Exact computation of spectral densities for a Langevin dynamic modelling the relaxation of a protein near its equilibrium

Abstract

The relaxation motion of a protein nearby its equilibrium is enhanced by the heat bath in which the protein is embedded. A classical approach will realize this heat bath through a molecular dynamic including a large number of molecules of the solvent at the cost of a large computing time. Here, we propose a modelling of the heat bath by a Langevin random force. Under this Langevin dynamic, an exact mathematical computation of the spectral densities can be made. The mathematical expression will depend upon the normal modes of the potential nearby its minimum. The mathematical computation is exact; it is, therefore, unnecessary to run an effective simulation through a molecular dynamic. The spectral densities will peak at these normal modes. Our computation provides a theoretical ground to the experimental determination of normal modes through a peak searching of observed spectral densities.