Extended Data Fig. 9: Quantification of mechanical parameters.
From: Mechanochemical bistability of intestinal organoids enables robust morphogenesis
A. Definitions of cellular aspect ratios \({(\frac{h}{d})}_{{\rm{c}}}\) and \({(\frac{h}{d})}_{{\rm{v}}}\), and in-plane contraction ratio \(\alpha =\frac{{({\Gamma }_{a}+{\Gamma }_{b})}_{{\rm{c}}}}{{({\Gamma }_{a}+{\Gamma }_{b})}_{{\rm{v}}}}\), with subscripts c and v respectively denoting crypt and villus. B. Quantification of Myh-9-GFP intensity and cell shape: top, crypt to villus Myh-9-GFP intensity ratios, including crypt apical (ca) to villus apical (va), and crypt basal (cb) to villus basal (vb); bottom, quantification of cellular aspect ratios in crypt \({(\frac{h}{d})}_{{\rm{c}}}\) and that in villus \({(\frac{h}{d})}_{{\rm{v}}}\). C. Inference of in-plane contraction ratio \(\alpha \,\) from both Myh-9-GFP intensity and cell shape: top, the ratio of in-plane Myh-9-GFP intensities (that is the sum of apical and basal intensities) of crypt to villus cell; bottom, the aspect ratio of crypt to villus cell \({(\frac{h}{d})}_{{\rm{c}}}/{(\frac{h}{d})}_{{\rm{v}}}\). In panel B and C, both bulged (N = 11) and budded (N = 28) samples are quantified. Bulged samples with lumen breakage (labelled as \(v\approx 1\), also used in Fig. 2e) are chosen to quantify cellular aspect ratio as their cell shapes give direct inference of \(\alpha\) (see SI Note section 3.2 for details). D, E. Fitting of the lumen inflation-induced morphometric variation with analytic formulae derived from the model. The images (top) show the organoid morphology and cell shape before and after lumen inflation by PGE treatment. Morphometric variation in cells is tracked by (middle) normalized aspect ratio of crypt cell \({(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ifl}}}/{(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ctr}}}\) (that is the value after lumen inflation \({(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ifl}}}\) normalized by that before inflation \({(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ctr}}}\), presented as mean ± SD, with data of \({(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ctr}}}\) and \({(\frac{h}{d})}_{{\rm{c}}}^{{\rm{ifl}}}\) shown in the right panel), and (bottom) aspect ratio of crypt to villus cell \({(\frac{h}{d})}_{{\rm{c}}}/{(\frac{h}{d})}_{{\rm{v}}}\) (mean ± SD, with raw data shown in the right panel), in both bulged (panel D, N = 24) and budded (panel E, N = 19) organoids. F. Quantification of cell numbers in crypt and villus cross-sections (2D) from organoid images, which are used to estimate parameters in panel G (see SI Note section 3.3 and 4.3 for details). G. Measurement of shape factor \({\kappa }_{\tt{c}}\) (left) and crypt size \(\varphi\) (right) in bulged (N = 11) and budded (N = 28) crypts. The box-plot elements show the 25% (Q1, lower bound), 50% (median, line within the box) and 75% (Q3, upper bound) quartiles, and the whiskers denote 1.5× the interquartile range (minimum = Q1–1.5\(\times\)(Q3–Q1), maximum = Q3\(+\)1.5\(\times\)(Q3–Q1)) with outliers (rhombuses). Scale bars: 50 µm.
