Understanding epistatic networks in the B1 β-lactamases through coevolutionary statistical modeling and deep mutational scanning

Throughout evolution, protein families undergo substantial sequence divergence while preserving structure and function. Although most mutations are deleterious, evolution can explore sequence space via epistatic networks of intramolecular interactions that alleviate the harmful mutations. However, comprehensive analysis of such epistatic networks across protein families remains limited. Thus, we conduct a family wide analysis of the B1 metallo-β-lactamases, combining experiments (deep mutational scanning, DMS) on two distant homologs (NDM-1 and VIM-2) and computational analyses (in silico DMS based on Direct Coupling Analysis, DCA) of 100 homologs. The methods jointly reveal and quantify prevalent epistasis, as ~1/3rd of equivalent mutations are epistatic in DMS. From DCA, half of the positions have a >6.5 fold difference in effective number of tolerated mutations across the entire family. Notably, both methods locate residues with the strongest epistasis in regions of intermediate residue burial, suggesting a balance of residue packing and mutational freedom in forming epistatic networks. We identify entrenched WT residues between NDM-1 and VIM-2 in DMS, which display statistically distinct behaviors in DCA from non-entrenched residues. Entrenched residues are not easily compensated by changes in single nearby interactions, reinforcing existing findings where a complex epistatic network compounds smaller effects from many interacting residues.