How the diffusivity profile reduces the arbitrariness of protein folding free energies

TL;DR

This paper demonstrates that incorporating diffusivity profiles into free energy calculations reduces the dependence on the choice of reaction coordinate, leading to more consistent predictions of protein folding kinetics.

Contribution

It introduces a method to rescale free energy profiles with diffusivity, minimizing the arbitrariness caused by different reaction coordinates in protein folding analysis.

Findings

Rescaled free energy profiles show less variation across different reaction coordinates.

Properly accounting for diffusivity profiles aligns folding kinetics predictions.

The method is applicable to experimental single molecule data.

Abstract

The concept of a protein diffusing in its free energy folding landscape has been fruitful for both theory and experiment. Yet the choice of the reaction coordinate (RC) introduces an undesirable degree of arbitrariness into the problem. We analyze extensive simulation data of an alpha-helix in explicit water solvent as it stochastically folds and unfolds. The free energy profiles for different RCs exhibit significant variation, some having an activation barrier, others not. We show that this variation has little effect on the predicted folding kinetics if the diffusivity profiles are properly taken into account. This kinetic quasi-universality is rationalized by an RC rescaling, which, due to the reparameterization invariance of the Fokker-Planck equation, allows the combination of free energy and diffusivity effects into a single function, the rescaled free energy profile. This rescaled free energy indeed shows less variation among different RCs than the bare free energy and diffusivity profiles separately do, if we properly distinguish between RCs that contain knowledge of the native state and those that are purely geometric in nature. Our method for extracting diffusivity profiles is easily applied to experimental single molecule time series data and might help to reconcile conflicts that arise when comparing results from different experimental probes for the same protein.