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

Abstract

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.

Opposing, Polarity-Driven Nuclear Migrations Underpin Asymmetric Divisions to Pattern Arabidopsis Stomata

“…The random nuclear movements in basl and the incorrectly oriented nuclear migrations in MYR-BRX create roughly equivalent outcomes on daughter cell sizes; in both cases, nuclei are frequently offset from the cell center pre-ACD but in an inappropriate place relative to neighbor cells of specific identities ( Figure 2G). Combining the decentering of nuclei, the irregular cell shapes of stomatal progenitors and the minimalwall rule that broadly governs division plane placement in plant cells [25][26][27] provides a parsimonious explanation for how differentially sized daughter cells are created from stomatal progenitor divisions, even without directed nuclear migrations (Figure 2H). However, without NM pre and NM post , tissue-wide spacing of meristemoids is incorrect owing to an inability to orient ACDs relative to neighbor cells ( Figure 2G).…”

Synergistic Pectin Degradation and Guard Cell Pressurization Underlie Stomatal Pore Formation

“…To map the morphogenesis of stomatal pores in detail, we performed stacklapse imaging experiments with an interval of 0.5 h for up to 48 h in cotyledons of 4d-old seedlings (Martinez et al, 2018) expressing LOW TEMPERATURE INDUCED PROTEIN 6B-green fluorescent protein (LTI6b-GFP), a plasma membrane marker (Supplemental Movies S1 and S2;Cutler et al, 2000). We focused on guard mother cells at the beginning of image collection.…”

“…Z-stack images of COS 488 staining, PGX1-GFP, and LTI6b-GFP were collected with a step size of 0.5 mm. Long-term z-stack time-lapse (stacklapse) imaging was performed as previously described (Peterson and Torii, 2012;Martinez et al, 2018): in brief, a cotyledon was cut from a 4-d-old light-grown LTI6b-GFP seedling and placed under a 0.5% (w/v) agar pad in a Nunc Lab-Tek chambered coverglass (Thermo Fisher; catalog no. 155360).…”

Action at a distance: Defects in division plane positioning in the root meristematic zone affect cell organization in the differentiation zone

“…The PPB is a ring of microtubules, microfilaments and associated proteins that marks the future position of the new cell wall, called the division site (Li et al, 2015;Pickett-Heaps et al, 1999;Rasmussen and Bellinger, 2018;Smertenko et al, 2017;Van Damme, 2009). Nuclear and PPB positioning often match division predictions based on cell geometry (Martinez et al, 2018;Moukhtar et al, 2019). PPB disassembly upon nuclear envelope breakdown precedes spindle formation (Dixit and Cyr, 2002).…”