Topological Metric Detects Hidden Order in Disordered Media

Skinner, Dominic J. and Song, Boya and Jeckel, Hannah and Jelli, Eric and Drescher, Knut and Dunkel, Jörn. (2021) Topological Metric Detects Hidden Order in Disordered Media. Physical Review Letters, 126 (4). 048101.

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Official URL: https://edoc.unibas.ch/83603/

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Recent advances in microscopy techniques make it possible to study the growth, dynamics, and response of complex biophysical systems at single-cell resolution, from bacterial communities to tissues and organoids. In contrast to ordered crystals, it is less obvious how one can reliably distinguish two amorphous yet structurally different cellular materials. Here, we introduce a topological earth mover's (TEM) distance between disordered structures that compares local graph neighborhoods of the microscopic cell-centroid networks. Leveraging structural information contained in the neighborhood motif distributions, the TEM metric allows an interpretable reconstruction of equilibrium and nonequilibrium phase spaces and embedded pathways from static system snapshots alone. Applied to cell-resolution imaging data, the framework recovers time ordering without prior knowledge about the underlying dynamics, revealing that fly wing development solves a topological optimal transport problem. Extending our topological analysis to bacterial swarms, we find a universal neighborhood size distribution consistent with a Tracy-Widom law.
Faculties and Departments:05 Faculty of Science > Departement Biozentrum > Infection Biology > Microbiology and Biophysics (Drescher)
UniBasel Contributors:Drescher, Knut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:25 Jun 2021 09:40
Deposited On:25 Jun 2021 09:40

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