During cleavage, different cellular processes cause the zygote to become partitioned into a set of cells with a specific spatial arrangement. These processes include the orientation of cell division according to: an animal-vegetal gradient; the main axis (Hertwig's rule) of the cell; and the contact areas between cells or the perpendicularity between consecutive cell divisions (Sachs' rule). Cell adhesion and cortical rotation have also been proposed to be involved in spiral cleavage. We use a computational model of cell and tissue biomechanics to account for the different existing hypotheses about how the specific spatial arrangement of cells in spiral cleavage arises during development. Cell polarization by an animal-vegetal gradient, a bias to perpendicularity between consecutive cell divisions (Sachs' rule), cortical rotation and cell adhesion, when combined, reproduce the spiral cleavage, whereas other combinations of processes cannot. Specifically, cortical rotation is necessary at the 8-cell stage to direct all micromeres in the same direction. By varying the relative strength of these processes, we reproduce the spatial arrangement of cells in the blastulae of seven different invertebrate species.
Author contributions
M.B.-U. and I.S.-C. conceived the study and wrote the manuscript with some input from all other authors. M.B.-U. performed the experiments. M.B.-U., M.M.-R. and I.S.-C. equally contributed to modelling and data analysis. C.G. and M.T.-G. processed and measured the real embryos.
Funding
This research was funded by the Academy of Finland (WBS 1250271), by the Ministerio de Ciencia y Tecnología (BFU2010-17044 to I.S.-C., BES2011-046641 to M.B.-U. and BES 2012-052214 to M.T.-G.), by the Generalitat de Catalunya (2013FI-B00439 to M.M.-R.), and by Universidad Autónoma de Madrid and Ministerio de Ciencia y Tecnología (CGL2011-29916 to C.G.).
