Chapter 20

For the following redox reaction, \\[ \mathrm{NAD}^{+}+2 \mathrm{H}^{+}+2 e^{-} \longrightarrow \mathrm{NADH}+\mathrm{H}^{+} \\] suggest an equation (analogous to Equation 20.12 ) that predicts the pH dependence of this reaction, and calculate the reduction potential for this reaction at \(\mathrm{pH} 8\)

A wealthy investor has come to you for advice. She has been approached by a biochemist who seeks financial backing for a company that would market dinitrophenol and dicumarol as weight-loss medications. The biochemist has explained to her that these agents are uncouplers and that they would dissipate metabolic energy as heat. The investor wants to know if you think she should invest in the biochemist's company. How do you respond?

a. What is the standard free energy change \(\left(\Delta G^{\circ}\right)\) for the reduction of coenzyme \(\mathrm{Q}\) by \(\mathrm{NADH}\) as carried out by Complex \(\mathrm{I}\) (NADH-coenzyme Q reductase) of the electron-transport pathway if \(\mathscr{E}_{\mathrm{o}}^{\prime}\left(\mathrm{NAD}^{+} / \mathrm{NADH}\right)=-0.320 \mathrm{V}\) and \(\mathscr{E}_{\mathrm{o}}^{\prime}\left(\mathrm{CoQ} / \mathrm{CoQH}_{2}\right)=\) \(+0.060 \mathrm{V}\) b. What is the equilibrium constant \(\left(K_{\mathrm{eq}}\right)\) for this reaction? c. Assume that (1) the actual free energy release accompanying the NADH- coenzyme Q reductase reaction is equal to the amount released under standard conditions (as calculated in part a \(),(2)\) this energy can be converted into the synthesis of ATP with an efficiency \(=0.75\) (that is, \(75 \%\) of the energy released upon NADH oxidation is captured in ATP synthesis), and (3) the oxidation of 1 equivalent of NADH by coenzyme Q leads to the phosphorylation of 1 equivalent of ATP. Under these conditions, what is the maximum ratio of [ATP]/ \([\mathrm{ADP}]\) attainable by oxidative phosphorylation when \(\left[\mathrm{P}_{\mathrm{i}}\right]=1 \mathrm{m} M ?\) (Assume \(\Delta G^{\circ \prime}\) for ATP synthesis \(=+30.5 \mathrm{kJ} / \mathrm{mol}\).)

Consider the oxidation of succinate by molecular oxygen as carried out via the electron-transport pathway \\[ \text { Succinate }+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \text { fumarate }+\mathrm{H}_{2} \mathrm{O} \\] a. What is the standard free energy change \(\left(\Delta G^{\circ}\right)\) for this reaction if \\[ \mathscr{E}_{\mathrm{o}}^{\prime}(\mathrm{Fum} / \mathrm{Succ})=+0.031 \mathrm{V} \text { and } \mathscr{E}_{\mathrm{o}}^{\prime}\left(\frac{1}{2} \mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}\right)=+0.816 \mathrm{V} \\] b. What is the equilibrium constant \(\left(K_{\mathrm{eq}}\right)\) for this reaction? c. Assume that (1) the actual free energy release accompanying succinate oxidation by the electron-transport pathway is equal to the amount released under standard conditions (as calculated in part a \(),(2)\) this energy can be converted into the synthesis of ATP with an efficiency \(=0.7\) (that is, \(70 \%\) of the energy released upon succinate oxidation is captured in ATP synthesis), and (3) the oxidation of 1 succinate leads to the phosphorylation of 2 equivalents of ATP. Under these conditions, what is the maximum ratio of [ATP]/ [ADP] attainable by oxidative phosphorylation when \(\left[\mathrm{P}_{\mathrm{i}}\right]=1 \mathrm{m} M ?\) (Assume \(\Delta G^{\circ \prime}\) for ATP synthesis \(=+30.5 \mathrm{kJ} / \mathrm{mol} .\) )

Consider the oxidation of NADH by molecular oxygen as carried out via the electron-transport pathway \\[ \mathrm{NADH}+\mathrm{H}^{+}+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{NAD}^{+}+\mathrm{H}_{2} \mathrm{O} \\] a. What is the standard free energy change \(\left(\Delta G^{\circ}\right)\) for this reaction if \(\mathscr{E}_{\mathrm{o}}^{\prime}\left(\mathrm{NAD}^{+} / \mathrm{NADH}\right)=-0.320 \mathrm{V}\) and \(\mathscr{E}_{\mathrm{o}}^{\prime}\left(\mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}\right)=\) \\[ +0.816 \mathrm{V} \\] b. What is the equilibrium constant \(\left(K_{\mathrm{cq}}\right)\) for this reaction? c. Assume that (1) the actual free energy release accompanying NADH oxidation by the electron-transport pathway is equal to the amount released under standard conditions (as calculated in part \(a),(2)\) this energy can be converted into the synthesis of ATP with an efficiency \(=0.75\) (that is, \(75 \%\) of the energy released upon NADH oxidation is captured in ATP synthesis), and (3) the oxidation of 1 NADH leads to the phosphorylation of 3 equivalents of ATP. Under these conditions, what is the maximum ratio of [ATP]/ \([\mathrm{ADP}]\) attainable by oxidative phosphorylation when \(\left[\mathrm{P}_{\mathrm{i}}\right]=2 \mathrm{m} M ?\) (Assume \(\Delta G^{\circ \prime}\) for ATP synthesis \(=+30.5 \mathrm{kJ} / \mathrm{mol}\).)

Write a balanced equation for the reduction of molecular oxygen by reduced cytochrome \(c\) as carried out by Complex IV (cytochrome oxidase \()\) of the electron-transport pathway. a. What is the standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for this reaction if \(\Delta \mathscr{E}_{\mathrm{o}}^{\prime}\) cyt \(c\left(\mathrm{Fe}^{3+}\right) / \mathrm{cyt} c\left(\mathrm{Fe}^{2+}\right)=+0.254\) volts and \\[ \mathscr{E}_{\mathrm{o}}^{\prime}\left(\frac{1}{2} \mathrm{O}_{2} / \mathrm{H}_{2} \mathrm{O}\right)=0.816 \text { volts } \\] b. What is the equilibrium constant \(\left(K_{\mathrm{eq}}\right)\) for this reaction? c. Assume that (1) the actual free energy release accompanying cytochrome \(c\) oxidation by the electron-transport pathway is equal to the amount released under standard conditions (as calculated in part a), (2) this energy can be converted into the synthesis of ATP with an efficiency \(=0.6\) (that is, \(60 \%\) of the energy released upon cytochrome \(c\) oxidation is captured in ATP synthesis), and (3) the reduction of 1 molecule of \(\mathrm{O}_{2}\) by reduced cytochrome \(c\) leads to the phosphorylation of 2 equivalents of ATP. Under these conditions, what is the maximum ratio of [ATP]/ \([\mathrm{ADP}]\) attainable by oxidative phosphorylation when \(\left[\mathrm{P}_{\mathrm{i}}\right]=3 \mathrm{m} M ?\) (Assume \(\Delta G^{\circ}\) for ATP synthesis \(=+30.5 \mathrm{kJ} / \mathrm{mol} .\)

The standard reduction potential for (NAD \(^{+} / \mathrm{NADH}\) ) is \(-0.320 \mathrm{V}\) and the standard reduction potential for (pyruvate/lactate) is \(-0.185 \mathrm{V}\) a. What is the standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for the lactate dehydrogenase reaction: \\[ \mathrm{NADH}+\mathrm{H}^{+}+\text {pyruvate } \longrightarrow \text { lactate }+\mathrm{NAD}^{+} \\] b. What is the equilibrium constant \(\left(K_{\mathrm{eq}}\right)\) for this reaction? c. If [pyruvate] \(=0.05 \mathrm{m} M \text { and [lactate }]=2.9 \mathrm{m} M\) and \(\Delta G\) for the lactate dehydrogenase reaction \(=-15 \mathrm{kJ} / \mathrm{mol}\) in erythrocytes, what is the \(\left[\mathrm{NAD}^{+}\right] /[\mathrm{NADH}]\) ratio under these conditions?

Assume that the free energy change \((\Delta G)\) associated with the movement of 1 mole of protons from the outside to the inside of a bacterial cell is \(-23 \mathrm{kJ} / \mathrm{mol}\) and \(3 \mathrm{H}^{+}\) must cross the bacterial plasma membrane per ATP formed by the bacterial \(\mathrm{F}_{1} \mathrm{F}_{0}-\mathrm{ATP}\) synthase. ATP synthesis thus takes place by the coupled process: $$3 \mathrm{H}_{\mathrm{out}}^{+}+\mathrm{ADP}+\mathrm{P}_{\mathrm{i}} \rightleftharpoons 3 \mathrm{H}_{\mathrm{in}}^{+}+\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O}$$ a. If the overall free energy change \(\left(\Delta G_{\text {overall }}\right)\) associated with ATP synthesis in these cells by the coupled process is \(-21 \mathrm{kJ} / \mathrm{mol}\), what is the equilibrium constant \(\left(K_{\mathrm{eq}}\right)\) for the process? b. What is \(\Delta G_{\text {synthesis }},\) the free energy change for ATP synthesis, in these bacteria under these conditions? c. The standard free energy change for ATP hydrolysis ( \(\Delta G^{\text {o' }}\) hydrolysis) is \(-30.5 \mathrm{kJ} /\) mol. If \(\left[\mathrm{P}_{\mathrm{i}}\right]=2 \mathrm{m} M\) in these bacterial cells, what is the \([\mathrm{ATP}] /[\mathrm{ADP}]\) ratio in these cells?

Describe in your own words the path of electrons through the \(\mathrm{Q}\) cycle of Complex III.

In the course of events triggering apoptosis, a fatty acid chain of cardiolipin undergoes peroxidation to release the associated cytochrome \(c .\) Lipid peroxidation occurs at a double bond. Suggest a mechanism for the reaction of hydrogen peroxide with an unsaturation in a lipid chain, and identify a likely product of the reaction.