Chain length scaling of protein folding time

TL;DR

This study uses Monte Carlo simulations to analyze how protein folding times scale with chain length, revealing different exponents for random and designed sequences and identifying an Arrhenius-like temperature dependence.

Contribution

It provides the first detailed analysis of chain length scaling of folding times for heteropolymers with different sequence types using lattice models.

Findings

Folding time scales as N^6 for random sequences.

Folding time scales as N^4 for designed sequences.

Folding exhibits Arrhenius behavior with a consistent energy barrier.

Abstract

Folding of protein-like heteropolymers into unique 3D structures is investigated using Monte Carlo simulations on a cubic lattice. We found that folding time of chains of length $N$ scales as $N^\lambda$ at temperature of fastest folding. For chains with random sequences of monomers $\lambda \approx 6$, and for chains with sequences designed to provide a pronounced minimum of energy to their ground state conformation $\lambda \approx 4$. Folding at low temperatures exhibits an Arrhenius-like behavior with the energy barrier $E_b \approx \phi |E_n|$, where $E_n$ is the energy of the native conformation. $\phi \approx 0.18$ both for random and designed sequences.