Driven diffusive systems with mutually interactive Langmuir kinetics

Abstract

We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules. In the proposed model, the attachment and detachment rates of a particle are modified depending upon the occupancy of neighboring sites. We first obtain continuum mean-field equations and in certain limiting cases obtain analytic solutions. We show how mutual interactions increase (decrease) the effects of boundaries on the phase behavior of the model. We perform Monte Carlo simulations and demonstrate that our analytical approximations are in good agreement with the numerics over a wide range of model parameters. We present phase diagrams over a selective range of parameters.

On-site residence time in a driven diffusive system: Violation and recovery of a mean-field description

“…The differential equation describing the steady-state solutions density profile to first order in is given by [34] …”

“…This equation has not been solved in general, but solutions are known for certain parameter regimes [34]. In the TASEP+MILK model, shock-type profiles have been found to occur as well [34].…”

“…In the TASEP+MILK model, shock-type profiles have been found to occur as well [34]. At the end of this section we apply our method to determine the residence time for these profiles, and compare with simulations.…”

“…In the model TASEP + MILK shown schematically in Fig. 7, the attachment and detachment rates are modified depending on the occupancy of the adjacent sites [34]. These additional interactions increase (decrease) the effects of boundaries on the phase behavior of the model.…”

“…1). A further modification in which TASEP is coupled to the mutually interactive Langmuir kinetics (TASEP + MILK) can lead to even stronger localization than the TASEP + LK model [34,35]. Despite the interaction with the bulk, the 1D system exhibits phase transition behavior under the mesoscopic scaling of kinetic rates (attachment/detachment rates from the lattice).…”