Question 19.1: DeVoe and Kistiakowsky [J. American Chemical Society 83 (196...
DeVoe and Kistiakowsky [J. American Chemical Society 83 (1961): 274] studied the kinetics of CO_{2} hydration catalyzed by the enzyme carbonic anhydrase:
CO_{2}+H_{2}O\rightleftharpoons HCO^{-}_{3}+H^{+}
In this reaction, CO_{2} is converted to bicarbonate ion. Bicarbonate is transported in the bloodstream and converted back to CO_{2} in the lungs, a reaction that is also catalyzed by carbonic anhydrase. The following initial reaction rates for the hydration reaction were obtained for an initial enzyme concentration of 2.3 nM and temperature of 0.5°C:
| Rate \left( M s^{-1} \right) | \left[ CO_{2} \right]\left( mM \right) |
| 2.78 ×10^{-5} | 1.25 |
| 5.00 ×10^{-5} | 2.5 |
| 8.33 ×10^{-5} | 5.0 |
| 1.67 ×10^{-4} | 20.0 |
Determine k_{m} and k_{2} for the enzyme at this temperature.
The Lineweaver–Burk plot of the rate^{-1} versus \left[ CO_{2} \right]^{-1} is shown here:
The y intercept for the best fit line to the data is 4000 M^{-1} s corresponding to R_{\max}=2.5×10^{-4} M s^{-1} . Using this value and \left[ E \right]_{0}=2.3 nM, k_{2} is
k_{2}=\frac{R_{\max}}{\left[ E \right]_{0}}=\frac{2.5×10^{-4} M s^{-1}}{2.3×10^{-9} M}=1.1×10^{5} s^{-1}Notice that the units of k_{2}, the turnover number, are consistent with a first-order process, in agreement with the Michaelis–Menten mechanism. The slope of the best fit line is 40 s such that, per Equation (19.56), k_{m} is given by
k_{m}=slope ×R_{\max}=\left( 40 s \right) \left( 2.5 ×10^{-4} M s^{-1} \right)=10 mM
