Entropy associated with conformation and density fluctuations in biomolecular solutions

TL;DR

This paper derives microscopic formulas for the entropy of biomolecular solutions, accounting for conformational and density fluctuations using Gibbs entropy, Langevin theory, and RISM/3D-RISM, enabling detailed entropy calculations.

Contribution

It introduces new formulas for entropy related to biomolecular conformations and solvent density fluctuations, combining multiple theoretical approaches.

Findings

Derived formulas for conformational entropy of biomolecules.

Formulas for solvent density fluctuation entropy around solutes.

Discussed the feasibility of calculating these entropies.

Abstract

Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned with the conformational fluctuation of a biomolecule, and the other with the density fluctuation of solvent around a solute. The formula derived for the entropy associated with the conformational fluctuation is where N is the number of atoms in the solute, and A is the determinant of the inverse of the variance-covariance matrix of conformational fluctuation. The formula for the entropy of solvent at a pair of positions around a solute is also derived to be, where n is the number of atoms in a solvent molecule, and B is essentially the determinant of the matrix of the density-pair-correlation functions. The entropy at a local position r may be obtained by integrating the expression by over the entire volume of the system. The feasibility of the calculation to find the entropies is discussed.