  We introduce a data-driven epistatic model of protein evolution, capable of
generating evolutionary trajectories spanning very different time scales
reaching from individual mutations to diverged homologs. Our in silico
evolution encompasses random nucleotide mutations, insertions and deletions,
and models selection using a fitness landscape, which is inferred via a
generative probabilistic model for protein families. We show that the proposed
framework accurately reproduces the sequence statistics of both short-time
(experimental) and long-time (natural) protein evolution, suggesting
applicability also to relatively data-poor intermediate evolutionary time
scales, which are currently inaccessible to evolution experiments. Our model
uncovers a highly collective nature of epistasis, gradually changing the
fitness effect of mutations in a diverging sequence context, rather than acting
via strong interactions between individual mutations. This collective nature
triggers the emergence of a long evolutionary time scale, separating fast
mutational processes inside a given sequence context, from the slow evolution
of the context itself. The model quantitatively reproduces the extent of
contingency and entrenchment, as well as the loss of predictability in protein
evolution observed in deep mutational scanning experiments of distant homologs.
It thereby deepens our understanding of the interplay between mutation and
selection in shaping protein diversity and novel functions, allows to
statistically forecast evolution, and challenges the prevailing
independent-site models of protein evolution, which are unable to capture the
fundamental importance of epistasis.
