Problem 17 - Biochemistry

Question

Plastoquinone oxidation by cytochrome \(b c_{1}\) and cytochrome \(b_{i} f\) complexes apparently leads to the translocation of \(4^{+} / 2 e^{-} .\) If \(\mathscr{E}_{0}^{\prime}\) for cytochrome \(f=0.365 \mathrm{V} \text { (Table } 20.1)\) and \(\mathrm{E}_{\mathrm{o}}^{\prime}\) for \(\mathrm{PQ} / \mathrm{PQH}_{2}=0.07 \mathrm{V},\) calculate \(\Delta G\) for the coupled reaction: \\[2 h v+4 \mathrm{H}^{+}_{\mathrm{in}} \longrightarrow 4 \mathrm{H}_{\mathrm{out}}^{+}\\] (Assume a value of \(23 \mathrm{kJ} / \mathrm{mol}\) for the free energy change \((\Delta G)\) associated with moving protons from inside to outside.

Step-by-Step Solution

Answer

\(\Delta G_{total} = -33.86 kJ/mol\)

Step 1: Calculate the Redox Potential

The standard redox potential (\(E_{0}\)) for the overall reaction can be calculated by subtracting the \(\mathscr{E}_{0}^{\prime}\) of the electron donor (PQH2) from the \(\mathscr{E}_{0}^{\prime}\) of the electron acceptor (cytochrome f). Given: \(\mathscr{E}_{0}^{\prime}\) for cytochrome \(f\) = 0.365V, \(\mathscr{E}_{0}^{\prime}\) for PQ/PQH2 = 0.07V. So, the overall redox potential = 0.365V - 0.07V = 0.295V.

Step 2: Calculate the Free Energy Change due to Electron Transfer

The free energy change (\(\Delta G_{el}\)) due to electron transfer can be calculated using the Nernst equation: \(\Delta G = -nFE\). Where \(n\) is the number of electrons transferred (n=2), \(F\) is Faraday's constant (\(F = 96485.33212 C mol^{-1}\)), and \(E\) is the overall redox potential from Step 1. So, \(\Delta G_{el} = -2 * 96485.33212 C mol^{-1} * 0.295V = -56864.97 Joules/mol = -56.86 kJ/mol.\

Step 3: Calculate the Total Free Energy Change

The total change in Gibbs free energy (\(\Delta G_{total}\)) of the coupled reaction is the summation of the \(\Delta G_{el}\) and the change in Gibbs free energy associated with moving protons from inside to outside. Assume the latter as given: \(23 kJ/mol\). So, \(\Delta G_{total} = -56.86 kJ/mol + 23 kJ/mol = -33.86 kJ/mol.\

Key Concepts

Cytochrome Complexes

Cytochrome complexes play a pivotal role in the electron transport chain, which is a crucial part of cellular respiration. These complexes are a group of proteins found in the mitochondrial inner membrane of eukaryotes and the plasma membrane of prokaryotes.

Specifically, cytochrome complexes like cytochrome b_c1 and cytochrome b_i f are involved in the transfer of electrons from donors to acceptors. In the process, they contribute to the proton motive force by translocating protons across the membrane.

A typical example of their activity can be observed during the oxidation of plastoquinone (PQ), where these complexes facilitate the transfer of electrons and thereby support the synthesis of ATP. The oxidation of plastoquinone (PQ) by these complexes results in the translocation of protons, hence creating the proton gradient that drives ATP production.

Redox Potential

Redox potential, which is also known as reduction potential, is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. It is represented by the symbol E₀ or ℓ_E0' when conditions are at standard state.

Understanding the Redox Potential in Electron Transport

In the electron transport chain, redox potentials are important because they determine in what sequence the electrons move from one component to the next. The greater the difference in redox potential between the electron donor and the electron acceptor, the greater the ability of the reaction to release energy.

For example, in the exercise provided, plastoquinone (PQ) has a lower redox potential compared to cytochrome f, meaning that it has a lesser tendency to gain electrons. The difference in redox potential between PQ/PQH₂ and cytochrome f is crucial for calculating the Gibbs free energy change of the reaction.

Gibbs Free Energy

Gibbs free energy, denoted as ΔG, is a thermodynamic quantity that represents the maximum amount of work that can be performed by a thermodynamic process at constant temperature and pressure.

Implications in Biochemical Reactions

The sign of the Gibbs free energy change (ΔG) indicates whether a reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0). In the context of the plastoquinone oxidation exercise, a negative ΔG implies that the process is energetically favorable and can proceed without the need for additional energy.

This concept is directly applied when combining the free energy changes due to electron transfer, calculated using the Nernst equation, and the free energy change associated with the translocation of protons across a membrane. The overall free energy change for the coupled reaction provides insights into the efficiency of proton pumping and its impact on the synthesis of ATP in cells.