Dependence of folding rates on protein length

TL;DR

This study examines how protein folding times depend on chain length using lattice models, revealing a power law growth with uniform interactions and a stretched exponential with heterogeneous interactions, highlighting the slowing effect of side chains.

Contribution

It demonstrates the impact of interaction heterogeneity and side chains on folding times, providing new insights into the scaling behavior of protein folding.

Findings

Folding time scales as N^3.6 with uniform interactions.

Heterogeneous interactions lead to stretched exponential dependence.

Side chains slow down folding due to frustration.

Abstract

Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power law with the chain length N with exponent $\lambda \approx 3.6$ for the Go model, in which all native interactions (i.e., between all side chains and backbone atoms) are uniform. If the interactions between side chains are given by pairwise statistical potentials, which introduce heterogeneity in the contact energies, then the power law fits yield large $\lambda$ values that typically signifies a crossover to an underlying activated process. Accordingly, the dependence of folding time is best described by the stretched exponential \exp(\sqrt{N}). The study also shows that the incorporation of side chains considerably slows down folding by introducing energetic and topological frustration.