## Membrane Potential and Ionic Permeability

As an example of how the actual value of membrane potential depends on the relative permeabilities of the competing ions, consider the situation illustrated in Figure 5-1. This model cell is much more permeable to K+ than to Na+. In other words, there are many channels that allow K+ to cross the membrane but

Figure 5-1 The resting membrane potential of a cell that is more permeable to potassium than to sodium. At the upward arrow, an apparatus that artificially holds the membrane potential at EK abruptly switched off, and Em is allowed to seek its own resting level.

Figure 5-1 The resting membrane potential of a cell that is more permeable to potassium than to sodium. At the upward arrow, an apparatus that artificially holds the membrane potential at EK abruptly switched off, and Em is allowed to seek its own resting level.

only a few that allow Na+ to cross. Imagine that initially we connect the cell to an apparatus that artificially maintains the resting membrane potential at EK, so that Em = Ek = -80 mV. (This could be accomplished experimentally using a voltage clamp apparatus, as described in Chapter 7.) What will happen to Em when we switch off the apparatus and allow Em to take on any value it wishes? In order to determine what will happen, it is necessary to keep in mind one important principle: if the membrane potential is not equal to the equilibrium potential for an ion, that ion will move across the membrane in such a way as to force Em toward the equilibrium potential for that ion. For example, Figure 5-2 illustrates the movement of K+ across a cell membrane in response to changes in Em. In this example, a cell is connected to an apparatus that allows us to set the membrane potential to any value we choose. Initially, we set Em to EK. Recall from Chapter 4 that when Em = EK there is a balance between the electrical force driving K+ into the cell and the concentrational force driving K+ out of the cell. At time = a, however, we suddenly make the interior of the cell less negative, reducing the electrical potential across the cell membrane and therefore decreasing the electrical force driving K+ into the cell. Such a reduction in the electrical potential across the membrane is called a depolarization of the membrane. The electrical force will then be weaker than the oppositely directed concentrational force, and there will be a net movement of K+ out of the cell.

-100

Em =E|<: No net movement of K+ because of balance between electrical and concentrational forces

Em less negative than Ek: K+ leaves cell because concentrational force driving exit is stronger than electrical force moving K+ into cell.

Time

Time a

Time b t

Time a

Time b

more negative than Ek: K+ enters cell because electrical force is now stronger than concentrational force.

Outward A

Net movement of K+ across membrane v Inward

Time t

Time a t

Time b

Figure 5-2 Effect of changes in membrane potential on the movement of potassium ions across the plasma membrane. (a) The membrane potential is artificially manipulated with respect to EK, as indicated. (b) In response to the changes in membrane potential, potassium ions move across the membrane in a direction governed by the difference between Em and EK.

Note that this movement is in the proper direction to make Em move back toward EK; that is, to make the interior of the cell more negative because of the efflux of positive charge. At time = b, we suddenly make Em more negative than Ek; that is, we hyperpolarize the membrane. Now the electrical force will be stronger than the concentrational force and there will be a net movement of K+ into the cell. Again, this is in the proper direction to make Em move toward Ek, in this case by adding positive charge to the interior of the cell.

Return now to Figure 5-1. We would expect that Na+, which has an equilibrium potential of +58 mV, will enter the cell. That is, Na+ will bring positive charge into the cell, and when we switch off the apparatus forcing Em to remain at EK, this influx of sodium ions will cause the membrane potential to become more positive (that is, move toward ENa). As Em moves toward ENa, however, it

Figure 5-3 The resting membrane potential of a cell that is more permeable to sodium than to potassium. As in Figure 5-1, an apparatus holding Em at EK is abruptly turned off at the upward arrow.

Na+

Hold Em at Release eK Em

will no longer be equal to EK, and K+ will move out of the cell in response to the resulting imbalance between the potassium concentrational force and electrical force. Thus, there will be a struggle between K+ efflux forcing Em toward EK and Na+ influx forcing Em toward ENa. Because K+ permeability is much higher than Na+ permeability, potassium ions can move out readily to counteract the electrical effect of the trickle of sodium ions into the cell. Thus, in this situation, the balance between the movement of Na+ into the cell and the exit of K+ from the cell would be struck relatively close to EK.

Figure 5-3 shows a different situation. In this case, everything is as before except that the sodium permeability is much greater than the potassium permeability. That is, there are more channels that allow Na+ across than allow K+ across. Once again, we start with Em = EK = -80 mV and then allow Em to seek its own value. Sodium, with ENa = +58 mV, enters the cell down its electrical and concentration gradients. The resulting accumulation of positive charge again causes the cell to depolarize, as before. Now, however, potassium cannot move out as readily as sodium can move in, and the influx of sodium will not be balanced as readily by efflux of potassium. Thus, Em will move farther from EK and will reach a steady value closer to ENa than to EK.

The point of the previous two examples is that the value of membrane potential will be governed by the relative permeabilities of the permeant ions. If a cell membrane is highly permeable to an ion, that ion can respond readily to deviations away from its equilibrium potential and Em will tend to be near that equilibrium potential.

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