Nonlinear cable properties of the giant axon of the cockroach Periplaneta americana

The steady state nonlinear properties of the giant axon membrane of the cockroach Periplaneta americana were studied by means of intracellular electrodes. The resistivity of this membrane markedly decreases in response to small subthreshold depolarizations. The specific slope resistance is reduced by twofold at 5 mV depolarization and by a factor of 14 at 20 mV depolarization. As a result, the spatial decay, V(X), of depolarizing potentials is enhanced when compared with the passive (exponential) decay. This enhancement is maximal at a distance of 1-1.5 mm from a point of subthreshold (0-20 mV) depolarizing perturbation. At that distance, the difference between the actual potential and the potential expected in the passive axon is approximately 30%. The effects of membrane rectification on V(X) were analyzed quantitatively with a novel derivation based on Cole's theorem, which enables one to calculate V(X) directly from the input current-voltage (I0-V) relation of a long axon. It is shown that when the experimental I0-V curve is replotted as (I0Rin)-1 against V (where Rin is the input resistance at the resting potential), the integral between any two potentials (V1 greater than V2) on this curve is the distance, in units of the resting space constant, over which V1 attenuates to V2. Excellent agreement was found between the experimental V(X) and the predicted value based solely on the input I0-V relation. The results demonstrate that the rectifying properties of the giant axon membrane must be taken into account when the electrotonic spread of even small subthreshold potentials is studied, and that, in the steady state, this behavior can be extracted from measurements at a single point. The effect of rectification on synaptic efficacy is also discussed.