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It was found for all cases studied (five serine proteases, lipase, acetylcholinesterase, lysozyme, and D-xylose isomerase) that the protein and substrate electrostatic potential patterns on the van der Waals envelope of the latter complement each other. This calls attention to a convergent evolution of the active-site potential in the cases of serine proteases, providing similar patterns for enzymes with very different primary structures. Enzyme activities, as characterized by log k(cat)/k(M) for the same substrate (succinyl-Ala-Ala-Pro-Phe-p-nitroanilide) of alpha-chymotrypsin, beta-trypsin, alpha-lytic protease, subtilisin Novo, and subtilisin Carlsberg, respectively, correlate well with the calculated electrostatic interaction energies between the protein environment: and the active site. To achieve a better fit between the calculated and experimental quantities, the geometry of the enzyme-substrate complexes had to be optimized by a technique based on molecular dynamics. For the same enzymes, it was found that a quantitative measure of the electrostatic complementarily between the active site. and protein environment correlates with the electrostatic interaction energies, as well. as the activities. 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