Modelling Physical Mechanisms Driving Tissue Self-Organisation in the Early Mammalian Embryo
In the mammalian embryo, between 3.5 and 4.5 days after fertilisation, the cells of the inner cell mass evolve from a uniform aggregate to an ordered structure with two distinct tissue layers - the primitive endoderm and epiblast. It was originally assumed that cells differentiated to form these layers in situ, but more recent evidence suggests that both cell types arise scattered throughout the inner cell mass, and it is thus proposed that the tissue layers self-organise by physical mechanisms after the specification of the two cell types. We have developed a computational model based on the subcellular element method to combine theoretical and experimental work and elucidate the mechanisms that drive this self-organisation. The subcellular element method models each cell as a cloud of infinitesimal points that interact with their nearest neighbours by local forces. Our method is built around the introduction of a tensile cortex in each cell by identifying boundary elements and using a Delaunay triangulation to define a network of forces that act within this boundary layer. Once the cortex has been established, we allow the tension in the network to vary locally at interfaces, modelling the exclusion of myosin at cell-cell interfaces and consequent reduction in tension. The model is validated by testing the simulated interfaces in cell doublets and comparing to experimental data and previous theoretical work. Furthermore, we introduce dynamic tension to model blebbing in primitive endoderm cells. We investigate the effects of cortical tension, differential interfacial tension, and blebbing on interfaces, rearrangement, and sorting. By establishing quantitative measurements of sorting we produce phase diagrams of sorting magnitude given system parameters and find that robust sorting in a 30 cell aggregate is best achieved by a combination of differential interfacial tension and blebbing.