Toward the Characterization of Fractional Stochastic Processes Underlying Methyl Dynamics in Proteins

In this article, we investigate the multiple-scale structure of methyl side chain dynamics in proteins. We show that the orientational correlation functions of CH₃ methyl groups are well described by a fractional Brownian dynamics model. Typical angular correlation functions involved in NMR relaxation were computed from MD simulations performed on two different proteins. These correlation functions were shown to be very well fitted by a fractional Ornstein–Uhlenbeck process in the presence of effective local potentials at the C–H and C–C methyl bonds. In addition, our analysis highlights the presence of the asymptotic power law decay of the waiting time probability density of the stochastic process involved, thereby illustrating the connection between approaches based on fractional diffusion equations and the continuous time random walk