20. Boolean Networks

Reconstruction of genetic regulatory networks from gene expression profiles and protein interaction data is a critical problem in systems biology. Boolean networks and their variants have been used for network reconstruction problems due to Boolean networks’ simplicity. In the graph of a Boolean network, nodes represent the statuses of genes while the edges represent relationships between genes. In a Boolean network model, the status of a gene is quantized as ‘on’ or ‘off’, representing the gene as being ‘active’ or ‘inactive’ respectively. In this chapter, we will introduce the basic definitions of Boolean networks and the analysis of their properties. We will also discuss a related model called probabilistic Boolean network, which extends Boolean networks in order to have the advantage of modeling with data uncertainty and model selection. Furthermore, we will also introduce directed acyclic Boolean network and the statistical method of SPAN to reconstruct Boolean networks from noisy array data by assigning an s-p-score for every pair of genes. At last, we will suggest possible directions for future developments on Boolean networks.