Bi-directional traffic of molecular motors in two antiparallel lanes with asymmetric lane changing rates

Abstract Inspired by the recent experimental observations on molecular motors accumulating on microtubule filament, we study an open system of two antiparallel lanes totally asymmetric simple exclusion processes (TASEP) in the presence of dynamic roadblocks. Particles following these TASEPs can also mutually interact with the surrounding environment through Langmuir Kinetics (LK) in both the lanes. Two antiparallel lanes TASEP are coupled with each other by asymmetric lane changing (coupling) rates. In the modified coupling conditions, the coupling rates depend on the configuration of nearest neighbouring sites. Both particles and roadblocks are interacting with each other by steric hardcore mutual interactions. In this paper, we have analysed (sophisticated) two lanes TASEP concerning novel stationary states as a result of the interactions and calculated observables such as that would be compared with experimental data if these are available in the future literature. Results of numerical integration of the master equations with mean-field approximation have been compared with Monte Carlo simulations.