1 Bioinformatics and Systems Biology Program , University of California , San Diego , UK.
2 Integrative Biology Laboratory, The Salk Institute for Biological Studies , La Jolla, CA 92037 , USA.
Proc Biol Sci. 2019 May 15;286(1902):20182727. doi: 10.1098/rspb.2018.2727.
Neural arbors (dendrites and axons) can be viewed as graphs connecting the cell body of a neuron to various pre- and post-synaptic partners. Several constraints have been proposed on the topology of these graphs, such as minimizing the amount of wire needed to construct the arbor (wiring cost), and minimizing the graph distances between the cell body and synaptic partners (conduction delay). These two objectives compete with each other-optimizing one results in poorer performance on the other. Here, we describe how well neural arbors resolve this network design trade-off using the theory of Pareto optimality. We develop an algorithm to generate arbors that near-optimally balance between these two objectives, and demonstrate that this algorithm improves over previous algorithms. We then use this algorithm to study how close neural arbors are to being Pareto optimal. Analysing 14 145 arbors across numerous brain regions, species and cell types, we find that neural arbors are much closer to being Pareto optimal than would be expected by chance and other reasonable baselines. We also investigate how the location of the arbor on the Pareto front, and the distance from the arbor to the Pareto front, can be used to classify between some arbor types (e.g. axons versus dendrites, or different cell types), highlighting a new potential connection between arbor structure and function. Finally, using this framework, we find that another biological branching structure-plant shoot architectures used to collect and distribute nutrients-are also Pareto optimal, suggesting shared principles of network design between two systems separated by millions of years of evolution.
神经树突（树突和轴突）可以被视为将神经元的细胞体连接到各种前突触和后突触伙伴的图。已经提出了几种拓扑约束条件，例如最小化构建树突所需的电线数量（布线成本），以及最小化细胞体和突触伙伴之间的图距离（传导延迟）。这两个目标相互竞争——优化一个目标会导致另一个目标的性能下降。在这里，我们描述了神经树突如何使用帕累托最优理论来解决这种网络设计权衡问题。我们开发了一种算法来生成接近在这两个目标之间平衡的树突，并证明该算法优于以前的算法。然后，我们使用该算法研究神经树突离帕累托最优有多近。分析了来自许多大脑区域、物种和细胞类型的 14145 个树突，我们发现神经树突比随机和其他合理的基准更接近帕累托最优。我们还研究了树突在帕累托前沿的位置以及树突到帕累托前沿的距离如何用于对某些树突类型（例如轴突与树突或不同的细胞类型）进行分类，这突出了树突结构和功能之间的新潜在联系。最后，使用该框架，我们发现另一种生物分支结构——用于收集和分配营养物质的植物茎结构也是帕累托最优的，这表明这两个系统之间存在网络设计的共享原则，这两个系统之间的进化时间相差数百万年。
