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

Proteins often exhibit subdiffusive configurational dynamics. The origins of this subdiffusion 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 (MD) simulations to be well-described by a hierarchical multi-exponential function, which gives rise to subdiffusion in the MSD over a finite range of time. We show that 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 for capturing 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 from memory effects, not from the free energy landscape and not from coordinate-dependent friction.