Collective Excitations in α-helical Protein Structures Interacting with the Water Environment

Abstract

Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic activity, energy/charge transport, protein folding, and others. To explain high effectiveness of energy storage and transport in proteins, two possible mechanisms of the long-lived excitation in proteins were proposed by H. Fröhlich and A.S. Davydov in the form of either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with their environment formed by water molecules. In the model, we distinguished three coupled subsystems, i.e. (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of side residuals which in turn interacts with (iii) the environment, surrounding water responsible for dissipation and fluctuation processes in the system. It was shown that under reasonable approximations the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation for order parameter which admits bifurcation into the solution corresponding to weak damped vibrational modes (Fröhlich-type regime). A bifurcation parameter in the model is derived through the strength of interaction between alpha-helical protein and its environment. As shown, in the bifurcation region, a solution corresponding to Davydov soliton can exist. The suggested mechanism underlying emerging macroscopic dissipative structures in the form of collective vibrational modes is discussed in connection with the recent experimental data on the long-lived collective protein excitations in the terahertz frequency region.