Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium

Abstract

The mechanics of the conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium have been considered. The variational principles for the energy-dissipation rate during conformational motions in a viscous medium and the rate of the potential energy decrease of a macromolecule during conformational relaxation have been analyzed. The seeming contradiction between this principle and the principle of the minimum energy-dissipation rate is resolved. It is shown that the energy-dissipation rate must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill the deterministic nature of classical trajectories. The generalization and analysis of the influence of thermal fluctuations and external forces on the variational principles for the conformational relaxation of macromolecules is carried out. A visual graphical geometric depiction has been developed using hyperspheres in the space of the velocities of chain nodes to describe conformational movements along many degrees of freedom in a viscous medium. The equipartition of the energy-dissipation rates (and the rates of potential energy decrease) among the conformational degrees of freedom is discussed.