Topological packing statistics distinguish living and non-living matter

Abstract

How much structural information is needed to distinguish living from non-living systems? Here, we show that the statistical properties of Delaunay tessellations suffice to differentiate prokaryotic and eukaroytic cell packings from a wide variety of inanimate physical structures. By introducing a mathematical framework for measuring topological distances between general 3D point clouds, we construct a universal topological atlas encompassing bacterial biofilms, snowflake yeast, plant shoots, zebrafish brain matter, organoids, and embryonic tissues as well as foams, colloidal packings, glassy materials, and stellar configurations. Living systems are found to localize within a bounded island-like region, reflecting that growth memory essentially distinguishes multicellular from physical packings. By detecting subtle topological differences, the underlying metric framework enables a unifying classification of 3D disordered media, from microbial populations, organoids and tissues to amorphous materials and astrophysical systems.

Updated link to online platform, added more examples to atlas

References in corpus (3)

• Voronoi cell analysis: The shapes of particle systems
• Towards the cellular-scale simulation of motor-driven cytoskeletal assemblies
• Computing foaming flows across scales: from breaking waves to microfluidics

Cited by in corpus (5)

• Persistent homology and topological statistics of hyperuniform point clouds
• Learning Dynamics from Multicellular Graphs with Deep Neural Networks
• Inferring traits of hyperuniformity from local structures via persistent homology
• Pair correlation function based on Voronoi topology
• Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics