arXiv subjects

Anatoly B. Kolomeisky

Publications and source records attributed to Anatoly B. Kolomeisky.

At least 19 recordsLinked to original sources

arXiv2026

Consistent time reversal and reliable and accurate inference in the presence of memory

Thermodynamic inference from coarse observations remains a key challenge. Memory, in particular correlations between consecutively observed mesostates, blur signatures of irreversibility and must be accounted for in defining physical time-reversal, which remains an open problem. We derive an experimentally accessible k-th order estimator for the entropy production rate. Using novel measure-theoretic techniques we prove necessary and sufficient conditions for guaranteed lower bounds on the dissipation even in the strongly non-Markovian setting. The proof reveals that estimators saturated in the order unravel the duration of memory which needs to be considered in defining physically consistent time-reversal. We show that Markovian estimators in absence of a time-scale separation lead to artifacts, which convey no physical meaning. Similarly, estimators not saturated in the order may overestimate the dissipation. The necessity of correctly accounting for memory in thermodynamic inference from strongly non-Markovian observations underscores the still underappreciated challenges and intricacies in defining and understanding irreversibility in presence of memory. Our results will hopefully stimulate experiments systematically considering thermodynamic inference on multiple scales consistently accounting for memory.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic inference from noisy single-molecule time series

Single-molecule or single-particle tracking measurements inherently yield noisy microscopic trajectories, often significantly constrained by the diffraction limit and by the finite rate at which photons are emitted and counted. Here we study systematically the resulting effects of finite spatial and temporal resolution on one's ability to discern and quantify the arrow of time in microscopic trajectories. Given an experimental time series Y(t) degraded by noise, we consider the problem of estimating the entropy production associated with the corresponding microscopic variable X(t) using two strategies. The first attempts to infer the statistical properties of X(t) from those of Y(t) before estimating the entropy production. The second uses the experimental observable as a proxy for the true microscopic observable, with the entropy production estimator applied directly to Y(t). We prove that both strategies result in lower bounds on the true entropy production. Importantly, noise-degraded observables Y(t) undergo non-Markovian dynamics even when X(t) are Markovian, and non-Markovian entropy production estimators are advantageous. We further note nontrivial interplay between spatial and temporal resolution: in the presence of detection noise, improving the temporal resolution alone may lead to poorer rather than better entropy production estimates.

cond-mat.stat-mech↗

arXiv2026

Stress relaxation in fiber networks via force-dependent stochastic severing

Fiber networks contribute to the mechanical stability of various biological systems, from cells to tissues. Such systems have been modeled by networks of springs or fibers that exhibit rigidity transitions as a function of either connectivity or applied strain. For a fiber network under constant applied strain, severing can reduce the connectivity and destabilize an initially rigid structure. Here, we investigate stress relaxation in spring and fiber networks in the presence of stochastic, force-dependent severing. A computational model to predict stress relaxation with mechanochemical feedback of stress on severing is developed. We also examine the effects of severing on the network topology and onset of rigidity transition. Using 2D triangular lattice-based computer simulations, we explore different limits of the feedback and demonstrate the shift in the onset of rigidity depending on the limit. The limit of tension-suppressed severing delays stress relaxation and shifts the transition into the bending-dominated regime to lower-than-expected connectivity. In contrast, tension-enhanced severing accelerates relaxation and shifts the transition to higher-than-expected connectivity. It is also found that the magnitude of this shift depends on the applied shear strain and the strength of the feedback. Our theoretical approach clarifies some microscopic aspects of these phenomena. Understanding the impact of such feedback mechanisms can provide valuable insights into designing systems by tuning the feedback to the desired response.

cond-mat.soft↗

arXiv2022

The energy cost and optimal design of networks for biological discrimination

Many biological processes discriminate between correct and incorrect substrates through the kinetic proofreading mechanism which enables lower error at the cost of higher energy dissipation. Elucidating physicochemical constraints for global minimization of dissipation and error is important for understanding enzyme evolution. Here, we identify theoretically a fundamental error-cost bound which tightly constrains the performance of proofreading networks under any parameter variations preserving the rate discrimination between substrates. The bound is kinetically controlled, i.e. completely determined by the difference between the transition state energies on the underlying free energy landscape. The importance of the bound is analyzed for three biological processes. DNA replication by T7 DNA polymerase is shown to be nearly optimized, i.e. its kinetic parameters place it in the immediate proximity of the error-cost bound. The isoleucyl-tRNA synthetase (IleRS) of E. coli also operates close to the bound, but further optimization is prevented by the need for reaction speed. In contrast, E. coli ribosome operates in a high-dissipation regime, potentially in order to speed up protein production. Together, these findings establish a fundamental error-dissipation relation in biological proofreading networks and provide a theoretical framework for studying error-dissipation trade-off in other systems with biological discrimination.

physics.bio-ph↗

arXiv2021

Surface-Facilitated Trapping by Active Sites: From Catalysts to Viruses

Trapping by active sites on surfaces plays important roles in various chemical and biological processes, including catalysis, enzymatic reactions, and viral entry into host cells. However, the mechanisms of these processes remain not well understood, mostly because the existing theoretical descriptions are not fully accounting for the role of the surfaces. Here we present a theoretical investigation on the dynamics of surface-assisted trapping by specific active sites. In our model, a diffusing particle can be occasionally reversibly bound to the surface and diffuse on it before reaching the final target site. An approximate theoretical framework is developed, and its predictions are tested by Brownian Dynamics computer simulations. It is found that the surface diffusion can be crucial in mediating the association to active sites. Our theoretical predictions work reasonably well as long as the size of the active site is much smaller than the overall surface area. Potential applications of our method are discussed.

cond-mat.soft↗

arXiv2021

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 four-sites 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 quantitative measuring the local deviations from equilibrium and the degrees of crowding.

cond-mat.stat-mech↗

arXiv2021

Steady-state dynamics of exclusion process with local reversible association of particles

Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these observations, we developed a theoretical model for collective dynamics of biological molecular motors that accounts for local association/dissociation events. In our approach, the particles interacting only via exclusion move along a lattice in the preferred direction, while the reversible associations are allowed at the specific site far away from the boundaries. Considering the association/dissociation site as a local defect, the inhomogeneous system is approximated as two coupled homogeneous sub-lattices. This allows us to obtain a full description of stationary dynamics in the system. It is found that the number and nature of steady-state phases strongly depend on the values of association and dissociation transition rates. Microscopic arguments to explain these observations, as well as biological implications, are also discussed. Theoretical predictions agree well with extensive Monte Carlo computer simulations.

cond-mat.stat-mech↗

arXiv2020

Asymmetry of forward/backward transition times as a non-equilibrium measure of complexity of microscopic mechanisms

In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition times in a random walk on a lattice of two lanes. We find that either transition times can be faster depending on the lattice's net current, and the symmetry is recovered only at equilibrium. Our analysis suggests that the forward/ backward transition times' asymmetry can be used as a measure of deviation from the equilibrium of the system.

cond-mat.stat-mech↗

arXiv2020

Different time scales in dynamic systems with multiple exits

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. But the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

cond-mat.stat-mech↗

arXiv2019

The Effect of Obstacles in Multi-Site Protein Target Search with DNA Looping

Many fundamental biological processes are regulated by protein-DNA complexes called {\it synaptosomes}, which possess multiple interaction sites. Despite the critical importance of synaptosomes, the mechanisms of their formation remain not well understood. Because of the multi-site nature of participating proteins, it is widely believed that their search for specific sites on DNA involves the formation and breaking of DNA loops and sliding in the looped configurations. In reality, DNA in live cells is densely covered by other biological molecules that might interfere with the formation of synaptosomes. In this work, we developed a theoretical approach to evaluate the role of obstacles in the target search of multi-site proteins when the formation of DNA loops and the sliding in looped configurations are possible. Our theoretical method is based on analysis of a discrete-state stochastic model that uses a master equations approach and extensive computer simulations. It is found that the obstacle slows down the search dynamics in the system when DNA loops are long-lived, but the effect is minimal for short-lived DNA loops. In addition, the relative positions of the target and the obstacle strongly influence the target search kinetics. Furthermore, the presence of the obstacle might increase the noise in the system. These observations are discussed using physical-chemical arguments. Our theoretical approach clarifies the molecular mechanisms of formation of protein-DNA complexes with multiple interactions sites.

cond-mat.soft↗

arXiv2019

Target search on DNA by interacting molecules: First-passage approach

Gene regulation is one of the most important fundamental biological processes in living cells. It involves multiple protein molecules that locate specific sites on DNA and assemble gene initiation or gene repression multi-molecular complexes. While the protein search dynamics for DNA targets has been intensively investigated, the role of inter-molecular interactions during the genetic activation or repression remains not well quantified. Here we present a simple one-dimensional model of target search for two interacting molecules that can reversibly form a dimer molecular complex, which also participates in the search process. In addition, the proteins have finite residence times on specific target sites, and the gene is activated or repressed when both proteins are simultaneously present at the target. The model is analyzed using first-passage analytical calculations and Monte Carlo computer simulations. It is shown that the search dynamics exhibits a complex behavior depending on the strength of inter-molecular interactions and on the target residence times. We also found that the search time shows a non-monotonic behavior as a function of the dissociation rate for the molecular complex. Physical-chemical arguments to explain these observations are presented. Our theoretical approach highlights the importance of molecular interactions in the complex process of gene activation/repression by multiple transcription factor proteins.

physics.bio-ph↗

arXiv2019

Facilitation of DNA loop formation by protein-DNA non-specific interactions

Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-specific interactions between protein and DNA molecules on the dynamics of loop formation. Our approach is based on analyzing a discrete-state stochastic model via a method of first-passage probabilities supplemented by Monte Carlo computer simulations. It is found that depending on a protein sliding length during the non-specific binding event three different dynamic regimes of the DNA loop formation might be observed. In addition, the loop formation time might be optimized by varying the protein sliding length, the size of the DNA molecule, and the position of the specific target sequences on DNA. Our results demonstrate the importance of non-specific protein-DNA interactions in the dynamics of DNA loop formations. Several quantitative predictions that can be experimentally tested are also presented.

cond-mat.soft↗

arXiv2018

Theoretical Insights into Mechanisms of Stochastic Gating in Channel-Facilitated Molecular Transport

Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically fluctuate between several conformations during the translocation. Although this phenomenon has been intensively investigated, many properties of translocation in dynamically changing environment remain not well understood microscopically. We developed a discrete-state stochastic framework to analyze the molecular mechanisms of transport processes with stochastic gating by explicitly calculating molecular fluxes through the pores. Two scenarios are specifically investigated: 1) symmetry preserving stochastic gating with free-energy changes, and 2) stochastic gating with symmetry changes but without modifications in the overall particle-pore interactions. It is found that stochastic gating can both accelerate or slow down the molecular translocation depending on the specific parameters of the system. We argue that biological systems might optimize their performance by utilizing conformational fluctuations of channels. Our theoretical analysis clarifies physical-chemical aspects of the molecular mechanisms of transport with stochastic gating.

physics.chem-ph↗

arXiv2018

First-passage processes on a filamentous track in a dense traffic: optimizing diffusive search for a target in crowding conditions

Several important biological processes are initiated by the binding of a protein to a specific site on the DNA. The strategy adopted by a protein, called transcription factor (TF), for searching its specific binding site on the DNA has been investigated over several decades. In recent times the effects obstacles, like DNA-binding proteins, on the search by TF has begun to receive attention. RNA polymerase (RNAP) motors collectively move along a segment of the DNA during a genomic process called transcription. This RNAP traffic is bound to affect the diffusive scanning of the same segment of the DNA by a TF searching for its binding site. Motivated by this phenomenon, here we develop a kinetic model where a `particle', that represents a TF, searches for a specific site on a one-dimensional lattice. On the same lattice another species of particles, each representing a RNAP, hop from left to right exactly as in a totally asymmetric simple exclusion process (TASEP) which forbids simultaneous occupation of any site by more than one particle, irrespective of their identities. Although the TF is allowed to attach to or detach from any lattice site, the RNAPs can attach only to the first site at the left edge and detach from only the last site on the right edge of the lattice. We formulate the search as a {\it first-passage} process; the time taken to reach the target site {\it for the first time}, starting from a well defined initial state, is the search time. By approximate analytical calculations and Monte Carlo (MC) computer simulations, we calculate the mean search time. We show that RNAP traffic rectifies the diffusive motion of TF to that of a Brownian ratchet, and the mean time of successful search can be even shorter than that required in the absence of RNAP traffic. Moreover, we show that there is an optimal rate of detachment that corresponds to the shortest mean search time.

physics.bio-ph↗

arXiv2018

Mechanisms of Protein Search for Targets on DNA: Theoretical Insights

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

q-bio.SC↗

arXiv2018

Molecular search with conformational change: One-dimensional discrete-state stochastic model

Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic modes. To understand the mechanisms of molecular search with alternating dynamics, we investigate the search dynamics with stochastic transitions between two conformations in a one-dimensional discrete-state stochastic model. It is explicitly analyzed using the first-passage time probabilities method to obtain a full dynamic description of the search process. A general dynamic phase diagram is developed. It is found that there are several dynamic regimes in the molecular search with conformational transitions, and they are determined by the relative values of the relevant length scales in the system. Theoretical predictions are fully supported by Monte Carlo computer simulations.

cond-mat.stat-mech↗

arXiv2018

Kinetics of Protein-DNA Interactions: First-Passage Analysis

All living systems can function only far away from equilibrium, and for this reason chemical kinetic methods are critically important for uncovering the mechanisms of biological processes. Here we present a new theoretical method of investigating dynamics of protein-DNA interactions, which govern all major biological processes. It is based on a first-passage analysis of biochemical and biophysical transitions, and it provides a fully analytic description of the processes. Our approach is explained for the case of a single protein searching for a specific binding site on DNA. In addition, the application of the method to investigations of the effect of DNA sequence heterogeneity, and the role multiple targets and traps in the protein search dynamics are discussed.

q-bio.SC↗

arXiv2017

Dynamics of relaxation to a stationary state for interacting molecular motors

Motor proteins are active enzymatic molecules that drive a variety of biological processes, including transfer of genetic information, cellular transport, cell motility and muscles contraction. It is known that these biological molecular motors usually perform their cellular tasks by acting collectively, and there are interactions between individual motors that specify the overall collective behavior. One of the fundamental issues related to the collective dynamics of motor proteins is the question if they function at stationary-state conditions. To investigate this problem, we analyze a relaxation to the stationary state for the system of interacting molecular motors. Our approach utilizes a recently developed theoretical framework, which views the collective dynamics of motor proteins as a totally asymmetric simple exclusion process of interacting particles, where interactions are taken into account via a thermodynamically consistent approach. The dynamics of relaxation to the stationary state is analyzed using a domain-wall method that relies on a mean-field description, which takes into account some correlations. It is found that the system quickly relaxes for repulsive interactions, while attractive interactions always slow down reaching the stationary state. It is also predicted that for some range of parameters the fastest relaxation might be achieved for a weak repulsive interaction. Our theoretical predictions are tested with Monte Carlo computer simulations. The implications of our findings for biological systems are briefly discussed.

cond-mat.soft↗