Variational Principles in Mechanics of Conformational Motions of Macromolecules in a Viscous Medium
Mechanics of conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium is considered. Variational principles for the energy dissipation rate during conformational motions in a viscous medium and the rate of a decrease of the potential energy of a macromolecule during conformational relaxation are analyzed. We show that the principle of the maximum decrease rate of the system's potential energy follows from the condition of the equality of the energy dissipation rate and the rate of the potential energy. The seeming contradiction between this principle and the principle of the minimum rate of energy dissipation is resolved. We show that the rate of the energy dissipation must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill deterministic nature of classical trajectories. Generalization and analysis of the effect of thermal fluctuations and external forces on the fulfillment of variational principles for the conformational relaxation of macromolecules are carried out. We have developed graphic geometric representations with the help of hyperspheres in the space of chain nodes velocities 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.