A Universal Property of Axonal and Dendritic Arbors

Axonal and dendritic arbors can be characterized statistically by their spatial density function, a function that specifies the probability of finding a branch of a particular arbor at each point in a neural circuit. Based on an analysis of over a thousand arbors from many neuron types in various species, we have discovered an unexpected simplicity in arbor structure: all of the arbors we have examined, both axonal and dendritic, can be described by a Gaussian density function truncated at about two standard deviations. Because all arbors are characterized by density functions with this single functional form, only four parameters are required to specify an arbor's size and shape: the total length of its branches and the standard deviations of the Gaussian in three orthogonal directions. This simplicity in arbor structure can have implications for the developmental wiring of neural circuits.