Figure 4

Dynamical mechanisms of hb border formation for various Bcd profiles. Each panel shows the Hb-Kr-Kni projections of the 4D phase portrait fragments from the hb-expressing and hb-nonexpressing border nuclei simultaneously. The hb-expressing and hb-nonexpressing border nuclei are the ones placed just anterior and just posterior to the hb border position, respectively. The axes labels for all panels are as for (A) and show the corresponding protein concentrations. The blue balls are the attractors from the hb-expressing border nucleus phase portraits, and the brown ones from the hb-nonexpressing nucleus portraits. The red balls are the saddles from the nuclei specified below for each panel. The cyan tubes are branches of the unstable manifolds for the hb-expressing border nuclei saddles, and the magenta ones for the hb-nonexpressing nuclei saddles. The green trajectories are the solutions for the biological initial conditions from the hb-expressing and hb-nonexpressing border nuclei. The initial conditions consist of the maternal Hb concentration and are zero for all other proteins. The trajectories gradually turn to red as time approaches the end of cleavage cycle 14A (t = τ) and become blue for later times. (A): The picture is for Bcd profile #1, with the hb-expressing border nucleus at 49%EL and the hb-nonexpressing border nucleus at 51%EL . (B): Bcd profile #71; the border nuclei at 49%EL and 51%EL ; the red saddle is from the hb-nonexpressing border nucleus. (C): Bcd profile #6; the border nuclei at 47%EL and 49%EL ; the red saddle is from the hb-expressing border nucleus. (D): Bcd profile #37; the border nuclei at 51%EL and 53%EL ; the red saddle is from the hb-expressing border nucleus.