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 \(=+30.5 \mathrm{kJ} / \mathrm{mol} .\)

Short Answer

Expert verified
a. The standard free energy change (\(\Delta G^{\circ '\}\)) for this reaction is -217 kJ/mol. b. The equilibrium constant (\(K'_{eq}\)) for this reaction is 6.9*10^{38}. c. The maximum ratio of [ATP]/[ADP] attainable by oxidative phosphorylation under these conditions, when \([P_{i}]\) equals 3 mM, is 1.03 × 10^5

Step by step solution

01

Write the balanced equation

The balanced equation for the reduction of molecular oxygen by reduced cytochrome c is: \[4 \text{cyt} c(\text{Fe}^{2+}) + O_2 + 4H^+ \rightarrow 4 \text{cyt} c(\text{Fe}^{3+}) + 2H_2O\]
02

Calculate the standard free energy change

The standard free energy change (\(\Delta G^{\circ \prime}\)) can be calculated from the standard reduction potentials using the equation \(\Delta G^{\circ \prime} = -nF\Delta E^{\circ \prime}\)Here, n equals 4 (the number of electrons transferred in the reaction), F stands for Faraday's constant (which is approximately 96,485 C·mol−1), and \(\Delta E^{\circ \prime}\) equals \(0.816V(1/2O_2 /H_2O) - 0.254V(cyt c(Fe^{3+}) /cyt c(Fe^{2+})) = 0.562 V\). Therefore, \[\Delta G^{\circ \prime} = -4 * 96,485 * 0.562 = -217 kJ / mol\]
03

Calculate the equilibrium constant

The equilibrium constant (\(K'_{eq}\)) can be calculated from the standard free energy change using the relationship between free energy and equilibrium constants. Using the equation \(\Delta G^{\circ' } = -RT \ln K'_{eq}\), where R is the ideal gas constant (8.314 J·K−1·mol−1) and T is the temperature in Kelvin (assume room temperature, 298K), first solve for \(\ln K'_{eq}\)\[\ln K'_{eq} = -\Delta G^{\circ' } / RT = 217,000 / (8.314 * 298) = 87.82\]Exponentiate to find \(K'_{eq}\)\[K'_{eq} = e^{87.82} = 6.9*10^{38}\]
04

Calculate the maximum ratio of [ATP]/[ADP]

Since 2 equivalents of ATP are produced per 1 equivalent of O2 reduced, and 60% of the energy released is captured in ATP synthesis, it implies that the energy captured by ATP synthesis can be calculated as\[\Delta G = \Delta G^{\circ \prime} * 0.6 / 2 = -65.1 kJ / mol ATP\]Now using this value, we can calculate the maximum attainable [ATP]/[ADP] using the phosphate potential. First solve for \(\Delta G_{P}\)\[ \Delta G_{P} = \Delta G^{\circ \prime} + RT \ln ([ADP][P_{i}] / [ATP])\]Rearrange to solve for [ATP]/[ADP]\[ [ATP]/[ADP] = e^((\Delta G_{P} - \Delta G^{\circ \prime})/RT) * [P_{i}]\]Input the known values\[ [ATP]/[ADP] = e^((30.5-(-65.1))/ RT) * 3 = 1.03 × 10^5\]

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Most popular questions from this chapter

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 \(=+30.5 \mathrm{kJ} / \mathrm{mol}\).)

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 \(=+30.5 \mathrm{kJ} / \mathrm{mol} .\) )

In problem 18 at the end of Chapter \(19,\) you might have calculated the number of molecules of oxaloacetate in a typical mitochondrion. What about protons? A typical mitochondrion can be thought of as a cylinder \(1 \mu \mathrm{m}\) in diameter and \(2 \mu \mathrm{m}\) in length. If the \(\mathrm{pH}\) in the matrix is \(7.8,\) how many protons are contained in the mitochondrial matrix?

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.

Considering that all other dehydrogenases of glycolysis and the TCA cycle use NADH as the electron donor, why does succinate dehydrogenase, a component of the TCA cycle and the electron transfer chain, use FAD as the electron acceptor from succinate, rather than \(\mathrm{NAD}^{+}\) ? Note that there are two justifications for the choice of FAD here-one based on energetics and one based on the mechanism of electron transfer for FAD versus \(\mathrm{NAD}^{+}\).

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