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

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.Author summary: The proper positioning of division planes is key for correct development and morphogenesis of organs, in particular in plants were cellular walls prevent cell rearrangements. Elucidating how division planes are selected is therefore essential to decipher the cellular bases of plant morphogenesis. Previous attempts to identify geometrical rules relating cell shape and division plane positioning in plants mostly focused on symmetric divisions in tissues reduced to 2D geometries. Here, we combined 3D quantitative image analysis and a new 3D cell division model to evaluate the existence of geometrical rules in asymmetrical and symmetrical divisions of complex cell shapes. We show that in the early embryo of the model plant Arabidopsis thaliana, which presents stereotyped but complex cell division patterns, a single geometrical rule (area minimization constrained on passing through the cell centroid) recapitulates the complete sequence of division events. This new rule, valid for both symmetrical and asymmetrical divisions, generalizes previously proposed cell division rules and can be interpreted based on the dynamics of the cytoskeleton and on the positioning of the nucleus, a hypothesis that we validated using leaf cell division patterns. This work highlights the importance of self-organization in plant early morphogenesis and the emergence of robust cellular organizations based on geometrical feedback loops between cell geometry and division plane selection.