Nervous systems, like other communication systems, use a sequence of impulses to carry information. The nature of nerve impulses, however, differs entirely from electromagnetic waves and sound waves. In every nerve cell, there is a membrane separating the cytoplasmic fluid from the extracellular solution. The membrane voltage (also called "membrane potential") is defined as the inside potential minus the outside potential. When a nerve cell is at rest, the membrane voltage is about -70 mV. The nerve impulse is a sharp change of the membrane voltage. Therefore, it is also known as action potential (Figure 2-1).

Ion Conductance

The generation of action potentials is mainly due to the changes of sodium (Na⁺) and potassium (K⁺) conductance. Figure 2-2 shows the concentrations of Na⁺ and K⁺ ions on both sides of a nerve membrane. For Na⁺, its concentration on the extracellular side is much higher than inside. We immediately notice that Na⁺ ions are far from electrochemical equilibrium: both the electric force due to electric potential difference and the chemical force due to ion concentration difference are pointing inward. How can the nerve membrane maintain such a stable state? This is because the conductance of Na⁺ ions is very small at the resting potential. Although the inward driving force is large, the resulting Na⁺ influx is small. This small influx can be balanced by the active transport of Na⁺ pump, which moves Na⁺ ions outward and simultaneously K⁺ ions inward.

The conductance of Na⁺ ions may change dramatically with the membrane voltage as demonstrated by voltage clamp experiments, in which the membrane voltage is displaced to a new value and maintained there (Figure 2-3). Because ions carry charges, the movement of ions across the membrane will change the membrane voltage. To maintain a constant membrane voltage, the voltage clamp circuit must generate electric currents to neutralize the membrane voltage change caused by the ionic flux. Thus, the ion current through the membrane is reflected in the electric current of the voltage clamp circuit outside the membrane.

A membrane is said to be depolarized if the new membrane voltage V_m is more positive than the resting potential V_m0, and hyperpolarized if V_m < V_m0. Since depolarization makes the inside potential more positive, we expect (from the consideration of electrochemical forces) the currents of all cations to increase in the outward direction. Figure 2-3 shows the experimental result for squid axons. The K⁺ current indeed increases in the outward direction. However, the behavior of Na⁺ current is totally unexpected. It first rises sharply in the inward direction and then declines with a slower rate to its resting value. Phenomenologically, the change of the Na⁺ current can be attributed to the change in Na⁺ conductance. Experimental results indicate that the Na⁺ conductance increases in the early stage of depolarization, which exceeds the reduction in the inward driving force. As time proceeds, the Na⁺ conductance decreases, resulting in the late decline of Na⁺ currents. The rise and fall of Na⁺ conductance are known as sodium activation and sodium inactivation, respectively. They play important roles in the generation of a nerve "impulse", which must contain a rising phase as well as a falling phase. Mathematically, the ion conductance is defined by

G_ion = I_ion/(V_m - V_ion)                (1)

where I_ion denotes the ion current through the membrane (outward current is defined as positive), and V_ion is the equilibrium potential for the ion. According to the Nernst equation,

V_ion = (RT/F) ln ([ion]_o/[ion]_i)       (2)

where R denotes the gas constant, T is the absolute temperature, F represents the Faraday constant, [ion]_o and [ion]_i are the ion concentrations in the extracellular and intracellular fluids, respectively.

At room temperature, the equilibrium potential for Na⁺ with concentrations given in Figure 2-2 is +55 mV. When the membrane voltage is depolarized, I_ion varies with time as shown in Figure 2-3. From eq.(1), we can obtain the time course of the ion conductance. Figure 2-4 shows the experimental results for a few depolarizations. We see that the peak of Na⁺ conductance increases with increasing depolarizations before it levels off at large depolarizations. It is also noteworthy that the rising rate of G_K is much slower than G_Na.

Generation of Action Potentials

In excitable cells, the action potential is elicited when the membrane voltage is depolarized to a critical value (the threshold). In most axons, the threshold is about 15 mV above the resting potential. Before the threshold is reached, the axon membrane behaves like an ordinary inactive substance with a certain resistance and capacitance. When a constant current I_s is applied to the inactive membrane, the membrane voltage becomes,

V_m(t) = I_sR_m[1 - exp(-t/R_mC_m)] + V_m0        (3)

where R_m and C_m are the effective resistance and capacitance of the membrane, respectively.

As shown in Figure 2-4, the peak of G_Na increases with increasing depolarizations. When the membrane is depolarized, more Na⁺ ions will flow into the intracellular fluid. Because the Na⁺ ions carry positive charges, the Na⁺ influx will make the membrane more depolarized, which in turn makes the Na⁺ conductance even larger. In the mean time, the K⁺ conductance also increases with increasing depolarization. In the physiological range of membrane voltages and ion concentrations, the electrochemical force on K⁺ is outward. The outflux of K⁺ will make the membrane more hyperpolarized, counteracting the Na⁺ influx. However, the rising rate of G_K is much slower than G_Na. In the early stage, the rise of K⁺ outflux will not be as large as the Na⁺ influx except at small depolarizations. Therefore, when the membrane is depolarized to a critical value, above which the Na⁺ influx exceeds the K⁺ outflux, the Na⁺ ions will flow inward at an accelerating rate. As a result, the membrane voltage rises sharply until it approaches the equilibrium potential for Na⁺. Subsequently, the sodium inactivation sets in and the K⁺ conductance rises significantly. The membrane voltage then returns to its resting value, constituting the falling phase of the action potential.

If the stimulus fails to raise the membrane voltage to the threshold, the intrinsic sharp voltage change cannot occur. This behavior is known as "all or none". Figure 2.5 illustrates the membrane response to two different current pulses, I₁ and I₂. The magnitude of I₁ is too small to charge the membrane above the threshold, but I₂ is strong enough to initiate an action potential.