Researchers Samuel Poincloux (currently at Aoyama Gakuin University) and Kazumasa A. Takeuchi of the University of Tokyo have clarified the conditions under which large numbers of "squishy" grains, which can change their shape in response to external forces, transition from acting like a solid to acting like a liquid. Similar transitions occur in many biological processes, including the development of an embryo: cells are "squishy" biological "grains" that form solid tissues and sometimes flow to form different organs. Thus, the experimental and theoretical framework elaborated here will help separate the roles of mechanical and biochemical processes, a critical challenge in biology. The findings were published in the journal Proceedings of the National Academy of Sciences (PNAS).
Imagine a pile of sand on a table. As we slowly raise one end of the table, it first sits undisturbed and acts like a solid. However, at a critical angle, the forces keeping the sandpile together yield to gravity: the pile breaks down and starts flowing, acting like a liquid. This is a yielding transition, a widely studied phenomenon with "grains" that do not change shape, such as sand or rocks. However, "grains" in biology are often "squishy," adapting their shape to external forces.
"Although our research revisits a well-studied problem," says Poincloux, the first author, "it hits the sweet spot of being complicated enough to be interesting and simple enough to develop various approaches. We incorporated interdisciplinary components, such as using a biomechanical tool that helped differentiate if the "grains" were changing shapes or positions."
Indeed, the researchers approached the challenge through experiments, computer modeling, and geometrical description. They used slender rubber rings as their "squishy" grains and stacked them in a container. They varied the number of rings, the density of "grains," and the strength of lateral forces applied to the rings. Then, using pictures, the researchers measured the rings' positions, shapes, and points of contact with each other as the batch of rings deformed. These measures allowed them to quantify how much the rings changed position (liquid-like behavior) or shape (solid-like behavior). Lastly, they performed computer simulations and geometric analyses to understand the role of friction and interactions between rings.
"We found the main surprise at the very end of the project," says Poincloux. "Surprisingly, a simple geometrical description underlies the yielding transition observed, despite involving large and complex shape changes coupled with frictional interactions."
These findings are the first steps toward understanding how "squishy" biological grains interact in living organisms, and Poincloux is already thinking of what to do next.
"To get closer to biological tissues, we could, for instance, modify the interactions and add ring adhesion to emulate linking proteins between cells. For those intending to use these squishy rings for experiments: do not forget to put a cover lid on top of the container to prevent the explosion of hundreds of rings across the laboratory… I will not disclose the number of times this incident happened."
