Power-law for axon diameters at branch point

Background: Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches? Results: We pursue the hypothesis that the axon caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. For a general cost function, we show that the optimal diameters of mother and daughter branches at a bifurcation satisfy a power law. The derivation relies on the fact that the axon conduction speed scales as a power of axon diameter. Although available data are consistent with the law, there is a large spread in the data. Future experimental tests will determine whether this spread is due to biological variability or measurement error. Conclusions: Minimization of arbor volume and signal propagation delay may have been an important factor in the evolution of the brain.