Figure 3

Figure 3

The blastoderm connectivity profile identifies key hallmarks of criticality during its rigidity percolation PT

(A–C) Exemplary 2D confocal sections at the 1^st–2^nd deep-cell layer of the central blastoderm of an e-cadherin-morpholino (MO)-injected embryo (A), of the marginal blastoderm of a WT embryo (B), and of the central blastoderm of a mesoderm-induced embryo (C) with overlaid connectivity maps (top) and their rigidity characteristics (bottom) during the fluidization/thickening process (color coded for 30 min intervals). Interstitial fluid is marked by dextran, nuclei by H2B-GFP, and membranes by membrane-RFP. Floppy areas are illustrated in gray, rigid areas in green, and the GC in red. Yellow- and purple-shaded areas indicate fluidized and rigid blastoderms, respectively.

(A’, B’, and C’) Plots of the time trajectory (color coded) of blastoderm viscosity (mean) as a function of its normalized connectivity <k> for e-cadherin-MO central blastoderm (A’; for viscosity n = 94, N = 6; for connectivity n = 54, N = 6), WT marginal blastoderm (B’; for viscosity n = 115, N = 9; for connectivity n = 15, N = 3), and mesoderm-induced central blastoderm (C’; for viscosity n = 42, N = 6; for connectivity n = 15, N = 3).

(A’’, B’’, and C’’) Plots of the time trajectory (color coded) of the GC relative size as a function of its normalized connectivity <k> for the samples described in (A’), (B’), and (C’).

(D) Plot of the fraction of the network occupied by the GC (mean ± 95% CI) as a function of normalized connectivity <k> in simulated random networks of the same size as the average size of WT experimental networks (black). Overlaid dot plot of the measured GC size as a function of the normalized network connectivity <k> of the central blastoderm in WT (n = 103, N = 11), e-cadherin-MO (n = 54, N = 6), control-MO (n = 15, N = 3), CAMypt1 (n = 89, N = 13), slb/wnt11f2 mutant (n = 10, N = 2), and mesoderm-induced WT (n = 15, N = 3) embryos and of the marginal blastoderm in WT (n = 15, N = 3) and slb/wnt11f2 mutant (n = 15, N = 3) embryos. n, number of networks; N, number of embryos.

(E) Plot of central blastoderm tissue viscosity (mean ± SEM) as a function of normalized connectivity <k> (mean ± SEM) for the experimental networks described in (D) (for viscosity: central blastoderm of WT n = 129, N = 11; e-cadherin-MO n = 94, N = 6; control-MO n = 71, N = 6; CAMypt1 n = 66, N = 7; slb/wnt11f2 mutant n = 54, N = 4; mesoderm-induced WT n = 42, N = 6; mesoderm-induced slb/wnt11f2 mutant n = 13, N = 3 embryos; marginal blastoderms of WT n = 115, N = 9; slb/wnt11f2 mutant n = 44, N = 5 embryos; for connectivity: samples described in D).

(F) Plot of the variance (Var) of the distribution of rigid cluster sizes p(s) other than the GC, as a function of their normalized connectivity <k>, in simulated networks of the same size as the average size of experimental networks (black) and in the experimental networks described in (D) (gray) (except marginal networks), showing divergence at the critical point, with good theory-experiment agreement.

(G) Plot of the cumulative distribution of rigid cluster sizes p(s) other than the GC near the critical point. The numerical experiment shows the scaling behavior of cluster size distribution p(s) for networks of arbitrary large size (∼1,200 nodes). The overlaid plot shows the cluster size distribution near criticality for real networks, showing excellent agreement with predictions. The dashed line shows a power-law p(s) ∼ s^−2.5.

The gray-shaded regions at the plots indicate the rigid regime above the theoretical k_c.

ρ Spearman correlation test (E). Scale bars: 50 μm in (A)–(C).

See also Figure S3 and Table S1.