  An abstract DNA-type system is defined by a set of nonlinear kinetic
equations with polynomial nonlinearities that admit soliton solutions
associated with helical geometry. The set of equations allows for two different
Lax representations: A von Neumann form and a Darboux-covariant Lax pair. We
explain why non-Kolmogorovian probability models occurring in soliton kinetics
are naturally associated with chemical reactions. The most general known
characterization of soliton kinetic equations is given and a class of explicit
soliton solutions is discussed. Switching between open and closed states is a
generic behaviour of the helices. The effect does not crucially depend on the
order of nonlinearity (i.e. types of reactions), a fact that may explain why
simplified models possess properties occuring in realistic systems. We explain
also why fluctuations based on Darboux transformations will not destroy the
dynamics but only switch between a finite number of helical structures.
