Axon arbor trade-off between wiring cost, delay, and synchronization in neuronal networks

The axonal signaling speed and synchronization are critical features that allow neural networks to communicate and compute. However, the axon arbor design with small latency and precise synchronization often incurs a high wiring cost, which leads to larger resources to build and maintain. We study the tradeoffs between wiring cost, signaling delays, and synchronization precision. We characterize the Pareto-optimal curve using a combinatorial geometric optimization problem and propose a numerical algorithm to solve it. The computed tradeoff space has a sweet spot in which low latency and precise synchronization can be achieved using moderate wiring cost. We observe that the axon arbor graph that realizes the performance sweet spot has its branching (bifurcation) angles to have a distribution that is similar to the branching angle distribution of the neocortical axon arbor. This resemblance supports that axon arbors may be designed to realize such sweet spots. Our proposed optimization procedure can be extended to account for other design considerations and to more realistic axon arbor models, and the implications of axon arbors designed to exploit the sweet spots merit further investigation.