"Methods from Computational Topology and Geometry for Analysing Neuronal Tree and Graph Data"

总结 随着科学的成熟，从描述到量化的进步是必不可少的。然而， 脑回路的基本单位--单个神经元--继续提出方法上的挑战。甚至 神经元树形的度量标准（度量）的定义仍然是一个开放的研究 问题.如果没有这样的指标，研究人员就无法准确地将神经元分类为细胞类型，这是一个至关重要的问题。 进一步了解电路组件以及它们如何协同工作。先进的方法， 计算拓扑学和几何学，直到最近才从纯数学发展到 数据分析，将被用来提取，表征，并以一种优雅的方式分类神经元形状， 结合了潜在的动态电生理特性。第一个具体目标将适用于新的 数学方法来定义和计算各种神经元形状的度量。一 称为"持久性摘要"的计算拓扑分析将用于生成不变量 然后可以使用不同的范数来比较神经元的表示。这其中的一个重要优势 方法的一个优点是，它可以灵活地处理定义在神经元上的任意函数，包括纯结构函数 (such如离索马的距离）或具有电生理意义的功能（如电紧张距离 或传播延迟），并且因此可以结合动态。一种更高级的方法， 度量空间之间的Gromov-Hausdorff距离也将被探索。这样生成的指标将是 用于分类和聚类，神经元形状空间的可视化，以及基于形状的 数据库搜索来自光学或电子显微镜的神经元重建。第二个目标将 使用莫尔斯理论从光显微镜数据中重建单个神经元，或将示踪剂注射 数据来总结投影模式的结构。这种方法保留了丢失的形状信息 当这样的数据在连接矩阵中被表征时。此外，这些方法将用于构建 共识树，它可以作为不同的重建产生的不同的总结， 算法这些工具将在适当的开源软件许可证下免费共享， 通过插件到广泛使用的软件平台以及网络服务到神经元的社区存储库， 形态学研究人员团队包括理论家，实验家，数据科学家和最终用户，所有 具有丰富的相关经验。除了能够理解正常的大脑回路， 它的组成神经元，提出的方法也将使研究人员能够表征的变化， 神经元的形状在病理改变的电路，与应用转基因动物模型的疾病。

Summary Progress from description to quantification is essential as a science matures. Yet numerical analysis of the elementary unit of brain circuitry—the individual neuron—continues to pose methodological challenges. Even the definition of a measurement yardstick (a metric) for the tree shape of a neuron remains an open research problem. Without such metrics, researchers cannot accurately classify neurons into cell types, an essential step toward understanding the circuit components and how they work together. Advanced methods from computational topology and geometry, which have only recently made their way from pure mathematics into data analysis, will be used to extract, characterize, and classify neuronal shapes in a way that elegantly incorporates the underlying dynamical electrophysiological properties. The first specific aim will apply new mathematical methods to define and compute metrics on the shapes of a wide variety of neurons. A computational topological analysis called “persistence summaries” will be used to generate invariant representations of the neurons that can then be compared using different norms. An important strength of this method is that it works flexibly with arbitrary functions defined on the neurons, including purely structural ones (such as distance from the soma) or functions with electrophysiological meaning (such as electrotonic distance or propagation delays) and can therefore incorporate dynamics. A more advanced approach based on the Gromov-Hausdorff distance between metric spaces will be also explored. The metrics so generated will be used for classification and clustering, visualization of the space of neuronal shapes, and shape-based database search for neuronal reconstructions derived from light or electron microscopy. The second aim will use Morse theory to reconstruct individual neurons from light microscopic data, or skeletonize tracer injection data to summarize the structure of projection patterns. This approach retains shape information, which is lost when such data are characterized in a connectivity matrix. Further, these methods will be applied to construct consensus trees, which can be used as a summary of different reconstructions produced by different algorithms. The tools will be freely shared under a suitable open-source software license, and made available via plugins to widely used software platforms as well as web services to a community repository of neuronal morphologies. The team of researchers includes theorists, experimentalists, data scientists, and end users, all with extensive relevant experience. Apart from enabling the understanding of normal brain circuitry in terms of its component neurons, the proposed methods will also allow researchers to characterize changes in the shape of neurons in pathologically altered circuits, with applications to transgenic animal models of disease.