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arXiv · 1604.00690

Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes

Hui-Shun Kuan·Meredith D. Betterton
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Abstract

Motor protein motion on biopolymers can be described by models related to the totally asymmetric simple exclusion process (TASEP). Inspired by experiments on the motion of kinesin-4 motors on antiparallel microtubule overlaps, we analyze a model incorporating the TASEP on two antiparallel lanes with binding kinetics and lane switching. We determine the steady-state motor density profiles using phase plane analysis of the steady-state mean field equations and kinetic Monte Carlo simulations. We focus on the the density-density phase plane, where we find an analytic solution to the mean-field model. By studying the phase space flows, we determine the model's fixed points and their changes with parameters. Phases previously identified for the single-lane model occur for low switching rate between lanes. We predict a new multiple coexistence phase due to additional fixed points that appear as the switching rate increases: switching moves motors from the higher-density to the lower-density lane, causing local jamming and creating multiple domain walls. We determine the phase diagram of the model for both symmetric and general boundary conditions.

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Hui-Shun Kuan, Meredith D. Betterton. 2016-07-12. Phase-plane analysis of the totally asymmetric simple exclusion process with binding kinetics and switching between antiparallel lanes. https://doi.org/10.1103/physreve.94.022419

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