Dendrites of cat's spinal motoneurones: relationship between stem diameter and predicted input conductance

1. The electroanatomy of motoneuronal dendrites was analysed using data from fifty-two dendritic trees of four completely reconstructed cat spinal motoneurones that had been labelled with intracellularly injected horseradish peroxidase. The cells belonged to m. triceps surae, and their physiological properties covered much of the known range for this muscle. 2. For each dendritic tree, the input conductance, as seen from the soma, was calculated by the method of Rall (1959), using anatomical measurements of the length and diameter of all branches and different assumed values for dendritic membrane resistivity. 3. There was a strong positive correlation between dendritic stem diameter and the calculated dendritic input conductance. Dendritic input conductance was approximately equal to a constant x (stem diameter)3/2 x (dendritic membrane resistivity)-0.76. 4. The relationship between dendritic stem diameter and computed input conductance was equal to that of Rall's equivalent-cylinder model of a dendritic tree. However, from a number of other points of view, the properties of the reconstructed dendrites differed from those of the model: (a) at branch points, the sum sigma(daughter diameters 3/2) was, on average, 19% greater than the 3/2 power of the parent diameter; (b) dendritic branches often showed a significant amount of tapering, and the mean overall degree of diameter decrease per branch was about 12%; (c) the termination of dendritic branches occurred at widely different distances from the soma within single dendritic trees (true for anatomical as well as for computed electrotonic distances). 5. When used in conjunction with previously published measurements of motoneuronal input resistance and proximal anatomy (Kernell & Zwaagstra, 1981), the present results gave further support to the conclusion that differences in membrane resistivity are of great importance for differences in motoneuronal input resistance. Furthermore, this conclusion was also confirmed by direct observation of the properties of the present four motoneurones: irrespective of the assumed ratio between somatic and dendritic membrane resistivity, there was a statistically significant positive correlation between the measured neuronal input resistance and the required membrane resistivity of soma and dendrites.