Three mechanisms and rapid-equilibrium rate equations for a type of reductase reaction

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful when the mechanism involves a number of pKs, but they are also useful when some reactants have stoichiometric numbers greater than one or hydrogen ions are produced or consumed in the rate-determining step. The pH dependencies of limiting velocities, Michaelis constants, and reaction velocities for the forward reaction are discussed for two examples of reductase reactions of the type mR + O -> products, where R is the reductant and O is the oxidant. For the nitrate reductase reaction (EC 1.9.6.1), m = 2 and two hydrogen ions are consumed. For the nitrite-ferredoxin reductase reaction (EC 1.7.7.1), m = 6 and eight hydrogen ions are consumed. The expressions for the limiting velocities, Michaelis constants, and rate equations for the forward reaction are derived for two ordered mechanisms and the random mechanism. Three Mathematica® programs are used to make plots of kinetic parameters as functions of pH and three-dimensional plots of rapid-equilibrium velocities as functions of [O] and [R] for arbitrary sets of input parameters.