pH–rate profile of a diprotic enzyme–substrate complex

Apparent maximal velocity when the ES complex bears one group that must be deprotonated and one that must stay protonated.

Vm,app = Vm 1 + 10(pKa1−pH) + 10(pH−pKa2)    equivalently 1 + [H⁺]/KES1 + KES2/[H⁺], with pH = −log[H⁺]
100
ceiling (fully protonation-competent) rate
4.0
group that must lose a proton to turn activity on
9.0
group that must stay protonated to keep activity on
Optimum pH6.50
Peak Vm,app99.4
Peak / Vm0.994
Usable width (½‑max)5.0

Vm,app curve   pKa1 (drag on axis)   pKa2 (drag on axis)   optimum pH. The two limbs are half‑maximal near pKa1 and pKa2; the peak sits at their midpoint and approaches Vm only when the pKas are well separated.