轴突的分支定律
Branching Law for Axons
摘要：
是什么决定了轴突分支的口径？我们追求的假设，轴突口径已经发展到最小化信号传播延迟，同时保持乔木体积最小。我们表明，对于一般的成本函数的最佳直径的母亲（$d_0$）和女儿（$d_1$，$d_2$）分支在一个分支服从分支律：$d_{0}^{ν+2}=d_{1}^{ν+2} + d_{2}^{ν+2}$。推导依赖于传导速度与轴突直径成比例的事实，即功率$ν$（有髓鞘轴突的$ν=1$和无髓鞘轴突的$ν=0.5$）。我们测试了现有的实验数据的分支法律，并找到一个合理的协议。
英文摘要：
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.
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