Let’s see how the membrane potential can be established in the first place. Later, we will see how we can calculate and even manipulate the value of the membrane potential. We will start by considering a hypothetical example of two solution compartments separated by a membrane. This example can later be extended to understand how the membrane potential is established in real cells. Assume that we have two solution compartments that are separated by a membrane, whose lipid and protein compositions can be altered depending on the unique cases considered (see Figs. 1–3). Because we want to understand the situation in biological cells, we will designate one compartment as the inside or intracellular compartment (i in Figs. 1–3) and another as the outside or extracellular compartment (o in Figs. 1–3). These compartments represent the intracellular and extracellular fluid compartments, respectively. In the intracellular compartment (i), we place a solution of 150 mM KCl. In the extracellular compartment (o), we have 5 mM KCl. Finally, we will set up a simple apparatus to measure the potential difference (membrane potential of V_m) across the membrane that separates the two compartments.

Here, our focus will be on K⁺ ions, and we have chosen these concentrations to resemble the physiological concentrations of K⁺ in intracellular and extracellular solutions. Also for the sake of this exercise, we will ignore osmotic forces that are caused by the differences in the concentration of solutes across the membrane. In real cells, the osmolarity of the intracellular and extracellular solutions must, of course, be the same in order to avoid cell swelling or shrinkage. Also, please remember that in real cells, the majority of intracellular anions are in fact carried on large proteins and, moreover, the extracellular Cl⁻ concentration is much higher (~110 mM). However, the KCl solutions used here have been chosen to simplify the numbers and, as we will see later in this lecture, the argument used here applies directly to real cells.

Let's first consider the situation where the membrane separating the two compartments is a pure lipid bilayer (i.e., devoid of membrane proteins) (Fig. 1). In this case, the voltage difference between the two compartments (i.e., the membrane potential) is zero. This is because in each compartment electroneutrality is perfectly obeyed. That is in each compartment, the sum of positive charges equals the sum of negative charges. Although, the KCl concentration is higher in the intracellular compartments, no diffusion of ions can occur due to the fact that no ionic pathways are present in the membrane for K⁺ and Cl⁻. Remember that ions cannot cross biological membranes without the aid of membrane transport proteins. Therefore, there can be no charge separation across the membrane and, therefore, there is no potential difference between the two compartments (Fig. 1). Although there is a concentration gradient, because there are no ionic pathways to allow the passage of ions, charge separation across the membrane cannot be established. Remember that a potential difference can only be established if there is charge separation across the membrane.

We now introduce large holes in the lipid bilayer that separates the two compartments (Fig. 2). Assume that the holes are large in diameter and non-selective, which will allow all solutes to pass through. In this case, both K⁺ and Cl⁻ diffuse from compartment i to o down their respective concentration gradients. In order to maintain electroneutrality, the same number of K⁺ and Cl⁻ move together from i to o. The movement of K⁺ and Cl⁻ from i to o will continue until equilibrium is established. At equilibrium, the KCl concentration will be the same in both compartments, and will be the algebraic average of the initial values ([KCl]_i = [KCl]_o = 77.5 mM). Again, electroneutrality is maintained in both compartments. No charge separation has taken place across the lipid bilayer and, thus, no voltage difference exists across the membrane. It is emphasized again that a potential difference can only be established if there is charge separation across the membrane.

We will now move to a scenario that is closer to what is seen in real cells (Fig. 3). If we insert K⁺-selective channels in the membrane, because of the concentration gradient, K⁺ ions will tend to move from compartment i to o. Therefore, there is a chemical gradient that causes K⁺ ions to move down their concentration gradient from compartment i to o. Cl⁻ cannot follow because the channels are highly selective for K⁺ and do not allow Cl⁻ to pass. Therefore, movement of K⁺ from i to o leads to charge separation across the membrane. Every K⁺ ion that moves from i to o adds a net positive charge to the extracellular side of the membrane and, simultaneously, leaves behind a net negative charge on the intracellular side of the membrane (Fig. 3A). This charge separation leads to the generation of an electrical gradient (i.e., electric field), which forms the basis for the establishment of the membrane potential. In this example, compartment i is negative with respect to compartment o. Note that the electrical gradient did not exist initially (prior to charge separation across the membrane), and only came into existence as K⁺ diffusion from i to o led to charge separation across the membrane (Fig. 3B). Because of the magnitude of the chemical gradient, K⁺ diffusion from i to o continues leading to excess positive charge on the extracellular side of the membrane and excess negative charge on the intracellular side of the membrane. As more K⁺ ions diffuse, the size of the electrical gradient increases. Ultimately, a point will be reached when diffusion of K⁺ ions from i to o down its concentration gradient is opposed by the excess positive and negative charges on the membrane (i.e., repelled by excess positive charge on opposite side of membrane and attracted by excess negative charge on the same side of the membrane). Thus, at some point the size of the electrical gradient is large enough to exactly balance and stop the net movement of K⁺ from i to o down its concentration gradient (Fig. 3B).

It is important to note that prior to the opening of the K⁺ channels, no potential difference existed between the two compartments (i.e., V_m = 0 mV). As soon as the first K⁺ ion diffuses from i to o, a small membrane potential is established, which grows in size until the magnitude of the electrical gradient equals the magnitude of the chemical gradient (Fig. 3, B and C). When the electrical gradient exactly balances the chemical gradient, K⁺ is said to be at electrochemical equilibrium. Based on the intracelluar and extracellular concentrations of K⁺ used in this example, the final (i.e., equilibrium) value of the membrane potential is about −90 mV (intracellular side negative with respect to the extracellular side). In the next two sections of this lecture, we will learn how to calculate the value of the membrane potential.

To summarize, while K⁺ is diffusing from i to o down its concentration gradient, a negative membrane potential is being established that favors the retention of K⁺ in compartment i. Therefore, two forces are now acting on K⁺:

At some point, a large enough electrical gradient will be established such that it will completely balance the chemical gradient driving K⁺ from compartment i to o. At this point, K⁺ is said to be in thermodynamic equilibrium. The membrane potential that is reached at the thermodynamic equilibrium is called the thermodynamic equilibrium potential (V_eq.) for K⁺. The equilibrium potential is the potential at which the chemical and the electrical forces acting on K⁺ ions exactly balance one another. At equilibrium, there is no net movement of K⁺ between the two compartments. Because we are considering K⁺, this potential is referred to as the K⁺ equilibrium potential, and is designated V_K.

The above example considered a situation where there were only K⁺-selective channels in the membrane. As a result, the established membrane potential (V_m) is at the K⁺ equilibrium potential (V_K). We can follow a similar logic and define the equilibrium potential for Na⁺ (V_Na), Cl⁻ (V_Cl), Ca²⁺ (V_Ca), etc. The important point to remember is that the membrane potential would only be at the equilibrium potential for any given ion if there are selective channels in the membrane only for that particular ion. Of course, the channels must be open to allow the passage of the ion. In real cells, the situation is more complicated because many different types of ions channels exist in the membrane. We will consider this case in a later section of this lecture (see In Real Cells, Multiple Ions Contribute to the Membrane Potential).

While we have focused on a hypothetical system in which only K⁺ ions contribute to the membrane potential, we will see shortly that K⁺ also plays the dominant role in most cells (with smaller contributions by Cl⁻ and Na⁺ ions). Before we discuss the situation in real cells, our next goal is to gain a quantitative understanding of the value of the membrane potential.