Fluctuation and linear analysis of Na-current kinetics in squid axon

The power spectrum of current fluctuations and the complex admittance of squid axon were determined in the frequency range 12.5 to 5,000 Hx during membrane voltage clamps to the same potentials in the same axon during internal perfusion with cesium. The complex admittance was determined rapidly and with high resolution by a fast Fourier transform computation of the current response, acquired after a steady state was attained, to a synthesized signal with predetermined spectral characteristics superposed as a continuous, repetitive, small perturbation on step voltage clamps. Linear conduction parameters were estimated directly from admittance data by fitting an admittance model, derived from the linearized Hodgkin-Huxley equations modified by replacing the membrane capacitance with a "constant-phase-angle" capacitance, to the data. The constant phase angle obtained was approximately 80 degrees. At depolarizations the phase of the admittance was 180 degrees, and the real part of the impedance locus was in the left-half complex plane for frequencies below 1 kHz, which indicates a steady-state negative Na conductance. The fits also yielded estimates of the natural frequencies of Na "activation" and "inactivation" processes. By fitting Na-current noise spectra with a double Lorentzian function, a lower and an upper corner frequency were obtained; these were compared with the two natural frequencies determined from admittance analysis at the corresponding potentials. The frequencies from fluctuation analyses ranged from 1.0 to 10.3 times higher than those from linear (admittance) analysis. This discrepancy is consistent with the concept that the fluctuations reflect a nonlinear rate process that cannot be fully characterized by linear perturbation analysis. Comparison of the real part of the admittance and the current noise spectrum shows that the Nyquist relation, which generally applies to equilibrium conductors, does not hold for the Na process in squid axon. The Na-channel conductance, gamma Na, was found to increase monotonically from 0.1 to 4.8 pS for depolarizations up to 50 mV from a holding potential of -60 mV, with no indication of a maximum value.