A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila
Fig 3
Canalizing properties and relaxation-like behavior of the gap gene damped oscillator.
(A, B) Canalizing properties: trajectories rapidly converge to the Kr-Kni and Kni-Gt planes in phase space. We simulated the nonautonomous diffusion-less circuit in the nucleus at 59% A–P position with Kni concentration fixed to zero and a set of initial conditions that were regularly distributed on the Kr-Gt plane. (A) Initial conditions shown in blue, embedded within the three-dimensional Kr-Kni-Gt space. (B) Two-dimensional projections of the Kr-Gt plane show converging system states as tiny blue dots at the end of cleavage cycle 12 (C12, initial conditions), cleavage cycle 13 (C13), as well as cleavage cycle 14A (C14A, time classes T1 and T8). (C) Fast-slow dynamics in posterior nuclei are caused by relaxation-like behavior. Unfolded, two-dimensional projections of the Kr-Kni and Kni-Gt planes are shown, as in Fig 2D at C13, C14A-T2, T4, and T6. Colored arrows indicate magnitude and direction of flow: large red arrows represent strong flow and small blue arrows represent weak flow. Simulated trajectories of posterior nuclei are superimposed on the flow (shown as black lines). Colored circles at the end of trajectories indicate current state at each time point. Stars mark trajectories experiencing a positive Gt component of the flow. See main text for further details. Gt, Giant; Kni, Knirps; Kr, Krüppel.