Dendritic caliber and the 3/2 power relationship of dentate granule cells

A quantitative examination of granule cell dendritic caliber and knowledge of dendritic lengths allows assessment of the distribution of dendritic membrane and the 3/2 power relationship at branch points. This paper presents caliber data of Golgi-impregnated rat dentate gyrus. We used camera lucida drawings of the dendritic trees of 15 dorsal leaf and 15 ventral leaf granule cells to quantify mean dendritic caliber, dendritic taper, the 3/2 power relationship of parent and sibling dendritic diameters at branch points, and surface area. First-order dendrites vary substantially in diameter. However, the mean caliber of all other dendrites is uniform across the proximal two-thirds of the molecular layer for the dorsal and ventral leaves. The average diameter here is 1 micron. More distally, only mean ventral leaf dendritic caliber declines. Granule cell dendritic taper is due primarily to caliber decreases at branch points and not to a gradual decline in diameter across the length of a dendritic segment. Comparing the parent segment diameter raised to the 3/2 power with the sum of the 3/2 powers of the two sibling segment diameters reveals, for the dendritic tree located within the distal two-thirds of the molecular layer, the desired 3/2 power relationship for the dorsal and ventral leaves. More proximally, where first-, second-, and third-order dendrites branch sequentially across a 60-100-micron extent, a 3/2 power relationship is not obtained. For the average dorsal leaf granule cell, dendritic surface area (without spines) is 11,984 micron2. The ratio of dendritic to somatic surface area is 28:1. Discussion of these data includes their implications for electrotonic modeling of the dentate granule cell.