Motorneurons of different geometry and the size principle

A scheme for constructing computer models of motorneurons is presented. These model neurons display both repetitive firing and action potentials of appropriate time course; the technique combines ideas of Dodge and Cooley (1973) and Kernell and Sjöholm (1972, 1973). This scheme is used to construct models of motorneurons of different input resistance (and hence different geometry) in order to examine Kernell's (1966) observations that (a) small motorneurons require a lower injected current to begin firing than do large motorneurons; but (b) the slope of the injected current-firing rate curve is less for small neurons than large. It is concluded that this behavior is not a simple consequence of the cell geometry, but requires different time courses for a slow conductance across the cell membrane. This observation is consistent with the experimentally observed differences in time course of afterhyperpolarization between large and small cells (Eccles et al., 1958). The models are used to study input-output relations for motorneurons when the input is a steady conductance change on the cell membrane, possibly in conjunction with an injected current. Comparisons are drawn with the experimental observations of Kernell (1965a, 1965b) and Chaplain and Schaupp (1973). It is shown that the observations of Henneman et al. (1965a, 1965b) and Milner-Brown et al. (1973a, 1973b) on the order of recruitment of motorneurons under conditions of natural stimulation may be explained by the following version of the size principle: a given input to a pool of motorneurons causes equivalent conductance changes on each cell of the pool—here equivalent means the input is distributed to corresponding portions of the soma-dendritic tree and is of equal magnitude in mhos. Hypotheses are offered as to how this distribution of input may be accomplished in Nature.