Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. IV. Topological stability of alpha helix and DNA structures

Abstract: The structural parameters of alpha helix and some forms of DNA-structures are determined by methods of algebraic topology. These structures are locally periodic and correspond to the bifurcation point for minimal surfaces given by Weierstrass representation. The index of an unstable surface equals zero for them. As predicted by a theory of catastrophes, formation of such structures corresponds to lifting of configurational degeneration. Formation turns by half- turns from different helices in the implementation of double-structure as a single system, may indicate a kind of local crossing-over between motherboard and paternal helices (at least for some part of the helix). The role of the exchange have yet to understand given the impossibility of exchange between different turns spirals going counter rotating and shifted axis.