The Narrowing of Dendrite Branches across Nodes follows a well-defined Scaling Law

Abstract

words)Branched networks are ubiquitous in nature, ranging in size from watercourses and trees to cellular organelles and the cytoskeleton [1][2][3][4][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 ( , ) is the mother (daughters) diameter and is the exponent. Among the most well-known laws are da Vinci's rule for trees 6 ( = ), Murray's law 7 for vascular and pulmonary systems ( = ), and Rall's law 8 in the nervous system ( = / ). While scaling laws have a strong theoretical foundation, based on optimality arguments, and there is some experimental support 9,10 , there is a dearth of critical tests and recent work in neurons, for example, finds sloppy morphology that defies optimization principles 11 . 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 morphogenesis 12 . 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 animals 13,14 and plants 15,16 .

Dynamic Instability of Dendrite Tips Generates the Highly Branched Morphologies of Sensory Neurons

“…An important difference between dendrite tips in class IV cells and the growth cones seen in these other cells is that the tips of class IV dendrites are much smaller. The diameter of class IV terminal dendrites is only ~200 nm (Liao et al, 2021), as small as a single filopodium, the finest feature of growth cones observed under the light microscope. Thus, tip-growth mechanisms in class IV dendrites likely differ from growth-cone-based growth.…”

“…Dendrite death occurred when the last point disappeared during a shrinkage event. Contact, defined as a tip getting closer than 0.15 m to another branch (roughly the radius of the terminal branch (Liao et al, 2021), switched a growing tip to a shrinking one with the post-contact dynamics (Table 1B).…”

Counting fluorescently labeled proteins in tissues in the spinning disk microscope using single-molecule calibrations

“…In each step of MC optimization method, a simulated image is generated based on , where A stands for the image intensity, N stands for image photon shot noise. The MC optimization aim to find the σ and λ that minimize the square of the difference (Liao et al ., 2021): , where I sim and I exp stand for 1D intensity profiles for simulated and experimental images separately, m stands for pixel number. Six 1000-step simulations were carried out for σ and λ detection.…”

Focal laser stimulation of fly nociceptors activates distinct axonal and dendritic Ca2+ signals

“…To see this figure in color, go online. (24). Therefore, both the narrower and wider stimuli will fall mostly within the proximal dendrites (and soma), whereas the wide stimulation will fall mostly outside the distal dendrites.…”