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

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

Author information

1
Center for Plant Cell Biology, Department of Botany and Plant Sciences, University of California, Riverside, California 92521.
2
Biochemistry and Molecular Biology Graduate Program, University of California, Riverside, California 92521.
3
Institute of Integrative Genome Biology, University of California, Riverside, California 92521.
4
Department of Mathematics, Susquehanna University, Selinsgrove, Pennsylvania 17870.
5
Center for Plant Cell Biology NSF-REU, Harvey Mudd College, Claremont, California 91711.
6
Department of Biology, The Pennsylvania State University, State College, Pennsylvania 16801.
7
Curriculum in Genetics and Molecular Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599.
8
Department of Biology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599.
9
Department of Mathematics, University of California, Riverside, California 92521.
10
Center for Plant Cell Biology, Department of Botany and Plant Sciences, University of California, Riverside, California 92521 carolyn.rasmussen@ucr.edu.

Abstract

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.

PMID:
30150312
PMCID:
PMC6241264
DOI:
10.1105/tpc.18.00401
[Indexed for MEDLINE]
Free PMC Article

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