A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties

To cope with the increasing complexity of regulatory networks, we define a reduction method for multi-valued logical models. Starting with a detailed model, this method enables the computation of a reduced model by iteratively "hiding" regulatory components. To keep a consistent behaviour, the logical rules associated with the targets of each hidden node are actualised to account for the (indirect) effects of its regulators. The construction of reduced models ensures the preservation of a number of dynamical properties of the original model. In particular, stable states and more complex attractors are conserved. More generally, we focus on the relationship between the attractor configuration of the original model and that of the reduced model, along with the issue of attractor reachability. The power of the reduction method is illustrated by its application to a multi-valued model of the segment-polarity network Controlling segmentation in the fly Drosophila melanogaster.