Kinetics of Enzymes with Iso-Mechanisms: Solvent Isotope Effects

Kinetic isotope effects on enzymatic reactions which employ general acid or general base catalytic mechanisms may arise during reprotonations of free enzyme. These effects reveal kinetically significant isomerizations of the free enzyme, or iso-mechanisms. The effects are expressed kinetically at high concentrations of substrate, onVmaxorkcat, but only thermodynamically at low substrate, onVmax/Km. The effects are also expressed on the noncompetitive inhibition constant of product inhibition,Kiip, because this parameter is dependent upon the steady-state concentration of the product form of free enzyme. A normal isotope effect on isomerization will decreaseVmaxandKiip, but not necessarily to the same degree. Which is greater will depend upon how rate-limiting the isomerization is to a complete turnover. Together they are related to the full effect on isomerization,Dkiso, by their product:Dkiso=DVmaxDKiip. Moreover, precisely how rate-limiting the isomerization is to a turnover can be shown to be numerically equal to (DVmax− 1)/(DKiipDVmax− 1), which surprisingly, holds whether there are other isotope effects present or not. The new relationships applied to published data on bovine carbonic anhydrase II reveal an intrinsic solvent isotope effect ofDk= 9 ± 4, and an iso step that is less than 80% rate-limiting. Applied to porcine pepsin, a significantDVis accompanied by excessive standard error onDKiip, precluding the calculation of a definitive intrinsic solvent isotope effect.