Stabilizing and Destabilizing Effects of Embedding 3-node Subgraphs on State Space of Boolean Networks

Oosawa, Chikoo
Savageau, Michael A.
Jarrah, Abdul S.
Laubenbacher, Reinhard C.
Sontag, Eduardo D.
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We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space that increases with longer length of attractors and greater number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can also provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with other six subgraphs show opposite effects on dynamics of the networks, is roughly consistent with Thomas's conjecture. These results suggest that feedforward subgraphs are one of the favorable local structures in biological complex networks.
Comment: 5 figures, 2 tables. accepted in ACRI2008, to appear in Lecture Notes in Computer Science
Nonlinear Sciences - Cellular Automata and Lattice Gases, Nonlinear Sciences - Adaptation and Self-Organizing Systems