  Expression of the Drosophila segment polarity genes is initiated by a
prepattern of pair-rule gene products and maintained by a network of regulatory
interactions throughout several stages of embryonic development. Analysis of a
model of gene interactions based on differential equations showed that
wild-type expression patterns of these genes can be obtained for a wide range
of kinetic parameters, which suggests that the steady states are determined by
the topology of the network and the type of regulatory interactions between
components, not the detailed form of the rate laws. To investigate this, we
propose and analyze a Boolean model of this network which is based on a binary
ON/OFF representation of transcription and protein levels, and in which the
interactions are formulated as logical functions. In this model the spatial and
temporal patterns of gene expression are determined by the topology of the
network and whether components are present or absent, rather than the absolute
levels of the mRNAs and proteins and the functional details of their
interactions. The model is able to reproduce the wild type gene expression
patterns, as well as the ectopic expression patterns observed in
over-expression experiments and various mutants. Furthermore, we compute
explicitly all steady states of the network and identify the basin of
attraction of each steady state. The model gives important insights into the
functioning of the segment polarity gene network, such as the crucial role of
the wingless and sloppy paired genes, and the network's ability to correct
errors in the prepattern.
