Random Boolean Networks and Attractors of their Intersecting Circuits

Jacques Demongeot (1) , Adrien Elena (1) , Mathilde Noual (2, 3) , Sylvain Sené (2, 4)

1 AGIM - AGeing and IMagery
2 IXXI - Institut Rhône-Alpin des systèmes complexes
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

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).

Keywords: genetic networks; immune networks; attractors counting; tangential circuits; intersected circuits

Domains: Discrete Mathematics [cs.DM]

Jacques Demongeot, Adrien Elena, Mathilde Noual, Sylvain Sené. Random Boolean Networks and Attractors of their Intersecting Circuits. IEEE Workshops of International Conference on Advanced Information Networking and Applications (WAINA 2011), Mar 2011, Biopolis, Singapore. pp.483--487, ⟨10.1109/WAINA.2011.154⟩. ⟨hal-00666589⟩