Our results show that the efficiency with which sodium entry is used for action potential formation varies considerably among different types of mouse central neurons, with sodium entry only ~25% more than the theoretical minimum in cortical pyramidal neurons but ~2-fold the minimum in cerebellar Purkinje neurons. In particular, the two types of fast-spiking GABAergic neurons we examined had substantially more "excess" sodium entry than cortical pyramidal neurons or most CA1 pyramidal neurons. The strong correlation of excess sodium entry with narrow action potentials suggests that the excess sodium entry associated with fast-spiking neurons is likely to be general, since there is a clear correlation between fast-spiking behavior and narrow action potentials (McCormick et al., 1985
; Nowak et al, 2003
; reviewed by Connors and Gutnick, 1990
; Bean, 2007
The experiments examining the pattern of sodium entry when cells are stimulated by the action potential waveforms of other cell types shows that the differences in sodium efficiency among different cell types is due primarily to the different shapes of action potentials, not to differences in sodium channel kinetics. Sodium channels do have different kinetics among different types of mammalian central neurons (e.g. Martina and Jonas, 1997
; Raman and Bean, 1997
), and differences in kinetics were apparent in the detailed time-course of sodium current elicited by a given spike shape applied to the four types of neurons (). For example, the sodium current in Purkinje neurons decayed faster than the current in CA1 neurons for all waveforms, at least up to the action potential peak; the difference in time-course was especially clear for the narrow Purkinje neuron spike. Nevertheless, the total amount of sodium entry and resulting efficiency was not dramatically different among sodium currents in the different cells in response to any given waveform. In Purkinje neurons, sodium current elicited by step depolarizations inactivates with a biphasic time-course, and repolarization is accompanied by activation of "resurgent" current that is associated with the slower phase of inactivation (Raman and Bean, 1997
; Raman and Bean, 2001
). This mechanism may produce extra sodium entry late in the spike waveform that balances more rapid inactivation early in the waveform.
There was a strong correlation between sodium efficiency and action potential width, with narrower action potentials having less efficiency. The most obvious reason for the correlation is that sodium channel inactivation is less complete during the falling phase of narrower action potentials. In addition, the action potential peak was on average less positive in the fast-spiking cells with narrower action potentials, which has two consequences: first, the rate of inactivation is slower at less positive voltages and second, the voltage is further from the sodium equilibrium potential so that the driving force on sodium ions is greater.
Action potential width is mainly determined by the potassium channels expressed in the neuron. Fast-spiking neurons with narrow action potentials use fast-activating Kv3 channels to repolarize the membrane (Wang et al., 1998
; Erisir et al., 1999
; reviewed by Rudy and McBain, 2001
). The presence of Kv3 channels not only produces narrow action potentials but also enables fast spiking (Lien and Jonas, 2003
). Our results suggest that there are two related mechanisms underlying this effect. One is that sodium channel inactivation is incomplete (simply because the narrow spikes rise and fall so rapidly). The other is that recovery begins sooner and from more hyperpolarized voltages. Both effects speed recovery and thereby reduce the refractory period, and both effects result from the rapid repolarization of the action potential in fast-spiking neurons. However, this rapid repolarization leads to reduced metabolic efficiency because the incomplete sodium channel inactivation allows extra sodium influx during the falling phase. Thus the rapid repolarization produced by Kv3 channels has a functional benefit in allowing repetitive fast spiking but with an additional metabolic cost.
Our experiments focused on the efficiency of sodium entry during the action potential. There is also a metabolic cost associated with the efflux of potassium ions. We could not easily directly quantify total spike-evoked potassium current because there is no blocker equivalent to TTX that is effective against all the multiple components of potassium current with different kinetics. However, for an action potential composed only of sodium and potassium currents, the total potassium efflux should be equal to the total sodium influx (because net inward charge movement must be counteracted by the same net outward charge movement by the end of the action potential, ignoring the after-hyperpolarization). Therefore, the extra sodium entry in fast-spiking neurons must be associated with an equal amount of extra potassium efflux, effectively doubling its metabolic cost.
Cell bodies of mammalian central neurons also have voltage-dependent calcium channels that are activated during the action potential and carry inward current during the falling phase of the spike. This calcium entry is another metabolic cost associated with the action potential. Spike-evoked calcium current is typically only 20–25% of sodium current when the two have been recorded in the same neuron (Raman and Bean, 1999
; Do and Bean, 2003
; Jackson et al., 2004
). Like sodium entry, calcium entry during the action potential must be countered by an equivalent amount of potassium efflux by the time the spike is over. Further work will be needed to quantify the extra metabolic cost associated with calcium entry (and associated potassium entry) during the action potential in various types of central neurons.
We analyzed sodium entry during somatic action potentials. It remains to be determined to what extent the efficiency of sodium entry might differ in a given cell type for somatic action potentials versus propagating axonal action potentials. Our measurements of sodium efficiency in the cell bodies of two glutamatergic cell types (sodium entry ratio of 1.2 ± 0.3 for cortical pyramidal neurons and 1.6 ± 0.7 for CA1 pyramidal neurons) are similar to the sodium entry ratio estimated for propagated action potentials measured in the en passant
synaptic boutons of glutamatergic hippocampal mossy fibers (1.3; Alle et al., 2009
). In at least some glutamatergic neurons, it has recently been found that both the action potential shape and the kinetic properties of voltage-dependent sodium channels can differ between the soma and the axon (Geiger and Jonas, 2000
; Engel and Jonas, 2005
; Kole et al.,2007
; Shu et al., 2007
). In particular, it is striking that the action potentials in hippocampal mossy fiber boutons are significantly narrower than in the parent cell bodies (Geiger and Jonas, 2000
; Alle et al., 2009
) and in fact are as narrow (0.25–0.38 msec at half-height; Geiger and Jonas, 2000
; Alle et al., 2009
) as the action potentials of many fast-spiking neurons. The fact that there is relatively little sodium current during the falling phase of the narrow action potential of mossy fiber boutons (Alle et al., 2009
) - in contrast to the narrow action potentials of fast-spiking GABAergic neurons - apparently reflects the fact that the sodium channels in the mossy fiber boutons inactivate unusually rapidly, nearly two-fold faster than those in granule neuron cell bodies (Engel and Jonas, 2005
). A comparison of how action potential shape or sodium channel kinetics might differ in the cell bodies and axons of fast-spiking neurons has not yet been made; it will be interesting to determine whether soma-axon differences are also present in these neurons.
Action potential shape can change with firing frequency, raising the possibility that sodium entry ratio and metabolic efficiency in a single neuronal type might be frequency-dependent. In preliminary experiments in Purkinje neurons, we found that although the action potential shape changes considerably in high-frequency firing stimulated by current injection (becoming smaller and broader), sodium entry during the falling phase was still present, and the sodium entry ratio changed very little at firing frequencies up to 300 Hz. By itself, action potential broadening might be expected to result in reduction in the sodium entry, but this is apparently counteracted by the reduction in action potential peak, which tends to reduce inactivation. It will be interesting to examine more systematically how the sodium entry ratio varies with frequency in different cell types.
Our results add to the recent results of Alle and colleagues (2009)
in suggesting that action potentials in mammalian neurons have more efficient use of sodium entry than action potentials in the squid giant axon. In cortical pyramidal neurons, we measured a sodium entry of 0.84 ± 0.30 pmole/spike, about 4-fold less than in squid axon (~ 4 pmole/spike, Hodgkin and Huxley, 1952
). It is striking that even in the least efficient examples we found, in Purkinje neurons, the sodium entry of 1.54 ± 0.54 pmole/spike is still much less than in the squid giant axon. It seems clear that the dramatic difference from the action potential in the squid giant axon is real and not because of different methods of estimation. The excess sodium entry in the squid axon action potential is because of a large sodium current during the falling phase, which was not only predicted from modeling (Hodgkin and Huxley, 1952
) but also shown by direct experimental measurements of the time course of sodium and potassium conductance during action potential waveforms (Bezanilla et al., 1970
). The predicted sodium entry from these electrophysiological measurements are also nicely consistent with experimental measurements of radiolabeled ion flux in squid axons (Keynes and Lewis,1951
; Shaw, 1966
; Atwater et al., 1970
). Interestingly, both modeling and direct experiments using action potential waveforms also showed incomplete sodium channel inactivation and a large amount of sodium entry during the falling phase of action potentials in the node of Ranvier of the toad Xenopus laevis
(Frankenhaeuser and Huxley, 1964
; de Haas and Vogel, 1989
), very similar to squid axon action potentials, suggesting that the more efficient use of sodium entry in mammalian central neurons compared to the squid axon is not general to all action potentials in vertebrate neurons.
Inefficiency of sodium entry in the action potential of the squid giant axon probably has very little overall metabolic cost to the animal. A single action potential fires during a startle-escape response (Otis and Gilly, 1990
), and such responses are likely needed only occasionally. Therefore, the evolutionary pressure for the squid axon action potential may be primarily for velocity of spike propagation rather than metabolic efficiency.
In contrast, it has been suggested that the metabolic demands associated with action potential firing in mammalian cortex may be a limiting factor in determining the range of firing frequencies used during normal operation of the cortex and can help explain sparse coding in the cortex (Laughlin and Sejnowski, 2003
; Lennie, 2003
). Previous quantitative calculations of the metabolic cost of cortical action potentials have assumed a 4-fold excess of sodium entry, as in the squid axon (Atwell and Laughlin, 2001). Our results show that in fact, action potentials in cortical pyramidal neurons (which make up ~90% of all neurons in the cortex) are far more metabolically efficient than this, with only ~25% excess sodium entry. The impact of the lower metabolic efficiency of action potentials in cortical interneurons is difficult to evaluate; on one hand, there are fewer interneurons than pyramidal neurons and each one likely has less total membrane surface area, but on the other hand, cortical interneurons fire 5–6-fold more spikes/sec than pyramidal neurons during physiological activity (Simons, 1978
; Contreras and Palmer, 2003
Our results are quantitatively consistent with those of Alle and colleagues (2009)
in the case of action potentials in glutamatergic neurons, suggesting very little extra sodium entry. However, the lower metabolic efficiency in the action potentials of cerebellar Purkinje neurons is quite striking, especially since these are large projection neurons. Indeed, the operation of Purkinje neurons could be viewed as a strong counter-example to the notion that metabolic efficiency is a particularly significant factor in the evolution of the nervous system. Not only is there substantial extra sodium entry in the Purkinje neuron spike, but these neurons fire spontaneously and continuously at average basal rates of ~40 Hz (Thach, 1968
; Latham and Paul, 1971
), even in the absence of synaptic stimulation (Hausser and Clark, 1997
; Raman and Bean, 1997
). This example suggests that whatever evolutionary pressure there may be to maximize metabolic efficiency can be balanced by functional benefits, conferred by mechanisms that also reduce metabolic efficiency. Specifically, our results suggest that in fast-spiking neurons, incomplete sodium channel inactivation during the action potential leads to an additional metabolic cost, but has a functional benefit by helping to enable high frequency firing.