Reaction scheme of diprotic model.

E represents the enzyme as a weak diprotic acid with its three protonation states EH2+, EH and E. The dissociation constants K1E, K2E, K1ES and K2ES describe rapid protonization equilibria of the free enzyme and the enzyme with bound substrate, i.e., K1E = [H+][EH]/[EH2+], K2E = [H+][E]/[EH], K1ES = [H+][ESH]/[ESH2+], K2ES = [H+][ES]/[ESH]. For the sake of simplicity, free protons are not shown in the scheme. The substrate affinity of the neutral enzyme EH is given by KM = [EH][S]/|ESH]. In case of steady-state kinetics, KM = (k−1+k2)/k1. The reaction rate of the system is given as d[P]/dt = k2[ESH]+k2′[ESH2+]+k2″[ES] leading to the final expression described by Eq. 2.

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