The membrane processes that enable neurons to communicate and process information are electrical in nature. Understanding them requires a few definitions of electrical terms.
Electricity is carried by electrons; the difference between concentrations of electrons in two places is voltage, or potential (E), and is measured in volts. The two poles of a flashlight battery, for instance, differ by 1.5 v, with a greater density of electrons at the negative pole. Each electron has a single negative charge.
When electrons flow through a wire, their rate of flow is expressed as a current, I, measured in amperes. The flow of electrons is reduced if it is impeded by a resistance, R, measured in ohms. The relationship of the potential (E), the current (I), and the resistance (R) is expressed in Ohm's law: E= IR. Thus more current (I) will flow if the potential (E) is increased or if the resistance (R) is lowered. Resistance is sometimes expressed in terms of conductance, defined as the reciprocal of resistance (1 /K) . Its unit is the mho (ohm spelled backward). In biological systems the charge is usually carried out by ions rather than electrons. An ion is a molecule in solution with one or more extra electrons (resulting in a negative charge) or with one or more missing electrons (resulting in a positive charge).
The next two sections of the chapter will examine two kinds of potentials across neural membranes: resting potentials and graded potentials. Resting potentials store energy in the membrane, and graded potentials enable neurons to process information. Later we will see how action potentials (defined in Chapter 1) allow information to be transmitted over great distances.
Two characteristics of neurons are crucial to their functioning: the differences in ion concentrations inside and outside the cell and the resulting differences in electrical potential across the membrane—the resting potential. The two are closely related.
The differences between potential inside and outside the cell can be observed only through recordings from an electrode (a small wire insulated except at the tip) placed inside a cell. This is usually a technically difficult feat because of the microscopic size of most neurons. Since we are still examining the properties of neurons that are common to all stages of evolution, it is of great advantage to record potential differences in the largest available neurons. Many invertebrates have a small number of giant neurons, with axons up to 1 mm in diameter; inserting an electrode in such an axon, which is easily visible to the naked eye, is no more difficult than threading a needle. Hence much of our knowledge of nerve cell membranes comes from the giant axons, such as those of the squid.
As an electrode is advanced toward a giant neuron, there is no difference in potential between it and a reference electrode until the cell membrane is penetrated. At that point the electrode's potential abruptly drops to about -70 mv with respect to the outside (see Figure 2.7). This is about one-twentieth the voltage across a flashlight battery. The potential is not constant at that level but continuously undergoes small variations, as Figure 2.7 indicates.
The next step in understanding resting potentials is to measure the concentrations of ions inside and outside the neuron. This can be done directly in the squid's giant axon, which is so large that a section of it can be squeezed, like a toothpaste tube, with a roller to force out the contents of the axon. The resulting concentrations of ions are shown in Figure 2.8. Obviously, the ion concentrations inside and outside the neuron are different, with the membrane maintaining the difference in ion concentrations. For most ions there is a concentration gradient, a difference in concentrations, across the membrane. How do the concentration gradients bring about the resting potential?
The Nernst Equation
The electrical potential across the neuron's membrane can be calculated from the ion concentrations using the Nernst equation. The equation depends on the insight that the electrical charge, or potential, measures the concentration of electrons or ions, so the electrical charge can be viewed as a concentration in chemical terms. Thus, to describe charge, we can use the language that describes concentrations of molecules or ions in solution.
The Nernst equation states that the potential, E, across the membrane is predicted by five relationships:
1. E is related to the "ideal gas constant," R, from chemistry, because the motion of ions is involved.
2. E is also proportional to the absolute temperature, T, because ions move faster at higher temperatures.
3. Ions will diffuse from a region of higher concentration across the membrane to a region of lower concentration along their concentration gradient. The ions are like a swarm of flies randomly buzzing about in a jar; when the jar is opened, they are more likely to fly from the jar into the room than from the room into the jar. After a while the flies will be evenly distributed across the room. Adding a net across the middle of the room to represent the membrane does not make any difference as long as the flies can move freely through it. In the Nernst equation, this diffusion along concentration gradients means that the potential across the membrane will depend on the logarithm of the concentrations of each ion inside (i) and outside (o) the membrane ([Xi]/[Xo]).
4. E is inversely proportional to the charge, n, on the ion in question because one needs fewer ions to yield the same difference in charge if each ion has a greater charge. 5. Finally, E is inversely proportional to F, the Faraday, a unit of electrical charge.
Summarizing these five relationships in a mathematical formula, we show the Nernst equation as
R and F are physical constants and T can also be held constant. Converting the ln into log10, we obtain
Now we can find the potentials (E) where various ions are in equilibrium — where ions will flow neither into nor out of a cell. We need to know only the charge of the ion and its concentration inside and outside the cell.