Modeling transcriptional factor cross-talk to understand parabolic kinetics, bimodal gene expression and retroactivity in biosensor design

•ODE-based kinetic model formulated to simulate transcriptional factor (TF) cross-talk.•TF repression, protein degradation, and cell growth dilution were considered.•The simulation fits well with the gene expression pattern from experimental data.•TF competitive binding leads to hysteresis and bimodal gene expression.•This ODE model may serve as diagnosis to troubleshoot biosensor design.