arXiv subjects

Aljaž Godec

Publications and source records attributed to Aljaž Godec.

45 records · Page 3Linked to original sources

arXiv2021

Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle's mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on "scattering fingerprints" of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures -- the intermediate scattering function and dynamic structure factor -- and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and X-ray scattering scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

cond-mat.stat-mech↗

arXiv2021

Emergent memory and kinetic hysteresis in strongly driven networks

Stochastic network-dynamics are typically assumed to be memory-less. Involving prolonged dwells interrupted by instantaneous transitions between nodes such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene expression, molecular machines, spreading of diseases, protein dynamics, diffusion in energy landscapes, epigenetics and many others. However, as soon as transitions cease to be negligibly short, as often observed in experiments, the dynamics develops a memory. That is, state-changes depend not only on the present state but also on the past. Here, we establish the first thermodynamically consistent -- dissipation-preserving -- mapping of continuous dynamics onto a network, which reveals ingrained dynamical symmetries and an unforeseen kinetic hysteresis. These symmetries impose three independent sources of fluctuations in state-to state kinetics that determine the `flavor of memory'. The hysteresis between the forward/backward in time coarse-graining of continuous trajectories implies a new paradigm for the thermodynamics of active molecular processes in the presence of memory, that is, beyond the assumption of local detailed balance. Our results provide a new understanding of fluctuations in the operation of molecular machines as well as catch-bonds involved in cellular adhesion.

cond-mat.stat-mech↗

arXiv2021

Criticality in Cell Adhesion

We illuminate the many-body effects underlying the structure, formation, and dissolution of cellular adhesion domains in the presence and absence of forces. We consider mixed Glauber-Kawasaki dynamics of a two-dimensional model of nearest-neighbor interacting adhesion bonds with intrinsic binding-affinity under the action of a shared pulling or pushing force. We consider adhesion bonds that are immobile due to being anchored to the underlying cytoskeleton as well as adhesion molecules that are transiently diffusing. Highly accurate analytical results are obtained on the pair-correlation level of the Bethe-Guggenheim approximation for the complete thermodynamics and kinetics of adhesion clusters of any size, including the thermodynamic limit. A new kind of dynamical phase transition is uncovered -- the mean formation and dissolution times per adhesion bond change discontinuously with respect to the bond-coupling parameter. At the respective critical points cluster formation and dissolution are fastest, while the statistically dominant transition path undergoes a qualitative change -- the entropic barrier to complete binding/unbinding is rate-limiting below, and the phase transition between dense and dilute phases above the dynamical critical point. In the context of the Ising model the dynamical phase transition reflects a first-order discontinuity in the magnetization-reversal time. Our results provide a potential explanation for the mechanical regulation of cell adhesion, and suggest that the quasi-static and kinetic response to changes in the membrane stiffness or applied forces is largest near the statical and dynamical critical point, respectively.

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arXiv2021

A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates

Memory effects in time-series of experimental observables are ubiquitous, have important cosequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time-series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic Molecular Dynamics simulations.

cond-mat.stat-mech↗

arXiv2021

Time- and ensemble-average statistical mechanics of the Gaussian Network Model

We present analytical results (up to a numerical diagonalization of a real symmetric matrix) for a set of time- and ensemble-average physical observables in the non-Hookean Gaussian Network Model (GNM) - a generalization of the Rouse model to elastic networks with links with a certain degree of extensional and rotational stiffness. We focus on a set of coarse-grained observables that may be of interest in the analysis of GNM in the context of internal motions in proteins and mechanical frames in contact with a heat bath. A C++ computer code is made available that implements all analytical results.

cond-mat.stat-mech↗

arXiv2021

Ubiquitous Dynamical Time Asymmetry in Measurements on Materials and Biological Systems

Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic and rheological response functions, and time series of distances derived from optical tweezers, single-molecule spectroscopy and molecular dynamics simulations. In many such systems the projection renders the reduced dynamics non-Markovian and the observable is not prepared in, or initially sampled from and averaged over, a stationary distribution. We prove that such systems always exhibit non-equilibrium, time asymmetric dynamics. That is, they evolve in time with a broken time-translation invariance in a manner closely resembling aging dynamics. We identify the entropy associated with the breaking of time-translation symmetry that is a measure of the instantaneous thermodynamic displacement of latent, hidden degrees of freedom from their stationary state. Dynamical time asymmetry is a general phenomenon, independent of the underlying energy surface, and is frequently even visible in measurements on systems that have fully reached equilibrium. This finding has fundamental implications for the interpretation of many experiments on, and simulations of, biological and materials systems.

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arXiv2020

Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle

We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model, we analyze tagged-particle diffusion in a single file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the "confining" (all background particles in front of the tagged-particle) and "pushing" (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.

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arXiv2020

Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations and correlations of time average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and discuss the results from a physical perspective. Feynman-Kac formulas are re-derived using Itô calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large deviation time-scales. For reversible dynamics with equilibrated initial conditions we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems.

cond-mat.stat-mech↗

arXiv2012

Exact Generalization of Local Thermodynamics of Inhomogeneous Fluids to Arbitrary Spatial Scales

In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local thermodynamic relations for the canonical and isothermal- isobaric ensembles without limitations with respect to the nature of intermolecular interactions. The inhomogeneity of the system is shown to result in two distinct entropic contributions. The intrinsic contribution is due the specific distribution of local environments experienced by a single molecule while the extrinsic one originates exclusively from the local variation of the density from its bulk value.

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