PMC

The transcription is regulated by the activators and the repressors binding to the binding sites of the gene.

Below the bifurcation or threshold , the equilibrium value of protein concentration is zero, while above it takes the value . The parameters are: , , and .

mRNAs hunchback and bicoid are represented by hb and bcd respectively. Arrows represent activations and are listed in the set of ordered pairs . Lines with perpendicular endings represent repressions and are listed in the set .

The steady state of protein shows a spiky profile, resulting from the inhibitory action of proteins and . In this model, we have considered that the concentrations of and are constant in time and non-homogeneous in space. The activator protein has been considered constant along the spatial region.

The mean distribution of the concentration of proteins has been calculated from the data of embryos, taken from the FlyEx database. The embryo length has been scaled from to , and the units in the vertical axis are proportional to protein concentration. The continuous curves show the predictions of the model of production of proteins HB and KNI. The model equations have been obtained with the software package GeneticNetworks.

The embryo length has been scaled from to , and the units in the vertical axis are proportional to protein concentration. The data has been taken from the FlyEx database. The continuous curves represent the fitted mean distribution of the concentration of proteins calculated from the data of embryos. These curves are the initial conditions for a model obtained with the software package GeneticNetworks for the production of the proteins KNI and zygotically produced HB, during cleavage cycle 14.