Quantifying the impact of changes in effective population size and expression level on the rate of coding sequence evolution

Molecular sequences are shaped by selection, where the strength of selection relative to drift is determined by effective population size (N-e). Populations with high N-e are expected to undergo stronger purifying selection, and consequently to show a lower substitution rate for selected mutations relative to the substitution rate for neutral mutations (omega). However, computational models based on biophysics of protein stability have suggested that w can also be independent of N-e. Together, the response of omega to changes in N-e depends on the specific mapping from sequence to fitness. Importantly, an increase in protein expression level has been found empirically to result in decrease of omega, an observation predicted by theoretical models assuming selection for protein stability. Here, we derive a theoretical approximation for the response of omega to changes in N-e and expression level, under an explicit genotype-phenotype-fitness map. The method is generally valid for additive traits and log-concave fitness functions. We applied these results to protein undergoing selection for their conformational stability and corroborate out findings with simulations under more complex models. We predict a weak response of omega to changes in either N-e or expression level, which are interchangeable. Based on empirical data, we propose that fitness based on the conformational stability may not be a sufficient mechanism to explain the empirically observed variation in omega across species. Other aspects of protein biophysics might be explored, such as protein-protein interactions, which can lead to a stronger response of omega to changes in N-e. (C) 2021 The Authors. Published by Elsevier Inc.

Automated summary

Molecular sequences are shaped by selection and drift, where populations with high effective population size undergo stronger purifying selection leading to a lower substitution rate for selected mutations. Increase in protein expression level decreases the substitution rate for selected mutations, but selection for protein stability may not fully explain the observed variation in substitution rate across species.