Figure 4. Spiny cell axon arbor wiring compared with minimum-length tree.

(A) Example putative excitatory pyramidal cell axon arbor (coronal view) showing the location of numerous boutons (upper), its Euclidean Steiner Minimal Tree (ESMT) graph (middle), and overlay of axon arbor and graph (lower) with dotted circles (white) showing locations where axon wiring was absent in minimum-length graph taken to connect same bouton set. (Key: axon wiring  =  grey lines, graph wiring  =  red lines, axonal bouton  =  yellow dots, cell body  =  green dot; anatomical axes: D, dorsal; L, lateral; P, posterior.) (B) Example of the shortest path from axon origin (root vertex) of this neuron to a selected bouton (upper, see region of interest) for the biological arbor (middle) was, after branching from the main descending axon, fairly direct (0.85 mm path length) but for the length-minimized tree (lower) the route was more circuitous (2.63 mm path length), including a trajectory reversal (marked by blue asterisk), because the artificial arbor lacked wire present in the axon arbor (dotted blue lines). Arrows show direction of flow from axon origin to bouton. (Key: shortest path  =  thick black lines, unvisited arbor wiring  =  grey lines, axon wiring absent in graph  =  dotted blue lines.).