COLLECTIVE EXCITATIONS IN ALPHA-HELICAL PROTEIN MOLECULE

Abstract

Continuous energy supply, a necessary condition for life, excites a state far from thermodynamic equilibrium, in particular coherent electric polar vibrations depending on water ordering in the cell. The collective, low-frequency vibrational excitations in protein macromolecules in the terahertz frequency region are suggested to orchestrate many protein processes such as enzymatic activity, electron/energy transport, conformation transitions and others. The most significant type of excitations is long-lived coherent vibronic modes and waves which are either spreading over large protein subdomains or being localised states. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested. We developed a unified quantum-mechanics approach to describe conditions of the formation of Fröhlich vibronic state and Davidov soliton in alphahelical protein molecules interacting with the environment. We distinguish three subsystems in the model, i.e., (i) oscillating peptide groups (PGs), interacting with (ii) the subsystem of side residuals of proteins, which in turn interacts with the environment (surrounding water), which is responsible for dissipation and fluctuation processes and modelled by a system of harmonic oscillators. It was shown that the equation of motion for dynamic variables of PG chain (phonon variables) can be transformed to the nonlinear Schrodinger equation for order parameters, which determines energy “pumping” due to protein interaction with a reservoir. Solution of the order parameter equation was shown to admit bifurcation into the solution corresponding to the formation of weak damped collective vibronic mode with growing amplitude. It was also shown that the solution corresponding to Davydov soliton can exist at certain boundary conditions in this bifurcation region. The suggested mechanism of emergent of macroscopic dissipative structures in the form of collective vibronic modes in proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region

Keywords

• alpha-helical proteinα-helical protein
• fröhlich condensation
• autolocalization states
• hydrogen bonds
• phonon
• dynamical regimes
• soliton