arXiv subjects

Anatoly B. Kolomeisky

Publications and source records attributed to Anatoly B. Kolomeisky.

At least 55 records · Page 3Linked to original sources

arXiv2009

Non-Equilibrium Dynamics of Single polymer Adsorption to Solid Surfaces

Adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption of a single polymer of length $N$ to a planar solid surface in the absence of hydrodynamic interactions. We find that for weak adsorption energies the adsorption time scales $ \sim N^{(1+2ν)/(1+ν)}$, where $ν$ is the Flory exponent for the polymer. We argue that in this regime the single chain adsorption is closely related to a field-driven polymer translocation through narrow pores. Surprisingly, for high adsorption energies the adsorption time becomes longer, as it scales $\sim N^{(1+ν)}$, which is explained by strong stretching of the unadsorbed part of the polymer close to the adsorbing surface. These two dynamic regimes are separated by an energy scale that is characterised by non-equilibrium contributions during the adsorption process.

cond-mat.soft↗

arXiv2008

Polymer translocation through pores with complex geometries

We propose a method for the theoretical investigation of polymer translocation through composite pore structures possessing arbitrarily specified geometries. Translocation through each constituent part of the composite is treated as being analogous to the diffusion of the translocation coordinate over the free energy landscape derived from the chain configurations within the pore. The proposed method accounts for possible reverse motions of the leading chain end at the interface between constituent parts of a composite pore, a possibility that has been neglected in prior studies. As an illustration of our method, we study the translocation of a Gaussian chain between two spherical compartments connected by a cylindrical pore, and by a composite pore consisting of two connected cylinders of different diameters, which is structurally similar to the $α$-hemolysin membrane channel. We demonstrate that reverse chain motions between the pore constituents may contribute significantly to the total translocation time. Our results further establish that translocation through a two-cylinder composite pore is faster when the chain is introduced into the pore on the cis (wide) side of the channel rather than the trans (narrow) side.

cond-mat.soft↗

arXiv2007

Molecular Motors Interacting with Their Own Tracks

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences non-monotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes.

cond-mat.soft↗

arXiv2007

Effect of charge distribution on the translocation of an inhomogeneously charged polymer through a nanopore

We investigate the voltage-driven translocation of an inhomogeneously charged polymer through a nanopore by utilizing discrete and continuous stochastic models. As a simplified illustration of the effect of charge distribution on translocation, we consider the translocation of a polymer with a single charged site in the presence and absence of interactions between the charge and the pore. We find that the position of the charge that minimizes the translocation time in the absence of pore--polymer interactions is determined by the entropic cost of translocation, with the optimum charge position being at the midpoint of the chain for a rodlike polymer and close to the leading chain end for an ideal chain. The presence of attractive or repulsive pore--charge interactions yields a shift in the optimum charge position towards the trailing end and the leading end of the chain, respectively. Moreover, our results show that strong attractive or repulsive interactions between the charge and the pore lengthen the translocation time relative to translocation through an inert pore. We generalize our results to accommodate the presence of multiple charged sites on the polymer. Our results provide insight into the effect of charge inhomogeneity on protein translocation through biological membranes.

cond-mat.soft↗

arXiv2007

Effect of Interactions on Molecular Fluxes and Fluctuations in the Transport Across Membrane Channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that in this case the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.

cond-mat.soft↗

arXiv2007

Transport of Molecular Motor Dimers in Burnt-Bridge Models

Dynamics of molecular motor dimers, consisting of rigidly bound particles that move along two parallel lattices and interact with underlying molecular tracks, is investigated theoretically by analyzing discrete-state stochastic continuous-time burnt-bridge models. In these models the motion of molecular motors is viewed as a random walk along the lattices with periodically distributed weak links (bridges). When the particle crosses the weak link it can be destroyed with a probability $p$, driving the molecular motor motion in one direction. Dynamic properties and effective generated forces of dimer molecular motors are calculated exactly as a function of a concentration of bridges $c$ and burning probability $p$ and compared with properties of the monomer motors. It is found that the ratio of the velocities of the dimer and the monomer can never exceed 2, while the dispersions of the dimer and the monomer are not very different. The relative effective generated force of the dimer (as compared to the monomer) also cannot be larger than 2 for most sets of parameters. However, a very large force can be produced by the dimer in the special case of $c=1/2$ for non-zero shift between the lattices. Our calculations do not show the significant increase in the force generated by collagenase motor proteins in real biological systems as predicted by previous computational studies. The observed behavior of dimer molecular motors is discussed by considering in detail the particle dynamics near burnt bridges.

cond-mat.stat-mech↗

arXiv2007

Translocation of polymers with folded configurations across nanopores

The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded segment through the channel followed by the linear part of the polymer. The transition rates vary for the folded and linear segments because of different interactions between the polymer molecule and the pore. It is shown that the translocation time depends non-monotonously on the length of the folded segment for short polymers and weak external fields, while it becomes monotonous for long molecules and large fields. Also, there is a critical interaction between the polymers and the pore that separates two dynamic regimes. For stronger interactions the folded polymer moves slower, while for weaker interactions the linear chain translocation is the fastest. In addition, our calculations show that the folding does not change the translocation scaling properties of the polymer. These phenomena can be explained by the interplay between the translocation distances and transition rates for the folded and linear segments of the polymer. Theoretical results are applied for analysis of experimental translocations through solid-state nanopores.

cond-mat.stat-mech↗

arXiv2007

Dynamic Properties of Molecular Motors in Burnt-Bridge Models

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed (``burned'') with probability p, providing a bias in the motion of the molecular motor. A new theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, at general conditions is presented. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.

cond-mat.soft↗

arXiv2007

Interaction Between Motor Domains Can Explain the Complex Dynamics of Heterodimeric Kinesins

Motor proteins are active enzyme molecules that play a crucial role in many biological processes. They transform the chemical energy into the mechanical work and move unidirectionally along rigid cytoskeleton filaments. Single-molecule experiments suggest that motor proteins, consisting of two motor domains, move in a hand-over-hand mechanism when each subunit changes between trailing and leading positions in alternating steps, and these subunits do not interact with each other. However, recent experiments on heterodimeric kinesins suggest that the motion of motor domains is not independent, but rather strongly coupled and coordinated, although the mechanism of these interactions are not known. We propose a simple discrete stochastic model to describe the dynamics of homodimeric and heterodimeric two-headed motor proteins. It is argued that interactions between motor domains modify free energy landscapes of each motor subunit, and motor proteins still move via the hand-over-hand mechanism but with different transitions rates. Our calculations of biophysical properties agree with experimental observations. Several ways to test the theoretical model are proposed.

cond-mat.soft↗

arXiv2006

Spontaneous Symmetry Breaking in Two-Channel Asymmetric Exclusion Processes with Narrow Entrances

Multi-particle non-equilibrium dynamics in two-channel asymmetric exclusion processes with narrow entrances is investigated theoretically. Particles move on two parallel lattices in opposite directions without changing them, while the channels are coupled only at the boundaries. A particle cannot enter the corresponding lane if the exit site of the other lane is occupied. Stationary phase diagrams, particle currents and densities are calculated in a mean-field approximation. It is shown that there are four stationary phases in the system, with two of them exhibiting spontaneous symmetry breaking phenomena. Extensive Monte Carlo computer simulations confirm qualitatively our predictions, although the phase boundaries and stationary properties deviate from the mean-field results. Computer simulations indicate that several dynamic and phase properties of the system have a strong size dependency, and one of the stationary phases predicted by the mean-field theory disappears in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2006

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability $p$, creating a biased directed motion for the particle. It is shown that for probability of burning $p=1$ the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of $p<1$ a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

cond-mat.soft↗

arXiv2006

Channel-Facilitated Molecular Transport Across Membranes: Attraction, Repulsion and Asymmetry

Transport of molecules across membrane channels is investigated theoretically using exactly solvable discrete stochastic site-binding models. It is shown that the interaction potential between molecules and the channel has a strong effect on translocation dynamics. The presence of attractive binding sites in the pore accelerates the particle current for small concentrations outside of the membrane, while for large concentrations, surprisingly, repulsive binding sites produce the most optimal transport. In addition, asymmetry of the interaction potential also strongly influences the channel transport. The mechanism of these phenomena are discussed using the details of particle dynamics at the binding sites.

cond-mat.soft↗

arXiv2006

Effect of Inhomogeneity in Translocation of Polymers through Nanopores

The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.

cond-mat.stat-mech↗

arXiv2006

Asymmetric Coupling in Two-Channel Simple Exclusion Processes

Simple exclusion processes for particles moving along two parallel lattices and jumping between them are theoretically investigated for asymmetric rates of transition between the channels. An approximate theoretical approach, that describes the particle dynamics exactly in any vertical cluster of two parallel sites and neglects the correlations between the different vertical clusters, is applied to calculate stationary-state density profiles, currents and phase diagrams. Surprisingly, it is found that asymmetry in the coupling between the channels leads to a very complex phase behavior that is very different from two-channel simple exclusion processes with symmetric coupling. There are seven stationary-state phases in the simple exclusion processes with asymmetric transition rates between the channels, in contrast to three phases found for the systems with symmetric coupling. In addition, a new maximal-current phase with a domain wall in the middle of the lattices, that has no analogs in other exclusion processes, is observed. Although the explicit calculations are presented only for the case of full asymmetry, when the particles can only jump between the channels in one direction, the properties of two-channel simple exclusion systems with general asymmetry are also discussed. Theoretical predictions are in excellent agreement with extensive computer Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2005

Transport of Single Molecules Along the Periodic Parallel Lattices with Coupling

General discrete one-dimensional stochastic models to describe the transport of single molecules along coupled parallel lattices with period $N$ are developed. Theoretical analysis that allows to calculate explicitly the steady-state dynamic properties of single molecules, such as mean velocity $V$ and dispersion $D$, is presented for N=1 and N=2 models. For the systems with $N>2$ exact analytic expressions for the large-time dynamic properties are obtained in the limit of strong coupling between the lattices that leads to dynamic equilibrium between two parallel kinetic pathways.

cond-mat.soft↗

arXiv2005

Dynamic Phase Transitions in Coupled Motor Proteins

The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, that allows to calculate explicitly the dynamic properties of the system, is developed. It is shown that there are two dynamic regimes, depending on the interaction between the particles. For strong interactions the motor proteins move as one tight cluster, while for weak interactions there is no correlation in the motion of the proteins, and the particle separation increases steadily with time. The boundary between two dynamic phases is specified by a critical interaction that has a non-zero value only for the coupling of the asymmetric motor proteins, and it depends on the temperature and the transitions rates. At the critical interaction there is a change in a slope for the mean velocities and a discontinuity in the dispersions of the motor proteins as a function of the interaction energy.

cond-mat.soft↗

arXiv2005

ATP hydrolysis stimulates large length fluctuations in single actin filaments

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for a mean growth velocity and for dispersion in length fluctuations. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers the mean size of unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach the maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration. Random and vectorial mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties. The possibility of attachment and detachment of oligomers is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.

cond-mat.soft↗

arXiv2005

Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branch. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain-wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions.

cond-mat.stat-mech↗