arXiv subjects

Peter G. Wolynes

Publications and source records attributed to Peter G. Wolynes.

At least 37 records · Page 2Linked to original sources

arXiv2013

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.

q-bio.BM↗

arXiv2013

Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: The comparative role of configurational entropy and elasticity

We compute the temperature-dependent barrier for alpha-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition(RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes, which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko, which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance---a kinetic quantity---from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.

cond-mat.dis-nn↗

arXiv2013

Fluctuating Mobility Generation and Transport in Glasses

In the context of the random first order transition theory we use an extended mode coupling theory of the glass transition that includes activated events to account for spatiotemporal structures in aging and rejuvenating glasses. We numerically solve fluctuating dynamical equations for mobility and fictive temperature fields which capture both mobility generation through activated events and facilitation effects. Upon rejuvenating, a source of high mobility at a glass surface initiates a growth front of mobility which propagates into the unstable low mobility region. The speed of the front is consistent with experiments on the rejuvenation of stable glasses, which "melt" from their surface.

cond-mat.dis-nn↗

arXiv2012

Microscopic theory of the glassy dynamics of passive and active network materials

Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active network materials. We construct a general microscopic network model that incorporates nonlinear elasticity of individual filaments and steric constraints due to crowding. Based on constructive analogies between structural glass forming liquids and random field Ising magnets implemented using a heterogeneous self-consistent phonon method, our scheme provides a microscopic approach to determine the mismatch surface tension and the configurational entropy, which compete in determining the barrier for structural rearrangements within the random first order transition theory of escape from a local energy minimum. The influence of crosslinking on the fragility of inorganic network glass formers is recapitulated by the model. For active network materials, the mapping, which correlates the glassy characteristics to the network architecture and properties of nonequilibrium motor processes, is shown to capture several key experimental observations on the cytoskeleton of living cells: Highly connected tense networks behave as strong glass formers; intense motor action promotes reconfiguration. The fact that our model assuming a negative motor susceptibility predicts the latter suggests that on average the motorized processes in living cells do resist the imposed mechanical load. Our calculations also identify a spinodal point where simultaneously the mismatch penalty vanishes and the mechanical stability of amorphous packing disappears.

cond-mat.stat-mech↗

arXiv2012

On the Strength of Glasses

The remarkable strength of glasses is examined using the random first order transition theory of the glass transition. The theory predicts that strength depends on elastic modulus but also on the configurational energy frozen in when the glass is prepared. The stress catalysis of cooperative rearrangements of the type responsible for the supercooled liquid's high viscosity account quantitatively for the measured strength of a range of metallic glasses, silica and a polymer glass.

cond-mat.dis-nn↗

arXiv2012

The Influence of Decoys on the Noise and Dynamics of Gene Expression

Many transcription factors bind to DNA with a remarkable lack of specificity, so that regulatory binding sites compete with an enormous number of non-regulatory 'decoy' sites. For an auto-regulated gene, we show decoy sites decrease noise in the number of unbound proteins to a Poisson limit that results from binding and unbinding. This noise buffering is optimized for a given protein concentration when decoys have a 1/2 probability of being occupied. Decoys linearly increase the time to approach steady state and exponentially increase the time to switch epigenetically between bistable states.

q-bio.MN↗

arXiv2012

Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.

physics.bio-ph↗

arXiv2012

Active contractility in actomyosin networks

Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of crosslink concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament sliding. Using computer simulations we examine how the concentration and susceptibility of motors contribute to their collective behavior and interplay with the network connectivity to regulate macroscopic contractility. Our model is shown to capture the formation and dynamics of contractile structures and agree with the observed dependence of active contractility on microscopic parameters including the contractility onset. Cooperative action of load-resisting motors in a force-percolating structure integrates local contraction/buckling events into a global contractile state via an active coarsening process, in contrast to the flow transition driven by uncorrelated kicks of susceptible motors.

physics.bio-ph↗

arXiv2011

The Interplay of Nonlinearity and Architecture in Equilibrium Cytoskeletal Mechanics

The interplay between cytoskeletal architecture and the nonlinearity of the interactions due to bucklable filaments plays a key role in modulating the cell's mechanical stability and affecting its structural rearrangements. We study a model of cytoskeletal structure treating it as an amorphous network of hard centers rigidly cross-linked by nonlinear elastic strings, neglecting the effects of motorization. Using simulations along with a self-consistent phonon method, we show that this minimal model exhibits diverse thermodynamically stable mechanical phases that depend on excluded volume, crosslink concentration, filament length and stiffness. Within the framework set by the free energy functional formulation and making use of the random first order transition theory of structural glasses, we further estimate the characteristic densities for a kinetic glass transition to occur in this model system. Network connectivity strongly modulates the transition boundaries between various equilibrium phases, as well as the kinetic glass transition density.

cond-mat.stat-mech↗

arXiv2011

On the spontaneous collective motion of active matter

Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are driven by energy-consuming motors. While systems driven by small-step motors are described by an effective temperature and are thus quiescent, at higher order in step size, both homogeneous and inhomogeneous, flowing and oscillating behavior emerges. Motors that respond with a negative susceptibility to imposed forces lead to an apparent negative-temperature system in which beautiful structures form resembling the asters seen in cell division.

cond-mat.soft↗

arXiv2011

Effective temperature and glassy dynamics of active matter

A systematic expansion of the many-body master equation for active matter, in which motors power configurational changes as in the cytoskeleton, is shown to yield a description of the steady state and responses in terms of an effective temperature. The effective temperature depends on the susceptibility of the motors and a Peclet number which measures their strength relative to thermal Brownian diffusion. The analytic prediction is shown to agree with previous numerical simulations and experiments. The mapping also establishes a description of aging in active matter that is also kinetically jammed.

cond-mat.soft↗

arXiv2011

Glassiness in Uniformly Frustrated Systems

We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the replica formalism developed for the spin glass systems to study the glass transition in uniformly frustrated many-body systems. Here a localization in configuration space emerges leading to an entropy crisis of the system. Using a combination of density functional theory and Landau theory of the glassy state, we first analyze the mean field glass transition within the saddle point approximation. We go beyond the saddle point approximation by considering the energy fluctuations around the saddle point and evaluate the barrier height distribution.

cond-mat.dis-nn↗

arXiv2010

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

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

q-bio.BM↗

arXiv2010

The Ultimate Fate of Supercooled Liquids

In recent years it has become widely accepted that a dynamical length scale ξ_α plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing ξ_α and the size of the crystal nucleus, ξ_M, which shrinks on cooling. We argue that at low temperatures where ξ_α > ξ_M a new crystallization mechanism emerges enabling rapid development of a large scale web of sparsely connected crystallinity. Though we predict this web percolates the system at too low a temperature to be easily seen in the laboratory, there are noticeable residual effects near the glass transition that can account for several previously observed unexplained phenomena of deeply supercooled liquids including Fischer clusters, and anomalous crystal growth near T_g.

cond-mat.dis-nn↗

arXiv2009

A universal origin for secondary relaxations in supercooled liquids and structural glasses

Nearly all glass forming liquids display secondary relaxations, dynamical modes seemingly distinct from the primary alpha relaxations. We show that accounting for driving force fluctuations and the diversity of reconfiguring shapes in the random first order transition theory yields a low free energy tail on the activation barrier distribution which shares many of the features ascribed to secondary relaxations. While primary relaxation takes place through activated events involving compact regions, secondary relaxation corresponding to the tail is governed by more ramified, string-like, or percolation-like clusters of particles. These secondary relaxations merge with the primary relaxation peak becoming dominant near the dynamical crossover temperature $T_c$, where they smooth the transition between continuous dynamics described by mode-coupling theory and activated events.

cond-mat.soft↗

arXiv2009

Wavenumber dependence of the structural relaxation time in the crossover regime of supercooled liquid dynamics

As a liquid is progressively supercooled an intriguing weakening of the wavenumber ($q$) dependence of the structural relaxation time $τ(q)$ in the large q limit is observed both in experiments and simulation studies. Neither the continuous Brownian diffusive dynamics nor the discontinuous activated events can alone explain the anomalous wavenumber dependence. Here we use our recently developed theory that unifies the mode coupling theory (MCT) for continuous dynamics and the random first order transition theory (RFOT) treatment of activated discontinuous motion as a nucleation (instanton) process, to understand the wavenumber dependence of density relaxation. The predicted smooth change in mechanism of relaxation from diffusive to activated, in the crossover regime, is wavevector dependent and is eventually responsible for sub-quadratic, almost linear, $q$ dependence of the relaxation time.

cond-mat.soft↗

arXiv2008

Spatiotemporal structures in aging and rejuvenating glasses

Complex spatiotemporal structures develop during the process of aging glasses after cooling and of rejuvenating glasses upon heating. The key to understanding these structures is the interplay between the activated reconfiguration events which generate mobility and the transport of mobility. These effects are both accounted for by combining the random first order transition theory of activated events with mode coupling theory in an inhomogeneous setting. The predicted modifications by mobility transport of the time course of the aging regime are modest. In contrast, the rejuvenation process is strongly affected through the propagation of fronts of enhanced mobility originating from the initial reconfiguration events. The structures in a rejuvenating glass resemble flames. An analysis along the lines of combustion theory provides an estimate of the front propagation speed. Heterogeneous rejuvenation naturally should occur for glasses with free surfaces. The analogy with combustion also provides a new way of looking at the uptake of diluents by glasses described by case II and super case II diffusion.

cond-mat.soft↗

arXiv2008

Gene-gene cooperativity in small networks

We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal footing we propose a mapping which connects the molecular level description of networks to the binary representation. We construct a phase diagram indicating when genes can be considered to be independent and when the coupling between them cannot be neglected leading to synchrony or correlations. We find that an appropriately mapped boolean description reproduces the probabilities of gene expression states of the full stochastic system very well and can be transfered to examples of self-regulatory systems with a larger number of gene copies.

q-bio.MN↗