New paper on maximum entropy cell packing

We have a new paper from grad student Tom Day, and in collaboration with Prof. Will Ratcliff (GT) and Prof. Ray Goldstein (Cambridge).

The success of multicellular organisms is due in part to their ability to assemble cells into complex, functional arrangements. However, self-assembly is subject to random noise that affects the final emergent structure. As the physiology of multicellular organisms can depend sensitively on structural details—in particular, the geometry of cellular packing—these fluctuations can directly impact fitness. Further, while extant multicellular organisms possess developmental mechanisms that can suppress or make use of random noise, nascent multicellular organisms do not possess such developmental programs, yet must generate repeatable multicellular structures to be successful. Understanding the origin and evolution of multicellularity thus requires understanding the impact of random noise on multicellular self-assembly.

Addressing this topic is particularly challenging as multicellularity has evolved independently over 25 times, and each separate lineage has evolved different rules for assembly. There are thus few, if any, general principles uniting multicellular organisms with different growth morphologies. For example, organisms that grow with persistent mother-daughter bonds (like plants or fungi) `freeze’ structural randomness in place; in contrast, organisms with ‘sticky’ cell-cell adhesion (like animals) can rearrange, so their final structure will be impacted by noise in reproduction and intercellular interactions. But this comparison only scratches the surface of the diversity of multicellular structures (e.g., from biofilms to trees to whales), which vary in dimensionality, topology, evolutionary history, and more. It thus would appear that random noise manifests uniquely in different kinds of multicellular organisms, without uniting rules.

In this paper, we show that random fluctuations in cell packing geometry follow a universal distribution, predictable from the maximum entropy principle. We experimentally observe this distribution in both snowflake yeast, a lab-created multicellular organism and the green alga Volvox carteri, which first evolved multicellularity in the Triassic. Maximum entropy cell packing statistics therefore unite organisms with and without canalized multicellular development, and organisms with markedly different growth morphologies. With these experimental observations and additional computational simulations, we show that maximum entropy packing is a fundamental property of multicellular groups, independent of growth morphology. 

Using snowflake yeast, we also show that maximum entropy cell packing plays a central role in the transition to multicellularity. The multicellular life cycle in this model system (growth of the group followed by fracture into multiple groups) arises directly from the maximum entropy distribution of free space within multicellular clusters. In fact, we show that the distribution of size across the population is completely predictable from maximum entropy considerations. Variation in the statistics of cellular packing therefore underlies the emergence of repeatable multicellular traits, such as group size at fracture, demonstrating how randomness can underlie the emergence of heritable multicellular traits prior to the evolution of multicellular development.

In a related vein, a theoretical analysis of V. carteri shows that the effects of fluctuations in intercellular space on the motility of green algae is small. These results show that the effects of random cell packing can be beneficial, detrimental, or neutral in character.

In summary, we show that the maximum entropy principle guides the organization of cellular space in organisms that are profoundly different: varying in their developmental regulation, and generating multicellular structures with different growth morphologies and dimensionalities. These fluctuations in multicellular packing appear as unavoidable as thermal fluctuations are to equilibrium phenomena, suggesting that maximum entropy packing statistics may represent a general principle, uniting all multicellular organisms.

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