Epistasis plays a limited role in driving entrenchment during neutral protein evolution

BACKGROUND: Substitutional entrenchment arising from epistatic interactions renders previously acceptable amino-acid states unfavorable over evolutionary time and has often been attributed to novel adaptive processes. However, recent simulations based on Potts-Hamiltonian models have suggested that entrenchment may also emerge during protein evolution governed by the neutral theory of molecular evolution (NTME). RESULTS: Here, we re-examine this conclusion by assessing whether substitutions permitted in such simulations are consistent with empirical expectations of NTME. Since Potts models are inferred from a large collection of homologous rather than orthologous sequences, they may allow substitutions that are incompatible with NTME. Our analysis revealed that Potts-based simulations permit amino-acid substitutions whose Hamiltonian energies (PHE, φ) often fall outside empirically derived NTME φ neighborhoods, thus allowing non-neutral evolution of domain sequences. To prevent such transgressions, we implement simulations that impose purifying selection whenever Potts-acceptable substitutions depart from the NTME φ neighborhood. When these substitutions are eliminated, we observed limited substitutional entrenchment, with site-specific amino-acid preferences remaining stable over biologically relevant timescales in neutral protein evolution. We further find that overdispersion of the molecular clock is modest and scales directly with the proportion of evolutionary lineages displaying epistasis-driven among-site rate heterogeneity, independent of entrenchment. CONCLUSIONS: These results demonstrate that significant entrenchment is not an inherent property of epistasis during protein evolution consistent with NTME. Our findings establish baseline expectations for neutral evolution with epistasis and suggest that pronounced entrenchment observed in natural protein evolution likely reflects non-neutral evolutionary histories, including adaptation.