  We present a general methodology in order to build mathematical models of
genetic regulatory networks. This approach is based on the mass action law and
on the Jacob and Monod operon model. The mathematical models are built
symbolically by the \emph{Mathematica} software package \emph{GeneticNetworks}.
This package accepts as input the interaction graphs of the transcriptional
activators and repressors and, as output, gives the mathematical model in the
form of a system of ordinary differential equations. All the relevant
biological parameters are chosen automatically by the software. Within this
framework, we show that threshold effects in biology emerge from the catalytic
properties of genes and its associated conservation laws. We apply this
methodology to the segment patterning in \emph{Drosophila} early development
and we calibrate and validate the genetic transcriptional network responsible
for the patterning of the gap proteins Hunchback and Knirps, along the
antero-posterior axis of the \emph{Drosophila} embryo. This shows that
patterning at the gap genes stage is a consequence of the relations between the
transcriptional regulators and their initial conditions along the embryo.
