Random Boolean Networks and Attractors of their Intersecting Circuits

The multi-scale strategy in studying biological regulatory networks analysis is based on two level of analysis. The first level is structural and consists in examining the architecture of the interaction graph underlying the network and the second level is functional and analyse the regulatory properties of the network. We apply this dual approach to the "immunetworks" involved in the control of the immune system. As a result, we show that the small number of attractors of these networks is due to the presence of intersecting circuits in their interaction graphs. We obtain an upper bound of the number of attractors of the whole network by multiplying the number of attractors of each of its strongly connected components. We detect first the strongly connected components in the architecture of the interaction digraph of the network. Secondly, we study the dynamical function of the attractors by looking further inside these components, notably when they form circuits (intersecting or not).