Eur. Phys. J. B (2013) 86: 413
https://doi.org/10.1140/epjb/e2013-40517-1

Regular Article

Long-range interactions in α-helical proteins with interspine coupling: Modulational instability and exact soliton solutions

¹ Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
² Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
³ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

^a e-mail: mvogal2009@yahoo.fr

Received: 23 May 2013
Received in final form: 21 June 2013
Published online: 2 October 2013

Abstract

The dynamics of α-helical proteins with interspine coupling by taking into account long-range dipole-dipole interactions and some additional higher order molecular excitations is studied. The model Hamiltonian is transformed into a set of three classical lattice equations, which are further reduced in the multiple scales analysis to a set of three coupled nonlinear Schrödinger (3-CNLS) equations. The linear stability analysis of continuous wave solutions of these 3-CNLS equations is performed and it reveals that the modulational instability (MI) gain is deeply influenced by the long-range interactions (LRI) parameter. Some classes of exact traveling wave solutions are constructed via the solutions of a φ⁴ model through the F-expansion method and representative wave structures are graphically displayed including localized and periodic solutions. In order to confirm the analytical approach, the numerical experiments show that the solitons are stable at 70 ps. These solitons, exhibited in the model, are a possible carrier of bio-energy transport in the protein molecules.