Hierarchical friction memory leads to subdiffusive configurational dynamics of fast-folding proteins

Proteins often exhibit subdiffusive configurational dynamics, the origins of which are still unresolved. We investigate the impact of non-Markovian friction and the free-energy landscape on the dynamics of fast-folding proteins in terms of the mean squared displacement (MSD) and the mean first-passage-time (MFPT) of the folding reaction coordinate. We find the friction memory kernel from published molecular dynamics simulations to be well-described by a hierarchical multiexponential function, which gives rise to subdiffusion in the MSD for times shorter than the longest memory time, while for longer times the confining free-energy landscape produces subdiffusion. Thus, for a wide range of times, friction memory effects in fast-folding proteins dominate the scaling behavior of the MSD compared to effects due to the folding free-energy landscape. As a consequence, Markovian models are insufficient to fully capture the folding dynamics, as quantified by the MSD and the MFPT, even when including coordinate-dependent friction. Our results demonstrate the importance of memory effects in protein folding and conformational dynamics and explicitly show that subdiffusion in fast-folding protein dynamics originates mainly from memory effects, not from the free-energy landscape and not from coordinate-dependent friction.