Eur. Phys. J. E (2010) 32: 327-332
https://doi.org/10.1140/epje/i2010-10627-x

Regular Article

Long-range interactions and wave patterns in a DNA model

¹ Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
² The African Institute for Mathematical Sciences, 6-8 Melrose Rd, 7945, Muizenberg, South Africa
³ Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
⁴ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

^* e-mail: contab408@hotmail.com

Received: 24 November 2009
Revised: 28 May 2010
Accepted: 24 June 2010
Published online: 30 July 2010

Abstract

We propose a spin-like model of DNA nonlinear dynamics with long-range interactions between adjacent base pairs. We show that the model equation is a modified sine-Gordon equation. We perform the linear stability analysis of a plane wave, which predicts high-amplitude and extended oscillating waves for high values of the long-range parameter. This is confirmed numerically and biological implications of the obtained patterns are suggested.