Nervous systems, like other communication systems, use a sequence of impulses to carry message. 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 transmembrane voltage (also called membrane potential) is defined as the inside potential minus the extracellular potential. When the nerve fiber is at rest, the membrane potential is about -70 mV. The nerve impulse is a sharp change of the membrane potential. Therefore, it is also known as the action potential (Fig. 2.1).

Figure 2.1. A typical nerve impulse (action potential).

Ion Conductances

The generation of action potentials is mainly due to the changes of sodium (Na⁺) and potassium (K⁺) conductances. 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 could the nerve membrane maintain such a stable state? This is because the conductance of Na⁺ ions in the membrane is very small at the resting membrane potential. Although the inward driving force is large, the resulting Na⁺ influx is small. This small influx can be balanced by a slow ion transport process, the Na⁺-K⁺ pump, which moves Na⁺ ions outward and simultaneously K⁺ ions inward.

Figure 2.2. Ion concentrations on both sides of a nerve membrane, which contains various types of proteins. Ions may move across the membrane through a special class of proteins called ion channels.

The conductance of Na⁺ ions may change dramatically with the membrane potential as demonstrated by voltage clamp experiments, in which the membrane potential is displaced to a new value and maintained there (Fig. 2.3). Because ions carry charges, the movement of ions across the membrane will change the membrane potential. To maintain a constant membrane potential, the voltage clamp circuit must generate electric currents to neutralize the membrane potential 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.

Figure 2.3. Ion currents measured from the voltage clamp circuit. (A) The membrane potential is depolarized from -70 mV to -10 mV at t = 0, and kept constant by the voltage clamp circuit. (B) The resulting Na⁺ and K⁺ currents through the membrane (outward positive) as measured from the voltage clamp circuit.

A membrane is said to be depolarized if the new potential 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. Fig. 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 Fig. 2.2 is +55 mV. When the membrane potential is depolarized, I_ion varies with time as shown in Fig. 2.3. From eq.(1), we can obtain the time course of the ion conductance. Fig. 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. Another feature to remember is that the rising rate of G_K is much slower than G_Na.

Figure 2.4. Time courses of Na⁺ and K⁺ conductances at a few depolarizations. The number next to each curve represents the depolarizing voltage from the resting potential -70 mV.

The ion conductance change is the collective results of many individual ion channels. Each ion channel may be in either "open" or "closed" state. The opening probability of each ion channel depends on the membrane potential, but the detailed mechanism is not known.

The Generation of action potentials

In excitable cells, the action potential is elicited when the membrane potential 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 potential 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 Fig. 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 potentials 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 potential rises sharply until it approaches the equilibrium potential for Na⁺. Subsequently, the sodium inactivation sets in and the K⁺ conductance rises significantly. The membrane potential then returns to its resting value, constituting the falling phase of the action potential.

Figure 2.5. The behavior of all or none. (A) A current pulse, I₁ or I₂, is applied to a nerve membrane. (B) I₁ fails to increase the membrane potential to the threshold whereas I₂ is strong enough to elicit a nerve impulse.

If the stimulus fails to raise the membrane potential to the threshold, the intrinsic sharp potential 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.