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

Abstract

AbstractMechanical forces of cell–cell interactions have been suggested to be critical for the emergence of diverse three-dimensional morphologies of multicellular organisms. The direct evaluation of the forces in living systems has been difficult due to technical limitations. Here, we developed a framework for inferring and modeling mechanical forces of cell–cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, cells were assumed to be spherical particles, where the mean forces (i.e. effective forces) of pairwise cell–cell interactions were considered. Then, the forces were statistically inferred from live imaging data, and subsequently, we successfully detected effective mechanical potentials of cell–cell interactions as a function of the cell–cell distances in Madin-Darby canine kidney (MDCK) cells, C.elegans early embryos, and mouse pre-implantation embryos. The qualitative and quantitative differences in the inferred potentials can be a control parameter for morphological transition during the mouse compaction process, and can also reproduce various three-dimensional morphologies including aggregates, cavities, tubes, cups, and two-dimensional sheets, which constitute basic structures observed during morphogenesis. We propose that effective potentials of cell–cell interactions are measurable, and their qualitative and quantitative features are critical for the emergence of diverse three-dimensional morphogenesis.Significance statementEmergence of diverse morphologies of multicellular organisms is one of the most intriguing phenomena in nature. Mechanical forces generated by cells play central roles in morphogenesis, however, their measurement is technically limited. Furthermore, due to the complex situations in living systems, a model for describing the emergent properties of multicellular systems has not been established. Here, we developed a method for inferring mechanical potential energy of cell–cell interactions, and showed that the quantitative differences in the potential is alone sufficient to describe basic three-dimensional morphologies observed during embryogenesis and organogenesis. This framework sheds light on the emergent properties of multicellular systems.