Computing Minimal Boolean Networks of Gene Regulatory Networks

Abstract

Models of Gene Regulatory Networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understand the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a-priori. Our goal in this work is to present a methodology for inferring this information from the data, and to provide a measure for comparing network states under different biological conditions. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. We also present a statistical approach for testing the similarity of inferred network states under different conditions. Finally, we extend our methodology into a heuristic that can handle large datasets that are generated by single-cell RNA-Sequencing(scRNA-Seq). We demonstrate the effectiveness of these tools using a public scRNA-Seq dataset and the GRN that is associated with it. Our methodology will enable researchers to obtain a better understanding of the dynamics of gene regulatory networks and their biological role.