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LETTER TO THE EDITOR

Letter

1) Sangrey and colleagues interpret the experimental results of Fernandez et al. (1982) as evidence that for the squid giant axon the maximum change of the voltage-dependent part of the capacitance occurs at the resting potential. Actually it is not possible to draw such a conclusion from these experiments. The measurements by Fernandez et al. were done at varying holding potentials in the frequency domain. Previous work by Bezanilla et al. (1982) measured Q_g versus V_m curves, which exhibit a rather unexpected behavior. The curves shift depending on the holding potential at which the measurements are done. For this reason the frequency domain measurements at different holding potentials do not translate in any transparent way into a voltage dependency of the gating capacitance during the propagated action potential. A more relevant description of the gating capacitance during the propagation was published by Armstrong and Bezanilla (1975). They measured the differential capacitance of an axon at 10-mV pulse intervals starting from a holding potential of –70 mV. This time course is more like the time course of an action potential than the measurements done at different holding potentials. Figure 9 of their work shows that the gating capacitance increases from –70 mV, reaches a maximum of 0.35 µF/cm² at –10 mV, and then decreases. The assumption that the gating capacitance starts at a maximum at the resting potential and then decreases as m(t)—the fraction of gating particles traversing the membrane—increases is incorrect.

2) Equation 3a of Sangrey et al. (2004)

(1)

implies that C_g(t) = Q_g(t)/V_m(t). However, the gating capacitance is voltage dependent and for the steady propagation of the action potential it can be described as an instantaneous function of the potential alone. A general definition of capacitance, which includes a nonlinear relation between Q and V, is the differential capacitance given by

Notice that when Q is a linear function of V, the above definition reduces to the well-known expression for capacitance of C = Q/V.

The correct, model-independent expression for the gating current I_g(t) during propagation is

and using the definition of differential capacitance introduced above we get

To estimate the velocity dependency on gating capacitance Hodgkin (1975) simply assumed that the charge transfer as a function of the potential is linear; in other words gating capacitance is a constant. Adrian (1975) assumed that the time evolution of the gating charge during propagation was given by

(2)

where m represents the fraction of m-particles in the position giving rise to open sodium channels and Q_g^max (t) is the maximum transferred charge. Assumption 2 is supported by a similar time evolution of Q_g(t) and m(t), both saturating at the foot and the peak of the action potential with fastest growth in between. The gating current is then

(3)

It turns out that numerical calculations using the H–H equations show that for the rising phase of the propagated action potential m(V_m) is approximately proportional to V_m (see, e.g., Fig. 1 of Hunter et al. 1975). Therefore

becomes a constant during the rising phase of the action potential. Thus the net result is that Adrian's gating current addition (Eq. 3) is approximately equivalent to increasing the capacitance of the membrane by a constant value independent of further modeling. The conclusion is that the gating charge of the sodium channel increases the membrane capacitance and affects the conduction velocity as Hodgkin correctly indicated in 1975.

REFERENCES

Adrian RH. Conduction velocity and gating current in the squid giant axon. Proc R Soc Lond B Biol Sci 189: 81–86, 1975.[Medline]

Armstrong CM and Bezanilla F. Currents associated with the ionic gating structures in nerve membrane. Ann NY Acad Sci 264: 265–277, 1975.[ISI][Medline]

Bezanilla F, Taylor RE, and Fernandez JM. Distribution and kinetics of membrane dielectric polarization. I. Long-term activation of gating currents. J Gen Physiol 79: 21–40, 1982.[Abstract/Free Full Text]

Fernandez JM, Bezanilla F, and Taylor RE. Distribution and kinetics of membrane dielectric polarization. II. Frequency domain studies of gating currents. J Gen Physiol 79: 41–67, 1982.[Abstract/Free Full Text]

Hodgkin AH. The optimum density of sodium channels in an unmyelinated nerve. Philos Trans R Soc Lond B Biol Sci 270: 297–300, 1975.[ISI][Medline]

Hunter PJ, McNaughton PA, and Noble D. Analytical models of propagation in excitable cells. Prog Biophys Mol Biol 30: 99–144, 1975.[Medline]

Sangrey TD, Friesen WO, and Levy WB. Analysis of the optimal channel density of the squid giant axon using a reparameterized Hodgkin–Huxley model. J Neurophysiol 91: 2541–2550, 2004.[Abstract/Free Full Text]

Nikola Jurisic
Jules Stein Eye Institute
Geffen School of Medicine
University of California
Los Angeles, CA 90095

Francisco Bezanilla
Institute for Molecular Pediatric Sciences
University of Chicago
Chicago, IL 60637

This article has been cited by other articles:

				W. B. Levy, P. Crotty, T. Sangrey, and O. Friesen Reply J Neurophysiol, August 1, 2006; 96(2): 960 - 960. [Full Text] [PDF]

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