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At least 1,261 records · Page 70Linked to original sources

arXiv2009

A model for bidirectional traffic of cytoskeletal motors

We introduce a stochastic lattice gas model including two particle species and two parallel lanes. One lane with exclusion interaction and directed motion and the other lane without exclusion and unbiased diffusion, mimicking a micotubule filament and the surrounding solution. For a high binding affinity to the filament, jam-like situations dominate the system's behaviour. The fundamental process of position exchange of two particles is approximated. In the case of a many-particle system, we were able to identify a regime in which the system is rather homogenous presenting only small accumulations of particles and a regime in which an important fraction of all particles accumulates in the same cluster. Numerical data proposes that this cluster formation will occur at all densities for large system sizes. Coupling of several filaments leads to an enhanced cluster formation compared to the uncoupled system, suggesting that efficient bidirectional transport on one-dimensional filaments relies on long-ranged interactions and track formation.

cond-mat.stat-mech↗

arXiv2009

RNA polymerase motors: dwell time distribution, velocity and dynamical phases

Polymerization of RNA from a template DNA is carried out by a molecular machine called RNA polymerase (RNAP). It also uses the template as a track on which it moves as a motor utilizing chemical energy input. The time it spends at each successive monomer of DNA is random; we derive the exact distribution of these "dwell times" in our model. The inverse of the mean dwell time satisfies a Michaelis-Menten-like equation and is also consistent with a general formula derived earlier by Fisher and Kolomeisky for molecular motors with unbranched mechano-chemical cycles. Often many RNAP motors move simultaneously on the same track. Incorporating the steric interactions among the RNAPs in our model, we also plot the three-dimensional phase diagram of our model for RNAP traffic using an extremum current hypothesis.

cond-mat.stat-mech↗

arXiv2011

Bidirectional transport and pulsing states in a multi-lane ASEP model

In this paper, we introduce an ASEP-like transport model for bidirectional motion of particles on a multi-lane lattice. The model is motivated by {\em in vivo} experiments on organelle motility along a microtubule (MT), consisting of thirteen protofilaments, where particles are propelled by molecular motors (dynein and kinesin). In the model, organelles (particles) can switch directions of motion due to "tug-of-war" events between counteracting motors. Collisions of particles on the same lane can be cleared by switching to adjacent protofilaments (lane changes). We analyze transport properties of the model with no-flux boundary conditions at one end of a MT ("plus-end" or tip). We show that the ability of lane changes can affect the transport efficiency and the particle-direction change rate obtained from experiments is close to optimal in order to achieve efficient motor and organelle transport in a living cell. In particular, we find a nonlinear scaling of the mean {\em tip size} (the number of particles accumulated at the tip) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system.

nlin.CG↗

arXiv2014

Boundary induced phase transition with stochastic entrance and exit

We study an open-chain totally asymmetric exclusion process (TASEP) with stochastic gates present at the two boundaries. The gating dynamics has been modeled keeping the physical system of ion-channel gating in mind. These gates can randomly switch between an open state and a closed state. In the open state, the gates are highly permeable such that any particle arriving at the gate immediately passes through. In the closed state, a particle gets trapped at the gate and cannot pass through until the gate switches open again. We calculate the phase-diagram of the system and find important and non-trivial differences with the phase-diagram of a regular open-chain TASEP. In particular, depending on switching rates of the two gates, the system may or may not admit a maximal current phase. Our analytic calculation within mean-field theory captures the main qualitative features of our Monte Carlo simulation results. We also perform a refined mean-field calculation where the correlations at the boundaries are taken into account. This theory shows significantly better quantitative agreement with our simulation results.

cond-mat.stat-mech↗

arXiv2014

A reaction-subdiffusion model of fluorescence recovery after photobleaching (FRAP)

Anomalous diffusion, in particular subdiffusion, is frequently invoked as a mechanism of motion in dense biological media, and may have a significant impact on the kinetics of binding/unbinding events at the cellular level. In this work we incorporate anomalous diffusion in a previously developed model for FRAP experiments. Our particular implementation of subdiffusive transport is based on a continuous time random walk (CTRW) description of the motion of fluorescent particles, as CTRWs lend themselves particularly well to the inclusion of binding/unbinding events. In order to model switching between bound and unbound states of fluorescent subdiffusive particles, we derive a fractional reaction-subdiffusion equation of rather general applicability. Using suitable initial and boundary conditions, this equation is then incorporated in the model describing two-dimensional kinetics of FRAP experiments. We find that this model can be used to obtain excellent fits to experimental data. Moreover, recovery curves corresponding to different radii of the circular bleach spot can be fitted by a single set of parameters. While not enough evidence has been collected to claim with certainty that CTRW is the underlying transport mechanism in FRAP experiments, the compatibility of our results with experimental data fuels the discussion as to whether normal diffusion or anomalous diffusion is the appropriate model, and as to whether anomalous diffusion effects are important to fully understand the outcomes of FRAP experiments. On a more technical side, we derive explicit analytic solutions of our model in certain limits.

cond-mat.stat-mech↗

arXiv2015

Energy dissipation in an adaptive molecular circuit

The ability to monitor nutrient and other environmental conditions with high sensitivity is crucial for cell growth and survival. Sensory adaptation allows a cell to recover its sensitivity after a transient response to a shift in the strength of extracellular stimulus. The working principles of adaptation have been established previously based on rate equations which do not consider fluctuations in a thermal environment. Recently, G. Lan et al. (Nature Phys., 8:422-8, 2012) performed a detailed analysis of a stochastic model for the E. coli sensory network. They showed that accurate adaptation is possible only when the system operates in a nonequilibrium steady-state (NESS). They further proposed an energy-speed-accuracy (ESA) trade-off relation. We present here analytic results on the NESS of the model through a mapping to a one-dimensional birth-death process. An exact expression for the entropy production rate is also derived. Based on these results, we are able to discuss the ESA relation in a more general setting. Our study suggests that the adaptation error can be reduced exponentially as the methylation range increases. Finally, we show that a nonequilibrium phase transition exists in the infinite methylation range limit, despite the fact that the model contains only two discrete variables.

q-bio.SC↗

arXiv2015

Collective cargo hauling by a bundle of parallel microtubules: bi-directional motion caused by load-dependent polymerization and depolymerization

A microtubule (MT) is a hollow tube of approximately 25 nm diameter. The two ends of the tube are dissimilar and are designated as `plus' and `minus' ends. Motivated by the collective push and pull exerted by a bundle of MTs during chromosome segregation in a living cell, we have developed here a much simplified theoretical model of a bundle of parallel dynamic MTs. The plus-end of all the MTs in the bundle are permanently attached to a movable `wall' by a device whose detailed structure is not treated explicitly in our model. The only requirement is that the device allows polymerization and depolymerization of each MT at the plus-end. In spite of the absence of external force and direct lateral interactions between the MTs, the group of polymerizing MTs attached to the wall create a load force against the group of depolymerizing MTs and vice-versa; the load against a group is shared equally by the members of that group. Such indirect interactions among the MTs gives rise to the rich variety of possible states of collective dynamics that we have identified by computer simulations of the model in different parameter regimes. The bi-directional motion of the cargo, caused by the load-dependence of the polymerization kinetics, is a "proof-of-principle" that the bi-directional motion of chromosomes before cell division does not necessarily need active participation of motor proteins.

q-bio.SC↗

arXiv2015

Correlations and Symmetry of Interactions Influence Collective Dynamics of Molecular Motors

Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and they frequently work together in large groups. To understand the mechanisms of collective behavior of motor proteins we study the effect of interactions in the transport of molecular motors along linear filaments. It is done by analyzing a recently introduced class of totally asymmetric exclusion processes that takes into account the intermolecular interactions via thermodynamically consistent approach. We develop a new theoretical method that allows us to compute analytically all dynamic properties of the system. Our analysis shows that correlations play important role in dynamics of interacting molecular motors. Surprisingly, we find that the correlations for repulsive interactions are weaker and more short-range than the correlations for the attractive interactions. In addition, it is shown that symmetry of interactions affect dynamic properties of molecular motors. The implications of these findings for motor proteins transport are discussed. Our theoretical predictions are tested by extensive Monte Carlo computer simulations.

physics.bio-ph↗

arXiv2015

Thermodynamics of accuracy in kinetic proofreading: Dissipation and efficiency trade-offs

The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e., by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide a consistent thermodynamic description of enzyme-assisted assembly processes involving competing substrates, in a Master Equation framework. We introduce and evaluate a measure of the efficiency based on rigorous non-equilibrium inequalities. The performance of several proofreading models are thus analyzed and the related time, dissipation and efficiency vs. error trade-offs exhibited for different discrimination regimes. We finally introduce and analyze in the same framework a simple model which takes into account correlations between consecutive enzyme-assisted assembly steps. This work highlights the relevance of the distinction between energetic and kinetic discrimination regimes in enzyme-substrate interactions.

cond-mat.stat-mech↗

arXiv2016

Persistent search in confined domains: a velocity-jump process model

We analyze velocity-jump process models of persistent search for a single target on a bounded domain. The searcher proceeds along ballistic trajectories and is absorbed upon collision with the target boundary. When reaching the domain boundary, the searcher chooses a random direction for its new trajectory. For circular domains and targets, we can approximate the mean first passage time (MFPT) using a Markov chain approximation of the search process. Our analysis and numerical simulations reveal that the time to find the target decreases for targets closer to the domain boundary. When there is a small probability of direction-switching within the domain, we find the time to find the target decreases slightly with the turning probability. We also extend our exit time analysis to the case of partitioned domains, where there is a single target within one of multiple disjoint subdomains. Given an average time of transition between domains $\langle T \rangle$, we find that the optimal rate of transition that minimizes the time to find the target obeys $β_{\rm min} \propto 1/ \sqrt{\langle T \rangle}$.

cond-mat.stat-mech↗

arXiv2017

A Multispecies Exclusion Model Inspired By Transcriptional Interference

We introduce exclusion models of two distinguishable species of hard rods with their distinct sites of entry and exit under open boundary conditions. In the first model both species of rods move in the same direction whereas in the other two models they move in the opposite direction. These models are motivated by the biological phenomenon known as Transcriptional Interference. Therefore, the rules for the kinetics of the models, particularly the rules for the outcome of the encounter of the rods, are also formulated to mimic those observed in Transcriptional Interference. By a combination of mean-field theory and computer simulation of these models we demonstrate how the flux of one species of rods is completely switched off by the other. Exploring the parameter space of the model we also establish the conditions under which switch-like regulation of two fluxes is possible; from the extensive analysis we discover more than one possible mechanism of this phenomenon.

physics.bio-ph↗

arXiv2016

From Conformational Spread to Allosteric and Cooperative models of E. coli flagellar motor

Escherichia coli swims using flagella activated by rotary motors. The direction of rotation of the motors is indirectly regulated by the binding of a single messenger protein. The conformational spread model has been shown to accurately describe the equilibrium properties as well as the dynamics of the flagellar motor. In this paper we study this model from an analytic point of view. By exploiting the separation of timescales observed in experiments, we show how to reduce the conformational spread model to a coarse-grained, cooperative binding model. We show that this simplified model reproduces very well the dynamics of the motor switch.

q-bio.QM↗

arXiv2018

A biologically inspired two-species exclusion model: effects of RNA polymerase motor traffic on simultaneous DNA replication

We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ($P$) represents RNAP motors while the other ($R$) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two $R$ particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of $P$ particles constitute a totally asymmetric simple exclusion process (TASEP) in a segment in the middle of the lattice. Consequently, the lattice consists of three segments; the encounters of the $P$ particles with the $R$ particles are confined within the middle segment (segment $2$) whereas only the $R$ particles can occupy the sites in the segments $1$ and $3$. The model captures three distinct pathways for resolving the co-directional as well as head-collision between the $P$ and $R$ particles. Using Monte Carlo simulations and heuristic analytical arguments that combine exact results for the TASEP with mean-field approximations, we predict the possible outcomes of the conflict between the traffic of RNAP motors ($P$ particles engaged in transcription) and the replication forks ($R$ particles). The outcomes, of course, depend on the dynamical phase of the TASEP of $P$ particles. In principle, the model can be adapted to the experimental conditions to account for the data quantitatively.

q-bio.SC↗

arXiv2018

Is Actin Filament and Microtubule Growth Reaction- or Diffusion-Limited?

Inside cells of living organisms, actin filaments and microtubules self-assemble and dissemble dynamically by incorporating actin or tubulin from the cell plasma or releasing it into their tips' surroundings. Such reaction-diffusion systems can show diffusion- or reaction-limited behaviour. However, neither limit explains the experimental data: while the offset of the linear relation between growth speed and bulk tubulin density contradicts the diffusion limit, the surprisingly large variance of the growth speed rejects a pure reaction limit. In this Letter, we accommodate both limits and use a Doi-Peliti field-theory model to estimate how diffusive transport is perturbing the chemical reactions at the filament tip. Furthermore, a crossover bulk density is predicted at which the limiting process changes from chemical reactions to diffusive transport. In addition, we explain and estimate larger variances of the growth speed.

physics.bio-ph↗

arXiv2019

Mean velocity and effective diffusion constant for translocation of biopolymer chains across membrane

Chaperone-assisted translocation through a nanopore embedded in membrane holds a prominent role in the transport of biopolymers. Inspired by classical Brownian ratchet, we develop a theoretical framework characterizing such translocation process through a master equation approach. In this framework, the polymer chain, provided with reversible binding of chaperones, undergoes forward/backward diffusion, which is rectified by chaperones. We drop the assumption of timescale separation and keep the length of a polymer chain finite, both of which happen to be the key points in most of the previous studies. Our framework makes it accessible to derive analytical expressions for mean translocation velocity and effective diffusion constant in stationary state, which is the basis of a comprehensive understanding towards the dynamics of such process. Generally, the translocation of polymer chain across membrane consists of three subprocesses: initiation, termination, and translocation of the main body part of a polymer chain, where the translocation of the main body part depends on the binding/unbinding kinetics of chaperones. That is the main concern of this study. Our results show that the increase of forward/backward diffusion rate of a polymer chain and the binding/unbinding ratio of chaperones both raise the mean translocation velocity of a polymer chain, and roughly speaking, the dependence of effective diffusion constant on these two factors achieves similar behavior.

physics.bio-ph↗

arXiv2021

Spin coherent states and stochastic hybrid path integrals

Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the system reduces to a piecewise deterministic Markov process (PDMP). Well known examples include stochastic gene expression, voltage fluctuations in neurons, and motor-driven intracellular transport. In this paper we use coherent spin states to construct a new path integral representation of the probability density functional for stochastic hybrid systems, which holds outside the weak noise regime. We use the path integral to derive a system of Langevin equations in the semi-classical limit, which extends previous diffusion approximations based on a quasi-steady-state reduction. We then show how in the weak noise limit the path integral is equivalent to an alternative representation that was previously derived using Doi-Peliti operators. The action functional of the latter is related to a large deviation principle for stochastic hybrid systems.

cond-mat.stat-mech↗

arXiv2021

Level crossing statistics in a biologically motivated model of a long dynamic protrusion: passage times, random and extreme excursions

Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures. Length of many such protrusions keep fluctuating about the mean value even in the the steady state. We develop here a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium). Exploiting the techniques developed for the calculation of level-crossing statistics of random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these model flagella. We identify different parameter regimes of this model flagellum that mimic those of the wildtype and mutants of a well known flagellated cell. By analysing our model in these different parameter regimes, we demonstrate how mutation can alter the level-crossing statistics even when the steady state length remains unaffected by the same mutation. Comparison of the theoretically predicted level crossing statistics, in addition to mean and variance of the length, in the steady state with the corresponding experimental data can be used in near future as stringent tests for the validity of the models of flagellar length control. The experimental data required for this purpose, though never reported till now, can be collected, in principle, using a method developed very recently for flagellar length fluctuations.

q-bio.SC↗

arXiv2011

On the distribution of estimators of diffusion constants for Brownian motion

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.

cond-mat.stat-mech↗