  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.
