Diameter scaling law

The systematic variation of diameters in branched networks has tantalized biologists since da Vinci’s rule for trees. Like trees, neuronal dendrites show systematic diameter changes across branch points with distal branches being narrower than proximal ones. These diameter changes have functional implications for the spread of electrical signals through dendrites (e.g. Rall’s Law). Using a super-resolution method that allows measurement of the diameters of all dendrites down to 200 nm in the highly branched Drosophila Class IV da sensory neurons, we have discovered a new diameter-scaling law: the cross-sectional area is proportional to the number of dendrite tips supported by the branch (plus a constant). The law accords with microtubules providing the force and transport for dendrite tip growth. Moreover, the law generalizes to motion-sensing T5 neurons in the Drosophila central nervous system. Our scaling law, which differs from Rall’s law and therefore has functional implications, will facilitate segmentation in connectomic studies.