Topological Metric Detects Hidden Order in Disordered Media
Name
PhysRevLett.126.048101.pdf
Description
Published version
Size
2.21 MB
Format
Adobe PDF
Checksum (MD5)
17a9e9cd6ee71741c687be933c6feeae
Author(s)
Skinner, Dominic J
Song, Boya
Jeckel, Hannah
Jelli, Eric
Drescher, Knut
Dunkel, Jörn
Date Issued
2021
Journal
Physical Review Letters
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
© 2021 American Physical Society. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.126.048101
