Analysis of interactions in totally asymmetric exclusion process with site-dependent hopping rates: theory and simulations

Abstract

Biological molecular motors are special enzymes that support biological processes such as intracellular transport, vesicle locomotion, RNA translation and manymore. Experimentalworks suggest that themotor proteins interact among each other and moreover they experience a push by other motors during the intracellular transport. To incorporate these dynamics, we consider a variant of open one-dimensional totally asymmetric simple exclusion process with sitedependent hopping rates and interactions. The qualitative properties of our system do not depend on the hopping rate function.We utilize the simplemean- eld, the cluster mean- eld, the correlated cluster mean- eld to theoretically calculate the stationary phase diagrams, density and the maximal particle current. The limitations of all the three theories are extensively discussed. It has been found that although the interactions do not change the number of phases in a phase diagram, it signi cantly changes the density pro les, the phase transition lines and the maximal particle current. The theoretical results obtained are supported by Monte Carlo simulations.