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Coaction of intercellular adhesion and cortical tension specifies tissue surface tension

  1. Eva-Maria Schoetzd,1
  1. aPrinceton Center for Theoretical Science, Princeton University, Princeton, NJ 08544;
  2. bUniversity of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School, Piscataway, NJ 08854;
  3. cDepartment of Molecular Biology, Princeton University, Princeton, NJ 08544; and
  4. dLewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544

  1. Edited* by Barry H. Honig, Columbia University/Howard Hughes Medical Institute, New York, NY, and approved June 7, 2010 (received for review March 20, 2010)

  1. Fig. 1.
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    Fig. 1.

    (A–C) Confocal sections of zebrafish aggregates. (Scale bar, 10 μm.) (A) Ectoderm cells in the bulk are densely packed into roughly polyhedral shapes. Membranes are labeled using Gap43-GFP, nuclei using Hoechst. (B) Surface cells in which E-cadherin is down-regulated. Cells have rounded edges and are compact. (C) Surface cells of an ectoderm aggregate. Bulk cells are compact, whereas surface cells are stretched. (D and E) Illustration of ordered packing of cells, where surface cells contact each other over a length Lside. (D) Cells along the interface with cell–culture medium maintain a compact shape (nstretch = 1). (E) Illustration of stretched surface cells with nstretch = 3. This arrangement satisfies force balance and the constant area constraint.

  2. Fig. 2.
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    Fig. 2.

    (A–C) Plot of aggregate surface tension in units of β as a function of γ/β. The dashed black line is the analytic calculation for ordered packing σordered. The solid blue line is the surface tension for a disordered aggregate. The dotted red line is σ = γ/2, which is equivalent to the DAH. (A) Two-dimensional aggregate, σrand = 1.05σordered. Magenta points are the average surface tensions of minimum energy aggregates generated numerically. (B, Inset) Scaled version of 2D data with error bars. (C) Three-dimensional aggregate. Blue line is conjectured disordered solution, σdisorder = 1.10σorder. (D and E) Minimum energy cell configurations generated using Surface Evolver at two different values of γ/β. Orange cells have six neighbors. (D) Sample aggregate with γ/β = 0.33. (E) Same initial conditions as D with γ/β = 1.667.

  3. Fig. 3.
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    Fig. 3.

    (A–C) SEM images of cell aggregates. (A) Control LP cell aggregate. (B) Cell aggregate treated with latrunculin A. (C) Cell aggregate treated with cytochalasin D. (D) Surface tension σ as measured by TST.

  4. Fig. 4.
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    Fig. 4.

    (A and B) Representative confocal slices of a 3D zebrafish ectoderm aggregate in planes tangent to the aggregate surface. A intersects the surface cells, whereas B is at a depth of > 25 μm and intersects a layer in the bulk. (Scale bar, 10 μm.) (C) Plot of the projected areas of all cells. Red points correspond to surface cells, whereas black points correspond to bulk cells, and the solid lines represent the mean of the entire dataset. Error bars represent errors on the aggregate mean. (D) Comparison of the relationship between σ, γ, and β as obtained from our extended model with α = MAX(0,(γ/2-β)/(2Phex)), for various surface cell configurations. The dash-dotted line corresponds to compact cell shapes, whereas the dashed and solid lines correspond to surface cells stretched over two or three cells, respectively. For γ/β < 2, compact cell shapes are optimal and the differential adhesion hypothesis is approximately satisfied, whereas for γ/β > 2, cells stretched over three interior cells are optimal and cortical tension dominates. (E, Inset) Magnification of crossover behavior in D.

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