Predicting Division Planes of Three-Dimensional Cells by Soap-Film Minimization

Plant Cell. 2018 Oct;30(10):2255-2266. doi: 10.1105/tpc.18.00401. Epub 2018 Aug 27.


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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Arabidopsis / cytology*
  • Bacterial Proteins / genetics
  • Bacterial Proteins / metabolism
  • Caenorhabditis elegans / cytology
  • Caenorhabditis elegans / embryology
  • Cell Division
  • Embryo, Nonmammalian / cytology
  • Luminescent Proteins / genetics
  • Luminescent Proteins / metabolism
  • Microtubules / metabolism
  • Microtubules / ultrastructure
  • Models, Biological*
  • Plant Cells / physiology*
  • Plant Leaves / cytology
  • Recombinant Proteins / genetics
  • Recombinant Proteins / metabolism
  • Soaps / chemistry
  • Time-Lapse Imaging
  • Zea mays / cytology*


  • Bacterial Proteins
  • Luminescent Proteins
  • Recombinant Proteins
  • Soaps
  • yellow fluorescent protein, Bacteria