A mutation-selection model of protein evolution under persistent positive selection

We use first principles of population genetics to model the evolution of proteins under persistent positive selection (PPS). PPS may occur when organisms are subjected to persistent environmental change, during adaptive radiations, or in host-pathogen interactions. Our mutation-selection model indicates protein evolution under PPS is an irreversible Markov process, and thus proteins under PPS show a strongly asymmetrical distribution of selection coefficients among amino acid substitutions. Our model shows the criteria ω > 1 (where ω is the ratio of non-synonymous over synonymous codon substitution rates) to detect positive selection is conservative and indeed arbitrary, because in real proteins many mutations are highly deleterious and are removed by selection even at positively-selected sites. We use a penalized-likelihood implementation of our model to successfully detect PPS in plant RuBisCO and influenza HA proteins. By directly estimating selection coefficients at protein sites, our inference procedure bypasses the need for using ω as a surrogate measure of selection and improves our ability to detect molecular adaptation in proteins. Significance Statement Understanding how natural selection acts on proteins is important as it can inform studies from adaptive radiations to host-pathogen co-evolution. Traditionally, selection on proteins is inferred indirectly by measuring the non-synonymous to synonymous rate ratio, ω , with ω > 1, = 1, and < 1 indicating positive (adaptive) selection, neutral evolution, and negative (purifying) selection respectively. However, the theoretical underpinnings of this ratio are not well understood. Here we use first-principles of population genetics to work out how persistent changes in selection affect protein evolution and we use our new model to detect adaptive sites in plant and influenza proteins. We show measuring selection directly improves detection of adaptation in proteins.