Neocortical Axon Arbors Trade-off Material and Conduction Delay Conservation
Figure 2
Artificial arbors were used to examine axonal tree optimization.
(A) Illustration of artificial arbors minimizing spatial (middle) and temporal (right) communication cost for a planar ring arrangement of bouton vertices (open circle) surrounding a cell body (filled circle) (left). For example, path p from cell body (v0) to bouton (v5) is p(v0, v5) = <v0,v1,v2,v3,v4,v5> and <v0,v5>, respectively, with corresponding path lengths dT(v0,v5) = r+4d and r. Note any given edge may be an element in more than one path but for wire length an edge is counted once only. (B) A simple 3D problem to illustrate the difference between minimum spanning tree (MST, left), where spatial cost is minimized using root and bouton vertices only, and Euclidean Steiner Minimal Tree (ESMT, right), where additional vertices called Steiner points (grey dots) may be inserted to further shorten total arbor length provided the interior angle between adjacent vertices and the Steiner point is 120°.