Totally asymmetric simple exclusion process with particle annihilation

The cargo transport in biological cells often happens under a crowded environment. Past experiments have revealed that cargoes have the ability to self-assemble by associating or dissociating multiple motor proteins, which can impede the forward motion of cargoes on biopolymeric tracks. Motivated by these processes, we study a totally asymmetric simple exclusion process with possibilities of annihilation of particles. The model consists of a one-dimensional track on which two species of particles, one carrying cargoes and the other representing free motor proteins, hop obeying the exclusion principle. Further, the cargo carrying particle can annihilate the other species of particles occupying the forward site at a rate r ( a ). The annihilation process causing particle non-conservation leads to a nonlinear coupling between the two species of particles. We show that this system undergoes boundary induced phase transitions in the state. Using the method of boundary-layer analysis, we find mean-field solutions for the average particle distribution profile across the lattice in the steady state. Analyzing these solutions and the phase portrait of the boundary-layer differential equation, we predict the phase diagram, which consists of a low-density, a high-density and a shock phase. We find that the shapes of the density profiles are affected differently in different phases by the annihilation process. The shapes of the density profiles in different phases agree qualitatively with results from numerical simulations.