Figure 1.
Control of Hb sharpness and position.
(A,B) An embryo in mid-nuclear cleavage cycle 14A, with immunostaining to Bicoid (Bcd) (A) and Hunchback (Hb) (B) proteins. Anterior pole on left, dorsal side on top. (C) Fluorescence profiles versus anteroposterior position for A (green) and B (blue). Hb position, 47.1% EL; sharpness, 82.7°. (D) Hb profiles for homozygotes of hb14F, an allele coding a non-DNA binding Hb protein [52], showing dramatically reduced sharpness (63.9°). Heavy blue line: hunchback self-regulatory (HSR) model (Figure 3) prediction for absence of self-regulation. (E) hb14F heterozygotes and wild-type together, showing similar position (44.3% EL) and sharpness (81.3°). See Figure S2 for non-normalized data. (F) Hb profiles from bcdE1/+ embryos (Bcd mRNA half-dosage). Heavy blue line: simulation for this background, by reducing Bcd synthesis in the HSR model. (G,H) Hb profiles from embryos expressing one copy of bcdK57R, an allele affecting Bcd cooperativity [54], gives two outcomes: a small anterior shift ((G); 3.0% change from bcdE1/+); and a strong anterior shift ((H); 36.7% change from bcdE1/+). Heavy blue lines: HSR model simulations for weakly and strongly reduced Bcd cooperative binding ((G) and (H), respectively). Maximum intensities are normalized to one, to allow comparison of profile sharpness from different experiments. All embryos are between 26 and 39 minutes into nuclear cleavage cycle 14A, as determined by membrane invagination and the relative position from surface to cortex (see Materials and Methods). In (D) there are two T7 embryos, showing normal posterior pattern (not used for sharpness or position measurements). Individual embryo images are shown in Figure S1.
Figure 2.
Dynamics of Hunchback (Hb) pattern formation.
(A) Fitting the hunchback self-regulatory (HSR) model (Figure 3) to the same profiles as in Figure 1C. Red and black lines: experimental Bicoid (Bcd) and Hb, respectively. Blue and green lines: fitting for total Bcd and Hb concentrations (Equations S1.1–2, in Text S1), respectively. (B) 47 Hb wild-type profiles at different ages (red lines). Black line is the oldest one (same as in (A)). Blue lines: Dynamic simulation of HSR model, using kinetic constants determined in (A). Green line is the same as in (A). (C) pattern positions change slightly over time. Red dots and blue line: Hb boundary positions measured from embryos and from simulation in (B), respectively. (D) The pattern quickly achieves mature sharpness, with little change after 10 minutes. Red dots: border inclination (from embryos in (B)) versus embryo age. Blue line: Model prediction for the progressive increase of border inclination, for the simulations in (B). Black arrows indicate the embryo used to fit the model (shown in (A)). See Figure S7 for a direct comparison between data and model time evolution profiles.
Table 1.
Mean positions and sharpness (inclination) for all embryos and simulations presented.
Figure 3.
The hunchback (hb) self-regulatory (HSR) model to simulate hb transcriptional activation by Bicoid (Bcd) and self-regulation.
(1): Bcd (B) synthesis from a source term; (2n, n = 1, …, 6): Bcd binding to hb promoter; (14, 16): Hb (H) binding to hb promoter; (1+2n, n = 1, …, 6) and (15, 17): Hb synthesis; (18 and 19): Hb and Bcd decay, respectively. bn and hn represent the fragments of hb promoters containing 6 Bcd and 2 Hb sites, respectively; subscripts n indicate how many Bcd or Hb molecules are bound. 0 denotes either inert or constant concentration species (e.g. mRNA). kb0,b1 indicates the transition from b0 to b1 states; kb1,H indicates production of H from b1, and so on. We introduced cooperativity by taking kb(n-1),bn = factorn.kb0,b1 and kbn,b(n-1) = kb1,b0 for n = 2, …, 6. In addition, we set kbn,H = (1+Synt_Factor).kb(n-1),H for n = 2, …, 6 to account for the effect of multiple protein binding to the gene promoter. These relations strongly reduced the number of parameters, and the model fitting was not sensitive to changes in them.
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).
Table 2.
Methods for obtaining expression patterns, for the specified numbers of WT and mutant embryos.