DNA encrypts the composition of the cellular material that is synthesized through transcription and translation. Never-theless, gene regulation mechanisms determine the final amount of transcribed and translated material. Transcription factors (TF) are a class of proteins that bind to DNA motifs and can either facilitate or prevent the RNA polymerase to transcribe a strand of DNA into an mRNA. These mechanisms allow the cell to sense the environment and adapt to different environmental conditions, e.g. presence of toxic compounds, oxidative stress or absence of nutrients. TF interactions with DNA are depicted by networks of molecular interactions. Some TFs bind to very specific DNA sites, and others have a broad range of binding sites. Moreover, TFs often interact each other, e.g. through heterodimerization prior to bind to DNA, leading to changes in their binding specificities. However, these effects remain poorly understood. By combining detailed mathematical modeling and high-throughput experimental techniques for quantification of molecular interactions, we built a heterodimer-DNA specificity model with higher predictive power than a one-site model. Bioreporters are living cells that emit a signal in the presence of a chemical compound. In arsenic bioreporters, a TF triggers the detoxification response in presence of arsenic. To better understand the key mechanisms involved in the response, we built a detailed mechanistic model of the gene regulatory circuits of different bioreporters. In this study, we used mathematical modeling (ODE, SSA) to create, calibrate and analyze detailed networks of molecular interactions involved in gene regulations. We quantified the cooperative binding of transcription factors forming heterodimers on a DNA library, and optimized bioreporters for the detection of arsenic by modeling feedback, uncoupled and toggle switched-based gene regulatory circuits.