Extended Data Fig. 8: Link between mechanical and morphometric parameters.
From: Mechanochemical bistability of intestinal organoids enables robust morphogenesis
A. Definitions of crypt cellular aspect ratio \({(\frac{h}{d})}_{{\rm{c}}}\) and in-plane to lateral tension ratio \({(\frac{{\Gamma }_{a}+{\Gamma }_{b}}{{\Gamma }_{l}})}_{{\rm{c}}}\) (see SI Note section 3.1 for details). B. Sensitivity analysis for how model parameters affect the correlation between aspect ratio \({(\frac{h}{d})}_{{\rm{c}}}\) and in-plane to lateral tension ratio \({(\frac{{\Gamma }_{a}+{\Gamma }_{b}}{{\Gamma }_{l}})}_{{\rm{c}}}\) in both bulged and budded crypts: the dependence of the normalized value \({(\frac{h}{d})}_{{\rm{c}}}/{(\frac{{\Gamma }_{a}+{\Gamma }_{b}}{{\Gamma }_{l}})}_{{\rm{c}}}\) on normalized volume \(v\) (left), in-plane contraction ratio \(\alpha\) (middle) and differential tension \({\sigma }_{{\rm{c}}}\)(right). We set \(v=1,\,\alpha =1.2\,\) and \({\sigma }_{{\rm{c}}}=\) 0.03 (bulged) or 0.15 (budded) unless the parameter is varying. C. Representative organoid image with Myh-9-GFP staining and extraction of cellular height \(h\) and width \(d\). D. Quantification of Myh-9-GFP intensity ratio: apical, basal, and in-plane (sum of apical and basal) intensities are normalized by lateral intensity in each crypt (bulged: N = 11, budded: N = 28). E. Quantification of cellular height \({h}_{{\rm{c}}}\), width \({d}_{{\rm{c}}}\) and aspect ratio \({(\frac{h}{d})}_{{\rm{c}}}\) in both bulged and budded crypts (bulged: N = 11, budded: N = 28). Bulged samples are those after lumen breakage (that is \(v\approx 1\), also shown in Fig. 2e), and in this state, cellular tension ratio and aspect ratio are expected to share the same value based on sensitive analysis B. F. Inference of in-plane to lateral tension ratio \({(\frac{{\Gamma }_{a}+{\Gamma }_{b}}{{\Gamma }_{l}})}_{{\rm{c}}}\) from corresponding Myh-9-GFP intensity ratio (that is right panel in D) and cellular aspect ratio (based on sensitive analysis B, tension ratio can also be inferred from aspect ratio in panel E). 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 (organoid) and 20 µm (magnification).
