FIGURE 3 Measurement of the space constant. (A) Experimental setup; (B) changes in membrane potential as a function of distance along the axon. A constant depolarizing current is applied to the cell body to depolarize the cell body from rest (—60 mV) to —50 mV. (Modified from Kandel ER. The cellular basis of behavior. San Francisco: Freeman, 1976.)
of the rod placed on the 50° C heat source became the same as the hot plate, the cell body is forced from its resting potential to a potential of —50 mV. After waiting a sufficient period of time for the potential changes to stabilize, the measurements are made. Very near the cell body the potential is —50 mV (Fig. 3B). However, the membrane potential sampled at various points away from the cell body has changed from the value of —50 mV at the cell body to more negative values distal from the cell body. Measurements made a great enough distance from the cell body reveal that the potential recorded is not changed from the resting potential (—60 mV). The potential profile is an exponential function of distance and can be used to define a space constant (denoted by the symbol A). The space constant is the distance it takes for the depolarizing displacement (i.e., 10 mV) to decay by 63% of its initial value. In this particular cell, the space constant is 1 mm. This means that 1 mm away from the cell body the potential would have changed from its value of —50 mV in the cell body to a value of —56.3 mV in the axon. The greater the space constant, the greater will be the extent of the propagation of this electrotonic potential. If the space constant is 2 mm, this potential profile would decay less so that at 2 mm the potential would be at —56.3 mV.
Just as it is possible to provide a formula for the time constant in terms of the physical properties of the membrane, it is also possible to derive a formula for the space constant. The space constant is equal to:
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