Now let’s examine the chemical and electrical gradients more closely so that we can gain a quantitative understanding of these two forces that act on ions. Our ultimate goal is to arrive at an equation that will allow us to calculate the value of the equilibrium potential based on the nature of ion (i.e., valence of the ion), as well as the ion concentration gradient that exists across the membrane. Here, we take a simplified approach to deriving this equation. A more rigorous approach is discussed under Derivation of the Nernst Equation. We will use K⁺ for this derivation and will later extend the equation to other ions. We begin by determining the free energy (ΔG) available from the chemical and electrical gradients. The chemical gradient (ΔG_Chemical) and the electrical gradient (ΔG_Electrical) can be defined as:

We should examine the Nernst equation closely in order to gain an intuitive understanding for the Nernst potential. First, it is reiterated here that for the Nernst potential to be established, selective channels must be present and open. Second, by examining the Nernst equation, it becomes immediately obvious that only three factors are important in determining the magnitude and direction of the Nernst potential. These three factors are (1) the concentration gradients, (2) the valence of the ionic species in question, and (3) temperature. If there is no concentration gradient across the plasma membrane, the ratio of the extracellular to intracellular concentration terms becomes 1. The natural logarithm of 1 is zero. Hence, there will be no potential difference across this membrane, even if the channels for the ion were fully open. Therefore, a concentration difference is essential in establishing a Nernst potential. The valence of the ion also influences the magnitude and direction of the Nernst potential for the ion. Note that the Nernst potential varies indirectly with the ionic valence. Temperature (T) also plays a small role in determining the magnitude of the Nernst potential. A few examples are presented below to show how the Nernst equation is used to determine the equilibrium potential for various ions.

For a typical mammalian cell in its natural environment (37 °C), the following ionic equilibrium potentials can be calculated. The Nernst Potential Calculator can be used to perform these calculations.

If there are only K⁺ channels in a cell, then V_m in this cell will be the same as the K⁺ equilibrium potential (V_K) which can be obtained from the Nernst potential for K⁺. Therefore, in this cell, V_m = V_rest = V_K, which is what you expect because K⁺ distributes itself across the membrane according to the Nernst equation which describes the situation at equilibrium (of course, the K⁺ channels have to be open to allow K⁺ to redistribute itself across the membrane according to the chemical and electrical potential gradients). At V_K, there is no net movement of K⁺ across the membrane. Similarly, if there are only Na⁺ channels in the cell (and are open), at equilibrium, V_m = V_rest = V_Na. If there are only Cl⁻ channels in the cell (and are open), at equilibrium, V_m = V_rest = V_Cl.

If there are more than one type of channels that are open at any given time, the situation is slightly more complex (see next section for details). Now the resting potential can no longer be described as an equilibrium potential because no ion is at equilibrium (V_m = V_rest ≠ V_eq.). This is because many ions are contributing to the resting potential, and the final value of the resting potential will depend on the concentration gradients and the relative membrane permeabilities of the ions in the system. When multiple ions are present, each ion is moving down its own electrochemical potential gradient. In this case, the system is said to be at steady-state. Although there are exceptions, in most mammalian cells, the major ions contributing to V_rest are K⁺, Na⁺, and Cl⁻. In the next section, we will describe how different ions contribute to the membrane potential in real cells.