Dynamically consistent reduction of logical regulatory graphs

To cope with the increasing complexity of regulatory networks, we define a reduction method for multi-valued logical models. Starting with a detailed model, we use decision diagrams to compute reduced models by iteratively ''removing'' regulatory components. To keep a consistent dynamical behaviour, the logical rules associated with the targets of each removed node are actualised to account for the (indirect) effects of its regulators. This construction of reduced models preserves crucial dynamical properties of the original model, including stable states and more complex attractors. In this respect, the relationship between the attractor configuration of the original model and those of reduced models is formally established. We further analyse the issue of attractor reachability. Finally, we illustrate the flexibility and efficiency of the proposed reduction method by its application to a multi-valued model of the fly segment polarity network, which is involved in the control of segmentation during early embryogenesis.