“Mutation Induced Extinction in Finite Populations: Lethal Mutagenesis and Lethal Isolation”, 2012-05-23 (; backlinks; similar):
Reproduction is inherently risky, in part because genomic replication can introduce new mutations that are usually deleterious toward fitness. This risk is especially severe for organisms whose genomes replicate “semi-conservatively”, eg. viruses and bacteria, where no master copy of the genome is preserved. Lethal mutagenesis refers to extinction of populations due to an unbearably high mutation rate (U), and is important both theoretically and clinically, where drugs can extinguish pathogens by increasing their mutation rate. Previous theoretical models of lethal mutagenesis assume infinite population size (N). However, in addition to high U, small N can accelerate extinction by strengthening genetic drift and relaxing selection. Here, we examine how the time until extinction depends jointly on N and U. We first analytically compute the mean time until extinction (τ) in a simplistic model where all mutations are either lethal or neutral. The solution motivates the definition of two distinct regimes: a survival phase and an extinction phase, which differ dramatically in both how τ scales with N and in the coefficient of variation in time until extinction. Next, we perform stochastic population-genetics simulations on a realistic fitness landscape that both (1) features an epistatic distribution of fitness effects that agrees with experimental data on viruses and (2) is based on the biophysics of protein folding. More specifically, we assume that mutations inflict fitness penalties proportional to the extent that they unfold proteins. We find that decreasing N can cause phase transition-like behavior from survival to extinction, which motivates the concept of “lethal isolation.” Furthermore, we find that lethal mutagenesis and lethal isolation interact synergistically, which may have clinical implications for treating infections. Broadly, we conclude that stably folded proteins are only possible in ecological settings that support sufficiently large populations.
Author Summary: Most spontaneous mutations hurt organismal fitness, eg. by destabilizing proteins. In many species, the normal mutation rate is strikingly high: on the order of one per genome per replication. In the face of these mutations, how can proteins maintain their native structure, and how can populations of organisms avoid extinction? Are there physics-based limits on how large the mutation rate of any species can be before the onslaught of mutations outpaces natural selection and melts-down proteins? Here, we address these questions with a computational model that combines protein folding thermodynamics with individual-based population genetics simulations. We calculate a theoretical “speed limit” equal to a few mutations per genome per replication—near the mutation rate of RNA viruses. Additionally, we find that the speed limit can be much lower in small populations where “random genetic drift” is strong. Thus, we conclude that stably folded proteins are only possible in ecological settings that support sufficiently large populations. These findings may have clinical implications for treating viral infections with drugs that elevate the viral mutation rate.