Fig. 4: Theoretical predictions of mechanochemical bistability for crypt morphogenesis.
From: Mechanochemical bistability of intestinal organoids enables robust morphogenesis
a, Theoretical bifurcation trajectories showing the evolution of crypt morphology and differential tension with lumen volume, specified as normal morphogenesis (black arrows), lumen inflation of both bulged and budded organoids (orange arrows), and tension inhibition (grey arrows). b, Comparison between experimental data (red dot, bulged (N = 11) samples; blue dots, budded (N = 28) samples; all data presented as mean ± s.d.) and predicted phase diagrams of crypt morphology as a function of tension asymmetry \(\epsilon\) and normalized volume v. Tension asymmetry of budded organoids agrees with the prediction considering crypt mechanosensation (right) rather than that without mechanosensation (left; see also Fig. 2f). c, Predicted evolution for tension asymmetry data (mean ± s.d.) of both bulged (N = 7) and budded (N = 19) samples with the theoretical model, where the intrinsic differential tension σ is the only free parameter fitted as 0.02 (Supplementary Note 4.3). d, Evolution of crypt shape with developmental time (N = 5), showing rapid changes in shape at a critical morphological point, as expected from bistability. The solid line represents mean values and the shaded region represents 95% confidence intervals. For different developmental stages, changes in the crypt profiles in a time interval of 20 min (red, start of interval; green, end of interval) are shown. Scale bars, 50 µm. e, Schematic of crypt morphogenesis driven by luminal pressure, and involved morphological bistability feature arising from mechanosensation.
