Fig. 3: Energetics of trans and cis fusion and pharmacological control of organoid morphogenesis.
From: Topological morphogenesis of neuroepithelial organoids
a, Change in bending energy ΔEb is depicted for trans and cis fusion. The conditions for ΔEb < 0 is denoted for both fusion modes in terms of topological rigidity \(\bar{\kappa }/\kappa\). b, State diagram of organoid morphology is shown as a function of reduced Gaussian rigidity \(\bar{\kappa }/\kappa\). Three regions depict the initial (yellow) and final (purple) morphologies. Region I, \(\bar{\kappa }/\kappa < -1\): an ensemble of spheres is stable and no fusion is favoured. Region II, \(\bar{\kappa }/\kappa > -1\): trans fusion leads to the formation of tubular lobules with spherical topology. Region III, \(\bar{\kappa }/\kappa > 0\): both trans and cis fusion are favoured and leads to lobules with wiffle ball morphology. c, Temporal evolution of scaled bending energy is shown for various values of \(\bar{\kappa }/\kappa\), estimated from triangulated meshes \({E}_{\mathrm{b}}/\kappa =\sum {H}_{i}^{2}{A}_{i}+4\uppi (\bar{\kappa }/\kappa )(N-g)\), where index i traverses all the faces in the system. Extended Data Fig. 4a shows the evolution of individual terms and Extended Data Fig. 4b shows the corresponding energy for the largest lobule in the system. Estimations were made for the same n = 3 untreated and n = 4 RA-treated organoids represented in Fig. 2. d, Treatment with HA130 leads to organoid morphologies that are consistent with the attenuation of epithelial fusion, both in the absence (top row) and presence (bottom row) of RA. Supplementary Videos 11 and 12 show the surface rendering examples. e, Shape of organoids cultured in varying concentrations of HA130. The error bar indicates 95% confidence interval for each condition (f shows the legend and n organoids). Organoid morphology is visualized by the surface renderings of the organoid outer boundary (magenta, transparent) and its apical surfaces (green) for day 4 samples shown in d. The parametric curves for the wiffle ball (four passages, d/R = 0.15; dashed line) and spherocylinders (solid line) serve as guides for the shape diagram. f, Topology of organoids cultured in varying concentrations of HA130.
