Branching out: A mathematical law of dendritic connectivity

Neuroscientists have derived a surprisingly simple and general equation that directly relates dendrite length with the number of branch points, dendrite spanning volume, and number of synapses. More specifically, they’ve shown that optimal dendritic wiring successfully predicts a 2/3 power law between these three factors. (A power law is a mathematical relationship between two quantities – found throughout the natural world – in which one quantity varies as a power of the other, often identifying simple rules underlying complex structures.) Their theory is both consistent with data gleaned from many types of neurons from a wide range of species yet specific to dendritic trees, leading them to conclude that their findings suggest that there are distinct design principles for dendritic arbors compared with vascular, bronchial, and botanical trees.