Topological analysis of multicellular structures

Recent advances in microscopy techniques make it possible to study the growth, dynamics and response of complex biological systems at single-cell resolution, from bacterial biofilms to tissues. When seeking to understand the formation and mechanical properties of these multicellular materials, the local spatial arrangement of their discrete cellular building blocks is of principal importance. To compare the similarity of crystals, we can compare lattice vectors or motifs, but when there is no crystal structure it is less obvious how one can reliably distinguish two amorphous yet structurally different materials. In this talk we introduce a topological distance between materials that needs only the coordinates of the centroid of each discrete object, and is based on the local graph structure around each centroid. Using this distance we will differentiate and classify structures formed from various ellipsoid and sphere packings, as well as biological cell data.