Multiple Scale Dynamics in Proteins Probed at Multiple Time Scales through Fluctuations of NMR Chemical Shifts

Fluctuations of NMR resonance frequency shifts and their relation with protein exchanging conformations are usually analyzed in terms of simple two-site jump processes. However, this description is unable to account for the presence of multiple time scale dynamics. In this work, we present an alternative model for the interpretation of the stochastic processes underlying these fluctuations of resonance frequencies. Time correlation functions of N-15 amide chemical shifts computed from molecular dynamics simulations (MD) were analyzed in terms of a transiently fractional diffusion process. The analysis of MD trajectories spanning dramatically different time scales (similar to 200 ns and 1 ms [Shaw, D. E.; et al. Science 2010, 330, 341-346]) allowed us to show that our model could capture the multiple scale structure of chemical shift fluctuations. Moreover, the predicted exchange contribution R-ex to the NMR transverse relaxation rate is in qualitative agreement with experimental results. These observations suggest that the proposed fractional diffusion model may provide significative improvement to the analysis of NMR dispersion experiments.