The variance of sodium current fluctuations at the node of Ranvier

Abstract

1. Single myelinated nerve fibres 12‐17 μm in diameter from Rana temporaria and Rana pipiens were voltage clamped at 2‐5 °C. Potassium currents were blocked by internal Cs+ and external tetraethylammonium ion. Series resistance compensation was employed. 2. Sets of 80‐512 identical, 20 ms depolarizations were applied, with the pulses repeated at intervals of 300‐600 ms. The resulting membrane current records, filtered at 5 kHz, showed record‐to‐record variations of the current on the order of 1%. From each set of records the time course of the mean current and the time course of the variance were calculated. 3. The variance was assumed to arise primarily from two independent sources of current fluctuations: the stochastic gating of sodium channels and the thermal noise background in the voltage clamp. Measurement of the passive properties of the nerve preparation allowed the thermal noise variance to be estimated, and these estimates accounted for the variance observed in the presence of tetrodotoxin and at the reversal potential. 4. After the variance σ 2 was corrected for the contribution from the background, its relationship to the mean current I could be fitted by the function σ 2 = iI—I 2/N expected for N independent channels having one non‐zero conductance level. The single channel currents i corresponded to a single‐channel chord conductance γ = 6·4 ± 0·9 pS (S.D.; n = 14). No significant difference in γ was observed between the two species of frogs. The size of the total population of channels ranged from 20,000 to 46,000. 5. The voltage dependence of i corresponded closely to the form of the instantaneous current—voltage relationship of the sodium conductance, except at the smallest depolarizations. The small values of i at small depolarizations may have resulted from the filtering of high‐frequency components of the fluctuations. 6. It is concluded that sodium channels have only two primary levels of conductance, corresponding to ‘open’ and ‘closed’ states of the channel. 7. The fraction pmax of channels open at the time of the peak conductance was found to be 0·59 ± 0·08 (S.D.; n = 5) and 0·9 ± 0·1 (S.D.; n = 3) for depolarizations to ‐5 and +125 mV, respectively. (50 ms hyperpolarizations to ‐105 mV preceded the depolarizations in each case.) These values are similar to those predicted by Hodgkin‐Huxley kinetics. 8. Fluctuations in the firing threshold of neurones are expected from the stochastic gating of sodium channels. A prediction of the size of these fluctuations based on the measured properties of the channels gives a value of about 1% for the relative spread, which agrees with experimental values in the literature.