Stochastic Modelling of Dynein Motors on a One-Dimensional Lattice: Dynamics and Stationary State

The motion of molecular motors inside cells constitutes an exciting and biologically motivated non-equilibrium physics problem. Experimental studies in recent years have shown that dynein motors can move with variable step sizes along the microtubule, depending on the load and ATP concentration. Inspired by the dynamics of dyneins, we have developed a model of an exclusion process on a one-dimensional lattice, where the motors can move in the forward direction up to four steps depending on the load attached to it. We study the dynamics of the mean-square displacement, stationary state current, and gap distribution for both open and periodic boundary conditions. In the transient regime, the fluctuation grows as t.log(t) for the periodic boundary conditions and is ballistic for open boundary conditions. The gap distribution between the motors in the stationary state for periodic boundary conditions shows discrete peaks of exponentially decaying amplitude at multiples of four gap size. We have also verified these interesting results using a mean-field analysis.