arXiv subjects

Anatoly B. Kolomeisky

Publications and source records attributed to Anatoly B. Kolomeisky.

71 records · Page 4Linked to original sources

arXiv2005

Dynamic Properties of Motor Proteins with Two Subunits

The dynamics of motor protein molecules that have two subunits is investigated using simple discrete stochastic models. Exact steady-state analytical expressions are obtained for velocities and dispersions for any number of intermediate states and conformations between the corresponding binding states of proteins. These models enabled a detailed description and comparison of two possible mechanisms of the motion of motor proteins along the linear tracks: the hand-over-hand mechanism when the motion of subunits alternate, and the inchworm mechanism when one subunit is always trailing another one. It is shown that particles in the hand-over-hand mechanism move faster and fluctuate more than the molecules in the inchworm mechanism. The effect of external forces on dynamic properties of motor proteins is discussed. Finally, a method is proposed for distinguishing between these two mechanisms based on experimental observations.

cond-mat.soft↗

arXiv2005

Coupling of Two Motor Proteins: a New Motor Can Move Faster

We study the effect of a coupling between two motor domains in highly-processive motor protein complexes. A simple stochastic discrete model, in which the two parts of the protein molecule interact through some energy potential, is presented. The exact analytical solutions for the dynamic properties of the combined motor species, such as the velocity and dispersion, are derived in terms of the properties of free individual motor domains and the interaction potential. It is shown that the coupling between the motor domains can create a more efficient motor protein that can move faster than individual particles. The results are applied to analyze the motion of helicase RecBCD molecules.

cond-mat.soft↗

arXiv2005

Thermodynamics and Phase Transitions of Electrolytes on Lattices with Different Discretization Parameters

Lattice models are crucial for studying thermodynamic properties in many physical, biological and chemical systems. We investigate Lattice Restricted Primitive Model (LRPM) of electrolytes with different discretization parameters in order to understand thermodynamics and the nature of phase transitions in the systems with charged particles. A discretization parameter is defined as a number of lattice sites that can be occupied by each particle, and it allows to study the transition from the discrete picture to the continuum-space description. Explicit analytic and numerical calculations are performed using lattice Debye-Hückel approach, which takes into account the formation of dipoles, the dipole-ion interactions and correct lattice Coulomb potentials. The gas-liquid phase separation is found at low densities of charged particles for different types of lattices. The increase in the discretization parameter lowers the critical temperature and the critical density, in agreement with Monte Carlo computer simulations results. In the limit of infinitely large discretization our results approach the predictions from the continuum model of electrolytes. However, for the very fine discretization, where each particle can only occupy one lattice site, the gas-liquid phase transitions are suppressed by order-disorder phase transformations.

cond-mat.stat-mech↗

arXiv2004

Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach

The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multi-layer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.

cond-mat.soft↗

arXiv2004

Two-Channel Totally Asymmetric Simple Exclusion Processes

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.

cond-mat.stat-mech↗

arXiv2004

Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of conventional motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is also explicitly taken into account. Using the method of first- passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly are the same, although the probabilities of these events are different. It is concluded that the current theoretical view, that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis, is consistent with all available experimental observations for kinesins.

cond-mat.soft↗

arXiv2004

Simple Growth Models of Rigid Multifilament Biopolymers

The growth dynamics of rigid biopolymers, consisting of $N$ parallel protofilaments, is investigated theoretically using simple approximate models. In our approach, the structure of a polymer's growing end and lateral interactions between protofilaments are explicitly taken into account, and it is argued that only few conformations are important for biopolymer's growth. As a result, exact analytic expressions for growth velocity and dispersion are obtained for {\it any} number of protofilaments and arbitrary geometry of the growing end of the biopolymer. Our theoretical predictions are compared with a full description of biopolymer growth dynamics for the simplest N=2 model. It is found that the results from the approximate theory are approaching the exact ones for large lateral interactions between the protofilaments. Our theory is also applied to analyze the experimental data on the growth of microtubules.

cond-mat.stat-mech↗

arXiv2003

Polymer Dynamics in Repton Model at Large Fields

Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit which is determined by the size of the neutral block. The theoretical arguments are supported by extensive numerical calculations by means of density-matrix renormalization group techniques.

cond-mat.stat-mech↗

arXiv2003

Local Inhomogeneity in Asymmetric Simple Exclusion Processes with Extended Objects

Totally asymmetric simple exclusion processes (TASEP) with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated. These non-equilibrium processes are relevant for the understanding of many biological and chemical phenomena. The steady-state phase diagrams, currents, and bulk densities are calculated using a simple approximate theory and extensive Monte Carlo computer simulations. It is found that the phase diagram for TASEP with a local inhomogeneity is qualitatively similar to homogeneous models, although the phase boundaries are significantly shifted. The complex dynamics is discussed in terms of domain-wall theory for driven lattice systems.

cond-mat.stat-mech↗

arXiv2003

Thermodynamics of Electrolytes on Anisotropic Lattices

The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space $1/r$ electrostatic interactions have been investigated. At all degrees of anisotropy, only coexistence between a disordered low-density phase and an ordered high-density phase with the structure similar to ionic crystal was found, in contrast to recent theoretical predictions. Tricritical parameters were determined to be monotonously increasing functions of anisotropy parameters which is consistent with theoretical calculations based on the Debye-Hückel approach. At large anisotropies a two-dimensional-like behavior is observed, from which we estimated the dimensionless tricritical temperature and density for the two-dimensional square lattice electrolyte to be $T^*_{tri}=0.14$ and $ρ^*_{tri} = 0.70$.

cond-mat.stat-mech↗

arXiv2002

A Simple Kinetic Model Describes the Processivity of Myosin-V

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness -- a quantitative measure of the stochastic deviations from uniform, constant-speed motion -- with ATP concentration under both resisting and assisting loads, and indicates a {\it sub}step of size $d_{0} \simeq$ 13-14 nm (from the ATP-binding site) that appears to accord with independent observations.

cond-mat.stat-mech↗

arXiv2002

Lattice Models of Ionic Systems with Charge Asymmetry

The thermodynamics of a charge-asymmetric lattice gas of positive ions carrying charge $q$ and negative ions with charge $-zq$ is investigated using Debye-Hückel theory. Explicit analytic and numerical calculations, which take into account the formation of neutral and charged clusters and cluster solvation by the residual ions, are performed for $z=2$, 3 and 4. As charge asymmetry increases, the predicted critical point shifts to lower temperatures and higher densities. This trend agrees well with the results from recent Monte Carlo simulations for continuum charge-asymmetric hard-sphere ionic fluids and with the corresponding predictions from continuum Debye-Hückel theory.

cond-mat.stat-mech↗

arXiv2002

Polymer Translocation Through a Long Nanopore

Polymer translocation through a nanopore in a membrane investigated theoretically. Recent experiments on voltage-driven DNA and RNA translocations through a nanopore indicate that the size and geometry of the pore are important factors in polymer dynamics. A theoretical approach is presented which explicitly takes into account the effect of the nanopore length and diameter for polymer motion across the membrane. It is shown that the length of the pore is crucial for polymer translocation dynamics. The present model predicts that for realistic conditions (long nanopores and large external fields) there are two regimes of translocation depending on polymer size: for polymer chains larger than the pore length, the velocity of translocation is nearly constant, while for polymer chains smaller than the pore length the velocity increases with decreasing polymer size. These results agree with experimental data.

cond-mat.stat-mech↗

arXiv2002

Anisotropic Lattice Models of Electrolytes

Systems of charged particles on anisotropic three-dimensional lattices are investigated theoretically using Debye-Huckel theory. It is found that the thermodynamics of these systems strongly depends on the degree of anisotropy. For weakly anisotropic simple cubic lattices, the results indicate the existence of order-disorder phase transitions and a tricritical point, while the possibility of low-density gas-liquid coexistence is suppressed. For strongly anisotropic lattices this picture changes dramatically: the low-density gas-liquid phase separation reappears and the phase diagram exhibits critical, tricritical and triple points. For body-centered lattices, the low-density gas-liquid phase coexistence is suppressed for all degrees of anisotropy. These results show that the effect of anisotropy in lattice models of electrolytes amounts to reduction of spatial dimensionality.

cond-mat.stat-mech↗

arXiv2001

Lattice Models of Ionic Systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Huckel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for 3D lattices. As for continuum electrolytes, low-density results for sc, bcc and fcc lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.

cond-mat.stat-mech↗

arXiv2000

Extended Kinetic Models with Waiting-Time Distributions: Exact Results

Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or one-dimensional random walks) with general waiting-time distributions. The concept of ``mechanicity'' is introduced in order to conveniently quantify departures from simple ``chemical,'' kinetic rate processes, and its significance is briefly indicated. The results are extended to more elaborate models that have finite side-branches and include death processes (to represent the detachment of a motor from the track).

cond-mat.stat-mech↗

arXiv1999

The Force Exerted by a Molecular Motor

The stochastic driving force exerted by a single molecular motor (e.g., a kinesin, or myosin) moving on a periodic molecular track (microtubule, actin filament, etc.) is discussed from a general viewpoint open to experimental test. An elementary "barometric" relation for the driving force is introduced that (i) applies to a range of kinetic and stochastic models, (ii) is consistent with more elaborate expressions entailing explicit representations of externally applied loads and, (iii) sufficiently close to thermal equilibrium, satisfies an Einstein-type relation in terms of the velocity and diffusion coefficient of the (load-free) motor. Even in the simplest two-state models, the velocity-vs.-load plots exhibit a variety of contrasting shapes (including nonmonotonic behavior). Previously suggested bounds on the driving force are shown to be inapplicable in general by analyzing discrete jump models with waiting time distributions.

cond-mat.stat-mech↗