Master equation of proteins in interaction with implicit or explicit solvent

TL;DR

This study compares explicit and mean-field solvent models in protein folding, revealing that effective solvent descriptions fail to accurately capture folding pathways, emphasizing the need for microscopic models for kinetic studies.

Contribution

The paper introduces a two-dimensional lattice model to compare explicit and effective solvent descriptions, demonstrating the limitations of mean-field approaches in folding pathway predictions.

Findings

Equilibrium predictions are identical for both models.

Kinetic pathways differ significantly between models.

Microscopic solvent models are necessary for accurate folding kinetics.

Abstract

Theoretical studies of protein folding on lattice models relie on the assumption that water close to amino-acids is always in thermal equilibrium all along the folding pathway. Within this framework, it has always been considered that out-of-equilibrium properties, such as folding time, could be evaluated equivalently from an averaging over a collection of trajectories of the protein with water described eitherexplicitly or through a mean-field approach. To critically assess this hypothesis, we built a two-dimensional lattice model of a protein in interaction with water molecules that can adopt a wide range of conformations. This microscopic description of the solvent has been used further to derive an effective model by averaging over all the degrees of freedom of the solvent. At thermal equilbrium, the two descriptions are rigourously equivalent, predicting the same folded conformation of the protein. The model allows exact calculations of some relaxation properties using the master equations associated to both solvent descriptions. The kinetic patterns associated to the folding pathways are remarkably different. In this work we demonstrate, that an effective description of the solvent can not described properly the folding pathway of a protein. The microscopic solvent model, that describes correctly the microscopic routes, appears to be the only candidate to study folding kinetics.