The Nernst Equation

 
In standard oxidation-reduction reactions you can usually tell whether a given compound will donate or receive electrons by looking at the standard reduction potential (ΔE°ʹ) [Oxidation-Reduction Reactions]. This is a big step toward understanding how electrons flow in biochemical reactions but we would like to know more about the energy of oxidation-reduction reactions since they are the fundamental energy-producing reactions in the cell.

The standard reduction potential for the transfer of electrons from one molecular species to another is related to the standard Gibbs free energy change (ΔG°ʹ) for the oxidation-reduction reaction by the equation

where n is the number of electrons transferred and ℱ (F) is Faraday’s constant (96.48 kJ V^-1 mol^-1). ΔE°ʹ is defined as the difference in volts between the standard reduction potential of the electron-acceptor system and that of the electron-donor system. The Δ (delta) symbol indicates a change or a difference between two values.

You may recall that electrons tend to flow from half-reactions with a more negative standard reduction potential to those with a more positive one. For example, in the pyruvate dehydrogenase reaction electrons flow from pyruvate (E°' = -0.48 V) to NAD⁺ (E°' = -0.32 V). We can calculate the change in standard reduction potentials; it's equal to +0.16 V [-0.32 - (-0.48) = +0.16].

Now we can calculate a standard Gibbs free energy change (ΔG°ʹ) for the electron transfer part of the pyruvate dehydrogenase reaction. Two electrons are transferred from pyruvate to NAD⁺ so the standard Gibbs free energy change is -31 kJ mol^-1 [-2(96.48)(0.16)]. This turns out to be a significant amount of energy that could be captured by the NADH molecule but you have to keep in mind that this is a standard Gibbs free energy change and conditions inside the cell are far from standard. The biggest difference is that standard Gibbs free energy changes are computed with equal concentrations of reactants and products at a concentration of 1M—about a thousand times higher than the concentrations inside the cell where, in addition, the concentrations of reactants and products are not equal.

Fortunately, we have a way of adjusting the values of the Gibbs free energy change and the change in the standard reduction potential to account for the actual concentrations inside the cell. The standard Gibbs free energy change is related to the equilibrium constant of a reaction K_eq by the equation

Just as the actual Gibbs free energy change for a reaction is related to the standard Gibbs free energy change by this equation, an observed difference in reduction potentials (ΔE) is related to the difference in the standard reduction potentials (ΔE°') by the Nernst equation.

By combining equations for ΔG°ʹ we get
For a reaction involving the oxidation and reduction of two molecules, A and B,
the Nernst equation is
where [A_ox] is the concentration of oxidized A inside the cell. The Nernst equation tells us the actual difference in reduction potential (ΔE) and not the artificial standard change in reduction potential (ΔE°ʹ).

At 298 K (25° C), this equation reduces to
where Q represents the ratio of the actual concentrations of reduced and oxidized species. To calculate the electromotive force of a reaction under nonstandard conditions, use the Nernst equation and substitute the actual concentrations of reactants and products. Keep in mind that a positive E value indicates that an oxidation-reduction reaction will have a negative value for the standard Gibbs free energy change.

The Nernst equation is very famous but it's actually not very useful. The problem is that many of the oxidation-reduction reactions take place within an enzyme complex such as the pyruvate dehydrogenase complex. The concentrations of the reactants and products are difficult to calculate under such conditions. That's why we usually use the standard reduction potentials instead of the actual reduction potentials, keeping in mind that these are only approximations of what goes on inside the cell.

Let's see what happens when we calculate the standard Gibbs free energy change for the reaction where NADH donates electrons to oxygen. Oxygen serves as an electron sink for getting rid of excess electrons [Oxidation-Reduction Reactions].

NAD⁺ is reduced to NADH in coupled reactions where electrons are transferred from a metabolite (e.g., pyruvate) to NAD⁺. The reduced form of the coenzyme (NADH) becomes a source of electrons in other oxidation-reduction reactions. The Gibbs free energy changes associated with the overall oxidation-reduction reaction under standard conditions can be calculated from the standard reduction potentials of the two half-reactions using the equations above.

As an example, let’s consider the reaction where NADH is oxidized and molecular oxygen is reduced. This represents the available free energy change during membrane-associated electron transport. This free energy is recovered in the form of ATP synthesis.

The two half-reactions from a table of standard reduction potentials are,

and
Since the NAD⁺ half-reaction has the more negative standard reduction potential, NADH is the electron donor and oxygen is the electron acceptor. The net reaction is
and the change in standard reduction potential is

Using the equations described above we get

What this tells us is that a great deal of energy can be released when electrons are passed from NADH to oxygen provided the conditions inside the cell resemble those for the standard reduction potentials (they do). The standard Gibbs free energy change for the formation of ATP from ADP + P_i is -32 kJ mol^-1 (the actual free-energy change is greater under the conditions of the living cell, it's about -45 kJ mol^-1). This strongly suggests that the energy released during the oxidation of NADH under cellular conditions is sufficient to drive the formation of several molecules of ATP. Actual measurements reveal that the oxidation of NADH can be connected to formation of 2.5 molecules of ATP giving us confidence that the theory behind oxidation-reduction reactions is sound.

[©Laurence A. Moran. Some of the text is from Principles of Biochemistry 4th ed. ©Pearson/Prentice Hall]