Nielsen BF et al. (2020), Model to Link Cell Shape and Polarity with Orga...

ECB-ART-48620

iScience 2020 Feb 21;232:100830. doi: 10.1016/j.isci.2020.100830.

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Model to Link Cell Shape and Polarity with Organogenesis.

Nielsen BF , Nissen SB , Sneppen K , Mathiesen J , Trusina A .

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How do flat sheets of cells form gut and neural tubes? Across systems, several mechanisms are at play: cells wedge, form actomyosin cables, or intercalate. As a result, the cell sheet bends, and the tube elongates. It is unclear to what extent each mechanism can drive tube formation on its own. To address this question, we computationally probe if one mechanism, either cell wedging or intercalation, may suffice for the entire sheet-to-tube transition. Using a physical model with epithelial cells represented by polarized point particles, we show that either cell intercalation or wedging alone can be sufficient and that each can both bend the sheet and extend the tube. When working in parallel, the two mechanisms increase the robustness of the tube formation. The successful simulations of the key features in Drosophila salivary gland budding, sea urchin gastrulation, and mammalian neurulation support the generality of our results.

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Genes referenced: LOC100887844 LOC115919910

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	Figure 1. Wedging Is Introduced through a Cell-Cell Interaction that Favors Tilted AB Polarity Vectorsα is the extent of wedging. The blue-red gradient indicates the apical-basal axis.(A) No wedging (α=0), AB polarities (arrows) tend to be parallel.(B) With isotropic wedging, the tilt α is the same in all directions.(C) With anisotropic wedging, the tilt has a preferred direction. Blue and red signify, respectively, basal and apical surfaces. pi and pj are the AB polarities of cells i and j.See also Figure S3 and S9, Video S1.
	Figure 2. Isotropic and Anisotropic Wedging Drive Budding and Wrapping, RespectivelyWedging cells are labeled in gray, with a shading that indicates the PCP direction.(A–C) Time evolution of budding simulation (similar to Drosophila salivary glands). Here, gray cells constrict basally and all cells on and inside the ring intercalate radially. The couplings are (λ1,λ2,λ3)=(0.5,0.4,0.1), the degree of wedging is \|α\|=0.5, and the annulus within which wedging occurs is given by the radii r0=5 and r1=15. See section Modeling budding from a plane for details, as well as Figure S5. Total number of time steps was 6.25×104 at dt=0.2. Snapshots correspond to times 5, 800, and 1.25×104. The width of the Gaussian noise was σ=0.05. See also Figures S1, S7, and S8, Video S2.(D–F) Time evolution of wrapping simulation (similar to neurulation). Here, gray cells representing neuroepithelium constrict apically and constriction is anisotropic, follows the direction of PCP (Eq 3). Cells proliferate only at the gray/colored boundary (with 7-h doubling time), mimicking differential proliferation at the neuroepithelium/ectoderm boundary. The couplings are (λ1,λ2,λ3)=(0.6,0.4,0), the degree of wedging is \|α\|=0.5. See section Modeling neurulation/wrapping for details, as well as Figure S4.Total number of time steps was 3.9×104 at dt=0.1, and snapshots were taken at times 5, 900, and 3.9×103. The cell cycle length in simulation time units is 600. This simulation was run without added Gaussian noise, but noise is supplied by proliferation, which is implemented as a Poisson process. See also Videos S4 and S5.
	Figure 3. Isotropic Wedging in Conjunction with PCP Is Sufficient to Drive Sea Urchin Gastrulation without External ForcingThe gray ring shows cells with (isotropic) basal constriction, and the shading indicates the direction of planar cell polarity, which curls around the vertical axis in our simulation. The couplings are (λ1,λ2,λ3)=(0.5,0.4,0.1), the degree of wedging is \|α\|=0.4, and the annulus within which wedging occurs is given by the radii r0=7 and r1=21. See section Modeling gastrulation for details. Total number of time steps was 1.25×105 at dt=0.1 and snapshots were taken at times 5, 1.5×103, and 1.25×104. The width of the Gaussian noise was σ=0.05.See also Video S3.
	Figure 4. The Cell Cycle Length at the Neuroepithelial-Ectoderm Boundary Affects Tube ClosureFor cell cycle lengths below 3.3 h and above 23 h the neural tube fails to close in our simulations. It should be noted that this broad interval also contains the cell cycle length of 4 h found for cells in the dorsolateral hinge points by McShane et al. (2015). The insets show outcomes of simulations run at short (2.6 h), intermediate (12 h), and long (26 h) cell cycle lengths. In simulation time, these correspond to 400, 1,800, and 4,000, respectively. See also Figures S2 and S6.

References [+] :

Andrew, Morphogenesis of epithelial tubes: Insights into tube formation, elongation, and elaboration. 2010, Pubmed