Living cells constantly perform work and thus require energy for the maintenance of highly organized structures, for the synthesis of cellular components, for movement, for the generation of electrical currents, for the production of light, and for many other processes. Bioenergetics is the quantitative study of energy relationships and energy conversions in biological systems. Biological energy transformations obey the laws of thermodynamics. All chemical reactions are influenced by two forces: the tendency to achieve the most stable bonding state (for which enthalpy, H, is a useful expression) and the tendency to achieve the highest degree of randomness, expressed as entropy, S. The net driving force in a reaction is ΔG, the free-energy change, which represents the net effect of these two factors: ΔG = ΔH - TΔS. Cells require sources of free energy to perform work.
The standard free-energy change, ΔG°', is a physical constant characteristic for a given reaction, and can be calculated from the equilibrium constant for the reaction: ΔG°' = -RT ln K'eq . The actual free-energy change, ΔG, is a variable, which depends on OΔG°' and on the concentrations of reactants and products: ΔG = ΔG°' + RT ln ([products]/[reactants]). When ΔG is large and negative, the reaction tends to go in the forward direction; when it is large and positive, the reaction tends to go in the reverse direction; and when ΔG = 0, the system is at equilibrium. The freeenergy change for a reaction is independent of the pathway by which the reaction occurs. Free-energy changes are also additive; the net chemical reaction that results from the successive occurrence of reactions sharing a common intermediate has an overall free-energy change that is the sum of the ΔG values for the individual reactions.
ATP is the chemical link between catabolism and anabolism. Its exergonic conversion to ADP and Pi, or to AMP and PPi, is coupled to a large number of endergonic reactions and processes. In general, it is not ATP hydrolysis, but the transfer of phosphate or adenylate from ATP to a substrate or enzyme molecule that couples the energy of ATP breakdown to endergonic transformations of substrates. By these group transfer reactions ATP provides the energy for anabolic reactions, including the synthesis of informational molecules, and for the transport of molecules and ions across membranes against concentration and electrical potential gradients. Muscle contraction is one of several exceptions to this generalization; ATP hydrolysis drives the conformational changes in myosin that produce contraction in muscle.
Cells contain other metabolites with large, negative, free energies of hydrolysis, including phosphoenolpyruvate, 1,3-bisphosphoglycerate, and phosphocreatine. These high-energy compounds, like ATP, have a high phosphate group transfer potential; they are good donors of the phosphate group. Thioesters also have high free energies of hydrolysis.
Biological oxidation-reduction reactions can be described in terms of two half reactions, each with a characteristic standard reduction potential, E'0. When two electrochemical half cells, each containing the components of a half reaction, are connected, electrons tend to flow to the half cell with the higher reduction potential. The strength of this tendency is proportional to the difference between the two reduction potentials (ΔE), and is a function of the concentrations of oxidized and reduced species. The standard free-energy change for an oxidation-reduction reaction is directly proportional to the difference in standard reduction potentials of the two half cells: ΔG°' - -nFΔE'0
Many biological oxidation reactions are dehydrogenations in which one or two hydrogen atoms (electron and proton> are transferred from a substrate to a hydrogen acceptor. Oxidationreduction reactions in cells involve specialized electron carrier cofactors. NAD and NADP are the freely diffusible cofactors of many dehydrogenases of cells. Both cofactors accept two electrons and one proton. FAD and FMN, the flavin nucleotides, serve as tightly bound prosthetic groups of flavoproteins. They can accept either one or two electrons. In many organisms, a central energyconserving process is the stepwise oxidation of glucose to CO2, in which the energy of oxidation is conserved in ATP as electrons are passed to O2.
Bioenergetics and Thermodynamics
Atkins, P.W. (1984) The Second Law, Scientiiic American Books, Inc., New York.
A well-illustrated and elementary discussion of the second law and its smplications.
Blum, H.F. (1968) Time's Arrow and Evolution, 3rd edn, Princeton University Press, Princeton, NJ.
Cantor, C.R. & Schimmel, P.R. (1980) Biophysical Chemistry, W.H. Freeman and Company, San Francisco.
This and the next two books are outstanding advanced treatments of thermodynamics.
Dickerson, R.E. (1969) Molecular Thermodynamics, W.A. Benjamin, Inc., Menlo Park, CA.
Edsall, J.T. & Gutfreund, H. (1983) Biothermodynamics: The Study of Biochemical Processes at Equilibrium, John Wiley & Sons, Inc., New York.
Ingraham, L.L. & Pardee, A.B. (1967) Free energy and entropy in metabolism. In Metabolic Pathways, 3rd edn, Vol. I (Greenberg, D.M., ed), pp. 146, Academic Press, Inc., New York.
Klotz, I.M. (1967) Energy Changes in Biochemical Reactions, Academic Press, Inc., New York.
Brief and nonmathematical introduction to thermodynamics for biochemists, with many illustrative examples.
Morowitz, H.J. (1970) Entropy for Biologists: An Introduction to Thermodynamics, Academic Press, Inc., New York.
A good introduction to thermodynamics in biology, not Limited to a discussion of entropy.
Rothman, T. (1989) Science iz la Mode, Princeton University Press, Princeton, NJ.
Chapter 4, "The Evolution of Entropy," is an excellent discussion of entropy in biology.
van Holde, K.E. (1985) Physical Biochemistry, 2nd edn, Prentice-Hall, Inc., Englewood Cliffs, NJ.
Chapters 1 through 3 cover the thermodynamic concepts discussed in this chapter.
Phosphate Group Transfers and ATP
Alberty, R.A. (1969) Standard Gibbs free energy, enthalpy and entropy changes as a function of pH and pMg for several reactions involving adenosine phosphates. J. Biol. Chem. 244, 3290-3302.
This research paper documents the strong dependence of the free energy of ATP hydrolysis on the concentrations of H+ and Mg2+.
Bock, R.M. (1960) Adenine nucleotides and properties of pyrophosphate compounds. In The Enzymes, 2nd edn, Vol. 2 (Boyer, P.D., Lardy, H., & Myrback, K., eds), pp. 3-38, Academic Press, Inc., New York.
Bridger, W.A. & Henderson, J.F. (1983) Cell ATP, John Wiley & Sons, Inc., New York.
The chemistry of ATP, the role of ATP in metabolic regulation, and the catabolic and anabolic roles of ATP.
Hanson, R.W. (1989) The role of ATP in metabolism. Biochem. Educ. 17, 86-92.
Excellent summary of the chemistry and biology of ATP.
Harold, F.M. (1986) The Vital Force: A Study of Bioenergetics, W.H. Freeman and Company, New York.
A beautifully clear discussion of thermodynamics in biological processes.
Jencks, W.P. (1990) How does ATP make work? Chemtracts-Biochem. Mol. Biol. 1, 1-13.
A clear and sophisticated description of ATP energy transductions in ion transport, muscle contraction, oxidative phosphorylation, and photophosphorylation.
Kalckar, H.M. (1969) Biological Phosphorylations: Development of Concepts, Prentice-Hall, Inc., Englewood Cliffs, NJ.
An historical account by one of the central participants in the study of biological phosphorylations.
Lipmann, F. (1941) Metabolic generation and utilization of phosphate bond energy. Adv. Enzymol. 11, 99-162.
The classic description of the role of high-energy phosphate compounds in biology.
Pullman, B. & Pullman, A. (1960) Electronic structure of energy-rich phosphates. Radiat. Res. Suppl. 2, pp. 160-181.
An advanced discussion of the chemistry of ATP and other `energy-rich" compounds.
Westheimer, F.H. (1987) Why nature chose phosphates. Science 235, 1173-1178.
A chemist's description of the unique suitability of phosphate esters and anhydrides for metabolic trans formations.
Biological Oxidation-Reduction Reactions
Dolphin, D., Avramovic, O., & Poulson, R. (eds) (1987) Pyridine Nucleotide Coenzymes: Chemical, Biochemical, and Medical Aspects, John Wiley & Sons, Inc., New York.
An excellent two-volume collection of authoritative reuiews. Among the most useful of these are the chapters by Kaplan, Westheimer, Veech, and Ohno and Ushio.
Latimer, W.M. (1952) Oxidation Potentials, 2nd edn, Prentice-Hall, Inc., New York.
Montgomery, R. & Swenson, C.A. (1976) Quantitative Problems in the Biochemical Sciences, 2nd edn, W.H. Freeman and Company, San Francisco.
Segel, I.H. (1976) Biochemical Calculations, 2nd edn, John Wiley & Sons, Inc., New York.
l.Entropy Changes during Egg Development Consider an ecosystem 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 defme the system and surroundings.
2. Calculation of ΔG°' from Equilibrium Constants Calculate the standard free-energy changes of the following metabolically important enzyme-catalyzed reactions at 25 ? and pH 7.0 from the equilibrium constants given.aspartate
(a) Glutamate + oxaloacetate
aspartatw α-ketoglutarate K'eq = 6.8
(b) Dihydroxyacetone phosphate
(c) Fructose-6-phosphate + ATP
3. Calculation of Equilibrium Constants from ΔG°' Calculate the equilibrium constants Keq for each of the following reactions at pH 7.0 and 25 °C, using the ΔG°' values of Table 13-4:
(a) Glucose-6-phosphate + H2O
(b) Lactose + H2O
(c) Malate
4. Experimental Determination of K'eq and ΔG°' 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 until equilibrium is established. The equilibrium concentrations are
| Glucose-1-phosphate | |
glucose-6-phosphate |
| (4.5×10-3M) | (9.6×10-2M) |
5. Experimental Determination of ΔG°' 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 dif ficult to measure accurately. The value of ΔG°' can be calculated indirectly, however, from the equilibrium 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 K'eq = 890
Using this information, calculate the standard free energy of hydrolysis of ATP. Assume a temperature of 25 °C.
6. Difference between ΔG°' and ΔG Consider the following interconversion, which occurs in glycolysis (Chapter 14):
Fructose-6-phosphate glucose-6-phosphate K'eq = 1.97
(a) What is ΔG°' for the reaction (assuming that the temperature is 25 °C)?
(b) If the concentration of fructose-6-phosphate is adjusted to 1.5 M and that of glucose-6-phosphate is adjusted to 0.5 M, what is ΔG?
(c) Why are ΔG°'and ΔG different?
7. Dependence of ΔG 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? Why?
8. The ΔG°' for Coupled Reactions Glucose-1-phosphate is converted into fructose-6-phosphate in two successive reactions:
Glucose-1-phosphate glucose-6-phosphate
Glucose-6-phosphate fructose-6-phosphate
Using the ΔG°'
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 Ouercoming an Unfauorable Reaction: ATP-Dependent Chemical Coupling The phosphorylation 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 ΔG°' =
13.8 kJ/mol
(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 route represent a reasonable metabolic route 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 P; at 4.8 mM, how high would the intracellular concentration of glucose have to be to have an equilibrium concentration of glucose-6-phosphate of 250 μM (normal physiological concentration)? Would this route be a physiologically reasonable approach, 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 utilized to effect the endergonic phosphorylation of glucose:Glucose + Pi
ATP + H2O
Sum: Glucose + ATPCalculate K'eq for the overall reaction. When the ATP-dependent phosphorylation of glucose is carried out, what concentration of glucose is needed to achieve a 250 μM intracellular concentration of glucose-6-phosphate when the concentrations of ATP and ADP are 3.38 and 1.32 mM, respectively?Does this coupling process provide a feasible route, at least in principle, for the phosphorylation of glucose as it occurs in the cell? Explain.
(d) Although coupling ATP hydrolysis to glucose phosphorylation makes thermodynamic sense, how this coupling is to take place has not been specified. 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? Explain.
(e) The ATP-coupled phosphorylation of glucose is catalyzed in the hepatocyte by the enzyme glucokinase. This enzyme binds ATP and glucose to form a glucose-ATP-enzyme complex, and the phosphate is transferred directly from ATP to glucose. Explain the advantages of this route.
10. Calculations of ΔG°' for ATP-Coupled Reactions From data in Table 13-6 calculate the ΔG°' value for the reactions
(a) Phosphocreatine + ADP
(b) ATP + fructose
11. Coupling ATP Cleavage to an Unfauorable Reaction This
problem explores the consequences of coupling ATP hydrolysis
under physiological conditions to a thermodynamically unfavorable
biochemical reaction. Because we want to explore these
consequences in stages, we shall consider the hypothetical
transformation, X Y, a reaction for which ΔG°' = 20 kJ/mol.
(a) What is the ratio [Yl/[Xl at equilibrium?
(b) Suppose X and Y participate in a sequence of reactions during which ATP is hydrolyzed to ADP and Pi. The overall reaction is :
X+ATP+H2O
Calculate [Y]/[X] for this reaction at equilibrium. Assume for the purposes of this calculation that the concentrations of ATP, ADP, and Pi are all 1 hs when the reaction is at equilibrium.
(c) We know that [ATP], [ADP], and [Pi] are not 1 M under physiological conditions. Calculate the ratio [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 ΔG at Physiologicccl Concentrations
Calculate the physiological ΔG (not ΔG°') for the
reactionPhosphocreatine + ADP creatine + ATP at 25 °C as it
occurs in the cytosol of neurons, in which phosphocreatine is
present at 4.7 mM, creatine at 1.0 mM, ADP at 0.20 mM, and ATP
at 2.6 mM.
13. Free Energy Required for ATP Synthesis under Physiological Conditions In the cytosol of rat hepatocytes, the mass-action ratio is
| [ATP] [ADP][Pi] |
= 533 M-1 |
Calculate the free energy required to synthesize ATP in the 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 concentration (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 OG??. Calculate the free energy required to synthesize ATP in the human hepatocyte when the physiological concentrations of ATP, ADP, and Pi are 3.5, 1.50, and 5.0 mM, respectively.
(b) A normal 68 kg (150 lb) adult requires a caloric intake of 2,000 kcal (8,360 kJ) of food per day (24 h). This food is metabolized and the free energy used to synthesize ATP, which is then utilized to do 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 utilized by a human adult in a 24 h period. 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. ATP Reserve in Muscle Tissue The ATP concentration in muscle tissue (approximately 70% water) is about 8.0 mM. During strenuous activity each gram of muscle tissue uses ATP at the rate of 300 N,mol/min for contraction.
(a) How long would the reserve of ATP last during a 100 meter dash?
(b) The phosphocreatine level in muscle is about 40.0 mM. How does this help extend the reserve of muscle ATP?
(c) Given the size of the reserve ATP pool, how can a person run a marathon?
16. Rates of Turnover of γ- and β-Phosphates of ATP If a small amount of ATP labeled with radioactive phosphorus in the terminal position, [γ-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 3zP in the central position, [β-32p]ATP, the 32P does not appear in Pi within the same number of minutes. Why?
17. 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:
Acetate + CoA + ATP
acetyl-CoA + AMP + PPi
(a) The ΔG°' 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 ΔG°' for the ATP-dependent synthesis of acetyl-CoA.
(b) Almost all cells contain the enzyme inorganic pyrophosphatase, which catalyzes the hydrolysis of PPi to Pi. What effect does the presence of this enzyme have on the synthesis of acetyl-CoA? Explain.
18. Are All Metabolic Reactions at Equilibrium?
(a) Phosphoenolpyruvate is one of the two phosphate donors in the synthesis of ATP during glycolysis. In human erythrocytes, the steady-state concentration of ATP is 2.24 mM, that of ADP is 0.25 mM, and that of pyruvate is 0.051 mM. Calculate the concentration of phosphoenolpyruvate at 25 °C, assuming that the pyruvate kinase reaction (Fig. 13-3) is at equilibrium in the cell.
(b) The physiological concentration of phosphoenolpyruvate in human erythrocytes is 0.023 mM. Compare this with the value obtained in (a). What is the significance of this difference? Explain.
19. Standard Reduction Potentials The standard reduction potential, E'0, of any redox pair is defined for the half cell reaction:
Oxidizing agent + n electrons reducing agent
The E'0 values for the NAD+/NADH and pyruvate/lactate conjugate redox pairs are -0.32 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) If we begin with 1 M concentrations of each reactant and product at pH 7, in which direction will the following reaction proceed?Pyruvate + NADH + H
(d) What is the standard free-energy change (ΔG°') at 25 °C for this reaction?
(e) What is the equilibrium constant (Key) for this reaction?
20. Energy Span of the Respiratory Chain Electron transfer in the mitochondrial respiratory chain may be represented by the net reaction equation
NADH + H+ + ½O2 H2O + NAD+`
(a) Calculate the value of DEo for the net reaction of mitochondrial electron transfer.
(b) Calculate ΔG°' for this reaction.
(c) How many ATP molecules can theoretically be generated by this reaction if the standard free energy of ATP synthesis is 30.5 kJ/mol?
21. Dependence of Electromotiue 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.
(a) 1.0 mM NAD+ and 10 mM NADH
(b) 1.0 mM NAD+ and 1.0 mM NADH
(c) 10 mM NAD+ and 1.0 mM NADH
22. Electron Affinity of Compounds List the following substances in order of increasing tendency to accept electrons:
(a) α-ketoglutarate + CO2(yielding isocitrate),
(b) oxaloacetate,
(c) O2,
(d) NADP+.
23. Direction of Oxidation-Reduction Reactions Which of the following reactions would be expected to proceed in the direction shown under standard conditions, assuming that the appropriate enzymes are present to catalyze them?
(a) Malate + NAD+
(b) Acetoacetate + NADH + H+
(c) Pyruvate + NADH + H+
(d) Pyruvate + β-hydroxybutyrate
(e) Malate + pyruvate
(f ) Acetaldehyde + succinate
