Reservoir crowding in a totally asymmetric simple exclusion process with Langmuir kinetics

We study a totally asymmetric simple exclusion process equipped with Langmuir kinetics with boundaries connected to a common reservoir. The total number of particles in the system is conserved and controlled by filling factor mu. Additionally, crowding of reservoir is taken into account which regulates the entry and exit of particles from both boundary as well as bulk. In the framework of mean-field approximation, we express the density profiles in terms of Lambert-W functions and obtain phase diagrams in alpha - beta parameter space. Further, we elucidate the variation of phase diagram with respect to filling factor and Langmuir kinetics. In particular, the topology of the phase diagram is found to change in the vicinity of mu = 1 . Moreover, the interplay between reservoir crowding and Langmuir kinetics develops a novel feature in the form of back-and-forth transition. The theoretical phase boundaries and density profiles are validated through extensive Monte Carlo simulations. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

We investigate a totally asymmetric simple exclusion process with Langmuir kinetics and conservation of total particle number controlled by filling factor mu. Crowding of the reservoir is taken into account in addition to the entry and exit of particles. We use mean-field approximation to express density profiles and obtain phase diagrams in the alpha - beta parameter space, showing changes in topology near mu = 1. The interplay of reservoir crowding and Langmuir kinetics leads to a novel back-and-forth transition feature. Theoretical phase boundaries and density profiles are validated through extensive Monte Carlo simulations.