ИСТИНА

https://sbpreports.ru/conference/sbsp_2021/abstracts/17 Background All of important molecular and supramolecular biological processes occur in viscous media. The friction forces for a particle moving in a viscous medium are proportional to the viscosity and lead to the dissipation of the energy of motion into heat. However, viscosity has one more important function, which is discussed in the report. First, we consider an example of the molecular dynamics of folding of a polypeptide chain of 150 residues in a medium with a viscosity of the order of the viscosity of liquid water. The polypeptide chain folds into a helical conformation and then forms one of the characteristic folds found in proteins. A more careful correlation analysis of the motion of the polypeptide chain shows that the phi-type angles turn predominantly in one direction, and the psi-type angles - in the opposite side. Modeling the dynamics of the same system in a medium with a viscosity below the critical value demonstrates the absence of correlations between rotations of torsion angles and the macromolecule folds into a stochastic globule. This example demonstrates the "organizing" effect of viscosity on the dynamics of a system of a large number of interacting particles. Aims In the report, we analyze the dynamic properties of such systems from the first principles of mechanics and show that the dynamics of a system of a large number of interacting particles in a viscous medium obeys certain statistical laws. The more degrees of freedom are involved in the process the more accurately the system obeys these laws [ 1 ]. We use simple and intuitive geometric properties of multidimensional spheres and a theorem on the practically constant value of a good physical function of a large number of variables on the hypersphere surface of a finite radius (the cognitive dissonance of such a statement can be reduced by a simple argument - a volume bounded by a hypersphere of a finite radius approaches 0 for a large number of dimensions of the hypersphere, i.e. the hypersphere "tends" to a point). Methods The analysis of the dynamics of a system of a large number of particles in a viscous medium, carried out from the first principles of mechanics, shows that under practically significant conditions, several important principles for motion are implemented, which strongly influence the formation of the spatial structure of a system of particles during spontaneous folding. Results These principles are as follows: - The average rate of energy dissipation is uniformly distributed over all degrees of freedom. - The movement occurs in such a way that the conditions of the maximum possible rate of decrease in the potential energy of the total system and the minimum possible rate of energy dissipation are simultaneously fulfilled. The last statement may seem contradictory, since these values are equal to each other. But it should be taken into account that we are considering motion in a phase space of high dimension and these extreme principles work in different areas of this space. To illustrate these principles, the report presents the results of molecular modeling. Conclusions The above principles for the motion of a system of a large number of particles in a viscous medium are especially interesting for understanding the regularities of the spontaneous formation of spatial structures of linear biopolymers in a viscous (aqueous) medium. The movement of a representative point along the multidimensional energy landscape occurs along most smooth paths, avoiding sharp drops in potential energy over a relatively small number of degrees of freedom. This reduces the probability of a representative point falling into "energy traps" on the way to the global minimum energy. Библиографические ссылки: Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium K. Shaitan Biophysics. 2018, 63, 1-9 https://doi.org/10.1134/S0006350918010165