Predicting division planes of three-dimensional cells by soap-film minimization

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.