Does the dynamics of sine-Gordon solitons predict active regions of DNA?

Abstract

In this work we analyze the possibility that soliton dynamics in a simple nonlinear model allows functionally relevant predictions of the behaviour of DNA. This suggestion was first put forward by Salerno [Phys. Rev. A, vol. 44, p. 5292 (1991)] by showing results indicating that sine-Gordon kinks were set in motion at certain regions of a DNA sequence that include promoters. We revisit that system and show that the observed behaviour has nothing to do with promoters; on the contrary, it originates from the bases at the boundary, which are not part of the studied genome. We explain this phenomenology in terms of an effective potential for the kink center. This is further extended to disprove recent claims that the dynamics of kinks [Lenholm and H\"ornquist, Physica D, vol. 177, p. 233 (2003)] or breathers [Bashford, J. Biol. Phys., vol. 32, p. 27 (2006)] has functional significance. We conclude that no such information can be extracted from this simple nonlinear model or its associated effective potential.