Bioenergetics
and Biochemical
Reaction Types
S-142
1. Entropy Changes during Egg Development Consider a system consisting of an egg in an incuba-
tor. 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 ⌬Gⴕⴗ from an Equilibrium Constant Calculate the standard free-energy change
for each of the following metabolically important enzyme-catalyzed reactions, using the equilibrium
constants given for the reactions at 25 C and pH 7.0.
aspartate
aminotransferase
(a) Glutamate oxaloacetate aspartate a-ketoglutarate K
eq
6.8
triose phosphate
isomerase
(b) Dihydroxyacetone phosphate glyceraldehyde 3-phosphate K
eq
0.0475
phosphofructokinase
(c) Fructose 6-phosphate ATP fructose 1,6-bisphosphate ADP K
eq
254
Answer
88888888888888z
y8888888888888
888888888888z
y88888888888
888888888888z
y88888888888
chapter
13
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Chapter 13 Bioenergetics and Biochemical Reaction Types S-143
3. Calculation of the Equilibrium Constant from ⌬Gⴕⴗ Calculate the equilibrium constant K
eq
for
each of the following reactions at pH 7.0 and 25 C, using the G values in Table 13–4.
glucose
6-phosphatase
(a) Glucose 6-phosphate H
2
O glucose P
i
b-galactosidase
(b) Lactose H
2
O glucose galactose
fumarase
(c) Malate fumarate H
2
O
Answer
4. Experimental Determination of K
eq
and ⌬Gⴕⴗ If a 0.1
M
solution of glucose 1-phosphate at 25 C
is incubated with a catalytic amount of phosphoglucomutase, the glucose 1-phosphate is trans-
formed to glucose 6-phosphate. At equilibrium, the concentrations of the reaction components are
Glucose 1-phosphate 88z
y88 glucose 6-phosphate
4.5 10
3
M
9.6 10
2
M
Calculate K
eq
and G for this reaction.
Answer
888888z
y88888
888888888888z
y88888888888
8888888888z
y888888888
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5. Experimental Determination of ⌬Gⴕⴗ 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 G can be
calculated indirectly, however, from the equilibrium constants of two other enzymatic reactions having
less favorable equilibrium constants:
Glucose 6-phosphate H
2
O 88n glucose P
i
K
eq
270
ATP glucose 88n ADP glucose 6-phosphate K
eq
890
Using this information for equilibrium constants determined at 25 C, calculate the standard free energy
of hydrolysis of ATP.
6. Difference between ⌬Gⴕⴗ and ⌬GConsider the following interconversion, which occurs in glycoly-
sis (Chapter 14):
Fructose 6-phosphate 88z
y88 glucose 6-phosphate K
eq
1.97
(a) What is G for the reaction (K
eq
measured at 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 0.50
M
, what is G?
(c) Why are G and Gdifferent?
Chapter 13 Bioenergetics and Biochemical Reaction Types S-145
7. Free Energy of Hydrolysis of CTP Compare the structure of the nucleoside triphosphate CTP with
the structure of ATP.
Adenosine triphosphate (ATP)
OH
N
H
H
OH
H
O
O
PO
H
N
NN
O
O
P
O
O
P CH
2
NH
2
Cytidine triphosphate (CTP)
O
OH
H
H
OH
H
O
O
PO
H
NH
N
O
O
P
O
O
P CH
2
NH
2
Now predict the K
eq
and G for the following reaction:
ATP CDP 88n ADP CTP
8. Dependence of ⌬Gon pH The free energy released by the hydrolysis of ATP under standard condi-
tions at pH 7.0 is 30.5 kJ/mol. If ATP is hydrolyzed under standard conditions except at pH 5.0, is
more or less free energy released? Explain. Use the Living Graph to explore this relationship.
9. The ⌬Gⴕⴗ for Coupled Reactions Glucose 1-phosphate is converted into fructose 6-phosphate in
two successive reactions:
Glucose 1-phosphate 88n glucose 6-phosphate
Glucose 6-phosphate 88n fructose 6-phosphate
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S-146 Chapter 13 Bioenergetics and Biochemical Reaction Types
Using the G values in Table 13–4, calculate the equilibrium constant, K
eq
, for the sum of the two
reactions:
Glucose 1-phosphate 88n fructose 6-phosphate
Answer
10. Effect of [ATP]/[ADP] Ratio on Free Energy of Hydrolysis of ATP Using Equation 13–4, plot
Gagainst ln Q(mass-action ratio) at 25 C for the concentrations of ATP, ADP, and P
i
in the table
below. G for the reaction is –30.5 kJ/mol. Use the resulting plot to explain why metabolism is regu-
lated to keep the ratio [ATP]/[ADP] high.
Concentration (m
M
)
ATP 5 3 1 0.2 5
ADP 0.2 2.2 4.2 5.0 25
P
i
10 12.1 14.1 14.9 10
Chapter 13 Bioenergetics and Biochemical Reaction Types S-147
11. Strategy for Overcoming an Unfavorable 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 P
i
is described by the equation
Glucose P
i
88n glucose 6-phosphate H
2
OG 13.8 kJ/mol
(a) Calculate the equilibrium constant for the above reaction at 37 C. In the rat hepatocyte the
physiological concentrations of glucose and P
i
are maintained at approximately 4.8 m
M
. What is
the equilibrium concentration of glucose 6-phosphate obtained by the direct phosphorylation of
glucose by P
i
? 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
P
i
. Assuming a fixed concentration of P
i
at 4.8 m
M
, how high would the intracellular concentra-
tion of glucose have to be to give an equilibrium concentration of glucose 6-phosphate of 250 m
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:
(1) Glucose P
i
88n glucose 6-phosphate H
2
OG 13.8 kJ/mol
(2) ATP H
2
O 88n ADP P
i
G 30.5 kJ/mol
Sum: Glucose ATP 88n glucose 6-phosphate ADP
Calculate K
eq
at 37 C for the overall reaction. For the ATP-dependent phosphorylation of glu-
cose, what concentration of glucose is needed to achieve a 250 m
M
intracellular concentration of
glucose 6-phosphate when the concentrations of ATP and ADP are 3.38 m
M
and 1.32 m
M
, respec-
tively? Does this coupling process provide a feasible route, at least in principle, for the phospho-
rylation of glucose in the cell? Explain.
(d) Although coupling ATP hydrolysis to glucose phosphorylation 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 concentra-
tion of P
i
and thus drive the unfavorable phosphorylation of glucose by P
i
. 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 glucoki-
nase. This enzyme binds ATP and glucose to form a glucose-ATP-enzyme complex, and the phos-
phoryl group is transferred directly from ATP to glucose. Explain the advantages of this route.
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S-148 Chapter 13 Bioenergetics and Biochemical Reaction Types
Answer
12. Calculations of ⌬Gⴕⴗ for ATP-Coupled Reactions From data in Table 13–6 calculate the G
value for the reactions.
(a) Phosphocreatine ADP 88n creatine ATP
(b) ATP fructose 88n ADP fructose 6-phosphate
Answer
13. Coupling ATP Cleavage to an Unfavorable Reaction To explore the consequences of coupling
ATP hydrolysis under physiological conditions to a thermodynamically unfavorable biochemical reac-
tion, consider the hypothetical transformation X →Y, for which G 20 kJ/mol.
(a) What is the ratio [Y]/[X] at equilibrium?
(b) Suppose X and Y participate in a sequence of reactions during which ATP is hydrolyzed
to ADP and P
i
. The overall reaction is
X ATP H
2
O 88n Y ADP P
i
Calculate [Y]/[X] for this reaction at equilibrium. Assume that the temperature is 25 C
and the equilibrium concentrations of ATP, ADP, and P
i
are all 1
M
.
(c) We know that [ATP], [ADP], and [P
i
] are not 1
M
under physiological conditions. Calcu-
late [Y]/[X] for the ATP-coupled reaction when the values of [ATP], [ADP], and [P
i
] are
those found in rat myocytes (Table 13–5).
Answer
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S-150 Chapter 13 Bioenergetics and Biochemical Reaction Types
14. Calculations of ⌬Gat Physiological Concentrations Calculate the actual, physiological Gfor
the reaction
Phosphocreatine ADP 88n creatine ATP
at 37 C, as it occurs in the cytosol of neurons, with phosphocreatine at 4.7 m
M
, creatine at 1.0 m
M
, ADP
at 0.73 m
M
, and ATP at 2.6 m
M
.
Answer
15. Free Energy Required for ATP Synthesis under Physiological Conditions In the cytosol of rat
hepatocytes, the temperature is 37 C and the mass-action ratio, Q, is
5.33 10
2
M
1
Calculate the free energy required to synthesize ATP in a rat hepatocyte.
16. Chemical Logic In the glycolytic pathway, a six-carbon sugar (fructose 1,6-bisphosphate) is cleaved to
form two three-carbon sugars, which undergo further metabolism (see Fig. 14–6). In this pathway, an
isomerization of glucose 6-phosphate to fructose 6-phosphate (shown below) occurs two steps before
the cleavage reaction (the intervening step is phosphorylation of fructose 6-phosphate to fructose 1,6-
bisphosphate (p. 549)).
[ATP]
[ADP][P
i
]
OOOHH
C
C
JO
A
C
A
C
A
C
A
A
HG
OOHHO
OOOHH
OOOHH
H
C
C
A
OO
O
OHHC
A
H
A
C
A
C
A
A
O
OU
HO
OOOHH
OOOHH
Glucose 6-phosphate Fructose 6-phosphate
phosphohexose
isomerase
CH2OPO3
2CH2OPO3
2
What does the isomerization step accomplish from a chemical perspective? (Hint: Consider what might
happen if the C—C bond cleavage were to proceed without the preceding isomerization.)
17. Enzymatic Reaction Mechanisms I Lactate dehydrogenase is one of the many enzymes that require
NADH as coenzyme. It catalyzes the conversion of pyruvate to lactate:
NADH HNAD
HC
A
OOHO
C
O
O
C
A
A
OO
COUlactate
dehydrogenase A
CH3
A
CH3
Pyruvate L-Lactate
S-152 Chapter 13 Bioenergetics and Biochemical Reaction Types
Glyceraldehyde
3-phosphate
Erythrose
4-phosphate
Fructose
6-phosphate
transaldolase
O
C
H
C
CH2OPO3
2
HOH
CHOH
C
CH2OPO3
2
HOHC
CH2OPO3
2
HOH
C
OH
CHOH
CHO H
Sedoheptulose
7-phosphate
CHOH
C
HOH
C
CH2OPO3
2
HOH
C
HO H
CH2OH
C O CH2OH
C O
18. Enzymatic Reaction Mechanisms II Biochemical reactions often look more complex than they
really are. In the pentose phosphate pathway (Chapter 14), sedoheptulose 7-phosphate and glycer-
aldehyde 3-phosphate react to form erythrose 4-phosphate and fructose 6-phosphate in a reaction
catalyzed by transaldolase.
Draw the mechanism of this reaction (show electron-pushing arrows). (Hint: This is a common reaction
throughout metabolism; the mechanism is similar to that catalyzed by other dehydrogenases that use
NADH, such as alcohol dehydrogenase.)
Draw a mechanism for this reaction (show electron-pushing arrows). (Hint: Take another look at aldol
condensations, then consider the name of this enzyme.)
Chapter 13 Bioenergetics and Biochemical Reaction Types S-153
19. 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 P
i
when the re-
actants and products are at 1
M
concentrations and the temperature is 25 C (standard state).
Because the actual physiological concentrations of ATP, ADP, and P
i
are not 1
M
, and the temper-
ature is 37 C, the free energy required to synthesize ATP under physiological conditions is differ-
ent from G. Calculate the free energy required to synthesize ATP in the human hepatocyte
when the physiological concentrations of ATP, ADP, and P
i
are 3.5, 1.50, and 5.0 m
M
, respectively.
(b) A 68 kg (150 lb) adult requires a caloric intake of 2,000 kcal (8,360 kJ) of food per day (24 hours).
The food is metabolized and the free energy is used to synthesize ATP, which then provides en-
ergy for the body’s daily chemical and mechanical work. Assuming that the efficiency of convert-
ing food energy into ATP is 50%, calculate the weight of ATP used by a human adult in 24 hours.
What percentage of the body weight does this represent?
(c) Although adults synthesize large amounts of ATP daily, their body weight, structure, and compo-
sition do not change significantly during this period. Explain this apparent contradiction.
Answer
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S-154 Chapter 13 Bioenergetics and Biochemical Reaction Types
20. Rates of Turnover of gand bPhosphates of ATP If a small amount of ATP labeled with radioac-
tive phosphorus in the terminal position, [g–
32
P]ATP, is added to a yeast extract, about half of the
32
P
activity is found in P
i
within a few minutes, but the concentration of ATP remains unchanged.
Explain. If the same experiment is carried out using ATP labeled with
32
P in the central position,
[b–
32
P]ATP, the
32
P does not appear in P
i
within such a short time. Why?
21. Cleavage of ATP to AMP and PP
i
during Metabolism Synthesis of the activated form of acetate
(acetyl-CoA) is carried out in an ATP-dependent process:
Acetate CoA ATP 88n acetyl-CoA AMP PP
i
(a) The G for the hydrolysis of acetyl-CoA to acetate and CoA is 32.2 kJ/mol and that for hy-
drolysis of ATP to AMP and PP
i
is 30.5 kJ/mol. Calculate G for the ATP-dependent synthesis
of acetyl-CoA.
(b) Almost all cells contain the enzyme inorganic pyrophosphatase, which catalyzes the hydrolysis of
PP
i
to P
i
. What effect does the presence of this enzyme have on the synthesis of acetyl-CoA?
Explain.
Answer
22. Energy for H
ⴙ
Pumping The parietal cells of the stomach lining contain membrane “pumps” that
transport hydrogen ions from the cytosol (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 37 C.
23. Standard Reduction Potentials The standard reduction potential, E, of any redox pair is defined
for the half-cell reaction:
Oxidizing agent nelectrons 88n 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 redox pair has the greater tendency to lose electrons? Explain.
(b) Which pair is the stronger oxidizing agent? Explain.
(c) Beginning with 1
M
concentrations of each reactant and product at pH 7 and 25 C, in which
direction will the following reaction proceed?
Pyruvate NADH H
88z
y88 lactate NAD
(d) What is the standard free-energy change (G) for the conversion of pyruvate to lactate?
(e) What is the equilibrium constant (K
eq
) for this reaction?
Answer
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S-156 Chapter 13 Bioenergetics and Biochemical Reaction Types
24. Energy Span of the Respiratory Chain Electron transfer in the mitochondrial respiratory chain
may be represented by the net reaction equation
NADH H
1
2
O
2
88z
y88 H
2
O NAD
(a) Calculate E for the net reaction of mitochondrial electron transfer. Use E values from
Table 13–7.
(b) Calculate G 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?
Answer
25. 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.
(a) 1.0 m
M
NAD
and 10 mM NADH
(b) 1.0 m
M
NAD
and 1.0 mM NADH
(c) 10 m
M
NAD
and 1.0 mM NADH
26. Electron Affinity of Compounds List the following in order of increasing tendency to accept
electrons: (a), a-ketoglutarate CO
2
(yielding isocitrate); (b), oxaloacetate; (c), O
2
; (d), NADP
.
Chapter 13 Bioenergetics and Biochemical Reaction Types S-157
27. 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?
(a) Malate NAD
88n oxaloacetate NADH H
(b) Acetoacetate NADH H
88n b-hydroxybutyrate NAD
(c) Pyruvate NADH H
88n lactate NAD
(d) Pyruvate b-hydroxybutyrate 88n lactate acetoacetate
(e) Malate pyruvate 88n oxaloacetate lactate
(f) Acetaldehyde succinate 88n ethanol fumarate
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S-158 Chapter 13 Bioenergetics and Biochemical Reaction Types
Data Analysis Problem
28. Thermodynamics Can Be Tricky Thermodynamics is a challenging area of study and one with many
opportunities for confusion. An interesting example is found in an article by Robinson, Hampson, Munro,
and Vaney, published in Science in 1993. Robinson and colleagues studied the movement of small mole-
cules between neighboring cells of the nervous system through cell-to-cell channels (gap junctions).
They found that the dyes Lucifer yellow (a small, negatively charged molecule) and biocytin (a small
zwitterionic molecule) moved in only one direction between two particular types of glia (nonneuronal
cells of the nervous system). Dye injected into astrocytes would rapidly pass into adjacent astrocytes,
oligodendrocytes, or Müller cells, but dye injected into oligodendrocytes or Müller cells passed slowly if
at all into astrocytes. All of these cell types are connected by gap junctions.
Although it was not a central point of their article, the authors presented a molecular model for
how this unidirectional transport might occur, as shown in their Figure 3:
Astrocyte
Astrocyte
Oligodendrocyte
Oligodendrocyte
(A)
(B)
The figure legend reads: “Model of the unidirectional diffusion of dye between coupled oligodendro-
cytes and astrocytes, based on differences in connection pore diameter. Like a fish in a fish trap, dye
molecules (black circles) can pass from an astrocyte to an oligodendrocyte (A) but not back in the
other direction (B).”
Although this article clearly passed review at a well-respected journal, several letters to the editor
(1994) followed, showing that Robinson and coauthors’ model violated the second law of thermodynamics.
(a) Explain how the model violates the second law. Hint: Consider what would happen to the en-
tropy of the system if one started with equal concentrations of dye in the astrocyte and oligoden-
drocyte connected by the “fish trap” type of gap junctions.
(b) Explain why this model cannot work for small molecules, although it may allow one to catch fish.
(c) Explain why a fish trap does work for fish.
(d) Provide two plausible mechanisms for the unidirectional transport of dye molecules between the
cells that do not violate the second law of thermodynamics.
Answer
Chapter 13 Bioenergetics and Biochemical Reaction Types S-159
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