Abstract

In the course of evolution, proteins diversify their sequences via a complex interplay between random mutations and neutral selection. As a consequence, we can today observe protein sequences of common evolutionary origin, with almost identical three-dimensional folds and biological functions, which however differ by as much as 70-80% of their amino acids. In my presentation, I will review our efforts to model protein evolution across multiple timescales, from the emergence of single mutations in a protein up to deep evolutionary time scales. To this aim, we first model protein fitness landscapes via generative probabilistic models trained on genomic data, and we show that these models are able to predict the effect of individual mutations, and to generate non-natural but biologically functional proteins. Second, we describe evolution as a stochastic process in these landscapes. 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.