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Plant tissue architecture and organ morphogenesis rely on the proper orientation of cell divisions. Previous attempts to predict division planes from cell geometry in plants mostly focused on 2D symmetric divisions. Using the stereotyped division patterns of  Arabidopsis thaliana  early embryogenesis, we investigated geometrical principles underlying plane selection in symmetric and in asymmetric divisions within complex 3D cell shapes. Introducing a 3D computational model of cell division, we show that area minimization constrained on passing through the cell centroid predicts observed divisions. Our results suggest that the positioning of division planes ensues from cell geometry and gives rise to spatially organized cell types with stereotyped shapes, thus underlining the role of self-organization in the developing architecture of the embryo. Our data further suggested the rule could be interpreted as surface minimization constrained by the nucleus position, which was validated using live imaging of cell divisions in the stomatal cell lineage.

Cell geometry determines symmetric and asymmetric division plane selection in Arabidopsis early embryos