Electrosoliton dynamics in a thermalized molecular chain

The possibility of the electrosoliton formation in α-helical proteins which represents a localized state of an extra electron bound with the deformation region of the α-helix arising due to the electron interaction with chain of peptide groups is investigated in a quasiclassical approximation. Two possible mechanisms of the formation of collective dynamic modes in the form of Fröhlich collective mode and Davydov soliton were previously suggested by the authors. In this paper, we developed a unified quantum-mechanics approach to describe conditions of the formation of the Fröhlich vibronic state and Davydov soliton in α-helical protein molecules interacting with the environment. The concept of "soliton" is used not only in the strict mathematical sense, i.e. in the case of completely integrable Hamiltonian systems, but also to describe dynamically stable, nonlinear collective structures. Davydov solitons are stable due to a small probability of the dissipation of its energy into thermal energy which provides a high efficiency of soliton transport of energy, charges, and conformation changes in biosystems at a physiological temperature of 310 K.Electrosolitons can be formed if the value of electron–phonon interaction (EPI) parameter exceeds a certain threshold. One of the most important characteristics of the electrosoliton’s state is the coupling energy of a quasi-particle (exciton or electron) with molecular chain deformation, which also determines the soliton stability. Dynamic equations describing the motion of a one-dimensional electrosoliton in the continuum approximation are a self-consistent system which includes the time-dependent Schrödinger equation with a deformation potential and an inhomogeneous linear wave equation for this potential. This system, known as the Zakharov system, has significance in physics and, generally, describes the nonlinear interaction of two physical subsystems: fast and slow. Zakharov equations have a well-known soliton solution in the hyperbolic secant form, describing the envelope profile of the high-frequency vibrations of a fast subsystem, which can propagate with any subsonic velocity. The suggested mechanism of emergent of macroscopic dissipative structures in the form of electrosolitons in α-helical proteins is discussed in connection with recent experimental data on long-lived collective protein excitation in the terahertz frequency region.