Eur. Phys. J. Plus (2021) 136: 274
https://doi.org/10.1140/epjp/s13360-021-01279-1

Regular Article

Excitons dynamic in a three-stranded -helix protein chains with diagonal and off-diagonal couplings: effects of strong long-range interactions

¹ Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
² Department of Basic Scientific Teachings, National Advanced School of Engineering of Maroua, University of Maroua, P.O. Box 46, Maroua, Cameroon
³ Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
⁴ Department of Mathematics and Physical Sciences, National Advanced School of Engineering of Yaoundé, University 12 of Yaounde I, P.O. Box 8390, Yaounde, Cameroon
⁵ African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon
⁶ Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana

^a yanickondouar@yahoo.com

Received: 22 October 2020
Accepted: 24 February 2021
Published online: 2 March 2021

Abstract

Exciton dynamics through a three-stranded -helix protein chain in the presence of inter-spines and diagonal and off-diagonal couplings as well as long-range interactions are investigated. Its is shown that the behavior of the system is governed by three-coupled modified continuous nonlinear Schrödinger equations. Performing a modulational instability analysis, it appears that both the off-diagonal coupling and the long-range interaction reduce the instability regions and the amplitude of the growth rate. More analytical insights of the system dynamics are obtained by constructing its solutions with the F-expansion method. Many families of solutions are unveiled among them are bright and dark solitary waves, Jacobian elliptic function solutions and hyperbolic function solutions to name just a few. Intensive numerical simulations carried corroborate the analytical solutions found with a good accuracy. In addition, our numerical findings prove that the long-range interactions increase the energy of the waves propagating through the protein chain. From a biological point of view, the model used in the current work better describes the energy transport in protein chains.