Local optimization of neuron arbors

How parsimoniously is brain wiring laid out, that is, how well does a neuron minimize costs of connections among its synapses? Neural optimization of dendritic and axonic arbors can be evaluated using a generalization of the Steiner tree concept from combinatorial network optimization theory. Local branch-junction geometry of neuronal connecting structures fits a volume minimization model well. In addition, volume of the arborizations at this neighborhood level is significantly more strongly minimized than their length, signal propagation speed, or surface area. The mechanism of this local volume optimization resembles those involved in formation of nonliving tree structures such as river junctions and electric-discharge patterns, and appears to govern initial nerve growth-cone behavior through vector-mechanical energy minimization.