Effects of longrange dispersion in nonlinear dynamics of DNA molecules
Abstract
A discrete nonlinear Schrodinger (NLS) model with longrange dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence $r^{s}$ and the exponential dependence $e^{\beta r}$ on the distance, $r$, are studied. For $s$ less than some critical value, $s_{cr}$, and similarly for $\beta \leq \beta_{cr}$ there is an interval of bistability where two stable stationary states: narrow, pinned states and broad, mobile states exist at each value of the total energy. For cubic nonlinearity the bistability of the solitons occurs for dipoledipole dispersive interaction $(s=3)$, and for the inverse radius of the dispersive interaction $\beta \leq \beta_{cr}=1.67$. For increasing degree of nonlinearity, $\sigma$, the critical values $s_{cr}$ and $\beta_{cr}$ increase. The longdistance behavior of the intrinsically localized states depends on $s$. For $s>3$ their tails are exponential while for $2<s<3$ they are algebraic. A controlled switching between pinned and mobile states is demonstrated applying a spatially symmetric perturbation in the form of a parametric kick. The mechanism could be important for controlling energy storage and transport in DNA molecules.
 Publication:

arXiv eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:physics/9906006
 Bibcode:
 1999physics...6006G
 Keywords:

 Physics  Biological Physics;
 Quantitative Biology
 EPrint:
 19 pages, 6 figures, in Proc. "Nonlinear Cooperative Phenomena in Biological Systems", Ed.: L. Matsson (World Scientific, Singapore, 1998) pp. 176194