Research ArticleBIOPHYSICS

Surface tension determines tissue shape and growth kinetics

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Science Advances  11 Sep 2019:
Vol. 5, no. 9, eaav9394
DOI: 10.1126/sciadv.aav9394
  • Fig. 1 CB geometry as a means to control 3D tissue growth.

    (A) Composition of phase-contrast images of tissues grown on a CB taken after 4, 7, 21, 32, 39, and 47 days. The tissue is pinned at the edges of the CB (red circle) and shows a moving contact line in between the scaffold and the Teflon holder, reminiscent of a liquid. Dashed line indicates the CB surface, and red arrows point toward the tissue-medium interface. Scale bar, 500 μm. (B and C) Radial slices at the neck for two different CB sizes with initial volumes of 1.1 μl (B) and 2.8 μl (C) obtained with LSFM from five different views. (D) Sample geometry and orientation of the light sheet. κ1and κ2 are minimum and maximum principal curvatures. (E) 3D rendering of actin fibers on the sample shown in (F) color-coded according to fluorescence intensity. (F to I) Phase-contrast images of tissues grown on four different CB surfaces with initial volumes of 1.1 μl (F), 1.6 μl (G), 2.2 μl (H), and 2.8 μl (I). (J to L) CB surfaces with initial volumes of 1.1 μl (J), 1.3 μl (K), and 1.5 μl (L). Sample neck size increases from left to right. Green arrow indicates the interface of the initial shape, and red arrow indicates the position of the tissue-medium interface after 32 days. Scale bars, 400 μm.

  • Fig. 2 Tissues behave like liquids when constrained by curved surfaces.

    (A to D) Evolution of the surface mean curvature (A and C) and surface area (B and D) of the tissue interfaces as a function of total volume (CB volume V0 plus tissue volume) for the two different CB shapes shown in Fig. 1. (A and B) Tissues grown on CB surfaces with a height of ~1.2 mm and top/bottom radius of ~1 mm with initial volumes of 1.1 μl (size 1; blue), 1.6 μl (size 2; red), 2.2 μl (size 3; black), and 2.8 μl (size 4; orange). Colored areas delineate the theoretical predictions of liquid interfaces of the same dimension based on the scaffold geometries obtained from the experiment. Colored curves are the corresponding mean values. (C and D) Tissues grown on CB surfaces with a height of ~0.7 mm and top/bottom radius of ~1 mm with initial volumes of 1.1 μl (size 1; blue), 1.3 μl (size 2; red), and 1.5 μl (size 3; black). Curves are color-coded according to the corresponding theoretical predictions of the liquid interface (see the Supplementary Materials for the full data).

  • Fig. 3 The kinetics of tissue growth depend on the initial curvature.

    (A) Measured tissue volumes for the four different CBs presented in Fig. 1 (F to I) with initial volumes of 1.1 μl (size 1; blue), 1.6 μl (size 2; red), 2.2 μl (size 3; black), and 2.8 μl (size 4; yellow). (B) Rescaling of the current tissue volume VT with the maximum tissue volume VT* (average of days 24 to 32) for three independent experiments and different CB shapes. Data points are color-coded according to the experiment, where each symbol represents a different CB shape. (C) Average tissue thickness VT*/A0 as a function of initial minimum principal curvature κmin and a linear regression (gray line; R = –0.936). Inset shows the initial surface area A0. (D) Rate of growth per tissue volume as a function of culture time, which can be fitted with a decay function following a standard log-normal distribution (black curve).

  • Fig. 4 Spontaneous emergence of chiral structures.

    (A) Maximum projection of tissue grown on a CB with an initial volume of 1.1 μl imaged after 32 days of tissue culture. Tissues were stained for actin and visualized using LSFM. Actin fibers are oriented in a particular direction. Scale bar, 500 μm. (B) Example of the fiber angle distributions for five different views (72° increments) around the sample obtained using fast Fourier transform analysis. Red curve delineates the average fiber angle distribution over all views, and dashed line indicates the mean value. (C) Mean fiber angle distributions as a function of total volume for four different sample sizes (color-coded; n = 3) compared to asymptotic directions of corresponding CB surfaces (blue curve) and to hyperboloid surfaces (black curve). Red curve shows theoretical predictions of maximum tensile directions obtained using membrane theory.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaav9394/DC1

    Fig. S1. Principle of the scaffold preparation procedure.

    Fig. S2. Equilibrium surfaces of axially symmetric configurations.

    Fig. S3. Experimental measurements compared to theoretical predictions of a liquid interface.

    Fig. S4. Experimental results of blebbistatin and TGF-β1 treatments.

    Fig. S5. Membrane theory of thin shells of revolution applied to CB surfaces.

    Fig. S6. Asymptotic directions on hyperboloids compared to CB surfaces.

    Fig. S7. Method of quantifying actin fiber angles and asymptotics on CB surfaces.

    Fig. S8. Example of actin fiber-angle direction analysis and local correlations.

    Fig. S9. Actin fiber angle distributions on the CB surfaces.

    Fig. S10. Time evolution of actin fiber angle distributions on CB.

    Movie S1. 3D LSFM image of tissue grown on a capillary bridge surface.

    References (4244)

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. Principle of the scaffold preparation procedure.
    • Fig. S2. Equilibrium surfaces of axially symmetric configurations.
    • Fig. S3. Experimental measurements compared to theoretical predictions of a liquid interface.
    • Fig. S4. Experimental results of blebbistatin and TGF-β1 treatments.
    • Fig. S5. Membrane theory of thin shells of revolution applied to CB surfaces.
    • Fig. S6. Asymptotic directions on hyperboloids compared to CB surfaces.
    • Fig. S7. Method of quantifying actin fiber angles and asymptotics on CB surfaces.
    • Fig. S8. Example of actin fiber-angle direction analysis and local correlations.
    • Fig. S9. Actin fiber angle distributions on the CB surfaces.
    • Fig. S10. Time evolution of actin fiber angle distributions on CB.
    • References (4244)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mov format). 3D LSFM image of tissue grown on a capillary bridge surface.

    Files in this Data Supplement:

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