Chapter 13, Problem 9P

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 - I Measurement of the rate constants for a simple enzymatic reaction obeying Michaelis-Menten kinetics gave the following results:

$k_1=2\times {10}^8{M}^{-1}{\sec }^{-1}$ $k_{-1}=1\times {10}^3{\sec }^{-1}$ $k_2=5\times {10}^3{\sec }^{-1}$a. What is K_s, the dissociation constant for the enzyme-substrate complex?

b. What is K_m, the Michaelis constant for this enzyme?

c. What is k_cat (the turnover number) for this enzyme?

d. What is the catalytic efficiency (k_cat/K_m) for this enzyme?

e. Does this enzyme approach "kinetic perfection"? (That is, does k_cat/K_m approach the diffusion-controlled rate of enzyme association with substrate?)

f. If a kinetic measurement was made using 2 nanomoles of enzyme per mL and saturating amounts of substrate, what would V_max equal?

g. Again, using 2 nanomoles of enzyme per mL of reaction mixture, what concentration of substrate would give v = 0.75 V_max?

h. If a kinetic measurement was made using 4 nanomoles of enzyme per mL and saturating amounts of substrate, what would V_max equal? What would K_m equal under these conditions?