Rapid-equilibrium rate equations for the enzymatic catalysis of A + B = P + Q over a range of pH

This article shows how pKs for the enzymatic site and enzyme-substrate complexes can be obtained from kinetic experiments on the reaction A + B = P + Q, with and without the consumption of hydrogen ions. The rapid-equilibrium rate equation makes it possible to obtain the pKs and chemical equilibrium constants involved in the mechanism, the apparent equilibrium constant K′ for the catalyzed reaction, and the number of hydrogen ions consumed in the rate-determining reaction. Experimentally-determined Michaelis constants can be adjusted for the pKs of the substrates A, B, P, and Q so that it is easier to obtain the pKs of E, EA, EB, EAB, EQ, and EPQ, and the chemical equilibrium constants. Reaction rates are discussed for the forward reaction ordered A + B = ordered P + Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction and for random A + B = ordered P + Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction. When hydrogen ions are consumed in the rate-determining reaction, there is a new factor 10npH in the rate equation, where n is the number of hydrogen ions consumed in the rate-determining reaction for the forward reaction. The integer n can be obtained from rate measurements over a range of pH, but it cannot be determined from thermodynamic measurements.