Neutral evolution of model proteins: diffusion in sequence space and overdispersion

TL;DR

This study uses a lattice model to simulate neutral evolution in proteins, demonstrating the existence of extensive neutral networks and overdispersion in mutation rates, aligning with biological observations.

Contribution

It provides evidence for large neutral networks and overdispersion in neutral mutation rates using a lattice model, advancing understanding of protein evolution.

Findings

Existence of extended neutral networks in sequence space

Neutral mutation rates have a broad distribution

Substitution process is overdispersed, matching biological data

Abstract

We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space -- sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than one). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with biological data.