Figure 6. Simulation of Bcd scaling in the gene circuit model of gap genes.

(a–h) Model output for Hb, Kr, Gt and Kni during cleavage cycle 14, at 3.125 (early T1), 9.375 (late T1), 15.625 (early T2), 21.875 (late T2), 28.125 (T3), 34.375 (T4), 40.625 (T6) and 46.875 (T8) minutes after the thirteenth nuclear division. Simulations using control19 or scaled Bcd are shown as solid or dashed lines, respectively. The scaling of Bcd in large embryos was based on data from Cheung et al.46 (see Methods for details). The control Bcd profile was the median profile from wild-type embryos used by Manu et al.19 to fit the model. The invariance of the Bcd length scale in absolute units was represented by reducing the length scale by 20%—from 0.1651 EL to 0.1321 EL—in the relative position units utilized in the model. Furthermore, a stronger Bcd source, caused by the increased amount of bcd mRNA in large embryos46, was modelled by multiplying the source strength (A), and hence Bcd concentration, by 1.6. These values of Bcd amplitude and length scale imply a critical position at ξ=0.311 (see Supplementary Fig. 9 for simulation experiments of adjusting the critical position). Control and scaled simulations are indicated in the legend above a. (i) Time series of boundary positions in the model output; see above for time points. Anterior and posterior boundaries are represented by left- and right-pointing triangles, respectively. The colour key is shown in b. Control and scaled Bcd simulations are shown as open and filled triangles, respectively. (j) Time series of the expression level (in a.u.) at the peak of the posterior Hb, central Kr, posterior Gt and abdominal Kni domains. Control and scaled simulations are shown as solid and dashed lines, respectively. Kr2, Kni2, Kni3 and Gt5 boundaries shift to the anterior. The reduction in Kr expression at the domain peak is relatively constant in time, whereas the difference between control and scaled Bcd simulations for Gt and Kni increases in time.