Electrophysiology of a dendritic neuron model.

The development of a mathematical model of dendritic neurons was begun because of a need to combine three different kinds of knowledge into a coherent theory. First, we have the anatomical concept of the neuron, together with the anatomical fact that extensive dendritic branching is characteristic of many important neuron types. Second, we have the theoretical development of the nerve membrane models that Dr. Cole' has just reviewed for you. Finally, we have a detailed body of quantitative electrophysiological information that has been obtained from individual neurons by means of intracellular and extracellular microelectrodes. I doubt that any biophysicist will be surprised to be told that a mathematical model is essential to the development of a neuron theory that aims to satisfy simultaneously these three kinds of information. There are further objectives of such a neuron model that also deserve to be mentioned. The integration of synaptic excitation and inhibition at the neuronal level can be subjected to theoretical analysis in terms of such a model. This, in turm, has relevance to the next level of theoretical neurophysiology, namely, inter-actions between several neurons and also between large populations of neurons. The dendritic neuron model may even have relevance to the problem of learning. Having made that speculative remark, I now return to the well-established anatomical facts of dendritic branching. Three important examples of such branching are illustrated in Fig. 1. These illustrations have been reproduced from the work of Ramon y Cajal (1909), of more than fifty years ago; their validity has been confirmed by many histologists. I show them today to remind you that branching can be very extensive. In the case of the Purkinje cell, detailed measurements (Fox and Barnard, 1957) yield an estimate that the dendritic surface area is as much as eighty to one hundred times that of the soma; in the case of motoneurons or pyramidal cells of cat, the dendritic surface area has been estimated to be as much as ten