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

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.