Kinetics of enzymes with iso-mechanisms: dead-end inhibition of fumarase and carbonic anhydrase II.

Isomerization of free enzyme can be detected in kinetic patterns of dead-end inhibition because competitive substrate analogs yield noncompetitive inhibition versus product in reverse reaction kinetics. The ratio of slope and intercept inhibition constants allows a quantitative estimation of the relative kinetic significance of the isomerization to a catalytic turnover. Applying this kinetic analysis theoretically to inhibition data for bovine carbonic anhydrase II by anions [Y. Pocker and T. L. Deits (1982) J. Am. Chem. Soc. 104, 2424] provides an estimate of 43 +/- 13% for how rate-limiting the isomerization segment is at pH 6.6. Applying the analysis experimentally to porcine heart fumarase provides a competitive pattern of inhibition by trans-aconitate versus fumarate with Ki(s) = 2.0 +/- 0.5 mM, together with a non-competitive pattern versus malate, with Ki(s) = 0.8 +/- 0.1 mM and Kii = 2.3 +/- 0.4 mM. Assuming that the isomerization segment of fumarase is the reprotonation of an active site carboxyl and imidazole with pK1 = 5.53 and pK2 = 7.78 [Blanchard and Cleland (1980) Biochemistry 19, 4506], an apparent rate constant for the isomerization segment of fumarate hydration is estimated as 95 +/- 22 s-1, compared to 42 +/- 13 s-1 for the chemical segment and 29 +/- 0.7 s-1 for a complete turnover. In contrast, the values are 17000 +/- 5200, 82 +/- 25, and 82 +/- 3 s-1, respectively, for malate dehydration. Hence, the isomerization segment is 30 +/- 7% rate-limiting during fumarate hydration but less than 1% during malate dehydration.