A simple mathematical model recapitulates signaling dynamics and predicts cell fate patterning.

(A) (Left) Model equations. u and v represent WNT and NODAL signaling, respectively (parameter descriptions and values in S2 Model). (Right) Time evolution of WNT and NODAL to steady state. (B) The position of inner and outer edge of simulated WNT signaling levels as a function of time. (C) WNT levels at steady state (46 h) as a function of edge distance for different simulations. LDN addition was simulated by setting WNT’s dependence on BMP to 0 at indicated time points. IWP2 addition was simulated by setting autoactivation of WNT to 0 at indicated time points. (D) NODAL levels at steady state (46 h) for different simulations. (E, F) Fates assigned by the model on colonies of different sizes (E), shapes (F). (G) hESCs immunostained for CDX2, BRA, SOX2 after 44 h of BMP treatment on triangular and pacman colonies. Immunostaining data from n = 18 colonies were used to calculate average fate territory maps shown adjacent to image. Scale bar = 100 μm. Underlying data can be found in S10 Data. BMP, Bone Morphogenic Protein; BRA, BRACHYURY; hESC, human embryonic stem cell; LDN, LDN193189.