Solitary waves in an inhomogeneous chain of α-helical proteins

Abstract

The dynamics of Davydov's model of α-helical proteins is considered by including the influence of inhomogeneities in the monomer units. Using the D2 ansatz for the exciton–phonon quantum state, the model Hamiltonian is transformed into a pair of classical lattice equations, which is further reduced in the continuum limit to a sole perturbed nonlinear Schrödinger (NLS) equation. The results of the perturbation theory of this equation show that the inhomogeneities in the localized form do not affect the velocity and amplitude of the solitary waves during propagation. We employ also the sine–cosine functions method to construct the exact solitary wave solutions in the presence of a variety of nonlinear inhomogeneities such as biquadratic, exponential and periodic inhomogeneities and it reveals that the coherent energy transport in the α-helical proteins is very much influenced by these nonlinear inhomogeneities.