Branching Law for Axons

Dmitri B. Chklovskii; Armen Stepanyants

paper

Branching Law for Axons

arXiv:physics/0302039

Abstract

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: $d_{0}^{ν + 2} = d_{1}^{ν + 2} + d_{2}^{ν + 2}$ . The derivation relies on the fact that the conduction speed scales with the axon diameter to the power $ν$ ( $ν = 1$ for myelinated axons and $ν = 0.5$ for non-myelinated axons). We test the branching law on the available experimental data and find a reasonable agreement.

8 pages, 4 figures