Problem 16 - Biochemistry: Concepts and Connections

Question

(a) Calculate the standard free energy change as a pair of electrons is transferred from succinate to molecular oxygen in the mitochondrial respiratory chain. (b) Based on your answer in part a, calculate the maximum number of protons that could be pumped out of the matrix into the intermembrane space as these electrons are passed to oxygen. Assume \(25^{\circ} \mathrm{C}, \Delta \mathrm{pH}=1.4\); \(\Delta \psi=0.175 \mathrm{~V}\) (matrix negative). (c) At which site(s) are these protons pumped?

Step-by-Step Solution

Answer

(a) \(-151.34\, kJ/mol\); (b) Maximum 8 protons; (c) Protons pumped at Complexes III and IV.

Step 1: Calculate Standard Free Energy Change

The standard free energy change for the transfer of electrons can be calculated using the Nernst equation: \[\Delta G^0' = -nF\Delta E^0' \]where \(n\) is the number of moles of electrons transferred, \(F\) is Faraday’s constant \((96,480\, C/mol)\), and \(\Delta E^0'\) is the standard reduction potential difference between the half-reactions. For the transfer of electrons from succinate to oxygen, the redox potentials are:- Succinate to Fumarate: \(E^0' = +0.031 \) V- Oxygen to Water: \(E^0' = +0.816 \) VThus, \(\Delta E^0' = E_{acceptor}^0' - E_{donor}^0' = 0.816\, V - 0.031\, V = 0.785\, V\).Substituting these values into the Nernst equation, \(\Delta G^0' = -2 \times 96,480\, C/mol \times 0.785\, V = -151,344\, J/mol\) or \(-151.34\, kJ/mol\).

Step 2: Calculate Maximum Number of Protons Pumped

The energy requirement for pumping protons can be calculated using the equation: \[\Delta G = 2.3RT\Delta pH + nF\Delta \psi\]where \( R = 8.31 \text{ J/mol}\cdot\text{K} \), \( T = 298 \text{ K}\) (\(25^\circ C\)), \( n \) is the moles of protons, \( \Delta \psi = 0.175 \text{ V}\).To find the number of protons, equate this to the \(\Delta G^0'\) found from Step 1: \[-151,344 = 2.3 \times 8.31 \times 298 \times 1.4 + n \times 96,480 \times 0.175\]Solving for \(n\), we get the approximation:\[-151,344 = 7962.3 + 16,884n\]Solving, \( n \approx 8.5 \). Since partial protons are not feasible, anticipate a max of 8 protons.

Step 3: Determine Sites of Proton Pumping

In the mitochondrial respiratory chain, protons are pumped at complexes I, III, and IV. Since electrons from succinate feed into complex II and then move onto component III (cytochrome c oxidase), the sites of pumping associated with this transfer are complexes III and IV. Therefore, the electrons from succinate effectively lead to proton pumping majorly at complexes III and IV.

Key Concepts

Standard Free Energy Change

Standard free energy change is a vital concept in understanding biochemical processes, particularly in the mitochondrial electron transport chain. It is denoted by \( \Delta G^0' \). This measure indicates the amount of energy available from a reaction under standard conditions to do work. In biological systems, it helps predict which reactions are energetically favorable and how they can drive various cellular functions.
The formula used is:\[ \Delta G^0' = -nF\Delta E^0' \]

• \( n \) is the number of moles of electrons transferred.
• \( F \) represents Faraday's constant, \( 96,480 \text{ C/mol} \).
• \( \Delta E^0' \) is the standard reduction potential difference between the electron acceptor and donor.

The calculation of \( \Delta G^0' \) tells us how much energy can be harnessed when electrons move from a source, like succinate, to an acceptor, such as oxygen, within the mitochondria.

Proton Gradient

The proton gradient is crucial for ATP synthesis in mitochondrial function. It results from the pumping of protons (H⁺ ions) across the mitochondrial membrane, creating a concentration and electrical gradient. This gradient is essential, as it represents stored potential energy that can be converted into ATP by ATP synthase.
The formation of the proton gradient involves:

• The contribution of several mitochondrial complexes (I, III, IV) that pump protons from the matrix to the intermembrane space.
• Creating a higher concentration of protons outside the inner mitochondrial membrane.

This gradient enables the mitochondria to act efficiently as an energy powerhouse. Moreover, understanding the energy dynamics across the membrane potential and pH gradient can give insights into how efficient and powerful this energy conversion process is. By tying the proton transport process to changes in standard free energy, we can predict how many protons could be pumped for a given amount of electron transfer.

Nernst Equation

The Nernst equation is a fundamental formula used to calculate the reduction potential of a chemical reaction under non-standard conditions. In the context of mitochondrial electron transport, it aids in finding the difference in redox potential that drives electron flow.
The standard Nernst equation for a half-reaction is written as:\[ E = E^0' - \frac{RT}{nF} \ln \left( \frac{[Products]}{[Reactants]} \right) \]
Here,

• \( E \) is the cell potential under non-standard conditions.
• \( R \) is the universal gas constant, \( 8.31 \text{ J/mol K} \).
• \( T \) denotes the temperature in Kelvin.
• \( n \) represents the number of moles of electrons involved.
• \( F \) is Faraday's constant.

Understanding and applying the Nernst equation allows us to adjust the standard potential for the actual cellular environment, calculating more accurate free energy changes in biological systems.

Redox Potential

Redox potential, often represented as \( E^0' \), is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. This concept is fundamental in the electron transport chain because it dictates the direction of electron flow between different molecular species.
In biological systems, each component of the electron transport chain has its redox potential. With:

• Molecules with a higher \( E^0' \) accepting electrons more readily.
• Electrons moving from molecules with lower \( E^0' \) to those with higher \( E^0' \).

For example, electrons move from succinate, having a lower redox potential, to oxygen, which has a higher redox potential. Recognizing how these potentials drive electron flow is essential for understanding how energy is efficiently transferred and transformed in cellular respiration.