# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/2303.00278