Biomedical subjects

Peter G Wolynes

Publications and source records attributed to Peter G Wolynes.

At least 19 recordsLinked to original sources

PubMed2024

The physical and evolutionary energy landscapes of devolved protein sequences corresponding to pseudogenes.

Protein evolution is guided by structural, functional, and dynamical constraints ensuring organismal viability. Pseudogenes are genomic sequences identified in many eukaryotes that lack translational activity due to sequence degradation and thus over time have undergone "devolution." Previously pseudogenized genes sometimes regain their protein-coding function, suggesting they may still encode robust folding energy landscapes despite multiple mutations. We study both the physical folding landscapes of protein sequences corresponding to human pseudogenes using the Associative Memory, Water Mediated, Structure and Energy Model, and the evolutionary energy landscapes obtained using direct coupling analysis (DCA) on their parent protein families. We found that generally mutations that have occurred in pseudogene sequences have disrupted their native global network of stabilizing residue interactions, making it harder for them to fold if they were translated. In some cases, however, energetic frustration has apparently decreased when the functional constraints were removed. We analyzed this unexpected situation for Cyclophilin A, Profilin-1, and Small Ubiquitin-like Modifier 2 Protein. Our analysis reveals that when such mutations in the pseudogene ultimately stabilize folding, at the same time, they likely alter the pseudogenes' former biological activity, as estimated by DCA. We localize most of these stabilizing mutations generally to normally frustrated regions required for binding to other partners.

Cyclophilin A↗

PubMed2007

Theory of structural glasses and supercooled liquids.

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature T(g). These include the following: the viscosity catastrophe and heat-capacity jump at T(g), and their connection; the nonexponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractal cooperative rearrangements; deviations from the Stokes-Einstein relation close to T(g); aging and its correlation with fragility; and the excess density of states at cryogenic temperatures owing to two-level tunneling systems and the Boson peak.

Chemical Phenomena↗

PubMed2006

Simulation studies of the fidelity of biomolecular structure ensemble recreation.

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.

Algorithms↗

PubMed2006

Stabilizing IkappaBalpha by "consensus" design.

IkappaBalpha is the major regulator of transcription factor NF-kappaB function. The ankyrin repeat region of IkappaBalpha mediates specific interactions with NF-kappaB dimers, but ankyrin repeats 1, 5 and 6 display a highly dynamic character when not in complex with NF-kappaB. Using chemical denaturation, we show here that IkappaBalpha displays two folding transitions: a non-cooperative conversion under weak perturbation, and a major cooperative folding phase upon stronger insult. Taking advantage of a native Trp residue in ankyrin repeat (AR) 6 and engineered Trp residues in AR2, AR4 and AR5, we show that the cooperative transition involves AR2 and AR3, while the non-cooperative transition involves AR5 and AR6. The major structural transition can be affected by single amino acid substitutions converging to the "consensus" ankyrin repeat sequence, increasing the native state stability significantly. We further characterized the structural and dynamic properties of the native state ensemble of IkappaBalpha and the stabilized mutants by H/(2)H exchange mass spectrometry and NMR. The solution experiments were complemented with molecular dynamics simulations to elucidate the microscopic origins of the stabilizing effect of the consensus substitutions, which can be traced to the fast conformational dynamics of the folded ensemble.

Amino Acid Sequence↗

PubMed2006

Statistics of cellular signal transduction as a race to the nucleus by multiple random walkers in compartment/phosphorylation space.

Cellular signal transduction often involves a reaction network of phosphorylation and transport events arranged with a ladder topology. If we keep track of the location of the phosphate groups describing an abstract state space, a simple model of signal transduction involving enzymes can be mapped on to a problem of how multiple biased random walkers compete to reach their target in the nucleus yielding a signal. Here, the first passage time probability and the survival probability for multiple walkers can be used to characterize the response of the network. The statistics of the first passage through the network has an asymmetric distribution with a long tail arising from the hierarchical structure of the network. This distribution implies a significant difference between the mean and the most probable signal transduction time. The response patterns for various external inputs generated by our model agree with recent experiments. In addition, the model predicts that there is an optimal phosphorylation enzyme concentration for rapid signal transduction.

Active Transport, Cell Nucleus↗

PubMed2006

A variational approach to the stochastic aspects of cellular signal transduction.

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making the physical significance of the variational method more transparent. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational Ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.

Cells↗

PubMed2006

Multiple-basin energy landscapes for large-amplitude conformational motions of proteins: Structure-based molecular dynamics simulations.

Biomolecules often undergo large-amplitude motions when they bind or release other molecules. Unlike macroscopic machines, these biomolecular machines can partially disassemble (unfold) and then reassemble (fold) during such transitions. Here we put forward a minimal structure-based model, the "multiple-basin model," that can directly be used for molecular dynamics simulation of even very large biomolecular systems so long as the endpoints of the conformational change are known. We investigate the model by simulating large-scale motions of four proteins: glutamine-binding protein, S100A6, dihydrofolate reductase, and HIV-1 protease. The mechanisms of conformational transition depend on the protein basin topologies and change with temperature near the folding transition. The conformational transition rate varies linearly with driving force over a fairly large range. This linearity appears to be a consequence of partial unfolding during the conformational transition.

Carrier Proteins↗

PubMed2006

The experimental survey of protein-folding energy landscapes.

We review what has been learned about the protein-folding problem from experimental kinetic studies. These studies reveal patterns of both great richness and surprising simplicity. The patterns can be interpreted in terms of proteins possessing an energy landscape which is largely, but not completely, funnel-like. Issues such as speed limitations of folding, the robustness of folding, the origin of barriers and cooperativity and the ensemble nature of transition states, intermediate and traps are assessed using the results from several experimental groups highlighting energy-landscape ideas as an interpretive framework.

Energy Transfer↗

PubMed2006

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

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

Amino Acid Substitution↗

PubMed2006

Role of topology, nonadditivity, and water-mediated interactions in predicting the structures of alpha/beta proteins.

The folding of alpha/beta proteins involves most of the commonly known structural and dynamic complexities of the protein energy landscapes. Thus, the interplay among different structural components, taking into account the cooperative interactions, is important in determining the success of protein structure prediction. In this work we present further developments of our knowledge-based force field for alpha/beta proteins, introducing more realistic modeling of many-body interactions governing the folding of beta-sheets. The model's innovations highlight both specific topological characteristics of secondary structures and the generic nonadditive interactions that are mediated by water. We also investigate how a coarse biasing of the protein morphology can be used to understand the role of heterogeneity in protein collapse. Analysis of the simulation results for three test alpha/beta proteins indicates that the addition of the topological and many-body ingredients to the model helps to greatly reduce the roughness in the energy landscape. Consequently, high quality candidate structures for alpha/beta proteins can be generated from simulated annealing runs, using very modest amounts of computer time.

Protein Folding↗

PubMed2006

Effective temperature in stochastic kinetics and gene networks.

The fluctuation-dissipation theorem, one of the central theorems in thermal dynamics, breaks down in out-of-equilibrium systems. The idea of effective temperature coming from the extensions of that theorem has been recently introduced to study glasses and has proved to be a key concept for out-of-equilibrium systems. Gene networks involve stochastic chemical kinetics and are far from equilibrium. This leads us to try to use the notion of effective temperature to study them. To develop this idea, we study a simple birth-death process and a general two-species interacting process using the language of effective temperature. Furthermore, a model of a nonregulatory gene is studied as an example. The effective temperature may serves as an alternative and somewhat more fundamental language to describe the intrinsic-extrinsic noise distinction that has already provided a tool for qualifying gene networks.

Animals↗

PubMed2006

Nonequilibrium self-assembly of linear fibers: microscopic treatment of growth, decay, catastrophe and rescue.

Many of the large structures of cells are constructed from fibers. These fibers self-assemble from individual proteins in a far-from-equilibrium fashion. Nonequilibrium self-assembly results in a highly dynamic process at the subcellular level that can be regulated and tuned to carry out many of the biological functions of the cell: growth, division and locomotion. We construct and analyze a nonequilibrium model of the dynamic end of a biological fiber that possesses site-resolved resolution. We solve for the steady states of this nonequilibrium system using a variational method. The results are compared to exact numerical solutions for systems with modest size. Using an effective reaction coordinate, we construct an effective potential from the steady-state distribution. The stochastic transitions of the system can be analyzed in this representation. We then apply this method to model microtubule systems. Predictions for macroscopic catastrophe, rescue and dynamic instability in the steady states are analyzed. We find that the length of the cap of the microtubule is small. The relations between the catastrophe/rescue rate and the growth rate are also discussed.

Cell Physiological Phenomena↗

PubMed2006

P versus Q: structural reaction coordinates capture protein folding on smooth landscapes.

Minding your p's and q's has become as important to protein-folding theorists as it is for those being instructed in the rules of etiquette. To assess the quality of structural reaction coordinates in predicting the transition-state ensemble (TSE) of protein folding, we benchmarked the accuracy of four structural reaction coordinates against the kinetic measure P(fold), whose value of 0.50 defines the stochastic separatrix for a two-state folding mechanism. For two proteins that fold by a simple two-state mechanism, c-src SH3 and CI-2, the Phi-values of the TSEs predicted by native topology-based reaction coordinates (including Q, the fraction of native contacts) are almost identical to those of the TSE based on P(fold), with correlation coefficients of >0.90. For proteins with complex folding mechanisms that have especially broad, asymmetrical free energy barriers such as the designed 3-ankyrin repeating protein (3ANK) or proteins with distinct intermediates such as cyanovirin-N (CV-N), we show that the ensemble of structures with P(fold) = 0.50 generally does not include the chemically relevant transition states. This weakness of P(fold) limits its usefulness in protein folding studies. For such systems, elucidating the essential features of folding mechanisms requires using multiple reaction coordinates, although the number is still rather small. At the same time, for simple folding mechanisms, there is no indication of superiority for P(fold) over structurally chosen and thermodynamically relevant reaction coordinates that correctly measure the degree of nativeness.

CSK Tyrosine-Protein Kinase↗

PubMed2005

Absolute rate theories of epigenetic stability.

Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory of chemical reactions corrected by a transmission factor. Both the probability of the rare cellular states that allow epigenetic escape and the transmission factor depend on the rates of DNA binding and unbinding events and on the rates of protein synthesis and degradation. Different mechanisms of escape from the stable attractors occur in the nonadiabatic, weakly adiabatic, and strictly adiabatic regimes, characterized by the relative values of those input rates.

DNA↗

PubMed2005

Nonequilibrium statistical mechanical models for cytoskeletal assembly: towards understanding tensegrity in cells.

The cytoskeleton is not an equilibrium structure. To develop theoretical tools to investigate such nonequilibrium assemblies, we study a statistical physical model of motorized spherical particles. Though simple, it captures some of the key nonequilibrium features of the cytoskeletal networks. Variational solutions of the many-body master equation for a set of motorized particles accounts for their thermally induced Brownian motion as well as for the motorized kicking of the structural elements. These approximations yield stability limits for crystalline phases and for frozen amorphous structures. The methods allow one to compute the effects of nonequilibrium behavior and adhesion (effective cross-linking) on the mechanical stability of localized phases as a function of density, adhesion strength, and temperature. We find that nonequilibrium noise does not necessarily destabilize mechanically organized structures. The nonequilibrium forces strongly modulate the phase behavior and have comparable effect as the adhesion due to cross-linking. Modeling transitions such as these allows the mechanical properties of cytoskeleton to rapidly and adaptively change. The present model provides a statistical mechanical underpinning for a tensegrity picture of the cytoskeleton.

Animals↗

PubMed2005

The energy landscape of modular repeat proteins: topology determines folding mechanism in the ankyrin family.

Proteins consisting of repeating amino acid motifs are abundant in all kingdoms of life, especially in higher eukaryotes. Repeat-containing proteins self-organize into elongated non-globular structures. Do the same general underlying principles that dictate the folding of globular domains apply also to these extended topologies? Using a simplified structure-based model capturing a perfectly funneled energy landscape, we surveyed the predicted mechanism of folding for ankyrin repeat containing proteins. The ankyrin family is one of the most extensively studied classes of non-globular folds. The model based only on native contacts reproduces most of the experimental observations on the folding of these proteins, including a folding mechanism that is reminiscent of a nucleation propagation growth. The confluence of simulation and experimental results suggests that the folding of non-globular proteins is accurately described by a funneled energy landscape, in which topology plays a determinant role in the folding mechanism.

Algorithms↗

PubMed2005

Bridging the gap between the mode coupling and the random first order transition theories of structural relaxation in liquids.

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating, in a self-consistent way, the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated hopping events called instantons. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event. In the vertex, the probability is proportional to exp(-A/s(c)) where s(c) is the configurational entropy. Close to the glass transition temperature, Tg, since s(c) is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor, phi(t), in deeply supercooled liquid fairly well. We show that below the mode coupling transition temperature, T(c), phi(t) not only decays via the hopping channel but the otherwise frozen MCT part of phi(t) also shows a hopping induced decay. This decay is primarily due to the relaxation of the longitudinal viscosity which is otherwise divergent in the idealized MCT. We further show that although hopping motion induces a decay in the MCT part of phi(t), due to the self-consistent calculation, this effect is nonlinear in nature.

Journal Article↗

PubMed2005

A funneled energy landscape for cytochrome c directly predicts the sequential folding route inferred from hydrogen exchange experiments.

Proteins fold through a variety of mechanisms. For a given protein, folding routes largely depend on the protein's stability and its native-state geometry, because the landscape is funneled. These ideas are corroborated for cytochrome c by using a coarse-grained topology-based model with a perfect funnel landscape that includes explicit modeling of the heme. The results show the importance of the heme as a nucleation site and explain the observed hydrogen exchange patterns of cytochrome c within the context of energy landscape theory.

Biophysical Phenomena↗