Influence of a certain off-diagonal coupling on energy localization in an alpha-helix protein chain

In this study, we investigates the dynamics of exciton-phonon interactions in a one-dimensional α -helix chain, taking into account both diagonal and off-diagonal couplings. The governing framework for this dynamic is established through a discrete nonlinear Schrödinger equation. To derive a continuous integrable nonlinear Schrödinger equation, a continuous semi-discrete approximation approach is employed. The study of linear stability is carried out in this work using the phenomenon of modulational instability. The influence of the coupling parameters on the amplitude of the growth rate and the instability zone allowed us to predict the existence of solitary waves in the α -helix. A detailed analysis of the breather is conducted, along with the study of the energy behavior associated with this breather, considering the stability regions of the breather. Numerical simulations demonstrate that for high values of the off-diagonal coupling constant, the bright breather exhibits localization and stability over extended periods. Moreover, we investigates the interactions between two breather-like entities. During this interaction, the trapping phenomenon is observed, facilitated by the off-diagonal coupling. However, the increase in the dipole-dipole interaction between the amide groups of the α -helix appears to reduce the breather trapping time. These findings are novel within the context of protein chains and indicate a strong concordance between the analytical and numerical analyses conducted herein. Consequently, an appropriate selection of parameters for this model effectively ensures the coherent transport of energy within the alpha-helix.