Coexisting origins of subdiffusion in internal dynamics of proteins

Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.