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.