Quantitative description of the sodium conductance of the giant axon of Myxicola in terms of a generalized second-order variable

Goldman, Lawrence

doi:10.1016/s0006-3495(75)85796-1

Cited by 47 publications

(34 citation statements)

References 26 publications

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“…However, other considerations make the relevance of this result to our study questionable. Inactivation in Myxicola Na ϩ channels appears to be much more closely coupled with activation than it is in squid Na ϩ channels, making the Hodgkin-Huxley assumption of independent activation and inactivation processes (which also is part of our simulations) inaccurate for this particular channel (Bell and Cook 1979;Goldman 1975). We have also been unable to find experimental measurements of propagating action potential velocities in Myxicola giant axons.…”

Section: Discussionmentioning

confidence: 89%

Metabolic Energy Cost of Action Potential Velocity

Crotty

Sangrey²,

Levy³

2006

Journal of Neurophysiology

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. The action potential of the unmyelinated nerve is metabolically expensive. Using the energetic cost per unit length for the biophysically modeled action potential of the squid giant axon, we analyze this cost and identify one possible optimization. The energetic cost arising from an action potential is divided into three separate components: 1) the depolarization of the rising phase; 2) the hyperpolarization of the falling phase; and 3) the largest component, the overlapping of positive and negative currents, which has no electrical effect. Using both the Hodgkin-Huxley (HH) model and an improved version of the HH model (HHSFL), we investigate the variation of these three components as a function of easily evolvable parameters, axon diameter and ion channel densities. Assuming conduction velocity is well designed for each organism, the energy component associated with the rising phase attains a minimum near the biological values of the diameter and channel densities. This optimization is explained by the membrane capacitance per unit length. The functional capacitance is the sum of the intrinsic membrane capacitance and the gating capacitance associated with the sodium channel, and this capacitance minimizes at nearly the same values of diameter and channel density. Because capacitance is temperature independent and because this result is independent of the assumed velocity, the result generalizes to unmyelinated mammalian axons. That is, channel density is arguably an evolved property that goes hand-in-hand with the evolutionary stability of the sodium channel. I N T R O D U C T I O NIn the nervous system, the action potential is used for long-distance information transmission. Delivery of such information in a timely fashion requires an action potential of sufficient velocity. On the other hand, sufficient velocity has its costs. In what follows, we assume that across species and across the life span of the organism the velocity of any axon is appropriate to its role in information processing.In the neuropil of neocortex, where axons must be unmyelinated if each one is to make several thousand sequential or neighboring synapses, the metabolic costs are surprisingly large. Attwell and Laughlin (2001) estimated that 75% of the adenosine triphosphate (ATP) consumed by neurons in the rat brain is used for communication and computation. Of this, half is used by the unmyelinated axons.This metabolic perspective contrasts with and, as we will see, ultimately complements Hodgkin's conjectured constraint on action potential velocity. Both Hodgkin (1975) and Adrian (1975) proposed that the gating charge movement that inevitably accompanies rapid activation of a voltage-dependent channel leads to an optimal density of fast Na ϩ channels. This optimization occurs because the movement of charge specifically restricted to the transmembrane voltage field contributes, albeit transiently, to membrane capacitance. Because increasing capacitance slows action potential propagation, Hodgkin proposed that the Na ϩ channel dens...

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Section: Discussionmentioning

confidence: 89%

Metabolic Energy Cost of Action Potential Velocity

Crotty

Sangrey²,

Levy³

2006

Journal of Neurophysiology

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“…At present this possibility has not been explored. Several authors (Hoyt, 1963;Hoyt & Adelman, 1970;Goldman & Schauf, 1972;Goldman, 1975;Moore & Cox, 1976) have suggested that the development of inactivation may be linked to the rise of the sodium conductance. It is interesting to speculate that the increase in the delay for the development of inactivation may be related to the slower rise of the sodium conductance seen in higher concentrations of calcium.…”

Section: Discussionmentioning

confidence: 99%

Effect of calcium upon sodium inactivation in the giant axon ofLoligo pealei

Shoukimas

1978

J. Membrain Biol.

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Giant axons of Loligo pealei were voltage clamped in artificial seawater solutions containing varying concentrations of calcium from 10 to 100 mM, and the sodium conductance inactivation was measured with a series of two-pulse experiments. The h infinity vs. voltage curve showed a shift of about 10 mV in the depolarizing direction on the voltage axis for a tenfold increase in external calcium without substantial alteration in the slope of the voltage dependence. The kinetics of the inactivation process were found to be exponential for hyperpolarizing prepulses, but showed some indication of a sigmoidal decay for depolarizing prepulses in all calcium concentrations employed. Increasing calcium increased the delay in the sigmoidal response. The inactivation time constant tauh increased as a function of calcium concentration over the potential range studied, -10 to -90 mV. The values of the rate constants alphah and betah are decreased with an increase in calcium and these effects are not consistent with parallel shifts of the rate constant vs. voltage curves along the voltage axis for changes in calcium concentration. Magnesium does not behave as an equimolar substitute for calcium. The effect of a solution containing 10 mM calcium and 50 mM magnesium is intermediate to that of solutions containing 10 and 30 mM calcium alone. Predictions of a recent model for the sodium conductance (Moore, J.W., Cox, E.B., 1976 Biophys. J. 16:171) which employs calcium binding were compared with the experimental data.

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“…This latter formulation produces no significant changes in the model. As a further note, Gettes & Reuter (1974) discussed alternative formulations of iads activation and inactivation, for example, coupled activation-inactivation kinetics (Goldman, 1975). We have adopted the approach proposed by Haas et al (1971) Slow inward current The characterization of i8 has probably received more experimental attention than other current component.…”

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confidence: 99%

Reconstruction of the action potential of ventricular myocardial fibres

Beeler

Réuter

1977

The Journal of Physiology

1,304

708

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3. The iNa is primarily responsible for the rapid upstroke of the action potential, while the other current components determine the configuration of the plateau of the action potential and the re-polarization phase. The relative importance of inactivation of i8 and of activation of iL for termination of the plateau is evaluated by the model. 4. Experimental phenomena like slow recovery of the sodium system from inactivation, frequency dependence of the action potential duration, all-or-nothing re-polarization, membrane oscillations are adequately described by the model. 5. Possible inadequacies and shortcomings of the model are discussed.

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Quantitative description of the sodium conductance of the giant axon of Myxicola in terms of a generalized second-order variable

Cited by 47 publications

References 26 publications

Metabolic Energy Cost of Action Potential Velocity

Metabolic Energy Cost of Action Potential Velocity

Effect of calcium upon sodium inactivation in the giant axon ofLoligo pealei

Reconstruction of the action potential of ventricular myocardial fibres

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