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

Figure 8

The interactions between neuronal branching and the network context.

(A) Nine synthetic neuronal trees grown competitively on a sample square substrate of homogeneously distributed random carrier points: the competitive greedy growth results automatically in tiling of the available space. (B) Three out of 16 neuronal trees grown competitively on random carrier points distributed on a ring: this simulates well the sharp borders of Purkinje cells in the cerebellum. Whether Purkinje cell dendrites actually tile in sagittal planes of the cerebellum remains to be determined. (C) Hippocampal granule cells from Figure 4 were scaled and positioned along the contours of a human dentate gyrus obtained from a sketch by Camillo Golgi [31]. Growing synthetic CA3 hippocampal pyramidal cells competitively with the limits from the template resulted in realistic hippocampal pyramidal cells affected by mutual avoidance. Synthetic dendrites were overlaid on the background of the original sketch. (D) Bipolar cells (black) in the retina were grown competitively to connect an array of photoreceptors (yellow) to an array of starburst amacrine cells (green, obtained using the algorithm in Figure 3). In such a case the full morphology of bipolar cells is determined by the context of the circuitry, after prescribing soma locations of the bipolar cells. For all panels of Figure 8 precise scale bars would depend on the details of the preparations and were therefore omitted.

Figure 8