Out-of-equilibrium noise facilitates inference from protein sequence data

Homologous proteins have similar three-dimensional structures and biological functions that shape their sequences. The constrained sequence variability among homologs is exploited by statistical inference methods, such as Potts models, and by deep learning methods, such as AlphaFold, to infer protein structure and function. In a minimal model, we show that both fluctuating selection strength and the emergence of function facilitate coevolution-based inference of structural contacts. Our conclusions extend to realistic synthetic data. Thus, out-of-equilibrium noise arising from ubiquitous variations in natural selection promotes the success of inference from protein sequences.