TY - JOUR T1 - A Scaling Law Governing Branching Morphogenesis in Neuronal Dendrites JF - bioRxiv DO - 10.1101/2020.04.13.039388 SP - 2020.04.13.039388 AU - Maijia Liao AU - Jonathon Howard Y1 - 2020/01/01 UR - http://biorxiv.org/content/early/2020/04/13/2020.04.13.039388.abstract N2 - Branched networks are ubiquitous in nature, ranging in size from watercourses and trees to cellular organelles and the cytoskeleton1–5. Often, the branch diameters change systematically throughout the network, with the proximal branches frequently thicker than the distal ones. This variation is usually interpreted as an adaptation to, or consequence of, the flow of materials and/or information through the network. To describe the changes in diameter over branch points, scaling or allometric relations of the form , have been proposed where dm (dd1,dd2) is the mother (daughters) diameter and p is the exponent. Among the most well-known laws are da Vinci’s rule for trees6 (p = 2), Murray’s law7 for vascular and pulmonary systems (p = 3), and Rall’s law8 in the nervous system (p = 3/2). While scaling laws have a strong theoretical foundation, based on optimality arguments, and there is some experimental support9,10, there is a dearth of critical tests and recent work in neurons, for example, finds sloppy morphology that defies optimization principles11. To test quantitatively scaling laws in the nervous system, we have established a new image-analysis method that allows us to resolve dendrite diameters down to 200 nm allowing us to measure the diameters of all branches in Drosophila Class IV dendritic arborization neurons, a model cell to study branching morphogenesis12. Unexpectedly, although the branch diameters vary systematically throughout the dendritic networks in these cells, they do not follow any of the known scaling laws. We propose a new scaling law governing dendritic morphology development. The law follows from two concepts: there is an incremental cross-sectional area needed to support each terminal branch, and there is a minimum branch diameter. The law is consistent with microtubule-based transport and tip extension in these cells. The new scaling law may also apply more generally to branching in other biological networks including the circulatory systems of animals13,14 and plants15,16.Competing Interest StatementThe authors have declared no competing interest. ER -