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Generation of a diffusion potential across a membrane that contains only potassium channels. Arrows represent ion movements.
This initial state will not, however, last. Because of the potassium channels, potassium will diffuse down its concentration gradient from compartment 2 into compartment 1. After a few potassium ions have moved into compartment 1, that compartment will have an excess of positive charge, leaving behind an excess of negative charge in compartment 2. Thus, a potential difference has been created across the membrane.
Now we introduce a second factor that can cause net movement of ions across a membrane: an electrical potential. As compartment 1 becomes increasingly positive and compartment 2 increasingly negative, the membrane potential difference begins to influence the movement of the potassium ions. They are attracted by the negative charge of compartment 2 and repulsed by the positive charge of compartment 1.
As long as the flux due to the potassium concentration gradient is greater than the flux due to the membrane potential, there will be net movement of potassium from compartment 2 to compartment 1, and the membrane potential will progressively increase. However, eventually the membrane potential will become negative enough to produce a flux equal but opposite the flux due to the concentration gradient. The membrane potential at which these two fluxes become equal in magnitude but opposite in direction is called the equilibrium potential for that type of ion—in this case, potassium. At the equilibrium potential for an ion, there is no net movement of the ion because the opposing fluxes are equal, and the potential will undergo no further change.
The value of the equilibrium potential for any type of ion depends on the concentration gradient for that ion across the membrane. If the concentrations on the two sides were equal, the flux due to the concentration gradient would be zero, and the equilibrium potential would also be zero. The larger the concentration gradient, the larger the equilibrium potential because a larger electrically driven movement of ions will be required to balance the larger movement due to the concentration difference.
If the membrane separating the two compartments is replaced with one that contains only sodium channels, a parallel situation will occur (Figure 8-10). A sodium equilibrium potential will eventually be established, but compartment 2 will be positive with respect to compartment 1, at which point net movement of sodium will cease. Again, at the equilibrium potential the movement of ions due to the concentration gradient is equal but opposite to the movement due to the electrical gradient.
Thus, the equilibrium potential for one ion species can be different in magnitude and direction from those for other ion species, depending on the concentration gradients for each ion. (Given the concentration gradient for any ion, the equilibrium potential for that ion can be calculated by means of the Nernst equation, Appendix D.)
Compartment 1 Compartment 2
0.15 M NaCl
0.15 M KCl
FIGURE 8-10
Generation of a diffusion potential across a membrane that contains only sodium channels. Arrows represent ion movements.
PART TWO Biological Control Systems
Vander et al.: Human Physiology: The Mechanism of Body Function, Eighth Edition
PART TWO Biological Control Systems
Our examples were based on the membrane being permeable to only one ion at a time. When more than one ion species can diffuse across the membrane, the permeabilities and concentration gradients for all the ions must be considered when accounting for the membrane potential. For a given concentration gradient, the greater the membrane permeability to an ion species, the greater the contribution that ion species will make to the membrane potential. (Given the concentration gradients and membrane permeabilities for several ion species, the potential of a membrane permeable to these species can be calculated by the Goldman equation, Appendix D.)
It is not difficult to move from these hypothetical examples to a nerve cell at rest where (1) the potassium concentration is much greater inside than outside (Figure 8-11a) and the sodium concentration profile is just the opposite (Figure 8-12a); and (2) the plasma membrane contains 50 to 75 times as many open potassium channels as open sodium channels.
Given the actual potassium and sodium concentration differences, one can calculate that the potassium equilibrium potential will be approximately —90 mV (Figure 8-11b) and the sodium equilibrium potential about +60 mV (Figure 8-12b). However, since the membrane is permeable, to some extent, to both
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FIGURE 8-12
Forces acting on sodium when the membrane of a neuron is at (a) the resting potential (-70 mV, inside negative), and (b) the sodium equilibrium potential (+60 mV, inside positive).
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FIGURE 8-11
Forces acting on potassium when the membrane of a neuron is at (a) the resting potential (-70 mV, inside negative), and (b) the potassium equilibrium potential (-90 mV, inside negative).
potassium and sodium, the resting membrane potential cannot be equal to either of these two equilibrium potentials. The resting potential will be much closer to the potassium equilibrium potential because the membrane is so much more permeable to potassium than to sodium.
In other words, a potential is generated across the plasma membrane largely because of the movement of potassium out of the cell down its concentration gradient through open potassium channels, so that the inside of the cell becomes negative with respect to the outside. To repeat, the experimentally measured resting membrane potential is not equal to the potassium equilibrium potential, because a small number of sodium channels are open in the resting state, and some sodium ions continually move into the cell, canceling the effect of an equivalent number of potassium ions simultaneously moving out.
An actual resting membrane potential when recorded is about -70 mV, a typical value for neurons, and neither sodium nor potassium is at its equilibrium potential. Thus, there is net movement through ion channels of sodium into the cell and potassium out. The concentration of intracellular sodium and potassium ions does not change, however, because active-transport mechanisms in the plasma membrane utilize
Vander et al.: Human Physiology: The Mechanism of Body Function, Eighth Edition
Neural Control Mechanisms CHAPTER EIGHT
Neural Control Mechanisms CHAPTER EIGHT
energy derived from cellular metabolism to pump the sodium back out of the cell and the potassium back in. Actually, the pumping of these ions is linked because they are both transported by the Na,K-ATPase pumps in the membrane (Chapter 6).
In a resting cell, the number of ions moved by the pump equals the number of ions that move in the opposite direction through membrane channels down their concentration and/or electrical gradients. Therefore the concentrations of sodium and potassium in the cell do not change. As long as the concentration gradients remain stable and the ion permeabilities of the plasma membrane do not change, the electric potential across the resting membrane will also remain constant.
Thus far, we have described the membrane potential as due purely and directly to the passive movement of ions down their electrical and concentration gradients, the concentration gradients having been established by membrane pumps. There is, however, as mentioned in Chapter 6, another component to the membrane potential that reflects the direct separation of charge across the membrane by the transport of ions by the membrane Na,K-ATPase pumps. These pumps actually move three sodium ions out of the cell for every two potassium ions that they bring in. This unequal transport of positive ions makes the inside of the cell more negative than it would be from ion diffusion alone. A pump that moves net charge across the membrane contributes directly to the membrane potential and is known as an electrogenic pump.
In most cells (but by no means all), the electrogenic contribution to the membrane potential is quite small. It must be reemphasized, however, that even when the electrogenic contribution of the Na,K-ATPase pump is small, the pump always makes an essential indirect contribution to the membrane potential because it maintains the concentration gradients down which the ions diffuse to produce most of the charge separation that makes up the potential.
Figure 8-13 summarizes the information we have been presenting. This figure may mistakenly be seen to present a conflict: The development of the resting membrane potential depends predominantly on the diffusion of potassium out of the cell, yet in the steady state, sodium diffusion into the cell, indicated by the black Na+ arrow in Figure 8-13, is greater than potassium diffusion out of the cell. The reason is that although there are relatively few open sodium channels, sodium has a much larger electrochemical force acting upon it—that is, it is far from its equilibrium potential. The greater diffusion of sodium into the cell than potassium out compensates for the fact that the membrane pump moves three sodium ions out of the cell
Plasma
Intracellular fluid membrane Extracellular fluid 
FIGURE 8-13
Movements of sodium and potassium ions across the plasma membrane of a resting neuron in the steady state. The passive movements (black arrows) are exactly balanced by the active transport (red arrows) of the ions in the opposite direction.
FIGURE 8-13
Movements of sodium and potassium ions across the plasma membrane of a resting neuron in the steady state. The passive movements (black arrows) are exactly balanced by the active transport (red arrows) of the ions in the opposite direction.
for every two potassium ions that are moved in. Figure 8-13 shows ion movements once steady state has been achieved, not during its achievement.
We have not yet dealt with chloride ions. The plasma membranes of many cells have chloride channels but do not contain chloride-ion pumps. Therefore, in these cells chloride concentrations simply shift until the equilibrium potential for chloride is equal to the resting membrane potential. In other words, the negative membrane potential moves chloride out of the cell, and the chloride concentration outside the cell becomes higher than that inside. This concentration gradient produces a diffusion of chloride back into the cell that exactly opposes the movement out because of the electric potential.
In contrast, some cells have a non-electrogenic active transport system that moves chloride out of the cell. In these cells, the membrane potential is not at the chloride equilibrium potential, and net chloride diffusion into the cell contributes to the excess negative charge inside the cell; that is, net chloride diffusion makes the membrane potential more negative than it would otherwise be.
We noted earlier that most of the negative charge in neurons is accounted for not by chloride ions but by negatively charged organic molecules, such as proteins and phosphate compounds. Unlike chloride, however, these molecules do not readily cross the plasma membrane but remain inside the cell, where their charge contributes to the total negative charge within the cell.
PART TWO Biological Control Systems
Vander et al.: Human Physiology: The Mechanism of Body Function, Eighth Edition
II. Biological Control Systems
PART TWO Biological Control Systems
8. Neural Control Mechanisms
© The McGraw-Hill Companies, 2001
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