Exchange of labeled nuclei in the CO2--HCO3--solvent system catalyzed by carbonic anhydrase

Silverman et al. (1979. J. Am. Chem. Soc. 101:6734-6740) have reported measurements of the loss of 18O to solvent from the isotopically labeled CO2--HCO3-system and of the mixing of 18O and 13C labels within the system, as catalyzed by human carbonic anhydrase C in the pH range 6-8. This work is an extension of earlier work (Silverman and Tu. 1976. J. Am. Chem. Soc. 98:978-984) on the very similar bovine enzyme. The more recent work is analyzed by its authors in terms of the "hydroxide" model for the apparent pH-dependence of enzymatic activity, a model in which the pH-dependence is associated with the presumed ionization of an H2O ligand of the active-site metal ion to OH-. From a comparison of their data with a solution of the coupled differential equations that describe the kinetics of isotope exchange in terms of the model, Silverman et al. derived a pH-dependent rate of exchange for the water molecule which is formed at the active site of the enzyme during dehydration. By contrast, using the same data and a model in which active enzyme has a water molecule on the metal ion at the active site, and similar differential equations, we derive a value for the rate of exchange of water that is pH-independent. This model has the attraction that it explains the magnetic relaxation rate of solvent water protons in the Co2+-substituted enzyme, whereas the hydroxide mechanism cannot explain these data without the introduction of unfounded ad hoc assumptions; further, the presence of an OH- ligand of the metal has never been demonstrated. We also include an analysis of analogous data for the bovine enzyme. One result of our analysis is that the pKa for activity of the enzyme samples used is near 6.0, implying that the bulk of the data were taken when the enzyme was essentially all active. It is straightforward to account for the pH-dependence of the data near and below the pKa by using an empirically-derived value for the pKa. However, we have recently developed a model for the low pH (inactive) enzyme that has been successful in interpreting a wide range of data, and we show that this new view can explain the few points at low pH quite adequately. Additionally, we consider the recent kinetic results for the human C enzyme, obtained at chemical equilibrium by studies of the linewidths of nuclear magnetic resonances of 13C in labeled substrate (Simonsson et al. 1979. Eur. J. Biochem. 93:409-417) and show that these experiments and those of Silverman et al. are all consistent with kinetic data from nonequilibrium stopped-flow experiments, viewed in terms of our model, in the limit of low substrate concentration. Results at higher concentrations indicate that the Michaelis constants and equilibrium constants differ somewhat.