• Home
  • Textbooks
  • Lehninger Principles of Biochemistry
  • Bioenergetics and Biochemical Reaction Types

Lehninger Principles of Biochemistry

David L. Nelson, Michael M. Cox

Chapter 13

Bioenergetics and Biochemical Reaction Types - all with Video Answers

Educators

Chapter Questions

05:40

Problem 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.

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:39

Problem 2

Calculation of $\Delta G^{\prime \circ}$ 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 $25^{\circ} \mathrm{C}$ and $\mathrm{pH} 7.0$
(a) Glutamate + oxaloacetate $\quad \rightleftharpoons \quad$ aspartate $+\alpha$ -ketogluta
(b) Dihydroxyacetone phosphate $\rightleftharpoons \quad$ glyceraldehyde 3 -phosphate
(c) Fructose 6 -phosphate $+$ ATP $\rightleftharpoons \quad$ fructose 1,6 -bisphosphate $+$ ADP

Hailey Tomashek
Hailey Tomashek
Numerade Educator
01:39

Problem 3

Calculation of the Equilibrium Constant from $\Delta G^{\prime \circ}$ Calculate the equilibrium constant $\boldsymbol{K}_{\mathrm{eq}}^{\prime}$ for each of the following reactions at $\mathrm{pH} 7.0$ and $25^{\circ} \mathrm{C},$ using the $\Delta G^{\prime \circ}$ values in Table $13-4$
(a) Glucose 6-phosphate $+\mathrm{H}_{2} \mathrm{O} \quad \rightleftharpoons \quad$ glucose $+\mathrm{P}_{\mathrm{i}}$
(b) Lactose $+\mathrm{H}_{2} \mathrm{O} \quad \rightleftharpoons \quad$ glucose $+$ galactose
(c) Malate $\rightleftharpoons$ fumarate $+\mathrm{H}_{2} \mathrm{O}$

Hailey Tomashek
Hailey Tomashek
Numerade Educator
01:24

Problem 4

Experimental Determination of $K_{\mathrm{eq}}^{\prime}$ and $\Delta G^{\prime \circ}$ If a $0.1 \mathrm{M}$ solution of glucose 1 phosphate at $25^{\circ} \mathrm{C}$ 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 $\rightleftharpoons$ glucose 6 -phosphate
\[
4.5 \times 10^{-3} \mathrm{M} \quad 9.6 \times 10^{-2} \mathrm{M}
\]
Calculate $\boldsymbol{K}_{\mathbf{e q}}^{\prime}$ and $\Delta G^{\prime \circ}$ for this reaction.

David Collins
David Collins
Numerade Educator
01:21

Problem 5

Experimental Determination of $\Delta G^{\prime \circ}$ 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 $\Delta G^{\prime \circ}$ can be calculated indirectly, however, from the equilibrium constants of two other enzymatic reactions having less favorable equilibrium constants:
$$\begin{array}{ll}
\text { Glucose } 6 \text { -phosphate }+\mathrm{H}_{2} \mathrm{O} \rightarrow \text { glucose }+\mathrm{P}_{\mathrm{i}} & K_{\mathrm{eq}}^{\prime}=270 \\
\mathrm{ATP}+\text { glucose } \rightarrow \mathrm{ADP}+\text { glucose } 6 \text { -phosphate } & K_{\mathrm{eq}}^{\prime}=890
\end{array}$$
Using this information for equilibrium constants determined at $25^{\circ} \mathrm{C},$ calculate the standard free energy of hydrolysis of ATP.

Prashant Bana
Prashant Bana
Numerade Educator
02:21

Problem 6

Difference between $\Delta G^{\prime \circ}$ and $\Delta G$ Consider the following interconversion, which occurs in glycolysis (Chapter 14 ):
Fructose 6 -phosphate $\rightleftharpoons$ glucose 6 -phosphate $K_{\mathrm{eq}}^{\prime}=1.97$
(a) What is $\Delta G^{\prime \circ}$ for the reaction $\left(\boldsymbol{K}_{\mathbf{e q}}^{\prime} \text { measured at } 25^{\circ} \mathrm{C}\right) ?$
(b) If the concentration of fructose 6 -phosphate is adjusted to $1.5 \mathrm{M}$ and that of glucose 6-phosphate is adjusted to $0.50 \mathrm{M}$, what is $\Delta G ?$
(c) Why are $\Delta G^{\prime \circ}$ and $\Delta G$ different?

Hailey Tomashek
Hailey Tomashek
Numerade Educator
03:56

Problem 7

Free Energy of Hydrolysis of CTP Compare the structure of the nucleoside triphosphate CTP with the structure of ATP.
Cytidine triphosphate (CTP)
Adenosine triphosphate (ATP)
Now predict the $\boldsymbol{K}_{\mathbf{e q}}^{\prime}$ and $\Delta G^{\prime \circ}$ for the following reaction:
\[
\mathbf{A T P}+\mathbf{C D P} \rightarrow \mathbf{A D P}+\mathbf{C T P}
\]

Prashant Bana
Prashant Bana
Numerade Educator
04:03

Problem 8

Dependence of $\Delta G$ on pH The free energy released by the hydrolysis of ATP under standard conditions is $-30.5 \mathrm{kJ} / \mathrm{mol}$. If $\mathrm{ATP}$ is hydrolyzed under standard conditions except at $\mathrm{pH} 5.0$, is more or less free energy released? Explain.

Eric Goldman
Eric Goldman
Numerade Educator
02:22

Problem 9

The $\Delta G^{\text {ro }}$ for Coupled Reactions Glucose 1 -phosphate is converted into fructose 6 phosphate in two successive reactions:
Glucose 1-phosphate $\rightarrow$ glucose 6 -phosphate
Glucose 6 -phosphate $\rightarrow$ fructose 6 -phosphate
Using the $\Delta G^{\prime \circ}$ values in Table $13-4$, calculate the equilibrium constant, $\boldsymbol{K}_{\mathbf{e q}}^{\prime},$ for the sum of the two reactions:
Glucose 1-phosphate $\rightarrow$ fructose 6 -phosphate

Prashant Bana
Prashant Bana
Numerade Educator
09:20

Problem 10

Effect of $|\mathrm{ATP}| /|\mathrm{ADP}|$ Ratio on Free Energy of Hydrolysis of ATP Using Equation $13-4,$ plot $\Delta G$ against $\ln Q(\text { mass-action ratio })$ at $25^{\circ} \mathrm{C}$ for the concentrations of $\mathrm{ATP}$ ADP, and $P_{i}$ in the table below. $\Delta G^{\prime \circ}$ for the reaction is -30.5 kJ/mol. Use the resulting plot to explain why metabolism is regulated to keep the ratio [ATP]/[ADP] high.
$$\begin{array}{lccccc}
& \multicolumn{4}{c} {\text { Concentration (mM) }} \\
\hline \mathrm{ATP} & 5 & 3 & 1 & 0.2 & 5 \\
\mathrm{ADP} & 0.2 & 2.2 & 4.2 & 5.0 & 25 \\
\mathrm{P}_{\mathrm{i}} & 10 & 12.1 & 14.1 & 14.9 & 10 \\
\hline
\end{array}$$

Niamat Khuda
Niamat Khuda
Numerade Educator
06:02

Problem 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 $\mathrm{P}_{\mathrm{i}}$ is described by the equation
$$\text { Glucose }+\mathbf{P}_{i} \rightarrow \text { glucose } 6 \text { -phosphate }+\mathbf{H}_{2} \mathbf{O} \quad \Delta G^{\prime \prime}=\mathbf{1 3 . 8} \mathbf{k J} / \mathrm{mol}$$
(a) Calculate the equilibrium constant for the above reaction at $37^{\circ} \mathrm{C}$. In the rat hepatocyte, the physiological concentrations of glucose and $P_{i}$ are maintained at approximately $4.8 \mathrm{mM}$. What is the equilibrium concentration of glucose 6 -phosphate obtained by the direct phosphorylation of glucose by $\mathrm{P}_{\mathrm{i}} ?$ 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 $\mathrm{P}_{\mathrm{i}}$. Assuming a fixed concentration of $\mathrm{P}_{\mathrm{i}}$ at $4.8 \mathrm{mM}$, how high would the intracellular concentration of glucose have to be to give an equilibrium concentration of glucose 6 -phosphate of $250 \mu \mathrm{M}$ (the normal physiological concentration)? Would this route be physiologically reasonable, given that the maximum solubility of glucose is less than $1 \mathrm{M} ?$
(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 $+P_{i} \rightarrow$ glucose 6 -phosphate $+H_{2} O \quad \Delta G^{\prime \prime}=13.8 k J /$
(2) $A T P+H_{2} O \rightarrow A D P+P_{1} \quad \Delta G^{\prime \prime}=-30.5$.
Sum: Glucose $+$ ATP $\rightarrow$ glucose 6 -phosphate $+$ ADP
Calculate $\boldsymbol{K}_{\mathbf{e q}}^{\prime}$ at $37^{\circ} \mathrm{C}$ for the overall reaction. For the ATP-dependent phosphorylation of glucose, what concentration of glucose is needed to achieve a $250 \mu \mathrm{M}$ intracellular concentration of glucose 6 -phosphate when the concentrations of $A$ TP and $A D P$ are 3.38 $\mathrm{mM}$ and $1.32 \mathrm{mM}$, 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 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 concentration of $\mathrm{P}_{\mathrm{i}}$ and thus drive the unfavorable phosphorylation of glucose by $\mathrm{P}_{\mathrm{i}}$. Is this a reasonable route? (Think about the solubility product, $K_{\mathrm{sp}},$ 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.

Sana Riaz
Sana Riaz
Numerade Educator
01:34

Problem 12

Calculations of $\Delta G^{\text {to }}$ for ATP-Coupled Reactions From data in Table $13-6,$ calculate the $\Delta G^{\prime \circ}$ value for the following reactions:
(a) Phosphocreatine $+\mathrm{ADP} \rightarrow$ creatine $+\mathrm{ATP}$
(b) $\mathrm{ATP}+$ fructose $\rightarrow$ ADP $+$ fructose 6 -phosphate

Prashant Bana
Prashant Bana
Numerade Educator
08:20

Problem 13

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 $\mathrm{X} \rightarrow \mathrm{Y},$ for which $\Delta G^{\prime \circ}=20.0 \mathrm{kJ} / \mathrm{mol}$
(a) What is the ratio $[\mathrm{Y}] /[\mathrm{X}]$ at equilibrium?
(b) Suppose $\mathrm{X}$ and $\mathrm{Y}$ participate in a sequence of reactions during which ATP is hydrolyzed to ADP and $\mathrm{P}_{\mathrm{i}}$. The overall reaction is

Niamat Khuda
Niamat Khuda
Numerade Educator
02:01

Problem 14

Calculations of $\Delta G$ at Physiological Concentrations Calculate the actual, physiological $\Delta G$ for the reaction
Phosphocreatine $+\mathrm{ADP} \rightarrow$ creatine $+\mathrm{ATP}$
at $37^{\circ} \mathrm{C}$, as it occurs in the cytosol of neurons, with phosphocreatine at $4.7 \mathrm{mM}$, creatine at $1.0 \mathrm{mM},$ ADP at $0.73 \mathrm{mM}$, and $\mathrm{ATP}$ at $2.6 \mathrm{mM}$

Caroline Jones
Caroline Jones
Numerade Educator
03:10

Problem 15

Free Energy Required for ATP Synthesis under Physiological Conditions In the cytosol of rat hepatocytes, the temperature is $37^{\circ} \mathrm{C}$ and the mass-action ratio, $Q,$ is
$$\frac{[\mathrm{ATP}]}{[\mathrm{ADP}]\left[\mathrm{P}_{1}\right]}=5.33 \times 10^{2} \mathrm{M}^{-1}$$
Calculate the free energy required to synthesize ATP in a rat hepatocyte.

Niamat Khuda
Niamat Khuda
Numerade Educator
08:02

Problem 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 $(\mathrm{p}$ 539)
What does the isomerization step accomplish from a chemical perspective? (Hint: Consider what might happen if the $\mathrm{C}-\mathrm{C}$ bond cleavage were to proceed without the preceding isomerization.)

Prashant Bana
Prashant Bana
Numerade Educator
03:47

Problem 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:
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.)

Niamat Khuda
Niamat Khuda
Numerade Educator
06:28

Problem 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 glyceraldehyde 3 -phosphate react to form erythrose 4 -phosphate and fructose 6 -phosphate in a reaction catalyzed by transaldolase.
Draw a mechanism for this reaction (show electron-pushing arrows). (Hint: Take another look at aldol condensations, then consider the name of this enzyme.)

Lara Gossage
Lara Gossage
Numerade Educator
09:41

Problem 19

Recognizing Reaction Types For the following pairs of biomolecules, identify the type of reaction (oxidation-reduction, hydrolysis, isomerization, group transfer, or internal rearrangement) required to convert the first molecule to the second. In each case, indicate the general type of enzyme and cofactor(s) or reactants that would be required, and any other products that would result.

Eric Goldman
Eric Goldman
Numerade Educator
03:20

Problem 20

Effect of Structure on Group Transfer Potential Some invertebrates contain phosphoarginine. Is the standard free energy of hydrolysis of this molecule more similar to that of glucose 6 -phosphate or of ATP? Explain your answer.

Niamat Khuda
Niamat Khuda
Numerade Educator
02:28

Problem 21

Polyphosphate as a Possible Energy Source The standard free energy of hydrolysis of inorganic polyphosphate (polyP) is about $-20 \mathrm{kJ} / \mathrm{mol}$ for each $\mathrm{P}_{\mathrm{i}}$ released. We calculated in Worked Example $13-2$ that, in a cell, it takes about $50 \mathrm{kJ} / \mathrm{mol}$ of energy to synthesize ATP from ADP and $\mathrm{P}_{\mathrm{i}}$. Is it feasible for a cell to use polyphosphate to synthesize ATP from ADP? Explain your answer.

Niamat Khuda
Niamat Khuda
Numerade Educator
11:32

Problem 22

Daily ATP Utilization by Human Adults
(a) A total of $30.5 \mathrm{kJ} / \mathrm{mol}$ of free energy is needed to synthesize ATP from ADP and $\mathrm{P}_{\mathrm{i}}$ when the reactants and products are at $1 \mathrm{M}$ concentrations and the temperature is $25^{\circ} \mathrm{C}$ (standard state). Because the actual physiological concentrations of ATP, ADP, and $P_{i}$ are not $1 \mathrm{M},$ and the temperature is $37^{\circ} \mathrm{C},$ the free energy required to synthesize ATP under physiological conditions is different from $\Delta G^{\prime \circ} .$ 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 $5.0 \mathrm{mM},$ respectively.
(b) $\mathrm{A} 68 \mathrm{kg}(150 \mathrm{lb})$ adult requires a caloric intake of $2,000 \mathrm{kcal}(8,360 \mathrm{kJ})$ of food per day (24 hours). 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 hours. 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.

Niamat Khuda
Niamat Khuda
Numerade Educator
07:02

Problem 23

Rates of Turnover of $\gamma$ and $\beta$ Phosphates of ATP If a small amount of ATP labeled with radioactive phosphorus in the terminal position, $\left[\gamma \text { - }^{32} \mathrm{P}\right]$ ATP, is added to a yeast extract, about half of the $^{32} \mathrm{P}$ activity is found in $\mathrm{P}_{\mathrm{i}}$ within a few minutes, but the concentration of ATP remains unchanged. Explain. If the same experiment is carried out using ATP labeled with $^{32} \mathrm{P}$ in the central position, $\left[\beta-^{32} \mathrm{P}\right] \mathrm{ATP},$ the $^{32} \mathrm{P}$ does not appear in $\mathrm{P}_{\mathrm{i}}$ within such a short time. Why?

Niamat Khuda
Niamat Khuda
Numerade Educator
05:13

Problem 24

Cleavage of ATP to AMP and PP $_{\mathbf{i}}$ during Metabolism Synthesis of the activated form of acetate (acetyl-CoA) is carried out in an ATP-dependent process:
$$\text { Acetate }+\mathrm{CoA}+\mathrm{ATP} \rightarrow \text { acetyl-Co } \mathrm{A}+\mathrm{AMP}+\mathrm{PP}_{\mathrm{i}}$$
(a) The $\Delta G^{\prime \circ}$ for hydrolysis of acetyl-CoA to acetate and CoA is $-32.2 \mathrm{kJ} / \mathrm{mol}$ and that for hydrolysis of ATP to AMP and PP is -30.5 kJ/mol. Calculate $\Delta G^{\prime \circ}$ for the ATPdependent synthesis of acetyl-CoA.
(b) Almost all cells contain the enzyme inorganic pyrophosphatase, which catalyzes the hydrolysis of $\mathrm{PP}_{\mathrm{i}}$ to $\mathrm{P}_{\mathrm{i}}$. What effect does the presence of this enzyme have on the synthesis of acetyl-CoA? Explain.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:57

Problem 25

Energy for $\mathbf{H}^{+}$ 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 $37^{\circ} \mathrm{C}$

Ronald Prasad
Ronald Prasad
Numerade Educator
13:20

Problem 26

Standard Reduction Potentials The standard reduction potential, $E^{\prime \circ},$ of any redox pair is defined for the half-cell reaction:
$$Oxidizing agent $+n$ electrons $\rightarrow$ reducing agent$$
The $E^{\prime \circ}$ values for the $\mathrm{NAD}^{+} / \mathrm{NADH}$ and pyruvate/lactate conjugate redox pairs are -0.32 $\mathrm{V}$ and $-0.19 \mathrm{V},$ 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 $\mathrm{pH} 7$ and $25^{\circ} \mathrm{C}$ in which direction will the following reaction proceed?
$$\text { Pyruvate }+\mathrm{NADH}+\mathrm{H}^{+} \rightleftharpoons \text { lactate }+\mathrm{NAD}^{+}$$
(d) What is the standard free-energy change $\left(\Delta G^{\prime \circ}\right)$ for the conversion of pyruvate to lactate?
(e) What is the equilibrium constant $\left(\boldsymbol{K}_{\mathbf{e q}}^{\prime}\right)$ for this reaction?

Niamat Khuda
Niamat Khuda
Numerade Educator
04:37

Problem 27

Energy Span of the Respiratory Chain Electron transfer in the mitochondrial respiratory chain may be represented by the net reaction equation
$$\mathrm{NADH}+\mathrm{H}^{+}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\mathrm{NAD}^{+}$$
(a) Calculate $\Delta E^{\prime \circ}$ for the net reaction of mitochondrial electron transfer. Use $E^{\prime \circ}$ values in Table $13-7$
(b) Calculate $\Delta G^{\prime \circ}$ 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 $52 \mathrm{kJ} / \mathrm{mol} ?$

Niamat Khuda
Niamat Khuda
Numerade Educator
05:08

Problem 28

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 $\mathrm{NAD}^{+}$ and $\mathrm{NADH}$ at $\mathrm{pH} 7.0$ and $25^{\circ} \mathrm{C}$, with reference to a half-cell of $E^{\prime \circ} 0.00$ $\mathrm{V}$
(a) $1.0 \mathrm{mM} \mathrm{NAD}^{+}$ and $10 \mathrm{mM}$ NADH
(b) $1.0 \mathrm{mM} \mathrm{NAD}^{+}$ and $1.0 \mathrm{mM}$ NADH
(c) $10 \mathrm{mM} \mathrm{NAD}^{+}$ and $1.0 \mathrm{mM}$ NADH

Niamat Khuda
Niamat Khuda
Numerade Educator
02:09

Problem 29

Electron Affinity of Compounds List the following in order of increasing tendency to accept electrons:
(a) $a$ -ketoglutarate $+\mathrm{CO}_{2}$ (yielding isocitrate)
(b) oxaloacetate;
(c) $\mathrm{O}_{2}$
(d) $\mathrm{NADP}^{+}$

Niamat Khuda
Niamat Khuda
Numerade Educator
11:52

Problem 30

Direction of Oxidation-Reduction Reactions Which of the following reactions would you expect to proceed in the direction shown, under standard conditions, in the presence of the appropriate enzymes?
(a) Malate $+\mathrm{NAD}^{+} \rightarrow$ oxaloacetate $+\mathrm{NADH}+\mathrm{H}^{+}$
(b) Acetoacetate $+\mathrm{NADH}+\mathrm{H}^{+} \rightarrow \beta$ -hydroxybutyrate $+\mathrm{NAD}^{+}$
(c) Pyruvate $+\mathrm{NADH}+\mathrm{H}^{+} \rightarrow$ lactate $+\mathrm{NAD}^{+}$
(d) Pyruvate $+\beta$ -hydroxybutyrate $\rightarrow$ lactate $+$ acetoacetate
(e) Malate $+$ pyruvate $\rightarrow$ oxaloacetate $+$ lactate
(f) Acetaldehyde + succinate $\rightarrow$ ethanol + fumarate

Niamat Khuda
Niamat Khuda
Numerade Educator
02:43

Problem 31

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 molecules 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 Muller 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 :
(A) Astrocyte Oligodendrocyte
(B) Astrocyte Oligodendrocyte
The figure legend reads: "Model of the unidirectional diffusion of dye between coupled oligodendrocytes 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 entropy of the system if one started with equal concentrations of dye in the astrocyte and oligodendrocyte 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.

Rashmi Sinha
Rashmi Sinha
Numerade Educator