As explained earlier, due to the action of the Na+-K+ pump, there is little Na+ inside the cell, and other intracellular inorganic cations have to be plentiful enough to balance the charge carried by the cell’s fixed anions—the negatively charged organic molecules that are confined inside the cell. This balancing role is performed largely by K+, which is actively pumped into the cell by the Na+K+ pump and can also move freely in or out through the K+ leak channels in the plasma membrane. Because of the presence of these channels, K+ comes almost to equilibrium, where an electrical force exerted by an excess of negative charges attracting K+ into the cell balances the tendency of K+ to leak out down its concentration gradient. The membrane potential (of the plasma membrane) is the manifestation of this electrical force, and we can calculate its equilibrium value from the steepness of the K+ concentration gradient. The following argument may help to make this clear.
Suppose that initially there is no voltage gradient across the plasma membrane (the membrane potential is zero) but the concentration of K+ is high inside the cell and low outside. K+ will tend to leave the cell through the K+ leak channels, driven by its concentration gradient. As K+ begins to move out, each ion leaves behind an unbalanced negative charge, thereby creating an electrical field, or membrane potential, which will tend to oppose the further efflux of K+. The net efflux of K+ halts when the membrane potential reaches a value at which this electrical driving force on K+ exactly balances the effect of its concentration gradient—that is, when the electrochemical gradient for K+ is zero. Although Cl– ions also equilibrate across the membrane, the membrane potential keeps most of these ions out of the cell because their charge is negative.
The equilibrium condition, in which there is no net flow of ions across the plasma membrane, defines the resting membrane potential for this idealized cell. A simple but very important formula, the Nernst equation, quantifies the equilibrium condition and, as explained in Panel 11–1, makes it possible to calculate the theoretical resting membrane potential if we know the ratio of internal and external ion concentrations. As the plasma membrane of a real cell is not exclusively permeable to K+ and Cl–, however, the actual resting membrane potential is usually not exactly equal to that predicted by the Nernst equation for K+ or Cl–.
The Resting Potential Decays Only Slowly When the Na+-K+ Pump Is Stopped
Movement of only a minute number of inorganic ions across the plasma membrane through ion channels suffices to set up the membrane potential. Thus, we can think of the membrane potential as arising from movements of charge that leave ion concentrations practically unaffected and result in only a very slight discrepancy in the number of positive and negative ions on the two sides of the membrane (Figure 11–23). Moreover, these movements of charge are generally rapid, taking only a few milliseconds or less.
Consider the change in the membrane potential in a real cell after the sudden inactivation of the Na+-K+ pump. A slight drop in the membrane potential occurs immediately. This is because the pump is electrogenic and, when active, makes a
The fow of any inorganic ion through a membrane channel is driven by the electrochemical gradient for that ion. This gradient represents the combination of two infuences: the voltage gradient and the concentration gradient of the ion across the membrane. When these two infuences just balance each other, the electrochemical gradient for the ion is zero, and there is no net fow of the ion through the channel. The voltage gradient (membrane potential) at which this equilibrium is reached is called the equilibrium potential for the ion. It can be calculated from an equation that will be derived below, called the Nernst equation.
The Nernst equation is V = RT In Co zF Ci
V = the equilibrium potential in volts (internal
Co and Ci = outside and inside concentrations of the ion, respectively
R = the gas constant (8.3 J mol–1 K–1)
T = the absolute temperature (K)
F = Faraday’s constant (9.6 × 104 J V–1 mol–1) z = the valence (charge) of the ion
In = logarithm to the base e