Nonlinearity-induced conformational instability and dynamics of biopolymers

Abstract

We propose a simple phenomenological model for describing the conformational dynamics of biopolymers via the nonlinearity-induced buckling and collapse (i.e. coiling up) instabilities. Taking into account the coupling between the internal and mechanical degrees of freedom of a semiflexible biopolymer chain, we show that self-trapped internal excitations (such as amide-I vibrations in proteins, base-pair vibrations in DNA, or polarons in proteins) may produce the buckling and collapse instabilities of an initially straight chain. These instabilities remain latent in a straight infinitely long chain, because the bending of such a chain would require an infinite energy. However, they manifest themselves as soon as we consider more realistic cases and take into account a finite length of the chain. In this case the nonlinear localized modes may act as drivers giving impetus to the conformational dynamics of biopolymers. The buckling instability is responsible, in particular, for the large-amplitude localized bending waves which accompany the nonlinear modes propagating along the chain. In the case of the collapse instability, the chain folds into a compact three-dimensional coil. The viscous damping of the aqueous environment only slows down the folding of the chain, but does not stop it even for a large damping. We find that these effects are only weakly affected by the peculiarities of the interaction potentials, and thus they should be generic for different models of semiflexible chains carrying nonlinear localized excitations.