where P is a catalytic parameter (either the catalytic efficiency, kcat/KM, or the catalytic rate constant, kcat), P0 is the value of the catalytic parameter at a sufficiently high pH and pKa refers specifically to the pK of the (conjugate acid of the) catalytic base. This equation assumes a single pKa value for the catalytic base, which, when P is catalytic efficiency, would describe ionization in the free enzyme while, when P is the catalytic rate constant, would describe ionization in the Michaelis complex (see the Supplementary Discussion).