Effects of Langmuir Kinetics of Two-Lane Totally Asymmetric Exclusion Processes in Protein Traffic

Abstract

In this paper, we study a two-lane totally asymmetric simple exclusion process (TASEP) coupled with random attachment and detachment of particles (Langmuir kinetics) in both lanes under open boundary conditions. Our model can describe the directed motion of molecular motors, attachment and detachment of motors, and free inter-lane transition of motors between filaments. In this paper, we focus on some finite-size effects of the system because normally the sizes of most real systems are finite and small (e.g., size $\le 10,000$). A special finite-size effect of the two-lane system has been observed, which is that the density wall moves left first and then move towards the right with the increase of the lane-changing rate. We called it the jumping effect. We find that increasing attachment and detachment rates will weaken the jumping effect. We also confirmed that when the size of the two-lane system is large enough, the jumping effect disappears, and the two-lane system has a similar density profile to a single-lane TASEP coupled with Langmuir kinetics. Increasing lane-changing rates has little effect on density and current after the density reaches maximum. Also, lane-changing rate has no effect on density profiles of a two-lane TASEP coupled with Langmuir kinetics at a large attachment/detachment rate and/or a large system size. Mean-field approximation is presented and it agrees with our Monte Carlo simulations.

arXiv comment15 pages, 8 figures. To be published in IJMPC

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• Collective dynamics of an inhomogeneous two-channel exclusion process: Theory and Monte Carlo simulations
• Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site-assignments
• Effect of walking-distance on a queuing system of totally asymmetric simple exclusion process equipped with functions of site assignments
• Throughput reduction on an air-ground transport system by the simultaneous effect of multiple traveling routes equipped with parking sites