Mutational paths in protein-sequence landscapes: from sampling to low-dimensional characterization

Eugenio Mauri (1) , Simona Cocco (1) , Rémi Monasson (1)

1 LPENS - Laboratoire de physique de l'ENS - ENS Paris

Understanding how protein functionalities vary along mutational paths is an important issue in evolutionary biology and in bioengineering. We here propose an algorithm to sample mutational paths in the sequence space, realizing a trade-off between protein optimality and path stiffness. The algorithm is benchmarked on exactly solvable models of proteins in silico, and applied to data-driven models of natural proteins learned from sequence data. Using mean-field theory, we monitor the projections of the sequence on relevant modes along the path, allowing for an interpretation of the protein sequence trajectory. Qualitative changes observed in paths as their lengths are varied can be explained by the existence of a phase transition in infinitely-long strings of strongly coupled Hopfield models.

Domaines: Biophysique; Mécanique statistique [cond-mat.stat-mech]

Eugenio Mauri, Simona Cocco, Rémi Monasson. Mutational paths in protein-sequence landscapes: from sampling to low-dimensional characterization. 2022. ⟨hal-03645394v1⟩