Topological packing statistics distinguish living and non-living matter

TL;DR

This paper introduces a topological framework based on Delaunay tessellations to effectively distinguish living biological structures from non-living physical systems by analyzing their 3D point cloud data.

Contribution

It develops a universal topological atlas and a mathematical framework for measuring topological distances, enabling classification of diverse 3D disordered media including biological and physical systems.

Findings

Living systems occupy a distinct topological region in the atlas.

Topological differences correlate with growth memory in multicellular structures.

Framework unifies classification across biological and physical 3D structures.

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.