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Peter G. Wolynes

Publications and source records attributed to Peter G. Wolynes.

At least 73 records · Page 4Linked to original sources
arXiv2004

Self consistent proteomic field theory of stochastic gene switches

We present a self-consistent field approximation to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the probability distribution and its moments. A much larger class of problems, such as genetic networks and cascades also remain exactly solvable with this approximation. We discuss in depth certain specific types of basic switches, which are used by biological systems and compare their behavior to the expectation for a deterministic switch.

q-bio.MN↗
arXiv2004

Comment on the ``Novel Isotope Effects Observed in Polarization Echo Experiments in Glasses''

The novel isotope and magnetic effects on two level system echoes in glasses observed by Nagel et al.(Phys.Rev.Lett. 92, 245511 (2004)) provide unique experimental insight into the nature of tunneling systems in amorphous solids. We show their observations are consistent with tunneling systems being extended systems having of order 100 moving units, as predicted by theory (Phys.Rev.Lett. 87, 195901 (2001)). The numerous nuclear quadrupole interactions within a tunneling center explain the magnitude of the magnetic and frequency dependence observed in deuterated glycerol. The extended nature of two level systems explains why a small residual effect can still be observed in regular glycerol even with its low abundance of quadrupolar nuclei.

cond-mat.dis-nn↗
arXiv2004

Theory of Aging in Structural Glasses

The random first order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of ``entropic droplets'' in terms of libraries of local energy landscapes is introduced which treats in a uniform way the supercooled liquid (reproducing earlier results) and glassy regimes. The resulting microscopic theory of aging makes contact with the Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both approaches are predicted and shown to be consistent with experiment. The nonlinearity of glassy relaxation is shown to quantitatively correlate with liquid fragility. The residual nonArrhenius temperature dependence of relaxation observed in quenched glasses is explained. The broadening of relaxation spectra in the nonequilibrium glass with decreasing temperature is quantitatively predicted. The theory leads to the prediction of spatially fluctuating fictive temperatures in the long-aged glassy state, which have non-Gaussian statistics. This can give rise to ``ultra-slow'' relaxations in systems after deep quenches.

cond-mat.soft↗
arXiv2004

Stability and Dynamics of Crystals and Glasses of Motorized Particles

Many of the large structures of the cell, such as the cytoskeleton, are assembled and maintained far from equilibrium. We study the stabilities of various structures for a simple model of such a far-from-equilibrium organized assembly in which spherical particles move under the influence of attached motors. From the variational solutions of the manybody master equation for Brownian motion with motorized kicking we obtain a closed equation for the order parameter of localization. Thus we obtain the transition criterion for localization and stability limits for the crystalline phase and frozen amorphous structures of motorized particles. The theory also allows an estimate of nonequilibrium effective temperatures characterizing the response and fluctuations of motorized crystals and glasses.

cond-mat.soft↗
arXiv2003

Reply to Comment on "Microscopic theory of network glasses"

In a Comment (cond-mat/0310030) on our recent paper on network glasses (Phys. Rev. Lett., 2003, 90, 085505), Micoulaut and Boolchand (MB) compare our predictions on glass transitions in network systems for the ratios of the transition temperatures TA/TG and TK/TG with experimental data. They claim significant differences between experiment and theory are seen and claim the lack of agreement is due to flaws in our theory. Their comparison of TA/TG is incorrect as they do not measure the same quantity that our theory predicts. The TK/TG comparison shows remarkable agreement between theory and experiment.

cond-mat.mtrl-sci↗
arXiv2003

Barrier Softening near the onset of Non-Activated Transport in Supercooled Liquids: Implications for Establishing Detailed Connection between Thermodynamic and Kinetic Anomalies in Supercooled Liquids

According to the Random First Order Transition (RFOT) theory of glasses, the barriers for activated dynamics in supercooled liquids vanish as the temperature of a viscous liquid approaches the dynamical transition temperature from below. This occurs due to a decrease of the surface tension between local meta-stable molecular arrangements much like at a spinodal. The dynamical transition thus represents a crossover from the low $T$ activated bevavior to a collisional transport regime at high $T$. This barrier softening explains the deviation of the relaxation times, as a function of temperature, from the simple $\log τ\propto 1/s_c$ dependence at the high viscosity to a mode-mode coupling dominated result at lower viscosity. By calculating the barrier softening effects, the RFOT theory provides a {\em unified} microscopic way to interpret structural relaxation data for many distinct classes of structural glass formers over the measured temperature range. The theory also provides an unambiguous procedure to determine the size of dynamically cooperative regions in the presence of barrier renormalization effects using the experimental temperature dependence of the relaxation times and the configurational entropy data. We use the RFOT theory framework to discuss data for tri-naphthyl benzene, salol, propanol and silica as representative systems.

cond-mat.dis-nn↗
arXiv2003

Stochastic gene expression as a many body problem

Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum many body problems. The dynamics of a single gene switch resembles the spin boson model of a two site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed, weakly frustrated stochastic networks than for randomly connected networks.

cond-mat.dis-nn↗
arXiv2003

Buffed energy landscapes: Another solution to the kinetic paradoxes of protein folding

The energy landscapes of proteins have evolved to be different from most random heteropolymers. Many studies have concluded that evolutionary selection for rapid and reliable folding to a given structure that is stable at biological temperatures leads to energy landscapes having a single dominant basin and an overall funnel topography. We show here that, while such a landscape topography is indeed a sufficient condition for folding, another possibility also exists, giving a new class of foldable sequences. These sequences have landscapes that are only weakly funneled in the conventional thermodynamic sense, but have unusually low kinetic barriers for reconfigurational motion. Traps have been specifically removed by selection. Here we examine the possibility of folding on these "buffed" landscapes, by mapping the determination of statistics of pathways for the heterogeneous nucleation processes involved in escaping from traps to the solution of an imaginary time Schroedinger equation. This equation is solved analytically in adiabatic and ``soft-wall'' approximations, and numerical results are shown for the general case. The fraction of funneled vs. buffed proteins in sequence space is estimated, suggesting the statistical dominance of the funneling mechanism for achieving foldability.

cond-mat.dis-nn↗
arXiv2003

Microscopic theory of network glasses

A molecular theory of the glass transition of network forming liquids is developed using a combination of self-consistent phonon and liquid state approaches. Both the dynamical transition and the entropy crisis characteristic of random first order transitions are mapped out as a function of the degree of bonding and the density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, the theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls relative to the laboratory transition. These results indicate why highly coordinated liquids should be "strong" while van der Waals liquids without coordination are "fragile".

cond-mat↗
arXiv2002

The Origin of the Boson Peak and the Thermal Conductivity Plateau in Low Temperature Glasses

We argue that the intrinsic glassy degrees of freedom in amorphous solids giving rise to the thermal conductivity plateau and the ``boson peak'' in the heat capacity at moderately low temperatures are directly connected to those motions giving rise to the two-level like excitations seen at still lower temperatures. These degrees of freedom can be thought of as strongly anharmonic transitions between the local minima of the glassy energy landscape that are accompanied by ripplon-like domain wall motions of the glassy mosaic structure predicted to occur at $T_g$ by the random first order transition theory. The energy spectrum of the vibrations of the mosaic depends on the glass transition temperature, the Debye frequency and the molecular length scale. The resulting spectrum reproduces the experimental low temperature Boson peak. The ``non-universality'' of the thermal conductivity plateau depends on $k_B T_g/\hbar ω_D$ and arises from calculable interactions with the phonons.

cond-mat.dis-nn↗
arXiv2001

The Intrinsic Quantum Excitations of Low Temperature Glasses

Several puzzling regularities concerning the low temperature excitations of glasses are quantitatively explained by quantizing domain wall motions of the random first order glass transition theory. The density of excitations agrees with experiment and scales with the size of a dynamically coherent region at $T_g$, being about 200 molecules. The phonon coupling depends on the Lindemann ratio for vitrification yielding the observed universal relation $l/λ\simeq 150$ between phonon wavelength $λ$ and mean free path $l$. Multilevel behavior is predicted to occur in the temperature range of the thermal conductivity plateau.

cond-mat.dis-nn↗
arXiv2001

Theory of Microemulsion Glasses

We show that the tendency towards microphase separation in microemulsions leads to the formation of a glassy state after sufficiently strong correlations between polar and hydrophobic regions have been established. Glassiness is predicted to occur above a critical volume fraction of surfactant, which is determined by the length of the amphiphilic molecules. Our results are obtained by solving the dynamical equations for the correlation functions of the system and by using a replica approach.

cond-mat.dis-nn↗
arXiv2001

Self generated randomness, defect wandering and viscous flow in stripe glasses

We show that the competition between interactions on different length scales, as relevant for the formation of stripes in doped Mott insulators, can cause a glass transition in a system with no explicitly quenched disorder. We analytically determine a universal criterion for the emergence of an exponentially large number of metastable configurations that leads to a finite configurational entropy and a landscape dominated viscous flow. We demonstrate that glassines is unambiguously tied to a new length scale which characterizes the typical length over which defects and imperfections in the stripe pattern are allowed to wander over long times.

cond-mat.dis-nn↗
arXiv2001

Reply to Comment on "Stripe glasses: self generated randomness in a uniformly frustrated system"

Using our previous results for the configurational entropy of a stripe glass as well as a variational result for the bare surface tension of entropic droplets we show that there is no disagreement between the numerical simulations of Grousson et al. and our theory. The claim that our theory disagrees with numerical simulations is based on the assumption that the surface tension is independent of the frustration parameter Q of the model. However, we show in this Reply that it varies strongly with Q and that the resulting Q-dependence of the kinetic fragility agrees with the one obtained by Grousson et al. We believe that this answers the questions raised in the Comment by Grousson et al.

cond-mat.dis-nn↗
arXiv2001

Diffusion and the Mesoscopic Hydrodynamics of Supercooled Liquids

The description of molecular motion by macroscopic hydrodynamics has a long and continuing history. The Stokes-Einstein relation between the diffusion coefficient of a solute and the solvent viscosity predicted using macroscopic continuum hydrodynamics, is well satisfied for liquids under ordinary to high temperature conditions, even for solutes as small as the solvent. Diffusion in supercooled liquids near their glass transition temperature has been found to deviate by as much as 3 orders of magnitude from that predicted by the Stokes-Einstein Relation [1]. Based on the random first order transition theory [2-4], supercooled liquids possess a mosaic structure. The size- and temperature-dependence of the transport anomalies are quantitatively explained with an effective medium hydrodynamics model based on the microscopic theory of this mesoscale, mosaic structure.

cond-mat.dis-nn↗
arXiv2000

On the Number of Metastable States in a Stripe Glass

We estimate the number of metastable states of a self generated stripe glass, relevant for the formation of glassy doped Mott insulators. Using replica bound states, we demonstrate that the configurational entropy is the difference between the entropy of the stripe liquid and of an amorphous stripe solid with phonon-type excitations. Using simple scaling laws we then determine the relationship between the modulation length and the configurational entropy.

cond-mat.dis-nn↗
arXiv2000

Microscopic Theory of Protein Folding Rates.I: Fine Structure of the Free Energy Profile and Folding Routes from a Variational Approach

A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G. Wolynes, Phys. Rev. Lett. {\bf 81}, 5237 (1998)]. We choose the $λ$-repressor protein as an illustrative example and focus on how the polymer chain statistics influence free energy profiles and partially ordered ensembles of structures. In particular, we investigate the role of chain stiffness on the free energy profile and folding routes. We evaluate the applicability of simpler approximations in which the conformations of the protein molecule along the folding route are restricted to have residues that are either entirely folded or unfolded in contiguous stretches. We find that the folding routes obtained from only one contiguous folded region corresponds to a chain with a much greater persistence length than appropriate for natural protein chains, while the folding route obtained from two contiguous folded regions is able to capture the relatively folded regions calculated within the variational approach. The free energy profiles obtained from the contiguous sequence approximations have larger barriers than the more microscopic variational theory which is understood as a consequence of partial ordering.

cond-mat.soft↗