Hedgehog signaling controls pattern formation in many vertebrate tissues. The downstream effectors of the pathway are the bifunctional Gli transcription factors, which, depending on hedgehog concentration, act as either transcriptional activators or repressors. Quantitatively understanding the interplay between Gli activator and repressor forms for patterning complex tissues is an open challenge. Here, we describe a reductionist mathematical model for how Gli activators and repressors are integrated in space and time to regulate transcriptional outputs of hedgehog signaling, using the pathway readouts Gli1 and Ptch1 as a model system. Spatially resolved measurements of absolute transcript numbers for these genes allow us to infer spatiotemporal variations of Gli activator and repressor levels. We validate our model by successfully predicting expression changes of Gli1 and Ptch1 in mutants at different developmental stages and in different tissues. Our results provide a starting point for understanding gene regulation by bifunctional transcription factors during mammalian development.
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