Fig. 4.

The maximum entropy model for natural sequences is anticorrelated with the catalytic power of mutants in catalytic-active remote regions. Strong negative correlations between $E_{\text{MaxEnt}}$ and $\log k_{\text{cat}}/K_{\text{M}}$ (A) and $\log k_{\text{cat}}$ (B) for the catalytic-active remote region are shown with the least-squares regression lines included. Each dot represents one single mutation. We shifted $E_{\text{MaxEnt}}$ by a constant so that the best-evolved design has a zero value.