Generalized Langevin Mode Analysis (GLMA) for Local Density Fluctuation of Water in an Inhomogeneous Field of a Biomolecule

TL;DR

This paper introduces a generalized Langevin mode analysis (GLMA) method to study local density fluctuations of water molecules around biomolecules in inhomogeneous environments, extending previous homogeneous models.

Contribution

The paper develops a novel eigenvalue-based approach to analyze water density fluctuation modes modulated by biomolecular fields, enabling mode distinction with visual color coding.

Findings

Identified how biomolecular fields influence water fluctuation modes.

Extended previous homogeneous water fluctuation models to inhomogeneous environments.

Proposed applications in life sciences and medicine.

Abstract

An idea to analyze the fluctuational mode or/and spectrum of water molecules in an inhomogeneous environment around a biomolecule such as protein and DNA is proposed based on the generalized Langevin equation (GLE) for water interacting with a biomolecule. The idea is to solve an eigen-value problem of the collective frequency matrix of water, which has a physical meaning similar to the Hessian matrix in the case of a connected harmonic-oscillator. The diagonalization of the matrix gives the mode and frequency of the density fluctuation of water around the biomolecule. The treatment is a natural extension of that made for water in a homogeneous environment by Chong and Hirata in 2008, in which the authors have found the four modes for density fluctuation; one for an acoustic mode, and the other three for optical modes. It is the point of the new approach how the mode and frequency of the density fluctuation are modulated by the field from the biomolecule. The method provides a way to distinguish the mode of fluctuation with color. A few possible applications of the theoretical approach to problems of the life science including medicine are also proposed.