Topological Metric Detects Hidden Order in Disordered Media

Dominic J. Skinner, Boya Song, Hannah Jeckel, Eric Jelli, Knut Drescher, Jörn Dunkel
2021 Physical Review Letters  
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
more » ... croscopic 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.
doi:10.1103/physrevlett.126.048101 pmid:33576647 fatcat:47vvajuntnhwpgiyzgpxamjhd4