041 An electric model of nerve
In general, it is legitimate to study a model of a mysterious process if three conditions are fulfilled: 1. Several features of the mystery must be known. 2. The model must contain the absolute minimum of working parts to reproduce the known features. 3. The model must reproduce other features, either as predictions, or as unexpected combinations.
There are several legitimate models of nerve. The earliest ones were simple circuits containing resistance and capacitance, and copied only the passive properties of nerve — they did not propagate an impulse or even suggest how an impulse would be propagated. They had the advantage of drawing attention to the similarity of a nerve to a leaky cable such as a submarine telegraph line. Since the mathematical equations relating to leaky cables were worked out during the last century, physiologists could apply rigorous and well-tested notions to those passive features of nerve which the „leaky cable“ models reproduced. Later, electro-chemical models were discovered. The best known of these is, incongruously enough, an iron wire in strong nitric acid. The acid forms an oxide film on the wire so that the iron within does not dissolve. This film is „passive“ but breaks down when scratched or stimulated electrically, for example, when the wire is touched with a piece of zinc. When stimulated, an impulse passes quite quickly down the wire, and this impulse has many of the properties of a nerve impulse: it is a vortex ring of electro-chemical action. During the passage of the impulse the passive film is decomposed momentarily, and the nitric acid attacks the iron with the evolution of nitric oxide. A fresh passive film is formed and this is „refractory“ for a short time; the wire cannot propagate another impulse immediately after one has passed by. This is a good dynamic model but has the disadvantage that the nature of the passive film is almost as mysterious as the nerve fibre itself; it is not very satisfactory to equate two unknowns.
It is possible to retain the simplicity of the leaky cable models and add to them a dynamic element to represent the mechanism in a nerve which provides the miniature electro-chemical explosion seen as an impulse. The circuit of a working model is shown in Figure 21. The capacitors and resistors provide the elements of a leaky cable, and the battery maintains a steady voltage such that the „inside“ of the model is negative to the outside. The addition to the circuit which endows it with the power to propagate an impulse is the neon tube, also connected, in effect, between the inside and outside and biased to a few volts below its striking voltage, which in the case of the miniature tubes used for the embodiment of this circuit, is between 50 and 60 volts. Every element (consisting of resistors R1, R2, R3, R4, the neon tube and the capacitor C) is connected to the adjacent elements on both sides through the capacitors C2, C3, C4 and C5. These capacitors join points of opposite polarity of the neon tubes, so that they may be envisaged as being in the form of a criss-cross connection, a sort of lazy-tongs arrangement extending down the chain of elements.
Providing all the neon tubes are below their striking voltage, the system is stable and inert. If, however, a voltage is applied as indicated by the external battery B1 or B2, the voltage across one of the neon tubes rises, and when it reaches the striking threshold the tube ionises and partially discharges the capacitor C1. When the tube ionises the voltage across it drops to the extinction level. This voltage drop is applied to adjacent tubes through C2, C3 and C4, C5, in such a sense as to increase the voltage across them (owing to the criss-cross connection) and they accordingly strike in their turn. The impulse is thus propagated to both ends of the chain at a velocity depending on the values of the capacitors and resistors.
Effects such as this are in fact seen in the central nervous system; a change in stimulus frequency has often been found to invert the response, and the anomalous effects of flicker have been described in some detail. It may well be that these otherwise rather puzzling phenomena may be explicable in terms of the peculiar properties of rapidly adapting inhibitory synapses, displayed so clearly in this simple model. The fact that this model is affected by and produces electrical rather than chemical or mechanical changes should be regarded as a convenience and a coincidence. It is not, of course, proof that the electrical changes in nerve are the essence of nervous action. The model is simply the analogue of one set of familiar mathematical expressions relating to passive networks linked by a non-linear operator in the form of a discharge tube. It could quite well be formed of chemical or mechanical parts and does not in theory contain more information than do the algebraic equations. Its advantage is that, being a real object, it has constant dimensions; hence its predictions are more explicit and detailed than those of the equations, in which the constants are rather more arbitrary and independent.