Comparison between phase-field model and coarse-grained model for characterizing cell-resolved morphological and mechanical properties in a multicellular system*

Embryonic development is a precise and complex process involving the cell morphology and mechanics interacting in space and time. The difficulty in quantitatively acquiring cellular morphological and mechanical information in vivo makes mathematical modeling a challenging problem and impedes model validation. Recently, the three-dimensional time-lapse live imaging and delineated developmental programs in the roundworm Caenorhabditis elegans provide an excellent platform for establishing quantitative models. In this paper, we study two popular computational models for multicellular systems, i.e., the phase-field model and the coarse-grained model, and compare their performance in characterizing the cell morphologies, cell adhesion, and cell stiffness in a real C. elegans embryo. We show that both models can capture cell-cell contact areas and heterogeneous cell adhesion, but only the phase-field model succeeds in inferring the heterogeneous cell stiffness by fitting cell shapes or cell-cell interface curvatures. Moreover, we demonstrate that the phase-field model converges to the coarse-grained model when increasing cell surface tension to dominance, obtaining a distance-dependent isotropic intercellular force.