By W. K. TAYLOR
Department of Anatomy, University College, London
The value of predictions made about the behaviour of the nervous system by models and analogues depends strongly on the accuracy of the assumptions concerning neuron properties on which their design is based. The most accurate assumptions that have been made for the properties of a particular neuron membrane are those of Hodgkin & Huxley ( 1952). These were based on careful measurement and led to equations for the membrane potential which were only solved after considerable labour. Extended solutions were obtained by Cole ( 1955) who used a high-speed digital computer. Minutes of computer time were required to predict msec. of membrane potential and as a digital computer can only handle one computation at any instant of time, a whole set of computers would be required for simultaneous calculation of the interactions between a set of nerve membranes. The alternative would be to compute each membrane potential in turn but the length and complexity of a programme based on the original equations would be prohibitive for two or more interacting membrane models.
Lack of quantitative physiological data has held up the extension of digital computer techniques to neural interaction problems and in particular to the mechanism of synaptic transmission that plays such an important part in the functioning of the nervous system. It is understandable, therefore, that there have been many suggestions for approximating the description of neural activity so that larger numbers of neurons can be considered simultaneously. Some approximations have led to the construction of electrical models but the value of their predictions is often difficult to assess.
Uttley ( 1954) follows a suggestion made by Eccles ( 1953) and assumes that a neuron fires if the post-synaptic potential rises by ten, or in general, n times the rise produced by a single synaptic impulse. This is probably quite correct for the single afferent volley to a motoneurone considered by Eccles but it does not tell us what firing-rate to expect if impulses continue to arrive and produce temporal summation. Temporal summation plays an important part in neurons like Renshaw cells that have post-synaptic potentials lasting up to 50 msec. or more. McIntyre ( 1956) has pointed out that many other neurons have a much longer lasting post-synaptic potential than the 4 msec. decay time constant of the motoneuron. We thus require, a different model for each neuron type or the same general model with suitably adjusted parameters. Several years ago, the author ( Taylor, 1955) constructed an approximate