Local inhomogeneity in two-lane asymmetric simple exclusion processes coupled with Langmuir kinetics

The effects of local inhomogeneity in a two-lane asymmetric simple exclusion process coupled with Langmuir kinetics are studied. The model is related to some biological processes such as the movement of molecular motors on parallel homogeneous and inhomogeneous filaments without restrictions for them to jump between these protofilaments as well as random motors (e.g., kinesin) attachments to and detachments from filaments. The local inhomogeneity is assumed to be located at one of the two lanes. The effects of such inhomogeneity on its neighboring lane are focused in this paper. Density and inter-lane current are investigated. It is found that when the value of the hopping rate (p) is small, the local inhomogeneity effect can be observed on both lanes due to particles changing lanes. The effect is weakened when either p and/or lane-changing rate (Ω) increases. Average density and average current of the two lanes are also calculated, and it is found that the average density profile exhibits a complex variation behavior with the increase of Ω when p, Ω_A (attachment rate) and Ω_D (detachment rate) are small. Mean-field approximation is presented and it agrees well with our Monte Carlo simulations.