Applications of persistent homology to spatial dynamics in cell biology

Abstract: Actin filaments are polymers that interact with motor proteins inside cells and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Datasets that describe the interaction of actin filaments with motors through time can either be generated used stochastic agent-based models or can come directly from experiments, typically in the form of fluorescence videos. In studying the emergence and maintenance of ring channel structures in such complex time-series data, we develop tools based on persistent homology that can distinguish between distinct filament organizations and experimental conditions. This work raises interesting questions about assessing the significance of topological features in topological summaries such as persistence diagrams.

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