Analysis of Interactions in Totally Asymmetric Exclusion Process with Site-Dependent Hopping Rates: Theory and Simulations

Biological molecular motors are special enzymes that support biological processes such as intracellular transport, vesicle locomotion, RNA translation and many more. Experimental works suggest that the motor 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 site-dependent hopping rates and interactions. The qualitative properties of our system do not depend on the hopping rate function. We utilize the simple mean-field, the cluster mean-field, the correlated cluster mean-field 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 significantly changes the density profiles, the phase transition lines and the maximal particle current. The theoretical results obtained are supported by Monte Carlo simulations.