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2.14: Steady-State and Equilibrium Kinetics of Carbonic Anhydrase-Catalyzed \(CO_{2}/HCO_{3}^{-}\) Interconversion

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    The CO2 \(\rightleftharpoons\) HCO3- interconversion catalyzed by CA is extremely fast. The usual kinetic parameters describing an enzymatic reaction are the turnover number or kinetic constant for the reaction, kcat, and the Michaelis constant Km. In the simple catalytic scheme

    \[E+S \xrightleftharpoons[k_{-1}]{k_{1}} ES \xrightarrow{k_{2}} E+P,\]

    where E stands for enzyme, S for substrate, and P for product, Km-1 is given by k1/(k-1 + k2). If k2 is small, kcat = k2 and Km-1 = k1/k-1, the latter corresponding to the thermodynamic affinity constant of the substrate for the enzyme. The pH dependences46 of kcat and Km for CO2 hydration for the high- and low-activity isoenzymes have been determined (Figure 2.2).33,36 It appears that Km is pH-independent, whereas kcat increases with pH, reaching a plateau above pH 8. For bicarbonate dehydration (the reverse of Equation 2.6), H+ is a cosubstrate of the enzyme. The pH dependence of kcat/Km for HCO3- dehydration is also mainly due to kcat, which shows the same pH profile as that for CO2 if the experimental kinetic data are divided by the available concentration of the H+ cosubstrate.47,48 Further measurements have shown that the pH dependence of kcat reflects at least two ionizations if the measurements are performed in the absence of anions.49 The value of kcat reaches its maximum at alkaline pH only when buffer concentrations exceed 10-2 M.50 In other words, the exchange of the proton with the solvent is the rate-limiting step along the catalytic pathway if relatively high concentrations of proton acceptors and proton donors are not provided by a buffer system. This limit results from the high turnover of the enzyme, which functions at the limit imposed by the diffusion rate of the H+ cosubstrate. At high buffer concentration, kcat shows an isotope effect consistent with the occurrence of an internal proton transfer as the new rate-limiting step.51

    Measurements of the catalyzed reaction performed at chemical equilibrium starting from mixtures of 12C-18O-labeled HCO3- and 13C-16O-labeled CO2 have shown the transient formation of 13C-18O-labeled species (both CO2 and HCO3-) before 18O-labeled water appears in solution.52 These experiments provided evidence that, at chemical equilibrium, an oxygen atom can pass from HCO3- to CO2 and vice versa several times before being released to water. Furthermore, maximal exchange rates are observed even in the absence of buffers.

    Under chemical equilibrium conditions, 13C NMR spectroscopy is particularly useful in investigating substrate interconversion rates, since the rates pass from a slow-exchange regime in the absence of enzyme to fast exchange at sufficient enzyme concentration. In the absence of enzyme two 13C signals are observed, one for CO2 and the other for HCO3-. In the presence of enzyme only one averaged signal is observed (Figure 2.6). Starting from the slow exchange situation, in the absence of enzyme, the increase in linewidth (\(\Delta\) \(\nu\)) of the substrate (A) and product (B) signals (caused by exchange broadening that is caused in turn by the presence of a small amount of catalyst) depends on the exchange rate and on the concentration of each species, according to the following relation:

    \[ \Delta \nu_{A}[A] = \Delta \nu_{B}[B] = \tau_{esch}^{-1} \tag{2.9}\]

    Therefore, the exchange rate \(\tau_{esch}^{-1}\) can be calculated.53 The appearance of the NMR spectrum for different \(\tau_{esch}^{-1}\) values is illustrated in Figure 2.6 under the condition [A] = [B]. For the high-activity enzyme it was found that the maximal exchange rates are larger than the maximal turnover rates under steady-state conditions; the ratio between kexch of the high-activity (type II) and low-activity (type I) forms is 50, i.e., larger than the ratio in kcat49,54 This result is consistent with the idea that the rate-limiting step in the steady-state process is an intramolecular proton transfer in the presence of buffer for type II enzymes, whereas it may not be so for the type I enzymes. The exchange is pH-independent in the pH range 5.7 - 8, and does not show a proton-deuteron isotope effect. The apparent substrate binding (HCO3-) is weaker than steady-state Km values, indicating that these values are not true dissociation constants. Chloride is a competitive inhibitor of the exchange.49

    clipboard_ed9bd15db4e061fbd98b401014763dab5
    Figure 2.6 - Calculated lineshape for the NMR signals of nuclei equally distributed between two sites ([A] = [B]), as a function of the exchange rate \(\tau^{-1}\). \(\Delta \omega\) is the peak separation in rad s-1.

    A similar investigation was conducted for type I CoHCA at pH 6.3, where the concentrations of CO2 and HCO3- are equal.55 The two lines for the two substrates were found to have different linewidths but equal T 1 values. Measurements at two magnetic fields indicate that the line broadening of the HCO3- resonance is caused by substrate exchange and by a paramagnetic contribution due to bonding. The temperature dependence of the linewidth shows that the latter is determined by the dissociation rate. Such a value is only about 2.5 times larger than the overall CO2 \(\rightleftharpoons\) HCO3- exchange-rate constant. Therefore the exchange rate between bound and free HCO3- is close to the threshold for the rate-limiting step. Such an exchange rate is related to the higher affinity of the substrate and anions in general for type I isoenzymes than for type II isoenzymes. This behavior can be accounted for in terms of the pKa of coordinated water (see Section C).


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