A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila
Fig 1
Dynamics of gap gene pattern formation in Drosophila melanogaster.
(A) Gap protein expression data (colored areas) and model output (dots), shown at cleavage cycle 13 (C13) and 14A (C14A, time classes T4 and T8). Hb is in yellow, Kr in green, Kni in red, Gt in blue (see key). See S1 Data for the whole data set, previously published in [32]. X-axes: % A–P position (where 0% is the anterior pole); y-axes: relative protein concentration (in au’s). Dashed vertical line indicates bifurcation boundary between static and shifting gap domain borders (at 52% A–P position). (B) Dynamical regimes governing gap gene expression in the anterior versus the posterior of the embryo. Static anterior boundaries are set by attractors in a multi-stable regime, as shown in the stylized phase portrait on the left. In this region, initial concentrations of maternal factors determine which basin of attraction a given nucleus will eventually fall into. It will either converge towards a high Hb and Gt state, a high Hb and Kr state, or a high Kr-only state. Shifting posterior boundaries are driven by a damped oscillator regulatory mechanism. This mechanism is implemented by a mono-stable spiral sink, a single stable state towards which spiralling trajectories converge. These are arranged around a color wheel that illustrates the different states composing the oscillator. The spiral sink is represented by the central black dot. Trajectories are represented by black curves with transient dynamics shown as solid, and asymptotic convergence is indicated by dotted curves. As in the anterior trunk region of the embryo, initial concentrations of maternal factors—Hb in particular—determine the starting points of the trajectories. (See text for details). A–P, anteroposterior; au, arbitrary unit; Conc., concentration; Gt, Giant; Hb, Hunchback; Kni, Knirps; Kr, Krüppel; Rel., relative.