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

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.