation among unfolded oligomers is kinetically favored; these oligomers very slowly transform into aggregates of helical structures with greater thermodynamic stability. The folded-unfolded conformational switch thus takes place with the free (nonaggregated) molecules, and the very slow folding transition is due to the low concentration of molecularly dispersed oligomers. PMID:27374725

  10. The prosegment catalyzes native folding of Plasmodium falciparum plasmepsin II.

    PubMed

    Jaafar, Ahmad Haniff; Xiao, Huogen; Dee, Derek R; Bryksa, Brian C; Bhaumik, Prasenjit; Yada, Rickey Y

    2016-10-01

    Plasmepsin II is a malarial pepsin-like aspartic protease produced as a zymogen containing an N-terminal prosegment domain that is removed during activation. Despite structural similarities between active plasmepsin II and pepsin, their prosegments adopt different conformations in the respective zymogens. In contrast to pepsinogen, the proplasmepsin II prosegment is 80 residues longer, contains a transmembrane region and is non-essential for recombinant expression in an active form, thus calling into question the prosegment's precise function. The present study examines the role of the prosegment in the folding mechanism of plasmepsin II. Both a shorter (residues 77-124) and a longer (residues 65-124) prosegment catalyze plasmepsin II folding at rates more than four orders of magnitude faster compared to folding without prosegment. Native plasmepsin II is kinetically trapped and requires the prosegment both to catalyze folding and to shift the folding equilibrium towards the native conformation. Thus, despite low sequence identity and distinct zymogen conformations, the folding landscapes of plasmepsin II and pepsin, both with and without prosegment, are qualitatively identical. These results imply a conserved and unusual feature of the pepsin-like protease topology that necessitates prosegment-assisted folding. PMID:27378574

  11. 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

  12. Universality Classes in Folding Times of Proteins

    PubMed Central

    Cieplak, Marek; Hoang, Trinh Xuan

    2003-01-01

    Molecular dynamics simulations in simplified models allow one to study the scaling properties of folding times for many proteins together under a controlled setting. We consider three variants of the Go models with different contact potentials and demonstrate scaling described by power laws and no correlation with the relative contact order parameter. We demonstrate existence of at least three kinetic universality classes that are correlated with the types of structure: the α-, α-β-, and β- proteins have the scaling exponents of ∼1.7, 2.5, and 3.2, respectively. The three classes merge into one when the contact range is truncated at a reasonable value. We elucidate the role of the potential associated with the chirality of a protein. PMID:12524300

  13. Fog spontaneously folds mosquito wings

    NASA Astrophysics Data System (ADS)

    Dickerson, Andrew K.; Liu, Xing; Zhu, Ting; Hu, David L.

    2015-02-01

    The flexibility of insect wings confers aerodynamic benefits, but can also present a hazard if exposed to fog or dew. Fog can cause water to accumulate on wings, bending them into tight taco shapes and rendering them useless for flight. In this combined experimental and theoretical study, we use high-speed video to film the spontaneous folding of isolated mosquito wings due to the evaporation of a water drop. We predict shapes of the deformed wing using two-dimensional elastica theory, considering both surface tension and Laplace pressure. We also recommend fold-resistant geometries for the wings of flapping micro-aerial vehicles. Our work reveals the mechanism of insect wing folding and provides a framework for further study of capillarity-driven folding in both natural and biomimetic systems at small scales.

  14. 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. PMID:24499973

  15. Folding of Layers of Finite Length

    NASA Astrophysics Data System (ADS)

    Schmid, D. W.; Podladchikov, Yu. Yu.; Marques, F.

    All existing folding theories assume that the layers are infinitely long or, which is mathematically equivalent, that the compression is directly applied to the lateral boundaries. These assumptions are not always justified for natural geological sys- tems. In fact we can observe that on all scales, from veins to sub-ducting slabs, the layers are of finite length and that there are no distinct, rigid walls pushing the lay- ers from the side. Using the method of Muskhelishvili we have derived the complete two-dimensional solution of an elliptic object embedded in a matrix and subject to far field boundary conditions; pure shear, simple shear and arbitrary combinations thereof. The rheology of the matrix is viscous, the layer may behave either elastically or viscous. Using the values from this background state analysis, stress, pressure and strain rate, we performed the classical linear stability analysis to examine the mech- anism of folding in the described setup. The resulting expressions maximum growth rates and dominant wavelengths are applicable to general geological systems; in the limit of an infinite aspect ratio of the layer the classical expressions of Biot are ob- tained for all other cases new expressions result. Our main results are: 1. Folding of finite length layers is controlled by the ratio of aspect ratio to competence contrast. 2. The described setup explains why in nature only folds can be observed with a rela- tively small wavelength to thickness ratio, suggesting small viscosity contrast 3. The problem of the unknown compressive stress value for the elastic layer is solved. 4. For finite length elastic layers the dominant wavelength selection shows a cubic, instead of square, root dependence. 5. A complete table, describing the folding in all the possible limits is presented and the applicability to natural systems discussed. All the presented results were checked numerically and/or with analogue models.

  16. Protein folding by motion planning

    NASA Astrophysics Data System (ADS)

    Thomas, Shawna; Song, Guang; Amato, Nancy M.

    2005-12-01

    We investigate a novel approach for studying protein folding that has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs). Our focus is to study issues related to the folding process, such as the formation of secondary and tertiary structures, assuming we know the native fold. A feature of our PRM-based framework is that the large sets of folding pathways in the roadmaps it produces, in just a few hours on a desktop PC, provide global information about the protein's energy landscape. This is an advantage over other simulation methods such as molecular dynamics or Monte Carlo methods which require more computation and produce only a single trajectory in each run. In our initial studies, we obtained encouraging results for several small proteins. In this paper, we investigate more sophisticated techniques for analyzing the folding pathways in our roadmaps. In addition to more formally revalidating our previous results, we present a case study showing that our technique captures known folding differences between the structurally similar proteins G and L. This research was supported in part by NSF CAREER Award CCR-9624315, NSF Grants ACI-9872126, EIA-9975018, EIA-0103742, EIA-9805823, ACR-0113971, CCR-0113974, EIA-9810937, EIA-0079874 and the Texas Higher Education Coordinating Board grant ATP-000512-0261-2001. ST was supported in part by an NSF Graduate Research Fellowship. GS was supported in part by an IBM PhD Fellowship.

  17. Protein folding: independent unrelated pathways or predetermined pathway with optional errors.

    PubMed

    Bédard, Sabrina; Krishna, Mallela M G; Mayne, Leland; Englander, S Walter

    2008-05-20

    The observation of heterogeneous protein folding kinetics has been widely interpreted in terms of multiple independent unrelated pathways (IUP model), both experimentally and in theoretical calculations. However, direct structural information on folding intermediates and their properties now indicates that all of a protein population folds through essentially the same stepwise pathway, determined by cooperative native-like foldon units and the way that the foldons fit together in the native protein. It is essential to decide between these fundamentally different folding mechanisms. This article shows, contrary to previous supposition, that the heterogeneous folding kinetics observed for the staphylococcal nuclease protein (SNase) does not require alternative parallel pathways. SNase folding kinetics can be fit equally well by a single predetermined pathway that allows for optional misfolding errors, which are known to occur ubiquitously in protein folding. Structural, kinetic, and thermodynamic information for the folding intermediates and pathways of many proteins is consistent with the predetermined pathway-optional error (PPOE) model but contrary to the properties implied in IUP models. PMID:18480257

  18. Kinetic Demonstration.

    ERIC Educational Resources Information Center

    Burgardt, Erik D.; Ryan, Hank

    1996-01-01

    Presents a unit on chemical reaction kinetics that consists of a predemonstration activity, the demonstration, and a set of postdemonstration activities that help students transfer the concepts to actual chemical reactions. Simulates various aspects of chemical reaction kinetics. (JRH)

  19. Kinetic Atom.

    ERIC Educational Resources Information Center

    Wilson, David B.

    1981-01-01

    Surveys the research of scientists like Joule, Kelvin, Maxwell, Clausius, and Boltzmann as it comments on the basic conceptual issues involved in the development of a more precise kinetic theory and the idea of a kinetic atom. (Author/SK)

  20. Enzyme Kinetics.

    ERIC Educational Resources Information Center

    Moe, Owen; Cornelius, Richard

    1988-01-01

    Conveys an appreciation of enzyme kinetic analysis by using a practical and intuitive approach. Discusses enzyme assays, kinetic models and rate laws, the kinetic constants (V, velocity, and Km, Michaels constant), evaluation of V and Km from experimental data, and enzyme inhibition. (CW)

  1. Folding and assembly of the large molecular machine Hsp90 studied in single-molecule experiments

    PubMed Central

    Jahn, Markus; Buchner, Johannes; Hugel, Thorsten; Rief, Matthias

    2016-01-01

    Folding of small proteins often occurs in a two-state manner and is well understood both experimentally and theoretically. However, many proteins are much larger and often populate misfolded states, complicating their folding process significantly. Here we study the complete folding and assembly process of the 1,418 amino acid, dimeric chaperone Hsp90 using single-molecule optical tweezers. Although the isolated C-terminal domain shows two-state folding, we find that the isolated N-terminal as well as the middle domain populate ensembles of fast-forming, misfolded states. These intradomain misfolds slow down folding by an order of magnitude. Modeling folding as a competition between productive and misfolding pathways allows us to fully describe the folding kinetics. Beyond intradomain misfolding, folding of the full-length protein is further slowed by the formation of interdomain misfolds, suggesting that with growing chain lengths, such misfolds will dominate folding kinetics. Interestingly, we find that small stretching forces applied to the chain can accelerate folding by preventing the formation of cross-domain misfolding intermediates by leading the protein along productive pathways to the native state. The same effect is achieved by cotranslational folding at the ribosome in vivo. PMID:26787848

  2. Efficient Estimation of Rare-Event Kinetics

    NASA Astrophysics Data System (ADS)

    Trendelkamp-Schroer, Benjamin; Noé, Frank

    2016-01-01

    The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles of short simulations and thus effectively parallelize the computational effort, but the rare events of interest still need to be spontaneously sampled in the data. Enhanced sampling approaches, such as parallel tempering or umbrella sampling, can accelerate the computation of equilibrium expectations massively, but sacrifice the ability to compute dynamical expectations. In this work we establish a principle to combine knowledge of the equilibrium distribution with kinetics from fast "downhill" relaxation trajectories using reversible Markov models. This approach is general, as it does not invoke any specific dynamical model and can provide accurate estimates of the rare-event kinetics. Large gains in sampling efficiency can be achieved whenever one direction of the process occurs more rapidly than its reverse, making the approach especially attractive for downhill processes such as folding and binding in biomolecules. Our method is implemented in the PyEMMA software.

  3. Efficient procedures for the numerical simulation of mid-size RNA kinetics

    PubMed Central

    2012-01-01

    Motivation Methods for simulating the kinetic folding of RNAs by numerically solving the chemical master equation have been developed since the late 90's, notably the programs Kinfold and Treekin with Barriers that are available in the Vienna RNA package. Our goal is to formulate extensions to the algorithms used, starting from the Gillespie algorithm, that will allow numerical simulations of mid-size (~ 60–150 nt) RNA kinetics in some practical cases where numerous distributions of folding times are desired. These extensions can contribute to analyses and predictions of RNA folding in biologically significant problems. Results By describing in a particular way the reduction of numerical simulations of RNA folding kinetics into the Gillespie stochastic simulation algorithm for chemical reactions, it is possible to formulate extensions to the basic algorithm that will exploit memoization and parallelism for efficient computations. These can be used to advance forward from the small examples demonstrated to larger examples of biological interest. Software The implementation that is described and used for the Gillespie algorithm is freely available by contacting the authors, noting that the efficient procedures suggested may also be applicable along with Vienna's Kinfold. PMID:22958879

  4. Globular Protein Folding In Vitro and In Vivo.

    PubMed

    Gruebele, Martin; Dave, Kapil; Sukenik, Shahar

    2016-07-01

    In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science. PMID:27391927

  5. Rapid compaction during RNA folding

    NASA Astrophysics Data System (ADS)

    Russell, Rick; Millett, Ian S.; Tate, Mark W.; Kwok, Lisa W.; Nakatani, Bradley; Gruner, Sol M.; Mochrie, Simon G. J.; Pande, Vijay; Doniach, Sebastian; Herschlag, Daniel; Pollack, Lois

    2002-04-01

    We have used small angle x-ray scattering and computer simulations with a coarse-grained model to provide a time-resolved picture of the global folding process of the Tetrahymena group I RNA over a time window of more than five orders of magnitude. A substantial phase of compaction is observed on the low millisecond timescale, and the overall compaction and global shape changes are largely complete within one second, earlier than any known tertiary contacts are formed. This finding indicates that the RNA forms a nonspecifically collapsed intermediate and then searches for its tertiary contacts within a highly restricted subset of conformational space. The collapsed intermediate early in folding of this RNA is grossly akin to molten globule intermediates in protein folding.

  6. 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…

  7. Protein Solubility and Folding Enhancement by Interaction with RNA

    PubMed Central

    Choi, Seong Il; Han, Kyoung Sim; Kim, Chul Woo; Ryu, Ki-Sun; Kim, Byung Hee; Kim, Kyun-Hwan; Kim, Seo-Il; Kang, Tae Hyun; Shin, Hang-Cheol; Lim, Keo-Heun; Kim, Hyo Kyung; Hyun, Jeong-Min; Seong, Baik L.

    2008-01-01

    While basic mechanisms of several major molecular chaperones are well understood, this machinery has been known to be involved in folding of only limited number of proteins inside the cells. Here, we report a chaperone type of protein folding facilitated by interaction with RNA. When an RNA-binding module is placed at the N-terminus of aggregation-prone target proteins, this module, upon binding with RNA, further promotes the solubility of passenger proteins, potentially leading to enhancement of proper protein folding. Studies on in vitro refolding in the presence of RNA, coexpression of RNA molecules in vivo and the mutants with impaired RNA binding ability suggests that RNA can exert chaperoning effect on their bound proteins. The results suggest that RNA binding could affect the overall kinetic network of protein folding pathway in favor of productive folding over off-pathway aggregation. In addition, the RNA binding-mediated solubility enhancement is extremely robust for increasing soluble yield of passenger proteins and could be usefully implemented for high-throughput protein expression for functional and structural genomic research initiatives. The RNA-mediated chaperone type presented here would give new insights into de novo folding in vivo. PMID:18628952

  8. Folding analysis of the most complex Stevedore's protein knot.

    PubMed

    Wang, Iren; Chen, Szu-Yu; Hsu, Shang-Te Danny

    2016-01-01

    DehI is a homodimeric haloacid dehalogenase from Pseudomonas putida that contains the most complex 61 Stevedore's protein knot within its folding topology. To examine how DehI attains such an intricate knotted topology we combined far-UV circular dichroism (CD), intrinsic fluorescence spectroscopy and small angle X-ray scattering (SAXS) to investigate its folding mechanism. Equilibrium unfolding of DehI by chemical denaturation indicated the presence of two highly populated folding intermediates, I and I'. While the two intermediates vary in secondary structure contents and tertiary packing according to CD and intrinsic fluorescence, respectively, their overall dimension and compactness are similar according to SAXS. Three single-tryptophan variants (W34, W53, and W196) were generated to probe non-cooperative unfolding events localized around the three fluorophores. Kinetic fluorescence measurements indicated that the transition from the intermediate I' to the unfolded state is rate limiting. Our multiparametric folding analyses suggest that DehI unfolds through a linear folding pathway with two distinct folding intermediates by initial hydrophobic collapse followed by nucleation condensation, and that knotting precedes the formation of secondary structures. PMID:27527519

  9. Ultrafast events in the folding of ferrocytochrome c.

    PubMed

    Kumar, Rajesh; Prabhu, N Prakash; Bhuyan, Abani K

    2005-07-01

    Laser flash photolysis and stopped-flow methods have been used to study the dynamic events in the micro- to millisecond time bin in the refolding of horse ferrocytochrome c in the full range of guanidine hydrochloride concentration at pH 12.8 (+/-0.1), 22 degrees C. Under the absolute refolding condition, the earliest relaxation time of the unfolded protein chain is less than 1 micros. The chain then undergoes diffusive dynamics-mediated contraction and expansion, in which intrapolypeptide ligands make transient contacts with the heme iron, giving rise to two distinct kinetic phases of approximately 0.4 and approximately 3 micros. Under moderate to absolute refolding conditions, the rates of these processes show little dependence on the denaturant concentration, indicating the absence of structural element in the incipient or the relaxed state. Chain expansion and contraction events continue until the polypeptide finds a stable and supportive transition state. The crossing of this transition barrier, which rate-limits the folding of alkaline ferrocytochrome c, is characterized by a stopped-flow measured time constant of approximately 3 ms in aqueous solvent. Observed kinetics thus implicate no submillisecond folding structure. The folding kinetics is effectively two state in which the unfolded polypeptide first relaxes to an unstructured chain and then crosses over a late rate-limiting barrier to achieve the native conformation. The experimentally observed rates as a function of guanidine hydrochloride concentration have been simulated by numerically calculated microscopic rates of a simple kinetic model that captures the essential features of folding. PMID:15982002

  10. 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.