Space Constant

Before discussing how the time constant is related to propagation velocity, the other passive membrane property, the space (or length) constant, will be discussed. To introduce this phenomenon, it is useful to turn again to a thermal analog. Instead of considering a small block on a hot plate, consider what might happen when one end of a long metal rod touches the hot plate. The hot plate is at constant 50° C, and the rod is initially at 25° C. If the one end of the rod is placed in contact with the hot plate and a sufficient period of time elapses for the temperature changes to stabilize, what will be the temperature gradient along the rod? It is obvious that the temperature at the end of the rod in contact with the hot plate will be 50°C (i.e., the same temperature as the hot plate). The temperature of the rod, however, will not be 50°C along its length. The temperature near the hot plate will be 50°C, but along the rod the temperature will gradually fall, and if the rod is long enough the temperature may still be 25°C at its other end. If the temperature of the rod at various distances from the hot plate is measured, the temperature will be found to decay as an exponential function of distance.

Just as there is a spatial degradation of temperature in a long rod, there is also a spatial degradation of potential along a nerve axon, which is referred to as electronic conduction. Figure 3A illustrates how it is possible to demonstrate this. One electrode is in the cell body and will be used to depolarize the cell artificially. A number of other electrodes are placed at various distances along the axon to record the potential gradient as a function of distance from the cell body. Initially, the cell body and all regions of its axon are at the resting potential of —60 mV. A sufficient subthreshold depolarization is then applied to the cell body to depolarize the cell body to —50 mV. Just as the temperature of the end

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