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

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2013-10, Vol.86 (10), Article 413
• Main Authors: Mvogo, Alain, Ben-Bolie, Germain Hubert, Crépin Kofané, Timoléon
• Format: Article
• Language: English
• Subjects: Analytical, structural and metabolic biochemistry; Biological and medical sciences; Complex Systems; Condensed Matter Physics; Fluid- and Aerodynamics; Fundamental and applied biological sciences. Psychology; General aspects, investigation methods; Physics; Physics and Astronomy; Proteins; Regular Article; Solid State Physics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2013-40517-1

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 φ 4 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.