Admittance To The Semicircle

We now turn to the frequency-dependent impedance and its reciprocal, the admittance, of excitable membranes. Although these are linear variables—while many of the interesting features of voltage-sensitive ion channels are nonlinear—measurement of these quantities is important because they can help us distinguish between competing theories of ion channel function.

As mentioned in Chapters 3 and 4, much pioneer work in this field was done by Kenneth S. Cole and his collaborators, who made impedance measurements on sea-urchin eggs, red blood cells and squid axons. These studies showed that, while membrane resistances vary greatly, all these cells have membrane capacitances of about 1 μF/cm². In 1939, Cole and Howard Curtis recorded the action potential and the impedance of the squid-axon membrane simultaneously, showing that the conductance of the axon membrane increases during the time the action potential passes over it.¹ This suggests that impedance measurements can give us valuable clues to the conformational changes in membrane molecules and the ion-conduction process, varying nonlinearly with both time and voltage. One such clue is a phenomenon called constant-phase capacitance, which is characterized by certain semicircular plots.