Because the activation curve of the voltage-gated Na
+ current in human cones was also fitted by a single Boltzmann function, the fraction of Na
+ channels that are still activated at those membrane potentials can be estimated from the Boltzmann function. In the activation curve,
V half was −35 mV and
K h −7.9 mV. Thus, at membrane potentials of −53, −63, and −68 mV, the estimated values of the activation curve are 0.093, 0.028, and 0.015, respectively. In the voltage-gated Na
+ current of the Hodgkin-Huxley model,
47 they settled on three
m-gating particles to control activation and one
h-gating particle for inactivation. Thus, the probability that all particles are in the permissive position is
m 3 ·
h. Therefore, at membrane potentials of −53, −63, and −68 mV, the estimated fraction of Na
+ channels that are still open is 1.5 × 10
−4, 1.0 × 10
−5, and 2.1 × 10
−6, respectively. This suggests that at those steady membrane potentials, the fraction of open Na
+ channels is decreased, as the membrane potentials of photoreceptors are more hyperpolarized. This result appears to contradict the spontaneous Na
+ spike generation in human photoreceptors. However, when membrane depolarization activates voltage-gated Na
+ channels, the fraction of activated Na
+ channels is mainly determined by the resting value of the
h parameter rather than that of the
m parameter, because the kinetics of the
h parameter is much slower than that of the
m parameter.
47 Thus, when the resting potentials of photoreceptors were hyperpolarized to between −63 and −68 mV by application of
h channel blockers, 46% to 62% of Na
+ channels were activated by depolarization. Therefore, it is likely that the fluctuations in the membrane voltage activate a significant amount of voltage-gated Na
+ channel and generate spontaneous Na
+ spikes in human photoreceptors.