2020/03/22 by Dhananjay Bhaskar, Bhaskar, Dhananjay, William Y. Zhang +3
Computer Science · Medicine · #Adaptation and Self-Organizing Systems (nlin.AO) #Clusterin in disease pathology #FOS: Biological sciences #FOS: Physical sciences #Quantitative Methods (q-bio.QM) #Soft Condensed Matter (cond-mat.soft) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2003.10008
openalex publication_date 2020/03/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Interacting, self-propelled particles such as epithelial cells can\ndynamically self-organize into complex multicellular patterns, which are\nchallenging to classify without a priori information. Classically, different\nphases and phase transitions have been described based on local ordering, which\nmay not capture structural features at larger length scales. Instead,\ntopological data analysis (TDA) determines the stability of spatial\nconnectivity at varying length scales (i.e. persistent homology) and can\ncompare different particle configurations based on the "cost" of reorganizing\none configuration into another. Here, we demonstrate a topology-based machine\nlearning approach for unsupervised profiling of individual and collective\nphases based on large-scale loops. We show that these topological loops (i.e.\ndimension 1 homology) are robust to variations in particle number and density,\nparticularly in comparison to connected components (i.e. dimension 0 homology).\nWe use TDA to map out phase diagrams for simulated particles with varying\nadhesion and propulsion, at constant population size as well as when\nproliferation is permitted. Next, we use this approach to profile our recent\nexperiments on the clustering of epithelial cells in varying growth factor\nconditions, which are compared to our simulations. Finally, we characterize the\nrobustness of this approach at varying length scales, with sparse sampling, and\nover time. Overall, we envision TDA will be broadly applicable as a\nmodel-agnostic approach to analyze active systems with varying population size,\nfrom cytoskeletal motors to motile cells to flocking or swarming animals.\n