4. Active Behavior of the Cell Membrane

When a stimulus current pulse is arranged to depolarize the resting membrane of a cell to or beyond the threshold voltage, then the membrane will respond with an action impulse. An example of this is seen in Figure 2.8 in the action potential responses 3b and 4 to the transthreshold stimuli 3 and 4, respectively. The response is characterized by an initially rapidly rising transmembrane potential, which reaches a positive peak and then more slowly recovers to the resting voltage. This phasic behavior typifies what is meant by an action impulse. A quantitative analysis of the action impulse was successfully undertaken by Alan L. Hodgkin and Andrew F. Huxley and colleagues in Cambridge (Hodgkin and Huxley, 1952abcd). Their work was made possible because of two important factors. The first was the selection of the giant axon of the squid, a nerve fiber whose diameter is around 0.5 mm, and consequently large enough to permit the insertion of the necessary two electrodes into the intracellular space. (Credit for discovering the applicability of the squid axon to electrophysiological studies is given to by J. Z. Young (1936). ) The second was the development of a feedback control device called the voltage clamp, capable of holding the transmembrane voltage at any prescribed value. This chapter describes the voltage clamp device, the experiments of Hodgkin and Huxley, the mathematical model into which their data were fitted, and the resulting simulation of a wide variety of recognized electrophysiological phenomena (activation, propagation, etc.). The voltage clamp procedure was developed in 1949 separately by K. S. Cole (1949) and G. Marmont (1949). Because of its importance, we first discuss the principle of the voltage clamp method in detail. The Hodgkin and Huxley work is important not only for its ability to describe quantitatively both the active and the passive membrane, but for its contribution to a deeper understanding of the membrane mechanisms that underlie its electrophysiological behavior. A remarkable improvement in the research of membrane electrophysiology was made by Erwin Neher and Bert Sakmann, who in 1976 published a method for the measurement of ionic currents in a single ionic channel (Neher and Sakmann, 1976). This method, called patch clamp, is a further development of the voltage clamp technique. The patch clamp technique allows the researcher to investigate the operation of single ion channels and receptors and has a wide application, for instance, in the pharmaceutical research. By measuring the capacitance of the plasma membrane with the patch clamp technique, the researcher may also investigate the regulation of exocytosis of the cell. The electric behavior of the axon membrane is, of course, described by the net ion flow through a great number of ion channels. The ion channels seem to behave "digitally" (as seen in the measurement result of the patch clamp experiment); however, because of the large number of ion channels, the electric currents of a large area of the axon membrane exhibit "analog" behavior, as seen in the measurement result obtained in a voltage clamp experiment. Logically, discussion of the electric behavior of the membrane should begin by examining the behavior of single ion channels and then proceed to by explain the electric behavior of the membrane as the summation of the behavior of a large number of its constituent ionic channels. For historical reasons, however, membrane behavior and the voltage clamp method are discussed here first, before ionic channel behavior and the patch clamp method are explored.