Transport of single molecules along the periodic parallel lattices with coupling

General discrete one-dimensional stochastic models to describe the transport of single molecules along coupled parallel lattices with period N are developed. Theoretical analysis that allows to calculate explicitly the steady-state dynamic properties of single molecules, such as mean velocity V and dispersion D, is presented for N=1 and N=2 models. For the systems with N>2 exact analytic expressions for the large-time dynamic properties are obtained in the limit of strong coupling between the lattices that leads to dynamic equilibrium between two parallel kinetic pathways. It is shown that for all systems dispersion is maximal when the coupling between channels is weak.