Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo
Figure 4
Bifurcation diagrams and simulations for the hunchback (hb) self-regulatory (HSR) model.
(A) Bistability: solid blue curves are the stable steady states for Hb total concentration [H]T (y-axis) for a given Bicoid (Bcd) total concentration [B]T (bottom axis), or as Bcd production rate (k0,B, top axis). Red curve is unstable steady states ([H]T will evolve away from such concentrations). Hb concentration will evolve to the low steady states (short dashed lines) at low Bcd concentration, but abruptly steps up to the high steady states (long dashed lines) as Bcd concentration, [B]T, moves out of the bistable region (31.2<[B]T<40.5; green line on bottom axis). (B) Loss of bistability in the absence of self-regulation: bifurcation diagram for HSR model without self-regulation reactions (14–17) shows no bistability. (C) Reduction in Bcd cooperative binding shifts bistable region toward high [B]T regions. Black and Red: bifurcation diagrams for heavy blue lines in Figure 1G and 1H, respectively (simulations for reduced Bcd cooperative binding (Figure 3; Table S2); blue line, wild-type diagram (same as in (A)); (D) Simulation for reduced number of Bcd binding sites (removing reactions 10–13) shows disrupted sharpness since Bcd concentrations (red line in the bifurcation diagram, small box) do not reach the bistable threshold (green dot).