Problem 1
Glycogen as Energy Storage: How Long Can a Game Bird Fly? Since ancient times, people have observed that certain game birds, such as grouse, quail, and pheasants, fatigue easily. The Greek historian Xenophon wrote: "The bustards ... can be caught if one is quick in starting them up, for they will fly only a short distance, like partridges, and soon tire; and their flesh is delicious." The flight muscles of game birds rely almost entirely on the use of glucose 1-phosphate to drive ATP synthesis (Chapter 14). The glucose 1-phosphate derives from the breakdown of stored muscle glycogen, catalyzed by the enzyme glycogen phosphorylase. The rate of ATP production is limited by the rate at which glycogen can be broken down. During a "panic flight," the game bird's rate of glycogen breakdown is quite high, approximately \(120 \mu \mathrm{mol} / \mathrm{min}\) of glucose 1-phosphate produced per gram of fresh tissue. Given that the flight muscles usually contain about \(0.35 \%\) glycogen by weight, calculate how long a game bird can fly. (Assume the average molecular weight of a glucose residue in glycogen is \(162 \mathrm{~g} / \mathrm{mol}\). )
Problem 2
Enzyme Activity and Physiological Function The \(V_{\max }\) of the glycogen phosphorylase from skeletal muscle is much greater than the \(V_{\max }\) of the same enzyme from liver tissue. a. What is the physiological function of glycogen phosphorylase in skeletal muscle? In liver tissue? b. Why does the \(V_{\max }\) of the muscle enzyme need to be greater than that of the liver enzyme?
Problem 4
Regulation of Glycogen Phosphorylase In muscle tissue, the rate of conversion of glycogen to glucose 6-phosphate is determined by the ratio of phosphorylase \(a\) (active) to phosphorylase \(b\) (less active). Determine what happens to the rate of glycogen breakdown if a broken cell extract of muscle containing glycogen phosphorylase is treated with (a) phosphorylase kinase and ATP (b) PP1 (c) epinephrine.
Problem 6
Glycogen Breakdown in Migrating Birds Unlike a rabbit, running all-out for a few moments to escape a predator, migratory birds require energy for extended periods of time. For example, ducks generally fly several thousand miles during their annual migration. The flight muscles of migratory birds have a high oxidative capacity and obtain the necessary ATP through the oxidation of acetyl-CoA (obtained from fats) via the citric acid cycle. Compare the regulation of muscle glycolysis during short-term intense activity, as in a fleeing rabbit, and during extended activity, as in a migrating duck. Why must the regulation in these two settings be different?
Problem 10
Metabolic Effects of Mutant Enzymes Predict and explain the effect on glycogen metabolism of each of the listed defects caused by mutation: (a) Loss of the cAMPbinding site on the regulatory subunit of protein kinase A (PKA) (b) Loss of the protein phosphatase inhibitor (inhibitor 1 in Fig. 15-16) (c) Overexpression of phosphorylase \(b\) kinase in liver (d) Defective glucagon receptors in liver.
Problem 11
Hormonal Control of Metabolic Fuel Between your evening meal and breakfast, your blood glucose drops and your liver becomes a net producer rather than consumer of glucose. Describe the hormonal basis for this switch, and explain how the hormonal change triggers glucose production by the liver.
Problem 13
13\. Optimal Glycogen Structure Muscle cells need rapid access to large amounts of glucose during heavy exercise. This glucose is stored in liver and skeletal muscle in polymeric form as particles of glycogen. The typical glycogen \(\beta\)-particle contains about 55,000 glucose residues (see Eig_ 15-2). Meléndez-Hevia, Waddell, and Shelton (1993), explored some theoretical aspects of the structure of glycogen, as described in this problem. a. The cellular concentration of glycogen in liver is about \(0.01 \mu \mathrm{M}\). What cellular concentration of free glucose would be required to store an equivalent amount of glucose? Why would this concentration of free glucose present a problem for the cell? Glucose is released from glycogen by glycogen phosphorylase, an enzyme that can remove glucose molecules, one at a time, from one end of a glycogen chain (see Eig. 15-3). Glycogen chains are branched (see Eig.15-2), and the degree of branching - the number of branches per chain - has a powerful influence on the rate at which glycogen phosphorylase can release glucose. b. Why would a degree of branching that was too low (i.e., below an optimum level) reduce the rate of glucose release? (Hint: Consider the extreme case of no branches in a chain of 55,000 glucose residues.) c. Why would a degree of branching that was too high also reduce the rate of glucose release? (Hint: Think of the physical constraints.) Meléndez-Hevia and colleagues did a series of calculations and found that two branches per chain (see Eig_15-2) was optimal for the constraints described above. This is what is found in glycogen stored in muscle and liver. To determine the optimum number of glucose residues per chain, Meléndez-Hevia and coauthors considered two key parameters that define the structure of a glycogen particle: \(t=\) the number of tiers of glucose chains in a particle (the mole-cule in Eig.15-2 has five tiers); \(g_{c}=\) the number of glucose residues in each chain. The \(y\) set out to find the values of \(t\) and \(g_{c}\) that would maximize three quantities: (1) the amount of glucose stored in the particle \(\left(G_{\mathrm{T}}\right)\) per unit volume; (2) the number of unbranched glucose chains \(\left(C_{A}\right)\) per unit volume (i.e., number of A chains in the outermost tier, readily accessible to glycogen phosphorylase); and (3) the amount of glucose available to phosphorylase in these unbranched chains \(\left(G_{\mathrm{PT}}\right)\). d. Show that \(C_{A}=2^{t-1}\). This is the number of chains available to glycogen phosphorylase before the action of the debranching enzyme. e. Show that \(C_{\mathrm{T}}\), the total number of chains in the particle, is given by \(C_{\mathrm{T}}=2^{t}-1\). For purposes of this calculation, consider the primers to be a single chain. Thus \(G_{\mathrm{T}}=g_{\mathrm{c}}\left(C_{\mathrm{T}}\right)=g_{c}\left(2^{t}-1\right)\), the total number of glucose residues in the particle. f. Glycogen phosphorylase cannot remove glucose from glycogen chains that are shorter than five glucose residues. Show that \(G_{\mathrm{PT}}=\left(g_{e}-4\right)\left(2^{t-1}\right)\). This is the amount of glucose readily available to glycogen phosphorylase.g. Based on the size of a glucose residue and the location of branches, the thickness of one tier of glycogen is \(0.12 g_{\mathrm{c}} \mathrm{nm}+0.35 \mathrm{~nm}\). Show that the volume of a particle, \(V_{5}\), is given by the equation $$ V_{\mathrm{s}}=4 / 3 \pi t^{3}\left(0.12 g_{\mathrm{c}}+0.35\right)^{3} \mathrm{~nm}^{3} $$ Meléndez-Hevia and coauthors then determined the optimum values of \(t\) and \(g_{c}\) - those that gave the maximum value of a quality function, \(f\), that maximizes \(G_{\mathrm{T}}, C_{A}\), and \(G_{P T}\), while minimizing \(V_{8}: f=\frac{G_{\mathrm{T}} C_{\mathrm{A}} G \mathrm{PT}}{V_{8}}\). They found that the optimum value of \(g_{c}\) is independent of \(t .\) h. Choose a value of \(t\) between 5 and 15 and find the optimum value of \(g_{\mathrm{c}}\). How does this compare with the \(g_{e}\) found in liver glycogen (see Egg.15-2)? (Hint: You may find it useful to use a spreadsheet program.)
