Cellular organization in lab-evolved and extant multicellular species obeys a maximum entropy law

TL;DR

This study reveals that cellular packing in multicellular organisms, both lab-evolved and natural, follows a maximum entropy law, indicating a universal statistical principle underlying cell organization despite biological differences.

Contribution

It demonstrates that cell neighborhood sizes in different multicellular species follow a gamma distribution predicted by maximum entropy principles, highlighting a conserved packing rule.

Findings

Cell neighborhoods fit a gamma distribution across species.

Cell packing obeys a maximum entropy law.

Results suggest a universal principle of multicellular organization.

Abstract

The prevalence of multicellular organisms is due in part to their ability to form complex structures. How cells pack in these structures is a fundamental biophysical issue, underlying their functional properties. However, much remains unknown about how cell packing geometries arise, and how they are affected by random noise during growth - especially absent developmental programs. Here, we quantify the statistics of cellular neighborhoods of two different multicellular eukaryotes: lab-evolved "snowflake" yeast and the green alga $Volvox~carteri$. We find that despite large differences in cellular organization, the free space associated with individual cells in both organisms closely fits a modified gamma distribution, consistent with maximum entropy predictions originally developed for granular materials. This 'entropic' cellular packing ensures a degree of predictability despite noise, facilitating parent-offspring fidelity even in the absence of developmental regulation. Together with simulations of diverse growth morphologies, these results suggest that gamma-distributed cell neighborhood sizes are a general feature of multicellularity, arising from conserved statistics of cellular packing.