Investigating Inter-Residue Interactions in Protein Evolution Using a Nonparametric Approach

Protein residues evolve through amino acid substitutions, with rates influenced by their structural environment. Among structural metrics, the side-chain weighted contact number () best correlates with evolutionary rates [1]. Because WCN measures distance-weighted coupling, it parallels stiffness describing mechanical connectivity. Stiffness–distance trends [2] suggest that a single power law may not capture multiscale effects. Distance weightings were systematically optimized and compared across 213 globular enzymes. Simple, broken, tempered, and logarithmic power laws yielded WCN-ER correlations of 0.6237, 0.6239, 0.6175, and 0.6249, respectively, with the broken and logarithmic forms performing marginally better but without substantial gain relative to their increased complexity.

References

[1] Shahmoradi A & Wilke CO (2016) J Theor Biol 406: 313–324.

[2] Dehouck Y & Mikhailov AS (2013) PLoS Comput Biol 9(8): e1003209.