Kinetics of Enzymes with Iso-Mechanisms: Dead-End Inhibition of Fumarase and Carbonic Anhydrase II

Isomerizations 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. Sec. 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 Kis = 2.0 ± 0.5 mM, together with a noncompetitive pattern versus malate, with Kis = 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.