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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 representing strong coupling of particles. 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. We then compare the dynamical properties of the proposed model with the earlier studied variant considering weakly coupled particles. Theoretical predictions agree well with extensive Monte Carlo computer simulations. [ABSTRACT FROM AUTHOR]

We introduce a one-dimensional non-equilibrium lattice gas model representing the processive motion of dynein molecular motors over the microtubule. We study both dynamical and stationary state properties for the model consisting of hardcore particles hopping on the lattice with variable step sizes. We find that the stationary state gap-distribution exhibits striking peaks around gap sizes that are multiples of the maximum step size, for both open and periodic boundary conditions. We verified this feature using a mean-field calculation. For open boundary conditions, we observe intriguing damped oscillator-like distribution of particles over the lattice with a periodicity equal to the maximum step size. To characterize transient dynamics, we measure the mean square displacement that shows weak superdiffusive growth with exponent γ ≈ 1.34 for periodic boundary and ballistic growth ( γ ≈ 2 ) for open boundary conditions at early times. We also study the effect of Langmuir dynamics on the density profile. [ABSTRACT FROM AUTHOR]

Cytoskeletal motors known as motor proteins are molecules that drive cellular transport along several parallel cytoskeletal filaments and support many biological processes. Experimental evidences suggest that they interact with the nearest molecules of their filament while performing any mechanical work. These interactions modify the microscopic level properties of motor proteins. In this work, a new version of two-channel totally asymmetric simple exclusion process, that incorporates the intra-channel interactions in a thermodynamically consistent way, is proposed. As the existing approaches for multi-channel systems deviate from analyzing the combined effect of inter and intra-channel interactions, a new approach known as modified vertical cluster mean field is developed. The approach along with Monte Carlo simulations successfully encounters some correlations and computes the complex dynamic properties of the system. Role of symmetry of interactions and inter-channel coupling is observed on the phase diagrams, maximal particle current and its corresponding optimal interaction strength. Surprisingly, for all values of coupling rate and most of the interaction splittings, the optimal interaction strength corresponding to maximal current belongs to the case of weak repulsive interactions. Moreover, for weak interaction splittings and with an increase in the coupling rate, the optimal interaction strength tends towards the known experimental results. The effect of coupling as well as interaction energy is also measured for correlations. They are found to be short-range and weaker for repulsive and weak attractive interactions while they are long-range and stronger for large attractions. [ABSTRACT FROM AUTHOR]

We consider random walks on quasi one dimensional lattices, as introduced in Faggionato and Silvestri (Random Walks on Quasi One Dimensional Lattices: Large Deviations and Fluctuation Theorems, ). This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general formulas for the asymptotic velocity and diffusion coefficient, and we show how to reduce their computation to suitable linear systems of the same degree of a single fundamental cell, with possible linear chain removals. We apply the above results to special families of kinetic models, also catching some errors in the biophysics literature. [ABSTRACT FROM AUTHOR]

Cargo transport by two molecular motors is studied by constructing a chemomechanical network for the whole transport system and analyzing the cargo and motor trajectories generated by this network. The theoretical description starts from the different nucleotide states of a single motor supplemented by chemical and mechanical transitions between these states. As an instructive example, we focus on kinesin-1, for which a detailed single-motor network has been developed previously. This network incorporates the chemical transitions arising from ATP hydrolysis on both motor heads. In addition, both the chemical and the mechanical transition rates of a single kinesin motor were found to depend on the load force experienced by the motor. When two such motors are attached via their stalks to a cargo particle, they become elastically coupled. This coupling can be effectively described by an elastic spring between the two motors. The spring extension, which is given by the deviation of the actual spring length from its rest length, determines the mutual interaction force between the motors and, thus, affects all chemical and mechanical transition rates of both motors. As a result, cargo transport by two motors leads to a combined chemomechanical network, which is quite complex and contains a large number of motor cycles. However, apart from the single motor parameters, this complex network involves only two additional parameters: (i) the spring constant of the elastic coupling between the motors and (ii) the rebinding rate for an unbound motor. We show that these two parameters can be determined directly from cargo trajectories and/or trajectories of individual motors. Both types of trajectories are accessible to experiment and, thus, can be used to obtain a complete set of parameters for cargo transport by two motors. [ABSTRACT FROM AUTHOR]

The “reversible ratchet” model of interacting Brownian motors, introduced by us earlier, is investigated using a one-site approximation of a mean-field type. We confirm the effect of enhanced efficiency due to repulsive interaction and we provide arguments suggesting that the enhancement is of energetic, rather than entropic, origin. We also check the validity of the fluctuation theorem for stationary particle current. [ABSTRACT FROM AUTHOR]

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors’ transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect. [ABSTRACT FROM AUTHOR]

Molecular motors convert chemical energy into mechanical work while operating in an environment dominated by Brownian motion. The aim of this paper is to explore the flow of energy between the molecular motors and its surroundings, in particular, its efficiency. Based on the Fokker-Planck equation with either N or infinite chemical states, we find that the energy efficiency of molecular motors, whether the Stokes efficiency or the usual thermodynamic efficiency, is strictly less than one, because of the dissipation of the energy in both the overdamped surroundings and in the process of the chemical reaction. [ABSTRACT FROM AUTHOR]

Intracellular transport is mediated by molecular motors that pull cargos along cytoskeletal filaments. Many cargos move bidirectionally and are transported by two teams of motors which move into opposite directions along the filament. We have recently introduced a stochastic tug-of-war model for this situation. This model describes the motion of the cargo as a Markov process on a two-dimensional state space defined by the numbers of active plus and active minus motors. In spite of its simplicity, this tug-of-war model leads to a complex dependence of the cargo motility on the motor parameters. We present new numerical results for the dependence on the number of involved motors. In addition, we derive a simple and intuitive sharp maxima approximation, from which one obtains the cargo motility state from only four simple inequalities. This approach provides a fast and reliable method to determine the cargo motility. [ABSTRACT FROM AUTHOR]

Bacterial chemotaxis relies on the clockwise-to-counterclockwise switching (and the reverse CCW-to-CW switching) of the flagellar motor’s rotational direction. Yet, despite its central role, the switch mechanism remains poorly understood. Here we study the switch statistics of the flagellar motor using computer simulations that combine first-passage time ideas and the property of dynamic binding of CheY-P to FliM. The simulated clockwise bias and switching frequency as a function of CheY-P concentration agree with the experimental results for E. coli. Moreover, the simulation results show a robust peak, which is present in some experimental reports, in the distribution of the time intervals of both clockwise and counterclockwise rotation. [ABSTRACT FROM AUTHOR]

We consider Markov chains with fast and slow variables and show that in a suitable scaling limit, the dynamics becomes deterministic, yet is far away from the standard mean field approximation. This new limit is an instance of self-induced stochastic resonance which arises due to matching between a rare event timescale on the one hand and the natural timescale separation in the underlying problem on the other. Here it is illustrated on a model of a molecular motor, where it is shown to explain the regularity of the motor gait observed in some experiments. [ABSTRACT FROM AUTHOR]

The traffic of molecular motors through open tube-like compartments is studied using lattice models. These models exhibit boundary-induced phase transitions related to those of the asymmetric simple exclusion process (ASEP) in one dimension. The location of the transition lines depends on the boundary conditions at the two ends of the tubes. Three types of boundary conditions are studied: (A) Periodic boundary conditions which correspond to a closed torus-like tube. (B) Fixed motor densities at the two tube ends where radial equilibrium holds locally; and (C) Diffusive motor injection at one end and diffusive motor extraction at the other end. In addition to the phase diagrams, we also determine the profiles for the bound and unbound motor densities using mean field approximations and Monte Carlo simulations. Our theoretical predictions are accessible to experiments. [ABSTRACT FROM AUTHOR]

We investigate the validity of a Markov approach for the motility of kinesin. We show in detail how the various mechanochemical states and reaction rates that are experimentally measured, can be used to create a Markov-chain model. We compare the performance of this model to motility data and we find global similarities in the load and ATP-concentration dependency of speed and mean run length. We also discuss the relation between the experimentally found stalling behavior and thermodynamic expectations. Finally, the Markov chain modelling provides a way to calculate the mean entropy production and the (power) efficiency. [ABSTRACT FROM AUTHOR]