Abstract
Low-frequency vibrational excitations of proteins macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic activity, molecular electron/energy transport, protein folding, and others. Two possible mechanisms of the formation of long-lived vibrational modes in protein were earlier proposed by H. Fröhlich and A.S. Davydov in the form of vibrational modes and solitary waves, respectively, to explain high effectiveness of energy storage and transport in proteins. In this paper, we developed a quantum dynamic model of vibrational mode excitation in alpha-helical protein interacting with environment. In the model we distinguish three coupled subsystems, i.e. (i) hydrogen bond peptide groups (PGs), interacting with (ii) the subsystem of side residuals which in turn interacts with (iii) environment (surrounding water) and is responsible for dissipation and fluctuation processes. It was shown that 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 was shown to determine interaction of a protein with environment and in part, energy pumping to the protein due to its interaction. In the bifurcation region, a solution corresponding to Davydov soliton was shown to exist. The suggested mechanism of emergence of the macroscopic dissipative structures in the form of collective vibrational modes in alpha-helical proteins is discussed in connection with the recent experimental data on the long-lived collective protein excitations in the terahertz frequency region.
