Effective mechanical potential of cell-cell interaction explains three-dimensional morphologies during early embryogenesis

Abstract

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. 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, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies. Author summaryEmergence of diverse three-dimensional morphologies of multicellular organisms is one of the most intriguing phenomena in nature. Due to the complex situations in living systems (e.g. a lot of genes are involved in morphogenesis.), a model for describing the emergent properties of multicellular systems has not been established. To approach this issue, approximation of the complex situations to limited numbers of parameters is required. Here, we searched for mechanical parameters for describing morphologies. We developed a statistical method for inferring mechanical potential energy of cell-cell interactions in three-dimensional tissues; the mechanical potential is an approximation of various mechanical components such as cell-cell adhesive forces, cell surface tensions, etc. Then, we showed that the quantitative differences in the potential is sufficient to reproduce basic three-dimensional morphologies observed during the mouse and C. elegans early embryogenesis, revealing a direct link between cellular level mechanical parameters and three-dimensional morphologies. Our framework provides a noninvasive tool for measuring spatiotemporal cellular forces, which would be useful for studying morphogenesis of larger tissues including organs and their regenerative therapy.