Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation

A two-dimensional generalized Langevin equation is proposed to describe the protein con-formational change, compatible to the electron transfer process governed by atomic packing density model. We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively, and introduce the coupling effect coming from both fluctuations and equilibrium variances. The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived, based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique. We explicitly elaborate the short time and long time approximations. The relationship between the two-dimensional description and the one-dimensional theory is also discussed.