Figure 2

The model and an illustration of the wave domain concept. (A) Diagram of the signaling motif. \(A\) and \(I\) represent active and inactive forms of the signaling molecule, while \(F\) represents a local inhibitor (see “Methods” for equations and Table 1 for parameter values). (B) The resulting distribution of component \(A\) in a snapshot of the simulation with \({k}_{0}=0.15\), \({s}_{2}=0.8\) using homogeneous initial conditions. (C) An image of two merged channels: green channel represents activator \(A\) and red channel represents inhibitor \(F\). The concentrations were scaled as \(\left[C-min(C)\right]/\left[\mathit{max}\left(C\right)-min\left(C\right)\right]\). (D) The colormap of the direction angles, \(\theta\), of the wave vectors at the same time point as B and C. Arrows represent the direction of wave vectors. (E) The colormap of the magnitude of a local change (gradient) in the directions of the wave vectors. Regions of high gradient are located at the edges of wave domains. (F) The colormap of our metric of the coherence distance. (G) Segmentation of the coherence distance with the modified watershed algorithm and after merging domains with similar values of the mean \(\theta\). (H) The dynamics of wave domains. The number of regions detected by the automated segmentation pipeline is decreasing (left panel), while the mean area of regions is increasing over time (right panel).