Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo
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.