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

TL;DR

This study reveals that subdiffusive behavior in fast-folding proteins is primarily caused by hierarchical friction memory effects rather than the free energy landscape, challenging traditional Markovian models.

Contribution

It demonstrates that non-Markovian friction memory effects are the main driver of subdiffusion in protein folding dynamics, highlighting the need to incorporate memory effects in models.

Findings

Friction memory kernel is well-described by a hierarchical multi-exponential function.

Friction memory effects dominate the scaling behavior of MSD over the free energy landscape.

Markovian models are insufficient to capture folding dynamics with subdiffusion.

Abstract

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.