A scaling law derived from optimal dendritic wiring

The wide diversity of dendritic trees is one of the most striking features of neural circuits. Here we develop a general quantitative theory relating the total length of dendritic wiring to the number of branch points and synapses. We show that optimal wiring predicts a 2/3 power law between these measures. We demonstrate that the theory is consistent with data from a wide variety of neurons across many different species and helps define the computational compartments in dendritic trees. Our results imply fundamentally distinct design principles for dendritic arbors compared with vascular, bronchial, and botanical trees.