In developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters. Supplementary Information The online version contains supplementary material available at 10.1007/s11538-020-00847-3.

中文翻译：

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揭示丝状网络中环结构开始时间的拓扑数据分析方法

在发育生物学以及其他生物系统中，可以使用蛋白质位置的时间序列数据捕获新兴结构和组织。在分析这些与时间相关的数据时，不仅要确定拓扑特征是否出现，而且要确定它们形成的时间，这是一个共同的挑战。例如，在大多数细胞中，肌动蛋白丝与肌球蛋白运动蛋白相互作用并组织成聚合物网络和高级结构。环形通道就是这种结构的例子，它们随着时间的推移保持恒定的直径，并在细胞分裂、发育和伤口愈合等过程中发挥关键作用。鉴于在体内研究肌动蛋白与肌球蛋白相互作用的局限性，我们使用基于复杂代理的模型生成细胞中蛋白质聚合物相互作用的时间序列数据。由于数据具有丝状结构，我们建议沿肌动蛋白丝采样并分析每次生成的点云的拓扑结构。基于持久同源性的现有工具，我们开发了一种拓扑数据分析 (TDA) 方法，用于评估此动态数据中的有效环生成。该方法在与数据中组织的出现相对应的路径中通过时间连接拓扑特征。在这项工作中，我们还提出了评估感兴趣的拓扑特征是否重要以及它们是否有助于在模拟蛋白质相互作用中形成新兴孔（环形通道）的方法。特别是，我们使用 MEDYAN 模拟平台来表明该技术可以区分由不同运动蛋白结合参数产生的肌动蛋白细胞骨架组织。补充信息 在线版本包含可从 10.1007/s11538-020-00847-3 获得的补充材料。