arXiv subjects
Publications and source records attributed to Yunxin Zhang.
In this research, methods of reducing a general periodic one-dimensional hopping model to a one- or two-state model, which keeps the basic properties of the original process, are discussed. This reduction also implies that, to some extent, many processes can be well described by simple two-state or even one-state models.
In cells, organelles and vesicles are usually transported by cooperation of several motor proteins, including plus-end directed motor kinesin and minus-end directed motor dynein. Many biophysical models have been constructed to understand the mechanism of this motion. However, so far, the basic principle about it remains unclosed. In this paper, based on the recent experimental results and existing theoretical models, a spider-like model is provided. In this model, each motor is regarded as a bead-spring system. The bead can bind to or unbind from the track stochastically, and step forward or backward with fixed step size L and force dependent transition rates. The spring connects the bead to cargo tightly. At any time, the position of cargo is determined by force balance condition. The obvious characteristics of our model are that, the motors interact with each other and they do not share the external load equally. Our results indicate, the stall force of cargo, under which the mean velocity of cargo vanishes, usually decreases with the interactions between motors. If the cargo is pulled by several motors from same motor species, the stall force of cargo is bigger than that of the single motor, but usually smaller than their sum. However, if the cargo is pulled by two motors with different directionality, the stall force of cargo might bigger or smaller than the difference of the two single motor stall forces. The results imply, cooperation of several motors is helpful to pull big cargoes, though it is not so good as might be expected and no obvious help to improve the velocity.
In this paper, the operation of totally asymmetric simple exclusion process with one or two shortcuts under open boundary conditions is discussed. Using both mathematical analysis and numerical simulations, we have found that, according to the method chosen by the particle at the bifurcation, the model can be separated into two different situations which lead to different results. The results obtained in this paper would be very useful in the road building, especially at the bifurcation of the road.
Periodic one dimensional hopping model is useful to study the motion of microscopic particles, which lie in thermal noise environment. The mean velocity $V_N$ and diffusion constant $D_N$ of this model have been obtained by Bernard Derrida [J. Stat. Phys. 31 (1983) 433]. In this research, we will give the limits $V_D$ and $D_D$ of $V_N$ and $D_N$ as the number $N$ of mechanochemical sates in one period tends to infinity by formal calculation. It is well known that the stochastic motion of microscopic particles also can be described by overdamped Langevin dynamics and Fokker-Planck equation. Up to now, the corresponding formulations of mean velocity and effective diffusion coefficient, $V_L$ and $D_L$ in the framework of Langevin dynamics and $V_P, D_P$ in the framework of Fokker-Planck equation, have also been known. In this research, we will find that the formulations $V_D$ and $V_L, V_P$ are theoretically equivalent, and numerical comparison indicates that $D_D, D_L$, and $D_P$ are almost the same. Through the discussion in this research, we also can know more about the relationship between the one dimensional hopping model and Fokker-Planck equation.
Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale. They convert chemical energy into mechanical work by moving along filamentous structures. In this paper, we study the velocity of two-head molecular motors in the framework of a mechanochemical network theory. The network model, a generalization of the recently work of Liepelt and Lipowsky (PRL 98, 258102 (2007)), is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for single cycle motor (PNAS(2001) 98(14) P7748-7753), we are able to obtain an explicit formula for the velocity of a molecular motor.
Molecular motors are essential components for the biophysical functions of the cell. Our current quantitative understanding of how multiple motors move along a single track is not complete; even though models and theories for single motor chemomechanics abound. Recently, M.J.I. M$\ddot{\rm u}$ller {\em et al.} have developed a tug-of-war model to describe the bidirectional movement of the cargo (PNAS(2008) 105(12) P4609-4614). Through Monte Carlo simulations, they discovered that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we carry out a thorough analysis of the tug-of-war model. All the stable, i.e., biophysically observable, steady states are obtained. Depending on several parameters, the system exhibits either uni-, bi- or tristability. Based on the separating boundary of the different stable states and the initial numbers of the different motor species that are bound to the track, the steady state of the cargo movement can be predicted, and consequently the steady state velocity can be obtained. It is found that, the velocity, even the direction, of the cargo movement change with the initial numbers of the motors which are bound to the track and several other parameters.
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 the molecular motors, whether the Stokes efficiency or the usual thermodynamic efficiency, is strictly bounded by 1, because of the dissipation of the energy in both the overdamped surroundings and in the process of the chemical reaction.
In this research, the totally asymmetric exclusion process without particle number conservation is discussed. Based on the mean field approximation and the Rankine-Hugoniot condition, the necessary and sufficient conditions of the existence of the domain wall have been obtained. Moreover, the properties of the domain wall, including the location and height, have been studied theoretically. All the theoretical results are demonstrated by the computer simulations.