Function perturbation impact on the topological structure of Boolean networks

This paper investigates the function perturbation impact on the topological structure of Boolean networks by using the semi-tensor product method, and presents a set of new results. First, a new necessary and sufficient condition is presented to guarantee that an attractor is invariant after function perturbations. Second, a necessary and sufficient condition is established to analyze how do the attractors of Boolean networks change with the Boolean function perturbations. Finally, as applications, the intervention problem of a WNT5A Boolean network and the function perturbation identification problem of a D. melanogaster segmentation polarity gene network are investigated, respectively. The study of the practical examples shows that the new results obtained in this paper are very effective in the function perturbations impact analysis of Boolean networks.