Training threshold Boolean networks: applications to gene regulatory network modeling

This study explores a Boolean model of the Arabidopsis thaliana flower organ specification gene regulatory network (FOS-GRN), consisting of thirteen genes with logical rules to update their states. We focus on the threshold Boolean network (TBN) variant, which simplifies gene network modeling by inferring weights and thresholds for each gene. This linear approach provides a more interpretable model compared to traditional Boolean networks with complex logical rules. To train the TBN for the FOS-GRN, we apply a machine learning method, using perceptrons to learn the linear relationships between genes. Our results indicate that three genes exhibit non-linear interactions, which cannot be captured by a TBN. Despite this, the inferred model closely approximates the original network. Additionally, the network’s asymptotic behavior correctly identifies biologically meaningful fixed points with the largest basins of attraction. When the goal of fully replicating the FOS-GRN state transition table was relaxed, and instead the focus shifted to identifying at least ten important fixed points, the inferred network succeeded in this objective. However, it also introduced spurious fixed points. Nevertheless, the perceptron-based training approach proves valuable for gene regulatory network inference within the TBN framework.