One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal plant body organization. To determine the importance of cell geometry in division plane orientation, we designed a three-dimensional probabilistic mathematical model to directly test the century-old hypothesis that cell divisions mimic soap-film minima. According to this hypothesis, daughter cells have equal volume and the division plane occurs where the surface area is at a minimum. We compared predicted division planes to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was directly adjacent to the predicted division site to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant cells (maize [Zea mays] epidermal cells and developing ligule cells and Arabidopsis thaliana guard cells) and animal cells (Caenorhabditis elegans embryonic cells) to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal organization of the plant body. To determine the importance of cell geometry in division plane orientation, we designed a threedimensional probabilistic mathematical modeling approach to directly test the century-old hypothesis that cell divisions mimic “soap-film minima” or that daughter cells have equal volume and the resulting division plane is a local surface area minimum. Predicted division planes were compared to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was observed directly adjacent to the predicted division site, to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant and animal cells to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

The maize ligule is an epidermis-derived structure that arises from the preligule band (PLB) at a boundary between the blade and sheath. A hinge-like auricle also develops immediately distal to the ligule and contributes to blade angle. Here, we characterize the stages of PLB and early ligule development in terms of topography, cell area, division orientation, cell wall rigidity, and auxin response dynamics. Differential thickening of epidermal cells and localized periclinal divisions contributed to the formation of a ridge within the PLB, which ultimately produces the ligule fringe. Patterns in cell wall rigidity were consistent with the subdivision of the PLB into two regions along a distinct line positioned at the nascent ridge. The proximal region produces the ligule, while the distal region contributes to one epidermal face of the auricles. Whereas the auxin transporter PIN1 accumulated in the PLB, observed differential auxin transcriptional response did not underlie the partitioning of the PLB. Our data demonstrate that two zones with contrasting cellular properties, the preligule and preauricle, are specified within the ligular region prior to ligule outgrowth.