Figure 6. AC/DC subcircuits and their possible role in the evolution of long-germband from short-germband segment determination.

(A) Phylogenetic relationships between the intermediate-germband insect T. castaneum and the two long-germband dipteran species analysed in this paper. Coloured bars indicate which dynamical regimes are active in which relative region along the A–P axis of the embryo (see key). (B) Visualisation of the dynamical regimes of an AC/DC circuit. We combine equation parameters into two composite control parameters which correspond to the $x$ and ${\tilde{\mathrm{\Gamma }}}^3$ parameters in Equations (28) and (29) of Appendix 1 and represent the strength of the positive feedback between two of the genes in the circuit (X-axis) and the strength of the negative feedback involving all three genes (Y-axis) respectively. We used simplified connectionist models (see ‘Materials and methods’)—with all degradation rates set to equal values, time-constant basal activation terms, and no auto-activation—to evaluate the dynamical regimes for varying values of these two control parameters. The results are colour-coded as indicated in the key. Possible dynamical regimes are: monostability and multistability without (grey), and with damped oscillations (light/dark red), as well as sustained limit-cycle oscillations (bright red) (see Appendix 1 for details).