Co-evolutionary constraints of globular proteins correlate with their folding rates

Folding rates (ln kf) of globular proteins correlate with their biophysical properties, but relationship between ln kf and patterns of sequence evolution remains elusive. We introduce 'relative co-evolution order' (rCEO) as length-normalized average primary chain separation of co-evolving pairs (CEPs), which negatively correlates with ln kf. In addition to pairs in native 3D contact, indirectly connected and structurally remote CEPs probably also play critical roles in protein folding. Correlation between rCEO and ln kf is stronger in multi-state proteins than two-state proteins, contrasting the case of contact order (co), where stronger correlation is found in two-state proteins. Finally, rCEO, co and ln kf are fitted into a 3D linear correlation.