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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 Hornquist, 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.
We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temp
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
The understanding of mechanisms that control epigenetic changes is an important research area in modern functional biology. Epigenetic modifications such as DNA methylation are in general very stable over many cell divisions. DNA methylation can howe
We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)],
The bipartite ground state entanglement in a finite linear harmonic chain of particles is numerically investigated. The particles are subjected to an external on-site periodic potential belonging to a family parametrized by the unit interval encompas