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Neurons use fractal networks for better connectivity

Neurons use fractal networks for better connectivity

Many of nature’s fractal objects benefit from the favorable functionality that comes from pattern repetition at various sizes. Examples from nature include beaches, lightning, rivers, and trees, as well as cardiovascular and respiratory systems such as the bronchial tree. Neurons, like trees, are thought to represent a common kind of fractal branching activity.

Although prior neuron research has calculated the scaling characteristics of their dendritic branches, this has generally been done to categorize neuron morphologies rather than quantify how neurons benefit from their fractal geometry.

Why does the body use fractal neurons rather than, say, the Euclidean wires seen in common electronics? Within the mammalian brain, neurons create vast networks, with individual neurons utilizing up to 60,000 connections in the hippocampus alone. They link to the retina’s photoreceptors, letting humans see, and to the limbs, allowing people to move and feel, in addition to their connections within the brain. Given its relevance as the body’s “wire,” the study focuses on the effect of fractal scaling in creating neuron connections.

“By distorting their branches and looking at what happens, we were able to show that the fractal weaving of the natural branches is balancing the ability of neurons to connect with their neighbors to form natural electric circuits while balancing the construction and operating costs of the circuits,” Rowland said.

(a) An example confocal micrograph (x–y layer) showing three neighboring dendritic arbors, each spanning the oriens (SO), pyramidale (SP), radiatum (SR), and lacunosum-moleculare (SLM) strata of the CA1 region. The dashed lines represent the strata boundaries and the bar corresponds to 100 μm. (b) A three-dimensional model of a dendritic arbor (reconstructed from a stack of micrographs in the z direction using Neurolucida and displayed using MATLAB) featuring the apical (blue) and basal (red) arbors and the soma (black). The neuron’s axon arbor is not shown. (c) Schematic showing the neuron parameters LWϕ, and θ. (d) Histogram of N, the number of neurons with a given D value, measured for the neurons’ apical and basal arbors.

D = 1.4 H-Tree fractal (generated using Mathematica and displayed using MATLAB) with W = 1 μm (a) and an example neuron’s basal arbor (reconstructed using Neurolucida and displayed using MATLAB) with median W = 1.4 μm (b). The branch level i is colored as follows: red (1st branch), orange (2nd), yellow (3rd), green (4th), blue (5th), and purple (6th). Histograms for an H-Tree (c) and neuron (d) plotting the number of branches N with a given value of L/Lmax. Panels (e) and (f) show the analysis of (c) and (d) plotted in log–log space. Panels (g) and (h) take the H-Tree and neuron shown in (a) and (b) and adjust all their branch lengths to be equal. Additionally, the H-Tree’s forking angle ϕ has been adjusted to 37° (the median value of the basal arbors).
(a) Schematic diagram of a coronal slice through the hippocampus at Bregma −4.52 mm showing the collection region (red box) within hippocampal CA1 (darkened area); the somata layer is denoted by the dashed line. (b) Confocal micrographs of Golgi-Cox stained cells. Three 774 by 774 µm cross-sections separated by 2 µm in the z-direction are shown. (c) A model showing a neuron’s soma (outlined in white) as well as its basal (red) and apical (blue) dendritic arbors superimposed on the original micrograph. The image in (c) was generated using Neurolucida.

Nature’s fractals benefit from the fact that they develop at various sizes, according to Taylor, who has long looked to fractals for bioinspiration. While trees are the most well-known example of fractal branching, he claims that this research shows how neurons vary from trees.

“Whereas the fractal character of trees originates predominantly from the distribution of branch sizes, the neurons also use the way their branches weave through space to generate their fractal character.”

See Also

Taylor, a Cottrell Scholar of the Research Council for Science Advancement, was given a broad U.S. patent in 2015 for not just his vision-related artificial fractal-based implants, but also for any such implants that link signaling activity with nerves for any purpose in animal and human biology.

How neurons exploit fractal geometry to optimize their network connectivity, Julian H. Smith, Conor Rowland, B. Harland, S. Moslehi, R. D. Montgomery, K. Schobert, W. J. Watterson, J. Dalrymple-Alford & R. P. Taylor

Published: January 2021, Scientific Reports volume 11, Article number: 2332
DOI: https://doi.org/10.1038/s41598-021-81421-2

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