  We propose a formalism for describing two-strand systems of a DNA type by
means of soliton von Neumann equations, and illustrate how it works on a simple
example exactly solvably by a Darboux transformation. The main idea behind the
construction is the link between solutions of von Neumann equations and
entangled states of systems consisting of two subsystems evolving in time in
opposite directions. Such a time evolution has analogies in realistic DNA where
the polymerazes move on leading and lagging strands in opposite directions.
