BIOCHEMISTRY - L. Stryer - 1984

VOLUME 1

PART I. CONFORMATION AND DYNAMICS

CHAPTER 6. INTRODUCTION TO ENZYMOLOGY

QUESTIONS AND PROBLEMS

1. The Hydrolysis of pyrophosphate to orthophosphate plays a crucial role in driving biosynthetic reactions, such as DNA Synthesis. In E. coli, this hydrolysis is catalyzed by pyrophosphatase, which has a Molecular Weight of 120 kDa and consists of 6 identical subunits. The V_max of the purified pyrophosphatase is 2,800 units per 1 mg of protein. One unit of enzyme activity is defined as The amount of enzyme that hydrolyzes 10 µmol of pyrophosphate in 15 min at 37°C under standard assay conditions.

a) How many moles of substrate are hydrolyzed per second by 1 mg of enzyme, provided that the Substrate Concentration is significantly higher than K_m?

b) How many moles of active sites are contained in 1 mg of enzyme? Assume that each subunit contains one Active Site.

c) What is the turnover number of this enzyme? Compare it with the turnover numbers of Other Enzymes mentioned in this chapter.

2. Penicillin is hydrolyzed and thereby inactivated by penicillinase, an enzyme found in various resistant strains of Bacteria. The molecular weight of penicillinase from Staphylococcus aureus is 29.6 kDa. The amount of penicillin hydrolyzed in 12 ml of solution over 1 min in the presence of 10^-9 g of purified penicillinase was measured as a function of penicillin concentration. Assume that the penicillin concentration remained practically unchanged during the assay.

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a) Plot these data as 1/V versus 1/[S]. Does penicillinase obey Michaelis-Menten kinetics? If so, what is the value of K_m?

b) What is the value of V_max?

c) What is the turnover number of penicillinase under these experimental conditions? Assume that each enzyme molecule has one active site.

3. The kinetics of an enzymatic reaction was measured as a function of substrate concentration in the presence and absence of an inhibitor (I), yielding the following data:

a) What are V_max and K_m in the absence of the inhibitor? In its presence?

b) What is the type of inhibition?

c) What is the inhibition binding constant?

d) If [S] = 1 • 10^-5 M and [I] = 2 • 10^-3 M, what fraction of the enzyme molecules have bound substrate? What fraction have bound inhibitor?

e) If [S] = 3 • 10^-5 M, what fraction of the enzyme molecules have bound substrate in the presence of 2 • 10^-3 M inhibitor versus in its absence? Compare The ratio of these values with the ratio of reaction rates under the same conditions.

4. The kinetics of the enzyme examined in Problem 3 was analyzed in the presence of another inhibitor added at a concentration of 10^-4 M:

a) What are The values of V_max and K_m in the presence of the inhibitor? Compare them with the values obtained in Problem 3.

b) What is the type of inhibition?

c) What is the dissociation constant of this inhibitor?

d) At [S] = 3 • 10^-5 M, what fraction of the enzyme molecules is bound to the substrate in the presence of 10^-4 M inhibitor? In its absence?

5. The plot of 1/V versus 1/[S] is known as the Lineweaver–Burk plot. Kinetic data can also be represented in V versus V/[S] coordinates, i.e., the Eadie–Hofstee plot.

a) Transform the Michaelis–Menten Equation to express V as a function of V/[S].

b) What is the physical Significance of the slope and the intercepts of the curve with the x-axis and y-axis in the V versus V/[S] plot?

c) Sketch how the dependence of V on V/[S] should appear in the absence of an inhibitor, in the presence of a competitive inhibitor, and in the presence of a noncompetitive inhibitor.

6. In the case of allosteric enzymes, an inhibitor at low concentrations often exerts an activating effect. Why? (Hint: consider the analogy with CO-Hemoglobin.)

7. The hormone progesterone contains two ketone groups. Very little is known about The properties of the receptor protein that recognizes progesterone. Which amino acid side chains could form Hydrogen Bonds with progesterone at pH 7? (Assume that the side chains in the receptor protein have the same pK values as in free Amino Acids dissolved in Water.)

8. Suppose that substrates A and B compete for an enzyme. Derive an expression relating the ratio of the utilization rates of A and B (V_A/V_B) to the concentrations of these substrates and their k₃ and K_m values. (Hint: express V_A as a function of k₃/K_m for substrate A and then do the same for substrate B.) Can it be assumed that Specificity is determined solely by K_m?