Chapter 13, Problem 12P

Answers to all problems are at the end of this book. Detailed solutions are available in the Student Solutions Manual, Study Guide, and Problems Book.

Quantitative Relationships Between Rate Constants to Calculate K_m, Kinetic Efficiency (k_cat/K_m) and V_max - IV Carbonic anhydrase catalyzes the hydration of ${\text{CO}}_{\text{2}}$:

${\text{CO}}_{\text{2}}{\text{+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}$The K_m of carbonic anhydrase for ${\text{CO}}_{\text{2}}$is 12 mM. Carbonic anhydrase gave an initial velocity $v_0=4.5\mu \text{mol}{\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\text{formed/mL}\cdot \text{sec}$when [ ${\text{CO}}_{\text{2}}$] = 36 mM.

a. What is V_max for this enzyme?

b. Assuming 5 pmol/mL ( $\text{5}\times {\text{10}}^{\text{-12}}$moles/mL) of enzyme were used in this experiment, what is k_cat for this enzyme?

c. What is the catalytic efficiency of this enzyme?

d. Does carbonic anhydrase approach "catalytic perfection"?