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

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.

The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability.

Variability is emerging as an integral part of development. It is therefore imperative to ask how to access the information contained in this variability. Yet most studies of development average their observations and, discarding the variability, seek to derive models, biological or physical, that explain these average observations. Here, we analyse this variability in a study of cell sheet folding in the green alga Volvox, whose spherical embryos turn themselves inside out in a process sharing invagination, expansion, involution, and peeling of a cell sheet with animal models of morphogenesis. We generalise our earlier, qualitative model of the initial stages of inversion by combining ideas from morphoelasticity and shell theory. Together with three-dimensional visualisations of inversion using light sheet microscopy, this yields a detailed, quantitative model of the entire inversion process. With this model, we show how the variability of inversion reveals that two separate, temporally uncoupled processes drive the initial invagination and subsequent expansion of the cell sheet. This implies a prototypical transition towards higher developmental complexity in the volvocine algae and provides proof of principle of analysing morphogenesis based on its variability.