Mean-field analysis of two-species totally asymmetric simple exclusion process (TASEP) with attachment and detachment

Abstract

In the field of statistical physics, unidirectional motion of a large number of particles along a single track can be described by totally asymmetric simple exclusion process (TASEP), from which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high particle density and low particle density along the motion track) and boundary layers, can be obtained. However, it is biologically general that a single track may be occupied by different particle species. For example, in cells each microtubule protofilament is usually occupied by different species of motor protein. So previous studies about TASEP that included only one particle species may not be reasonable enough to describe more detailed properties of particle motion processes in a real cell environment. To address this problem, TASEP including two particle species is discussed in this study. Theoretical methods to get particle densities of each species are provided. By which, phase transition related properties of particle densities are obtained. Our analysis shows that domain wall and boundary layers of single species densities always appear simultaneously with those of the total particle density. The height of the domain wall of total particle density is equal to the summation of those of single particle species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species.