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 K₁^E, K₂^E, K₁^ES and K₂^ES describe rapid protonization equilibria of the free enzyme and the enzyme with bound substrate, i.e., K₁^E = [H⁺][EH]/[EH₂⁺], K₂^E = [H⁺][E⁻]/[EH], K₁^ES = [H⁺][ESH]/[ESH₂⁺], K₂^ES = [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 K_M = [EH][S]/|ESH]. In case of steady-state kinetics, K_M = (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.