Reconstructing the multicellular structure of a developing metazoan embryo with repulsion-attraction model and cell-cell connection atlas in vivo

Abstract

Embryogenesis is a spatio-temporal multicellular evolutional process involved with intracellular biochemical activities and intercellular biophysical interactions. Reproducible and precise multicellular structures contribute to robustness of embryonic development by cell-cell communication, morphogenesis and other significant biological events. Using Caenorhabditis elegans as animal model, recently several researches established mechanical models to reconstruct the multicellular structures of this developmental system, in which cells interact via repulsive or attractive potentials inside an ellipsoidal eggshell. However, those models ignored some practical details and lack of test in depth. In this paper, we improved an in silico modeling framework based on previous models by revising formulae of interactive force and applying in vivo experimental information of eggshell shape, cell volume, cell position and cell-cell connection relationship. Cell pairs with and without empirically repeated connection were regarded to have different types of attractive force, which could help stabilize cells into their experimentally observed locations accompanied by correct neighbour relationships. Both previous models and our revised ones were tested, verified and compared to each other. Our modeling framework not only reproduces the multicellular structure patterns in an artificially compressed embryo with ∼50 cells, but also exhibits a potential to uncover active adjustments and controls on cell positioning.

Computable early Caenorhabditis elegans embryo with a phase field model

“…Intriguingly, the remarkable movement of ABpl and a persistent 3D embryo structure are rescued by the ABpl-E motif but not by the ABpl-C motif (Figs 3C and S7B and S6 Movie), indicating that a weak attraction in ABpl's posterior is essential for its migration in anteroventral direction. Besides, the cell-cell contact map is in agreement with the one conserved in real embryos, which however failed to be fully recaptured in a previous study using optimized coarse-grained models [22]. After weakening the attractive force between ABpl and E, the positions and contacts of the 8 cells exhibit mirror symmetry about the AP-DV plane, concerning both the geometric and mechanical topologies.…”

“…These optimization operations result in a parameter combination of γ = 0.25, c = 1.0 and g e = 16, which are used in all simulations in this work ( S19A and S19B and S20 Figs). Note that the embryo structure is insensitive to the exact value of g e , thus we assume that the stiffness of the eggshell is one magnitude larger than that of a cell, namely g e = 10 g = 16 ( S20 Fig ) [ 22 ]. Importantly, all the attraction coefficients between cells ( σ i , j ) are set as zero at the start and assigned with different values in later simulations for in-depth investigation, as a high-dimensional factor that may diversify the developmental paths.…”

“…To list a few, a multi-particle model was designed to analyze the structural evolution up to the 4-cell stage using groups of interactive particles to represent cell membranes, which however contained dozens of system parameters that were difficult to measure or fit [ 18 , 19 ]. Later, coarse-grained models were proposed to reproduce cell positions up to ~50-cell stage, which simplified the cells into mass particles and ignored most of the cellular morphological features [ 9 , 10 , 20 – 22 ]. These models revealed several physical factors that could affect the cell-arrangement patterns, such as cell division timing, cell division orientation, cell adhesion, and eggshell shape.…”

Delineating the mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

“…In 2020, Guan et al revised the coarse-grained model by optimizing the formulation and parameters and inputting experimentally measured cell volumes and eggshell shape to determine the latest developmental stage to which it can be applied with sufficient precision [76] , [201] . They found that the model can reproduce cell positions up to the 26-cell stage (at which time they are assumed to be at mechanical equilibrium) with positional variation that is less than a cell’s radius for all cells.…”

“…Moreover, they determined that the model performs well even at the 51-cell stage, except for three cells that exhibit a deviation larger than their radii, suggesting that the system at this stage remains largely governed by mechanical cues but that additional modifications (e.g., inhomogeneous cell stiffness and cell adhesion) might have a non-negligible effect on some cells. In addition, these researchers found that the cell–cell contact relationship conserved among embryos is poorly reproduced by the coarse-grained model, although the inclusion of a heterogeneous cell–cell adhesion map derived from cell–cell contact data somewhat improves the reconstruction performance of the model [201] .…”