Do proteins learn to evolve? The Hopfield network as a basis for the understanding of protein evolution

Correlations between amino-acid residues can be observed in sets of aligned protein sequences, and the analysis of their statistical and evolutionary significance and distribution has been thoroughly investigated. In this paper, we present a model based on such covariations in protein sequences in which the pairs of residues that have mutual influence combine to produce a system analogous to a Hopfield neural network. The emergent properties of such a network, such as soft failure and the connection between network architecture and stored memory, have close parallels in known proteins. This model suggests that an explanation for observed characters of proteins such as the diminution of function by substitutions distant from the active site, the existence of protein folds (superfolds) that can perform several functions based on one architecture, and structural and functional resilience to destabilizing substitutions might derive from their inherent network-like structure. This model may also provide a basis for mapping the relationship between structure, function and evolutionary history of a protein family, and thus be a powerful tool for rational engineering.