1.  Different orders. Differentiate between a first-order rate constant and a second-order rate constant. ✓ 3

2.  A fraudulent reaction? What is a pseudo-first-order reaction? ✓ 3

3.  Changing in concert. On the graph at the right, show how substrate and product concentrations of the simple enzyme-catalyzed reaction



change with time. ✓ 3



(a) For a reaction in which the equilibrium is in favor of product formation.

(b) For a reaction in which the equilibrium constant is 1.

4.  Active yet responsive. What is the biochemical advantage of having a K_M approximately equal to the substrate concentration normally available to an enzyme? ✓ 4

5.  Defining attributes. What is the defining characteristic for an enzyme catalyzing a sequential reaction? A double-displacement reaction? ✓ 4

6.  Affinity or not affinity? That is the question. The affinity between a protein and a molecule that binds to the protein is frequently measured as a dissociation constant K_D.



Does K_M measure the affinity of the enzyme complex? Under what circumstances might K_M approximately equal K_D? ✓ 4

8.  Hydrolytic driving force. The hydrolysis of pyrophosphate to orthophosphate is important in driving forward biosynthetic reactions such as the synthesis of DNA. This hydrolytic reaction is catalyzed in Escherichia coli by a pyrophosphatase that has a mass of 120 kDa and consists of six identical subunits. For this enzyme, a unit of activity is defined as the amount of enzyme that hydrolyzes 10 μmol of pyrophosphate in 15 minutes at 37°C under standard assay conditions. The purified enzyme has a V_max of 2800 units per milligram of enzyme. ✓ 4

(a) How many moles of substrate are hydrolyzed per second per milligram of enzyme when the substrate concentration is much greater than K_M?

(b) How many moles of active sites are there in 1 mg of enzyme? Assume that each subunit has one active site.

(c) What is the turnover number of the enzyme? Compare this value with others mentioned in this chapter.

9.  A fresh view. The plot of 1/V₀ versus 1/[S] is sometimes called a double-reciprocal or Lineweaver–Burk plot. Another way of expressing the kinetic data is to plot V₀ versus V₀/[S], which is known as an Eadie–Hofstee plot. ✓ 4

(a) Rearrange the Michaelis–Menten equation to give V₀ as a function of V₀/[S].

(b) What is the significance of the slope, the vertical intercept, and the horizontal intercept in a plot of V₀ versus V₀/[S]?

10.  More Michaelis–Menten. For an enzyme that follows simple Michaelis–Menten kinetics, what is the value of V_max if V₀ is equal to 1 mmol minute⁻¹ when [S] = 1/10 K_M? ✓ 4

11.  Fractional occupation. Starting with the Michaelis–Menten equation, derive an equation that shows the fraction of active sites filled (f_ES) at any V₀. ✓ 4

12.  They go together like spaghetti and meatballs. Match the term with the proper description.

13.  A new view of cooperativity. Draw a double-reciprocal plot for a typical Michaelis–Menten enzyme and an allosteric enzyme that have the same V_max. ✓ 5

14.  Angry biochemists. Many biochemists go bananas, and justifiably, when they see a Michaelis–Menten plot like the one shown below. To see why they go bananas, determine the V₀ as a fraction of V_max when the substrate concentration is equal to 10 K_M and 20 K_M. Please control your outrage. ✓ 4

15.  Knowing when to say when. What is feedback inhibition? Why is it a useful property? ✓ 5

16.  Turned upside down. An allosteric enzyme that follows the concerted mechanism has a T/R ratio of 300 in the absence of substrate. Suppose that a mutation reversed the ratio. How would this mutation affect the relation between the velocity of the reaction and the substrate concentration? ✓ 5

17.  RT equilibrium. Differentiate between homotropic and heterotropic effectors. ✓ 5

18.  Restoration project. Aspartate transcarbamoylase (ATCase) is an allosteric enzyme that regulates the synthesis of uridine triphosphate (UTP) and cytidine triphosphate (CTP). It can be separated into regulatory subunits and catalytic subunits. If isolated regulatory subunits and catalytic subunits of ATCase are mixed, the native enzyme is reconstituted. What is the biological significance of the observation? ✓ 5

19.  Negative cooperativity. You have isolated a dimeric enzyme that contains two identical active sites. The binding of substrate to one active site decreases the substrate affinity of the other active site. Can the concerted model account for this negative cooperativity? ✓ 5

21.  K_M matters. The amino acid asparagine is required by cancer cells to proliferate. Treating patients with the enzyme asparaginase is sometimes used as a chemotherapy treatment. Asparaginase hydrolyzes asparagine to aspartate and ammonia. The adjoining illustration shows the Michaelis–Menten curves for two asparaginases from different sources, as well as the concentration of asparagine in the environment (indicated by the arrow). Which enzyme would make a better chemotherapeutic agent? ✓ 4

22.  Varying the enzyme. For a one-substrate, enzyme-catalyzed reaction, double-reciprocal plots were determined for three different enzyme concentrations. Which of the following three families of curve would you expect to be obtained? Explain.

23.  Rate-limiting step. In the conversion of A into D in the following biochemical pathway, enzymes E_A, E_B, and E_C have the K_M values indicated under each enzyme. If all of the substrates and products are present at a concentration of 10⁻⁴ M and the enzymes have approximately the same V_max, which step will be rate limiting and why? ✓ 4

25.  Competing substrates. Suppose that two substrates, A and B, compete for an enzyme. Derive an expression relating the ratio of the rates of utilization of A and B, V_A/V_B, to the concentrations of these substrates and their values of k_cat and K_M. (Hint: Express V_A as a function of k_cat/K_M for substrate A, and do the same for V_B.) Is specificity determined by K_M alone? ✓ 4

26.  Colored luminosity. Tryptophan synthetase, a bacterial enzyme that contains a pyridoxal phosphate (PLP) prosthetic group, catalyzes the synthesis of l-tryptophan from l-serine and an indole derivative. The addition of l-serine to the enzyme produces a marked increase in the fluorescence of the PLP group, as the adjoining graph shows. The subsequent addition of indole, the second substrate, reduces this fluorescence to a level even lower than that produced by the enzyme alone. How do these changes in fluorescence support the notion that the enzyme interacts directly with its substrates? ✓ 5

27.  Too much of a good thing. A simple Michaelis–Menten enzyme, in the absence of any inhibitor, displayed the following kinetic behavior. The expected value of V_max is shown on the y axis. ✓ 4 ✓ 5



(a) Draw a double-reciprocal plot that corresponds to the velocity-versus-substrate curve.

(b) Provide an explanation for the kinetic results.

28.  Paradoxical at first glance. Phosphonacetyl-L-aspartate (PALA) is a potent inhibitor of the allosteric enzyme aspartate transcarbamoylase (ATCase), which has six active sites, because PALA mimics the two physiological substrates. ATCase controls the synthesis of pyrimidine nucleotides. However, low concentrations of this unreactive bisubstrate analog increase the reaction velocity. On the addition of PALA, the reaction velocity increases until an average of three molecules of PALA are bound per molecule of enzyme. This maximal velocity is 17-fold greater than it is in the absence of PALA. The reaction velocity then decreases to nearly zero on the addition of three more molecules of PALA per molecule of enzyme. Why do low concentrations of PALA activate ATCase? ✓ 5

29.  Distinguishing between models. The following graph shows the fraction of an allosteric enzyme in the R state (f_R) and the fraction of active sites bound to substrate (Y) as a function of substrate concentration. Which model, the concerted or sequential, best explains these results? ✓ 5

30.  Reporting live from ATCase 1. The allosteric enzyme aspartate transcarbamoylase (ATCase) has six active sites, arranged as two catalytic trimers. ATCase was modified with tetranitromethane to form a colored nitrotyrosine group (λ_max = 430 nm) in each of its catalytic chains. The absorption by this reporter group depends on its immediate environment. An essential lysine residue at each catalytic site also was modified to block the binding of substrate. Catalytic trimers from this doubly modified enzyme were then combined with native trimers to form a hybrid enzyme. The absorption by the nitrotyrosine group was measured on addition of the substrate analog succinate. What is the significance of the alteration in the absorbance at 430 nm? ✓ 5

31.  Reporting live from ATCase 2. A different ATCase hybrid was constructed to test the effects of allosteric activators and inhibitors. Normal regulatory subunits were combined with nitrotyrosine-containing catalytic subunits. The addition of ATP, an allosteric activator of ATCase, in the absence of substrate increased the absorbance at 430 nm, the same change elicited by the addition of succinate (see the graph in problem 30). Conversely, CTP, an allosteric inhibitor, in the absence of substrate decreased the absorbance at 430 nm. What is the significance of the changes in absorption of the reporter groups? ✓ 5