Solitary waves management in α-helix protein chain with long-range interactions and asymmetric molecular vibrations

Abstract

A three-stranded α-helix protein chain model with long-rangeinteractions, whose dynamic, in the continuum limit approximation isgoverned by three coupled nonlinear Schr\"{o}dinger equation typesis investigated. Applying the trial equation method, two- andfour-bright solitary wave solutions are constructed to explain theexciton dynamic through the protein chains. Intensive numericalsimulations allow to check the influence of key system parameters onthe dynamic of the solutions. It appears that nonlinear couplings,long-range interactions, asymmetric molecular vibrations, and thewave's velocity deeply alter the widths and amplitudes of oursolitary waves, two salient features which mean that the abovementioned parameters have a major impact on bioenergy transport inprotein chains. In the same vein, the number of solitary waves whichpropagate through the protein chain may be controlled by either thewave velocity, the asymmetric molecular vibrations strength or thelong-range interaction strength provided that values of the latterparameters are set below or above critical values identified.