Long-range energy modes in α-helix lattices with inter-spine coupling

A system for three-strand α-helix proteins, with long-range dispersive interactions among polypeptide units, is considered. The associate improved Davydov model is shown to be fully described by a set of modified coupled discrete nonlinear Schrödinger equations, which involve long-range interactions between peptide groups along the protein strands. By means of the modulational instability theory, the competition between nonlinearity and long-range intermolecular interactions are shown to modify the domain of instability of plane waves. The impact of the competition between nonlinearity and long-range interactions, on the process of energy transport and storage, is also addressed numerically. It is shown that nonlinearity and the long-range couplings conspire to the emergence of trains of solitonic structures, when parameters are well chosen within the domain of instability of plane waves. The relevance of the improved model as well as the biological implications of the account of long-range intermolecular interactions, are discussed in the contexts of energy transport and storage in hydrogen-bonded molecular structures in general, and in α-helix proteins in particular.