WNT signaling dynamics lie outside the Turing instability regime.

Abstract

(A) Schematic and equations of the model. (B) Evolution of activator levels from the initial state to the steady state. Inequalities define parameter regimes that display each of the 2 behaviors (S1 Model). In each case, the top row shows the model simulated on a circular colony, while the bottom shows it simulated in a domain with cells throughout. Simulation parameters: sA = 0.01, kI = 1, kA = 0, kdA = 0.001, DI = 0.4, sI = 0.01, kdI = 0.008. (left) DA = 0.014, (right) DA = 0.0025 for outside and inside Turing instability regime, respectively. Simulation domain: 190 × 190 pixel square lattice with periodic boundary conditions and random distribution of activator/inhibitor as initial conditions. To simulate the model in circular colonies, a circle (radius: 25 pixels) is defined at the center of the lattice. Outside the circle, sA = sI = 0, and kd = 0.01. (C) Snapshots of GFP-β-catenin hESCs from time-lapse imaging at indicated time points post BMP treatment. Marked regions are magnified in images shown below. (D) Average nonmembrane β-catenin intensity levels as a function of distance from the colony edge. The legend indicates the time post BMP treatment represented by each curve. Green and blue dots represent the front and back edges of the active signaling domain, respectively. (E) The positions of the inner and outer edge of the signaling domain as a function of time post BMP addition. Magenta line shows linear fit with equation 6.02 μm/h × t + 13.57 μm, R2 = 0.98. (F) Kymograph showing spatiotemporal evolution of nonmembrane β-catenin levels. At time points earlier than the first time plotted in D, signaling is below threshold signaling at all positions in the colony. Scale bar = 100 μm. Underlying data can be found in S3 Data. BMP; Bone Morphogenic Protein; GFP; Green Fluorescent Protein; hESC, human embryonic stem cell.</p