Interacting, self-propelled particles such as motile epithelial cells can dynamically URLanize into large-scale patterns. In such living systems, cell number and density can vary dramatically over time due to proliferation, which is not commonly considered in other active matter systems. As a consequence, it remains challenging to determine individual and collective phases over varying populations sizes without a priori information. Here, we demonstrate an unbiased machine learning approach to analyze multiparticle clusters based on topological structure, which is robust to changes in population size. For a given particle configuration , topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology) , and can compare different particle configurations based on the "cost" of URLanizing one configuration into another.  We show that TDA can accurately map out phase diagrams for interacting particles with varying adhesion and self-propulsion , at constant population size as well as when proliferation is permitted. Next, we use this approach to profile our recent experiments on the clustering of epithelial cells in varying growth factor conditions  . Finally, we characterize the statistical robustness of this approach over repeated simulations and with random particle removal . Overall, we envision TDA will be broadly applicable as a model-agnostic approach to analyze active systems with varying population size, from cytoskeletal motors to motile cells to flocking or swarming animals.
Interacting, self-propelled particles such as epithelial cells can dynamically URLanize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase transitions have been described based on local ordering, which may not capture structural features at larger length scales. Instead , topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology) and can compare different particle configurations based on the "cost" of URLanizing one configuration into another. Here, we demonstrate a topology-based machine learning approach for unsupervised profiling of individual and collective phases based on large-scale loops. We show that these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to map out phase diagrams for simulated particles with varying adhesion and propulsion , at constant population size as well as when proliferation is permitted. Next, we use this approach to profile our recent experiments on the clustering of epithelial cells in varying growth factor conditions , which are compared to our simulations . Finally, we characterize the robustness of this approach at varying length scales, with sparse sampling, and over time . Overall, we envision TDA will be broadly applicable as a model-agnostic approach to analyze active systems with varying population size, from cytoskeletal motors to motile cells to flocking or swarming animals.
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motile
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large-scale patterns. In such living systems, cell number and density can vary dramatically over time due to proliferation, which is not commonly considered in other active matter systems. As a consequence, it remains challenging to determine individual and collective phases over varying populations sizes
complex multicellular patterns, which are challenging to classify
R
Here, we demonstrate an unbiased machine learning approach to analyze multiparticle clusters based on topological structure, which is robust to changes in population size. For a given particle configuration
Classically, different phases and phase transitions have been described based on local ordering, which may not capture structural features at larger length scales. Instead
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,
A
Here, we demonstrate a topology-based machine learning approach for unsupervised profiling of individual and collective phases based on large-scale loops.
R
TDA can accurately
these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to
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interacting
simulated
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self-propulsion
propulsion
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, which are compared to our simulations
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statistical
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over repeated simulations and with random particle removal
at varying length scales, with sparse sampling, and over time