Figure 5
From: Mechanisms of gap gene expression canalization in the Drosophila blastoderm
Spatial configuration of attraction basins in the simplified model. (A,B): Basins of attraction at the eleven spatial positions (nuclei in cleavage cycle 13) for the two Bcd profiles from the ensemble (profiles (A) #1 and (B) #71, corresponding to the phase portraits from Fig. 4A and 4B, respectively), together with the initial Hb concentration profile (black curve) and highlighted positions of the hb borders in the model (dashed magenta lines). Each thick vertical line presents the domain Ω, which is the set of initial values 0 < vHb < 100 at the Hb axis, in which the attraction basins for attractors A1-A3 are marked by corresponding colors. The basins were calculated and shown at spatial positions ranging from 37% EL to 57% EL with 2% bins, and the width of the vertical lines containing these basins is arbitrarily chosen for better visibility. (C): Intersection of the initial Hb profile (black curve) and the attraction basin boundaries (blue and red curves) for all but one Bcd profiles classified in the two families in (D), as described in the text. The blue and red colors in both (C) and (D) correspond to the first and second Bcd families, respectively. For the first Bcd family, the initial Hb profile crosses a boundary separating either the attraction basins of A1 and A3 (see (A) for an example) or the basins of A2 and A3, and all these boundaries are shown as blue curves in (C) (see Methods for description of basin boundary calculation). For all Bcd profiles from the second family, the basin boundaries shown in (C) as red curves separate the basin of A2 and the lower part of the basin of A1 at various spatial positions (see (B) for an example). The two line segments at the bottom of (C) show the ranges of the hb border positions in solutions of the simplified model equations for Bcd profiles from the two families. The inset in (D) shows the correlation between the hb border positions in the model (vertical axis) and the positions of intersection points between the initial Hb profile and the basin boundaries from (C) (horizontal axis), for Bcd profiles from the two families.