Effective mechanical potential of cell–cell interaction explains basic structures of three-dimensional morphogenesis

Mechanical properties of cell–cell interactions have been suggested to be critical for the emergence of diverse three-dimensional morphologies of multicellular organisms. Mechanical potential energy of cell–cell interactions has been theoretically assumed, however, whether such potential can be detectable in living systems remains poorly understood. In this study, we developed a novel framework for inferring mechanical forces of cell–cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, cells were approximately assumed to be spherical particles, where microscopic features of cells such as polarities and shapes were not explicitly incorporated and the mean forces (i.e. effective forces) of cell–cell interactions were considered. Then, the forces were statistically inferred from live imaging data, and subsequently, we successfully detected potentials of cell–cell interactions. Finally, computational simulations based on these potentials were performed to test whether these potentials can reproduce the original morphologies. Our results from various systems, including Madin-Darby canine kidney (MDCK) cells, C.elegans early embryos, and mouse blastocysts, suggest that the method can accurately infer the effective potentials and capture the diverse three-dimensional morphologies. Importantly, energy barriers were predicted to exist at the distant regions of the interactions, and this mechanical property of cell–cell interactions was essential for formation of cavities, tubes, cups, and two-dimensional sheets. Collectively, these structures constitute basic structures observed during morphogenesis and organogenesis. We propose that effective potentials of cell– cell interactions are parameters that can be measured from living organisms, and represent a fundamental principle underlying the emergence of diverse three-dimensional morphogenesis.