  Interactions between genes and gene products give rise to complex circuits
that enable cells to process information and respond to external signals.
Theoretical studies often describe these interactions using continuous,
stochastic, or logical approaches. We propose a new modeling framework for gene
regulatory networks, that combines the intuitive appeal of a qualitative
description of gene states with a high flexibility in incorporating
stochasticity in the duration of cellular processes. We apply our methods to
the regulatory network of the segment polarity genes, thus gaining novel
insights into the development of gene expression patterns. For example, we show
that very short synthesis and decay times can perturb the wild type pattern. On
the other hand, separation of timescales between pre- and posttranslational
processes and a minimal prepattern ensure convergence to the wild type
expression pattern regardless of fluctuations.
