Reasoning About Monotonic Regulation Conditions for Boolean Gene Regulatory Networks: An Algorithmic Approach

Gene Regulatory Networks (GRNs) determine how genes interact and regulate each other, in order to control various biological processes in living organisms. Each component of the GRN may be regulated by other components in the network called regulators, often divided to activators or inhibitors, and the overall effect of these regulators is determined by a regulation function. Here, we study the possible form of regulation functions, termed regulation conditions, in Boolean networks, a well established formalism for GRN modeling. Many tools exist for analyzing and modeling GRNs to gain insights on the control mechanisms for biological processes. One such tool is the Reasoning Engine for Interaction Networks (RE:IN), a powerful formal verification-based method that has been used effectively to study various GRNs of developmental and stem cell systems. We formally explain the permitted regulation functions in RE:IN, while understanding the assumptions (monotonicity, symmetry-by-groups and first order logic) and restrictions. Motivated by the effective use of RE:IN, along with an interest in understanding its assumptions and extending its capabilities, we reduce the problem of specifying regulation conditions in Boolean Networks to a matrix representation. Using this representation, we study methods to count the number of regulation conditions, provide a simple proof for those currently supported, and suggest a systematic approach for extending the regulation conditions to handle biological cases that are currently not supported by RE:IN. By analyzing a database of Boolean networks developed by the research community, we provide support for the validity of the monotonicity assumption in Boolean Networks, and identify limitations imposed by currently supported regulation functions. Based on our extension, we implemented a prototype reasoning tool for networks with extended regulation conditions.