Theoretical investigation of biological transport: Asymmetric simple exclusion processes in two-channel systems
Kolomeisky, Anatoly B.
Doctor of Philosophy
Multi-particle non-equilibrium dynamics in two-channel biological transport systems is investigated theoretically within the framework of asymmetric simple exclusion processes (ASEP). In exclusion processes particles move along the lattice by hopping between neighboring sites that are vacant. We consider the systems with open boundaries, where particles enter the lattice on the entrance site and leave from the exit site with given rates. Four different ASEP models are studied. The first two models investigate interchannel coupling between parallel channels in a one-way transport system. The third model considers junction of two parallel tracks, while the last model investigates two-way transport system with narrow entrances with coupling on the boundaries. Theoretical investigation of these non-equilibrium systems reveal many interesting phenomena, such as unusual phase diagrams that contain up to seven stationary-state phases, localization of the domain wall in the bulk of the system, symmetry-breaking and strong interparticle correlation. Stationary phase diagrams, particle currents and bulk values of densities are calculated in a mean-field approximation for the systems in the thermodynamic limit. In addition, exact matrix product ansatz method and phenomenological domain-wall theory are applied to analyze dynamic properties. For several systems nearest-neighbour correlation and density distribution functions are computed and size-scaling effects are analyzed. Extensive Monte Carlo computer simulations are carried out for all systems to test predictions and they verify our theoretical results.