Problems

1. Entropy Changes during Egg Development Consider a system consisting of an egg in an incubator. The white and yolk of the egg contain proteins, carbohydrates, and lipids. If fertilized, the egg is transformed from a single cell to a complex organism. Discuss this irreversible process in terms of the entropy changes in the system, surroundings, and universe. Be sure that you first clearly define the system and surroundings.

2. Calculation of AG'" from an Equilibrium Constant

Calculate the standard free-energy changes of the following metabolically important enzyme-catalyzed reactions at 25 °C and pH 7.0, using the equilibrium constants given.

aspartate aminotransferase

(a) Glutamate + oxaloacetate 3

aspartate + a-ketoglutarate K'eq = 6.8

triose phosphate isomerase

(b) Dihydroxyacetone phosphate 3

glyceraldehyde 3-phosphate K'eq = 0.0475

phosphofructokinase

(c) Fructose 6-phosphate + ATP 4

fructose 1,6-bisphosphate + ADP kq = 254

3. Calculation of the Equilibrium Constant from AG'°

Calculate the equilibrium constants K'eq for each of the fol lowing reactions at pH 7.0 and 25 °C, using the AG'° values in Table 13-4.

glucose 6-phosphatase

(a) Glucose 6-phosphate + H2O 3

glucose + Pi b-galactosidase

(c) Malate 3 fumarate + H2O

4. Experimental Determination of KLq and AG'° If a 0.1

m solution of glucose 1-phosphate is incubated with a catalytic amount of phosphoglucomutase, the glucose 1-phosphate is transformed to glucose 6-phosphate. At equilibrium, the concentrations of the reaction components are

Glucose 1-phosphate 34 glucose 6-phosphate 4.5 X 10~3 m 9.6 X 10~2 m

Calculate K'eq and AG'° for this reaction at 25 °C.

5. Experimental Determination of AG'° for ATP Hydrolysis A direct measurement of the standard free-energy change associated with the hydrolysis of ATP is technically demanding because the minute amount of ATP remaining at equilibrium is difficult to measure accurately. The value of AG'° can be calculated indirectly, however, from the equilib rium constants of two other enzymatic reactions having less favorable equilibrium constants:

Glucose 6-phosphate + H2O —> glucose + Pi K'eq = 270 ATP + glucose —> ADP + glucose 6-phosphate

Using this information, calculate the standard free energy of hydrolysis of ATP at 25 °C.

6. Difference between AG'° and AG Consider the following interconversion, which occurs in glycolysis (Chapter 14):

Fructose 6-phosphate 34 glucose 6-phosphate

(b) If the concentration of fructose 6-phosphate is adjusted to 1.5 m and that of glucose 6-phosphate is adjusted to 0.50 m, what is AG?

7. Dependence of AG on pH The free energy released by the hydrolysis of ATP under standard conditions at pH 7.0 is —30.5 kJ/mol. If ATP is hydrolyzed under standard conditions but at pH 5.0, is more or less free energy released? Explain.

8. The AG'° for Coupled Reactions Glucose 1-phos-phate is converted into fructose 6-phosphate in two successive reactions:

Glucose 1-phosphate-> glucose 6-phosphate

Glucose 6-phosphate-> fructose 6-phosphate

Using the AG'° values in Table 13-4, calculate the equilibrium constant, K'eq, for the sum of the two reactions at 25 °C:

Glucose 1-phosphate-> fructose 6-phosphate

9. Strategy for Overcoming an Unfavorable Reaction: ATP-Dependent Chemical Coupling The phosphoryla-tion of glucose to glucose 6-phosphate is the initial step in the catabolism of glucose. The direct phosphorylation of glucose by Pi is described by the equation

Glucose + Pi-> glucose 6-phosphate + H2O

(a) Calculate the equilibrium constant for the above reaction. In the rat hepatocyte the physiological concentrations of glucose and Pi are maintained at approximately 4.8 mM. What is the equilibrium concentration of glucose 6-phosphate obtained by the direct phosphorylation of glucose by Pi? Does this reaction represent a reasonable metabolic step for the catabolism of glucose? Explain.

(b) In principle, at least, one way to increase the concentration of glucose 6-phosphate is to drive the equilibrium reaction to the right by increasing the intracellular concentrations of glucose and Pi. Assuming a fixed concentration of Pi at 4.8 mM, how high would the intracellular concentration of glucose have to be to give an equilibrium concentration of glucose 6-phosphate of 250 ^m (the normal physiological concentration)? Would this route be physiologically reasonable, given that the maximum solubility of glucose is less than 1 m?

(c) The phosphorylation of glucose in the cell is coupled to the hydrolysis of ATP; that is, part of the free energy of ATP hydrolysis is used to phosphorylate glucose:

Sum: Glucose + ATP —> glucose 6-phosphate + ADP

Calculate Keq for the overall reaction. For the ATP-dependent phosphorylation of glucose, what concentration of glucose is needed to achieve a 250 ^m intracellular concentration of glucose 6-phosphate when the concentrations of ATP and ADP are 3.38 mM and 1.32 mM, respectively? Does this coupling process provide a feasible route, at least in principle, for the phosphorylation of glucose in the cell? Explain.

(d) Although coupling ATP hydrolysis to glucose phos-phorylation makes thermodynamic sense, we have not yet specified how this coupling is to take place. Given that coupling requires a common intermediate, one conceivable route is to use ATP hydrolysis to raise the intracellular concentration of Pi and thus drive the unfavorable phosphorylation of glucose by Pi. Is this a reasonable route? (Think about the solubility products of metabolic intermediates.)

(e) The ATP-coupled phosphorylation of glucose is catalyzed in hepatocytes by the enzyme glucokinase. This enzyme binds ATP and glucose to form a glucose-ATP-enzyme complex, and the phosphoryl group is transferred directly from ATP to glucose. Explain the advantages of this route.

10. Calculations of AG'° for ATP-Coupled Reactions

From data in Table 13-6 calculate the AG'° value for the reactions

(b) ATP + fructose —> ADP + fructose 6-phosphate

11. Coupling ATP Cleavage to an Unfavorable Reaction

To explore the consequences of coupling ATP hydrolysis under physiological conditions to a thermodynamically unfavorable biochemical reaction, consider the hypothetical transformation X n Y, for which AG" = 20 kJ/mol.

(b) Suppose X and Y participate in a sequence of reactions during which ATP is hydrolyzed to ADP and Pi. The overall reaction is

Calculate [Y]/[X] for this reaction at equilibrium. Assume that the equilibrium concentrations of ATP, ADP, and Pi are 1 m.

(c) We know that [ATP], [ADP], and [Pi] are not 1 m under physiological conditions. Calculate [Y]/[X] for the ATP-coupled reaction when the values of [ATP], [ADP], and [Pi] are those found in rat myocytes (Table 13-5).

12. Calculations of AG at Physiological Concentrations

Calculate the physiological AG (not AG'°) for the reaction

Phosphocreatine + ADP —> creatine + ATP

at 25 °C, as it occurs in the cytosol of neurons, with phosphocreatine at 4.7 mM, creatine at 1.0 mM, ADP at 0.73 mM, and ATP at 2.6 mM.

13. Free Energy Required for ATP Synthesis under Physiological Conditions In the cytosol of rat hepato-cytes, the mass-action ratio, Q, is

Calculate the free energy required to synthesize ATP in a rat hepatocyte.

14. Daily ATP Utilization by Human Adults

(a) A total of 30.5 kJ/mol of free energy is needed to synthesize ATP from ADP and Pi when the reactants and products are at 1 M concentrations (standard state). Because the actual physiological concentrations of ATP, ADP, and Pi are not 1 M, the free energy required to synthesize ATP under physiological conditions is different from AG'°. Calculate the free energy required to synthesize ATP in the human he-patocyte when the physiological concentrations of ATP, ADP, and Pi are 3.5, 1.50, and 5.0 mM, respectively.

(b) A 68 kg (150 lb) adult requires a caloric intake of 2,000 kcal (8,360 kJ) of food per day (24 h). The food is metabolized and the free energy is used to synthesize ATP, which then provides energy for the body's daily chemical and mechanical work. Assuming that the efficiency of converting food energy into ATP is 50%, calculate the weight of ATP used by a human adult in 24 h. What percentage of the body weight does this represent?

(c) Although adults synthesize large amounts of ATP daily, their body weight, structure, and composition do not change significantly during this period. Explain this apparent contradiction.

15. Rates of Turnover of y and ft Phosphates of ATP

If a small amount of ATP labeled with radioactive phosphorus in the terminal position, [y-32P]ATP, is added to a yeast extract, about half of the 32P activity is found in Pi within a few minutes, but the concentration of ATP remains unchanged. Explain. If the same experiment is carried out using ATP labeled with 32P in the central position, [¡-32P]ATP, the 32P does not appear in Pi within such a short time. Why?

16. Cleavage of ATP to AMP and PPi during Metabolism The synthesis of the activated form of acetate (acetyl-CoA) is carried out in an ATP-dependent process:

(a) The AG'° for the hydrolysis of acetyl-CoA to acetate and CoA is -32.2 kJ/mol and that for hydrolysis of ATP to AMP and PPi is -30.5 kJ/mol. Calculate AG'° for the ATP-dependent synthesis of acetyl-CoA.

(b) Almost all cells contain the enzyme inorganic py-rophosphatase, which catalyzes the hydrolysis of PPi to Pi. What effect does the presence of this enzyme have on the synthesis of acetyl-CoA? Explain.

17. Energy for H+ Pumping The parietal cells of the stomach lining contain membrane "pumps" that transport hydrogen ions from the cytosol of these cells (pH 7.0) into the stomach, contributing to the acidity of gastric juice (pH 1.0). Calculate the free energy required to transport 1 mol of hydrogen ions through these pumps. (Hint: See Chapter 11.) Assume a temperature of 25 °C.

18. Standard Reduction Potentials The standard reduction potential, E'°, of any redox pair is defined for the half-cell reaction:

Oxidizing agent + n electrons —> reducing agent

The E'° values for the NAD+/NADH and pyruvate/lactate conjugate redox pairs are -0.32 V and -0.19 V, respectively.

(a) Which conjugate pair has the greater tendency to lose electrons? Explain.

(b) Which is the stronger oxidizing agent? Explain.

(c) Beginning with 1 M concentrations of each reactant and product at pH 7, in which direction will the following reaction proceed?

(d) What is the standard free-energy change (AG'°) at 25 °C for the conversion of pyruvate to lactate?

(e) What is the equilibrium constant (AjLq) for this reaction?

19. Energy Span of the Respiratory Chain Electron transfer in the mitochondrial respiratory chain may be represented by the net reaction equation

(a) Calculate the value of AE'° for the net reaction of mitochondrial electron transfer. Use E'° values from Table 13-7.

(b) Calculate AG'° for this reaction.

(c) How many ATP molecules can theoretically be generated by this reaction if the free energy of ATP synthesis under cellular conditions is 52 kJ/mol?

20. Dependence of Electromotive Force on Concentrations Calculate the electromotive force (in volts) registered by an electrode immersed in a solution containing the following mixtures of NAD+ and NADH at pH 7.0 and 25 °C, with reference to a half-cell of E'° 0.00 V.

21. Electron Affinity of Compounds List the following substances in order of increasing tendency to accept electrons: (a) a-ketoglutarate + CO2 (yielding isocitrate); (b) ox-aloacetate; (c) O2; (d) NADP+.

22. Direction of Oxidation-Reduction Reactions Which of the following reactions would you expect to proceed in the direction shown, under standard conditions, assuming that the appropriate enzymes are present to catalyze them?

lactate + acetoacetate

(e) Malate + pyruvate —> oxaloacetate + lactate

(f) Acetaldehyde + succinate-> ethanol + fumarate Diabetes 2

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