Boundary induced phase transition with stochastic entrance and exit

We study an open-chain totally asymmetric exclusion process (TASEP) with stochastic gates present at the two boundaries. The gating dynamics has been modeled keeping the physical system of ion-channel gating in mind. These gates can randomly switch between an open state and a closed state. In the open state, the gates are highly permeable such that any particle arriving at the gate immediately passes through. In the closed state, a particle gets trapped at the gate and cannot pass through until the gate switches open again. We calculate the phase-diagram of the system and find important and non-trivial differences with the phase-diagram of a regular open-chain TASEP. In particular, depending on switching rates of the two gates, the system may or may not admit a maximal current phase. Our analytic calculation within mean-field theory captures the main qualitative features of our Monte Carlo simulation results. We also perform a refined mean-field calculation where the correlations at the boundaries are taken into account. This theory shows significantly better quantitative agreement with our simulation results