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.

Therapeutic Basis of Electromagnetic Resonances and Signal-Modulation

“…The nonlinear, systemic collective harmony of macroscopic phenomena characterizes the biosolitons. The collectivity driven by the energy-transfer is well shown in large molecules like alpha-helix of proteins [143] in THz frequency region but also appears mass-movement at lower frequencies [144]. The soliton harmonization of the collective movements emerges when the cells starve and need collective efforts to survive, sharing the available energy as optimally as possible [145].…”

Contribution of the collective excitations to the coupled proton and energy transport along mitochondrial crista membrane in oxidative phosphorylation system

“…Theoretical consideration of the proton transport as a collective phenomenon emerging in molecular systems has been first carried out in the framework of Davydov soliton theory (Antonchenko et al 1983). Davydovs soliton (Davydov 1982) or other similar self-localized states (Austin et al 2003; Pang 2012) and collective excitations (Bolterauer et al 1991; Kadantsev and Goltsov 2020) have long been and still are considered as promising candidates for the role of charge and energy carriers within proteins (Kavitha et al 2016), along the membrane surface (Manousakis 2005; Kadantsev and Goltsov 2022) and on interfaces of biopolymers and artificial membranes (Matsui and Matsuo 2020). The concept of solitary waves was developed to described the mechanism underlying highly effective transport of charge and energy in molecular systems in the form of molecular excitations which are described by autolocalized solutions (solitons) of nonlinear wave equations (Davydov 1985).…”