Computable early Caenorhabditis elegans embryo with a phase field model*

Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at molecular level, how cell proliferation and migration together drive the morphogenesis at cellular and organismic levels is not well understood. Using Caenorhabditis elegans as the model animal, we present a phase field model to compute early embryonic morphogenesis within a confined eggshell. With physical information about cell division obtained from three-dimensional time-lapse cellular imaging experiments, the model can precisely reproduce the early morphogenesis process as seen in vivo, including time evolution of location and morphology of each cell. Furthermore, the model can be used to reveal key cell-cell attractions critical to the development of C. elegans embryo. Our work demonstrates how genetic programming and physical forces collaborate to drive morphogenesis and provides a predictive model to decipher the underlying mechanism.