A generalized Davydov model with interspine coupling and its integrable discretization

Abstract

We propose a generalized model for the dynamics of alpha helical proteins by including excitations of dipole and quadrupole types, nearest and next nearest-neighbour interactions and interspine coupling at higher order. We investigate the dynamics in the continuum limit by identifying the underlying completely integrable model for specific parameters and study the solitonic aspects including Lax pair, soliton solutions, etc. We analyse the energy sharing properties between the spines during the propagation of solitons through them by constructing multi-soliton solutions to the resulting completely integrable three-coupled fourth-order nonlinear Schrödinger equation. We identify the equivalent integrable higher-order discrete three-coupled equations through an appropriate generalization of the Lax pair of the original Ablowitz–Ladik lattice. By means of systematic simulations, we study the nature of energy transfer in discrete alpha helical protein lattice.