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

Exciton dynamics through a three-stranded α-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.