20.4 N&v 999 Mh

than expected from the models based on the HH formalism. Moreover, the voltage at which the spike takes off (the threshold) varies remarkably from spike to spike in the same neuron in vivo (Fig. 1, overleaf). Examining several HH-based models, the authors find that none of them can account for both observations — spike sharpness and threshold variability. Indeed, under the HH formalism the spike speed and onset-voltage variability seem to be antagonistic: if the model parameters are tweaked to fit the observations for spike speed, the variability in onset cannot occur and vice versa. Naundorf et al. conclude that the HH formalism is not valid for the neurons that they monitored, and they propose a complementary model that invokes cooperative voltage-gated sodium channels. They took as their basis a sodium-channel model that allowed for a slow voltage-independent transition from the open state to the inactivated closed state. This can produce the threshold variability: for slower inputs to the neuron the threshold is higher than for rapid inputs, as, during the slow depolarization phase, more channels are inactivated, so greater input is needed for activation. Naundorf et al. then make a radical addition to this model: they allow the threshold for the voltage-dependent transition from the closed state to the open state to depend directly on the number of open channels. This channel cooperativity means that the opening of one channel makes the neighbouring channels more likely to open, providing a positive-feedback mechanism over and above the intrinsic voltage dependence of the channels. This allows sharp spike onsets without affecting the inactivation rate, leaving the onset variability intact. If channel cooperativity does occur, it should depend on the channel density, with sparser channels producing less cooperativity. So Naundorf et al. tested their theory by reducing the effective channel density using the sodium-channel blocker tetrodotoxin. They found that the spikes did indeed become smoother and closer to the HH model. All in all, it’s a tall order to contest a theory as well established as the HH model. Even if Naundorf and colleagues’ theoretical proposals Neurons encode and transmit information by generating action potentials, or ‘spikes’ of voltage that sweep along their membranes (Box 1). It has been 50 years since Hodgkin and Huxley proposed a mechanistic model by which such spikes are generated in an electrically excitable membrane. The theoretical framework associated with their model, the socalled HH formalism, is the closest that neurophysiologists have to Newton’s laws of motion, and it underpins almost all modern models of how neurons work. In a bold and imaginative study, Naundorf et al. (page 1060 of this issue) challenge the HH theory and specifically its applicability to the neurons of the cerebral cortex. Hodgkin and Huxley showed that spikes in neuronal membranes are produced through the interaction of fast depolarizing and slower hyperpolarizing currents that are dynamically dependent on the voltage (Box 1). Without knowing that voltage-dependent ion channels existed, Hodgkin and Huxley reasoned that the experimentally observed activation and inactivation curves of these currents could be explained by the collective action of a population of channels acting independently. This theory was later backed up with thermodynamical arguments. A practical outcome of this framework is a family of computational models stating, in terms of differential equations, how the dynamics of the various voltage-dependent processes evolve with time. In this family of models, the currents are the product of the conductance per ion channel, the density of channels, the fraction of open channels, the membrane area and the electrical driving force due to the ion concentration gradient. One of the key tenets is that the fraction of the open channels is governed by the membrane voltage, with channels themselves being mutually independent. The HH formalism predicts that, when viewed at high temporal precision, spikes rise smoothly once the membrane voltage reaches the activation threshold. Naundorf et al. have tested this by recording spikes from a variety of cortical neurons in vitro and in vivo. They found that the spikes rise much more abruptly The membranes of all cells have a potential difference across them, as the cell interior is negative with respect to the exterior (a). In neurons, certain stimuli can reduce this potential difference by opening sodium-ion channels in the membrane. For example, neurotransmitters interact specifically with ligand-gated sodium-ion channels. So sodium ions flow into the cell, reducing the voltage across the membrane. Once the potential difference reaches a threshold voltage, the reduced voltage causes hundreds of voltage-gated sodium channels in that region of the membrane to open briefly. Sodium ions flood into the cell, completely depolarizing the membrane (b). This opens more voltage-gated ion channels in the adjacent membrane, and so a wave of depolarization courses along the cell — the action potential. As the action potential nears its peak, the sodium channels close, and potassium channels open, allowing ions to flow out of the cell (the hyperpolarizing current) to restore the normal potential of the membrane (c). Because action potentials are an all-or-nothing response, occurring only once the threshold voltage is reached, the strength of the stimulating signal will not produce a larger ‘spike’ in the neuron. Strong stimuli will instead produce a series of action potentials — so it is the frequency, number and timing of the spikes that encode neural information. B.G. & G.B.E. Box 1 | Action potentials in neurons