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One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application

Figure 3

Generating dendritic structures by constructing geometric spanning fields: I. the retinal starburst amacrine cell.

(A) Reconstruction of a starburst amacrine cell in the inner plexiform layer of the rabbit retina (data from [24]). (B) Synthetic starburst amacrine cell morphologies can be best obtained by distributing random carrier points along a density ring limited by a circular hull. (C) An example tree grown on random carrier points distributed according to B following the algorithm described in Figure 2. Spatial jitter was added to reproduce the wriggliness of the original structure. (D) A tree grown on exactly the same points as (C) with a lower balancing factor. (E) The number of randomly distributed carrier points and the balancing factor bf determine the synthetically generated morphology. Here, the areas are plotted in which the synthetic trees match the original according to certain criteria (blue: total cable length ±200 µm; red: total number of branch points ±5; green: mean path length to the root ±3 µm). The area of overlap corresponds to a reasonable parameter set for the synthetic trees. (F–H) Branch order distribution, path length distribution and Sholl intersections are compared for the original tree (red) and for one sample synthetic tree (grey).

Figure 3