Granular matter
Do living and nonliving packings differ in their neighbour topology?
Open access · cc by · source: Europe PMC
Counting how neighbouring points connect in 3D is enough to tell most living tissues apart from nonliving packings like granular piles and foams.
Study at a glance
- Design
- Computational / modelling — Delaunay tessellation motif counting plus a graph-based optimal-transport distance applied to published 3D point clouds
- N
- No single N; datasets include 15 biofilm colonies per species, nine zebrafish brain regions, 90 embryo time windows, and 40 nonliving-system points in the combined atlas
- Population
- 3D point clouds from bacterial biofilms, zebrafish brain and embryos, other tissues, simulated granular packings, foams and stars
- Outcome
- Topological diffusion distance between neighbourhood-motif distributions and clustering in a low-dimensional embedding
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Key findings
Biofilms from the four species separated cleanly, tracking cell aspect ratio. The embryo's time ordering could be recovered from topology alone, without using timestamps. In the combined atlas, of 40 nonliving points only an industrial foam fell inside the region occupied by living systems. Randomly shuffling brain cell positions and relaxing them produced a different topology closer to polyurethane foam, suggesting growth history shapes packing.
Methodology
The authors tessellated 3D point clouds (cell nuclei, bacteria, particles, stars) into Delaunay tetrahedra and counted how often each local neighbourhood motif appears. They then measured distances between motif distributions using a topological diffusion distance defined on a flip graph linking motifs one neighbour exchange apart. They applied this to biofilms of four bacterial species, zebrafish brain regions and developing embryos, and a combined atlas of living and nonliving systems.
Limitations
It is a descriptive comparison of existing datasets, so which physical features drive the separation is only partly tested (one randomisation control on one tissue). The atlas mixes very different data sources and imaging methods, and choices such as the boundary parameter alpha are set per dataset. The link between curvature of the developmental trajectory and biological transitions is suggestive and described mostly in supplementary material. Many details (motif labelling, convergence with sample size) are in supplements not included in this text.
How this study connects
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