Biased Random Walk in Crowded Environment: Breaking Uphill/Downhill Symmetry of Transition Times

Uphill Drift in the Absence of Current in Single-File Diffusion

Single-file diffusion is a paradigmatic model for the transport of Brownian colloidal particles in narrow one-dimensional channels, such as those found in certain porous media, where the particles cannot cross each other. We consider a system where a different external uniform potential is present to the right and left of an origin. For example, this is the case when two channels meeting at the origin have different radii. In equilibrium, the chemical potential of the particles are equal, the density is thus lower in the region with the higher potential, and by definition there is no net current in the system. Remarkably, a single-file tracer particle initially located at the origin, with position denoted by Y(t), exhibits an average uphill drift toward the region of highest potential. This drift has the late time behavior ⟨Y(t)⟩=Ct^{1/4}, where the prefactor C depends on the initial particle arrangement. This surprising result is shown analytically by computing the first two moments of Y(t) through a simple and physically illuminating method, and also via extensive numerical simulations.

Milestoning estimators of dissipation in systems observed at a coarse resolution

Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may-via a process called milestoning-improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.

Arrhenius law for interacting diffusive systems

Finding the mean time it takes for a particle to escape from a metastable state due to thermal fluctuations is a fundamental problem in physics, chemistry, and biology. Here, we consider the escape rate of interacting diffusive particles, from a deep potential trap within the framework of the macroscopic fluctuation theory-a nonequilibrium hydrodynamic theory. For systems without excluded volume, our investigation reveals adherence to the well-established Arrhenius law. However, in the presence of excluded volume, a universality class emerges, fundamentally altering the escape rate. Remarkably, the modified escape rate within this universality class is independent of the interactions at play. The universality class, demonstrating the importance of excluded volume effects, may bring insights to the interpretation of escape processes in the realm of chemical physics.

RNA polymerase drives ribonucleotide excision DNA repair in E. coli

Ribonuclease HII (RNaseHII) is the principal enzyme that removes misincorporated ribonucleoside monophosphates (rNMPs) from genomic DNA. Here, we present structural, biochemical, and genetic evidence demonstrating that ribonucleotide excision repair (RER) is directly coupled to transcription. Affinity pull-downs and mass-spectrometry-assisted mapping of in cellulo inter-protein cross-linking reveal the majority of RNaseHII molecules interacting with RNA polymerase (RNAP) in E. coli. Cryoelectron microscopy structures of RNaseHII bound to RNAP during elongation, with and without the target rNMP substrate, show specific protein-protein interactions that define the transcription-coupled RER (TC-RER) complex in engaged and unengaged states. The weakening of RNAP-RNaseHII interactions compromises RER in vivo. The structure-functional data support a model where RNaseHII scans DNA in one dimension in search for rNMPs while "riding" the RNAP. We further demonstrate that TC-RER accounts for a significant fraction of repair events, thereby establishing RNAP as a surveillance "vehicle" for detecting the most frequently occurring replication errors.

Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining

The entropy production rate (EPR) measures time-irreversibility in systems operating far from equilibrium. The challenge in estimating the EPR for a continuous variable system is the finite spatiotemporal resolution and the limited accessibility to all of the nonequilibrium degrees of freedom. Here, we estimate the irreversibility in partially observed systems following oscillatory dynamics governed by coupled overdamped Langevin equations. We coarse-grain an observed variable of a nonequilibrium driven system into a few discrete states and estimate a lower bound on the total EPR. As a model system, we use hair-cell bundle oscillations driven by molecular motors, such that the bundle tip position is observed, but the positions of the motors are hidden. In the observed variable space, the underlying driven process exhibits second-order semi-Markov statistics. The waiting time distributions (WTD), associated with transitions among the coarse-grained states, are non-exponential and convey the information on the broken time-reversal symmetry. By invoking the underlying time-irreversibility, we calculate a lower bound on the total EPR from the Kullback-Leibler divergence (KLD) between WTD. We show that the mean dwell-time asymmetry factor - the ratio between the mean dwell-times along the forward direction and the backward direction, can qualitatively measure the degree of broken time reversal symmetry and increases with finer spatial resolution. Finally, we apply our methodology to a continuous-time discrete Markov chain model, coarse-grained into a linear system exhibiting second-order semi-Markovian statistics, and demonstrate the estimation of a lower bound on the total EPR from irreversibility manifested only in the WTD.

Crowding breaks the forward/backward symmetry of transition times in biased random walks

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and provide a clear physical picture. Recent theoretical studies made a surprising discovery that in complex systems, the symmetry of molecular forward/backward transition times with respect to local bias in the dynamics may be broken and it may take longer to go downhill than uphill. The physical origins of these phenomena remain not fully understood. Here, we explore in more detail the microscopic features of the symmetry breaking in the forward/backward transition times by analyzing exactly solvable discrete-state stochastic models. In particular, we consider a specific case of two random walkers on a four-site periodic lattice as the way to represent the general systems with multiple pathways. It is found that the asymmetry in transition times depends on several factors that include the degree of deviation from equilibrium, the particle crowding, and methods of measurements of dynamic properties. Our theoretical analysis suggests that the asymmetry in transition times can be explored experimentally for determining the important microscopic features of natural processes by quantitatively measuring the local deviations from equilibrium and the degrees of crowding.

Cycle Completion Times Probe Interactions with Environment

Recent measurements of the durations of nonequilibrium processes provide valuable information on microscopic mechanisms and energetics. Theory for corresponding experiments to date is well-developed for single-particle systems only. Little is known for interacting systems in nonequilibrium environments. Here we introduce and study a basic model for cycle processes interacting with an environment that can exhibit a net particle flow. We find a surprising richness of cycle time variations with environmental conditions. This manifests itself in unequal cycle times τ⁺ and τ^- in forward and backward cycle directions with both asymmetries τ^- < τ⁺ and τ^- > τ⁺, speeding up of backward cycles by interactions, and dynamical phase transitions, where cycle times become multimodal functions of the bias. The model allows us to relate these effects to specific microscopic mechanisms, which can be helpful for interpreting experiments.