Cell models lead to understanding of multi-cellular morphogenesis consisting of successive self-construction of cells

Morphogenesis of multi-cellular organisms occurs through cell behaviours within a cell aggregate. Cell behaviours have been described using cell models involving equations of motion for cells. Cells in cell models construct shapes of the cell aggregate by themselves. Here, a history of cell models, the cell centre model and the vertex cell model, which we have constructed, are described. Furthermore, the application of these cell models is explained in detail. These cell models have been applied to transformation of cell aggregates to become spherical, formation of mammalian blastocysts and cell intercalation in elongating tissues. These are all elemental processes of morphogenesis and take place in succession during the whole developmental process. A chain of successive elemental processes leads to morphogenesis. Finally, we highlight that cell models are indispensable to understand the process whereby genes direct biological shapes.