Selection for cooperativity causes epistasis predominately between native contacts and enables epistasis-based structure reconstruction.

Epistasis and cooperativity of folding both result from networks of energetic interactions in proteins. Epistasis results from energetic interactions among mutants, whereas cooperativity results from energetic interactions during folding that reduce the presence of intermediate states. The two concepts seem intuitively related, but it is unknown how they are related, particularly in terms of selection. To investigate their relationship, we simulated protein evolution under selection for cooperativity and separately under selection for epistasis. Strong selection for cooperativity created strong epistasis between contacts in the native structure but weakened epistasis between nonnative contacts. In contrast, selection for epistasis increased epistasis in both native and nonnative contacts and reduced cooperativity. Because epistasis can be used to predict protein structure only if it preferentially occurs in native contacts, this result indicates that selection for cooperativity may be key for predicting structure using epistasis. To evaluate this inference, we simulated the evolution of guanine nucleotide-binding protein (GB1) with and without cooperativity. With cooperativity, strong epistatic interactions clearly map out the native GB1 structure, while allowing the presence of intermediate states (low cooperativity) obscured the structure. This indicates that using epistasis measurements to reconstruct protein structure may be inappropriate for proteins with stable intermediates.