Context please. The allosteric properties of aspartate transcarbamoylase have been discussed in detail in this chapter. What is the function of aspartate transcarbamoylase?

Activity profile. A histidine residue in the active site of aspartate transcarbamoylase is thought to be important in stabilizing the transition state of the bound substrates. Predict the pH dependence of the catalytic rate, assuming that this interaction is essential and dominates the pH-activity profile of the enzyme.

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

Knowing when to get going. What is the biochemical rationale for ATP serving as a positive regulator of ATCase?

No T. What would be the effect of a mutation in an allosteric enzyme that resulted in a T/R ratio of 0?

Turned upside down. An allosteric enzyme that follows the concerted model 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 rate of the reaction and the substrate concentration?

Partners. As shown in Figure 10.2, CTP inhibits ATCase; however, the inhibition is not complete. Can you suggest another molecule that might enhance the inhibition of ATCase? Hint: See Figure 25.2.

RT equilibrium. Differentiate between homotropic and heterotropic effectors.

Restoration project. If isolated regulatory subunits and catalytic subunits of ATCase are mixed, the native enzyme is reconstituted. What is the biological significance of the observation?

Because it’s an enzyme. X-ray crystallographic studies of ATCase in the R form required the use of the bisubstrate analog PALA. Why was this analog, a competitive inhibitor, used instead of the actual substrates?

Allosteric switching. A substrate binds 100 times as tightly to the R state of an allosteric enzyme as to its T state. Assume that the concerted (MWC) model applies to this enzyme. (See equations for the Concerted Model in the Appendix to Chapter 7.)

Allosteric transition. Consider an allosteric protein that obeys the concerted model. Suppose that the ratio of T to R formed in the absence of ligand is 10⁵, K_T = 2 mM, and K_R = 5 μM. The protein contains four binding sites for ligand. What is the fraction of molecules in the R form when 0, 1, 2, 3, and 4 ligands are bound? (See equations for the Concerted Model in the Appendix to Chapter 7.)

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? Hint: See Section 7.2.

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 and K_M. Draw a double reciprocal plot for the same allosteric enzyme in the presence of an allosteric inhibitor and an allosteric stimulator.

Paradoxical at first glance. Recall that phosphonacetyl-l-aspartate (PALA) is a potent inhibitor of ATCase because it mimics the two physiological substrates. However, in the presence of substrates, low concentrations of this unreactive bisubstrate analog increase the reaction velocity. On the addition of PALA, the reaction rate 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 rate 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?

Regulation energetics. The phosphorylation and dephosphorylation of proteins is a vital means of regulation. Protein kinases attach phosphoryl groups, whereas only a phosphatase will remove the phosphoryl group from the target protein. What is the energy cost of this means of covalent regulation?

Vive la différence. What is an isozyme?

Fine-tuning biochemistry. What is the advantage for an organism to have isozymic forms of an enzyme?

Making matches.

Powering change. Phosphorylation is a common covalent modification of proteins in all forms of life. What energetic advantages accrue from the use of ATP as the phosphoryl donor?

No going back. What is the key difference between regulation by covalent modification and specific proteolytic cleavage?

Zymogen activation. When very low concentrations of pepsinogen are added to acidic media, how does the half-time for activation depend on zymogen concentration?

No protein shakes advised. Predict the physiological effects of a mutation that resulted in a deficiency of enteropeptidase.

A revealing assay. Suppose that you have just examined a young boy with a bleeding disorder highly suggestive of classic hemophilia (factor VIII deficiency). Because of the late hour, the laboratory that carries out specialized coagulation assays is closed. However, you happen to have a sample of blood from a classic hemophiliac whom you admitted to the hospital an hour earlier. What is the simplest and most rapid test that you can perform to determine whether your present patient also is deficient in factor VIII activity?

Counterpoint. The synthesis of factor X, like that of prothrombin, requires vitamin K. Factor X also contains γ-carboxyglutamate residues in its amino-terminal region. However, activated factor X, in contrast with thrombin, retains this region of the molecule. What is a likely functional consequence of this difference between the two activated species?

A discerning inhibitor. Antithrombin III forms an irreversible complex with thrombin but not with prothrombin. What is the most likely reason for this difference in reactivity?

Drug design. A drug company has decided to use recombinant DNA methods to prepare a modified α₁-anti-trypsin that will be more resistant to oxidation than is the naturally occurring inhibitor. Which single amino acid substitution would you recommend?

Blood must flow. Why is inappropriate blood-clot formation dangerous?

Hemostasis. Thrombin functions in both coagulation and fibrinolysis. Explain.

Dissolution row. What is tissue-type plasminogen activator and what is its role in preventing heart attacks?

Joining together. What differentiates a soft clot from a mature clot?

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?

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Reporting live from ATCase 1. ATCase underwent reaction 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?

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 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 33). Conversely, CTP in the absence of substrate decreased the absorbance at 430 nm. What is the significance of the changes in absorption of the reporter groups?

Conviviality and PKA. Recent studies have suggested that protein kinase A may be important in establishing behaviors in many organisms, including humans. One study investigated the role of PKA in locust behavior. Certain species of locust live solitary lives until crowded, at which point they become gregarious—they prefer the crowded life.

Locusts were grouped together for one hour, and then allowed to stay with the group or move away. Prior to crowding, some insects were injected with a PKA inhibitor, a cyclic GMP-dependent kinase inhibitor or no inhibitor, as indicated. The results are shown above.

Repeating heptads. Each of the three types of fibrin chains contains repeating heptapeptide units (abcdefg) in which residues a and d are hydrophobic. Propose a reason for this regularity.

Density matters. The sedimentation value of aspartate transcarbamoylase decreases when the enzyme switches to the R state. On the basis of the allosteric properties of the enzyme, explain why the sedimentation value decreases.

Too tight a grip. Trypsin cleaves proteins on the carboxyl side of lysine. Trypsin inhibitor has a lysine residue, and binds to trypsin, yet it is not a substrate. Explain.

Apparently not the four-leaf variety. Cows that graze on spoiled sweet clover, which contains dicoumarol, die from hemorrhagic disease. The cause of death is defective prothrombin. However, the amino acid composition of the defective prothrombin is identical to that of normal prothrombin. What is the mechanism of action of dicoumarol? Why are the amino acid compositions of the defective and normal prothrombin the same?

Aspartate transcarbamoylase. Write the mechanism (in detail) for the conversion of aspartate and carbamoyl phosphate into N-carbamoylaspartate. Include a role for the histidine residue present in the active site.

Protein kinases. Write a mechanism (in detail) for phosphorylation of a serine residue by ATP catalyzed by protein kinase. What groups might you expect to find in the enzyme’s active site?