Dynamic disorder in a coupled two-lane exclusion process with Langmuir kinetics

In intracellular transport, the motor proteins may jump between the filaments due to structural deformity where the motion is hindered by presence of bound proteins. This motivates us to study a system of two parallel disordered exclusion processes with Langmuir kinetics under symmetric and asymmetric coupling conditions. Theoretically, continuum mean-field approximation is employed to obtain steady-state equations which are further solved numerically. The steady-state system dynamics are examined for different values of coupling constant C, which indicates ratio of lane-changing rates. The effect of binding constant K and defect parameters is also explored. Under the symmetric coupling case, the topological structure of phase diagram turns out to be similar to that in single-lane model, which differs significantly under fully asymmetric coupling. The asymmetric coupling increases magnitude of difference between densities in two lanes. At a very large attachment/detachment rate, the LK dynamics dominate the effect of asymmetric coupling in the lanes. The defect parameters are found to reduce particle flux in the steady state. The numerical results are validated through extensive Monte Carlo simulation.