What determines the caliber of axonal branches? We pursue the hypothesis that the axonal caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. We show that for a general cost function the optimal diameters of mother (d_0) and daughter (d_1, d_2) branches at a bifurcation obey a branching law: d_0~(v+2) = d_2~(v+2) . The derivation relies on the fact that the conduction speed scales with the axon diameter to the power v (v = 1 for myelinated axons and v = 0.5 for non-myelinated axons). We test the branching law on the available experimental data and find a reasonable agreement.
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