Robustness and fragility of Boolean models for genetic regulatory networks.

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 time-scales between pre- and post-translational processes and a minimal prepattern ensure convergence to the wild-type expression pattern regardless of fluctuations.