Viscosity Dependence of the Folding Rates of Proteins

TL;DR

This study investigates how solvent viscosity influences protein folding rates using off-lattice models, revealing a non-monotonic relationship with a maximum at intermediate viscosities and providing estimates for folding times of different protein structures.

Contribution

It introduces a quantitative analysis of viscosity effects on protein folding rates using Langevin dynamics and Kramers theory, with estimates for real protein folding times.

Findings

Folding rates increase linearly at low viscosities.

Folding rates decrease as 1/η at high viscosities.

Maximum folding rate occurs at intermediate viscosities.

Abstract

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.