Genes involved in detoxification of foreign compounds exhibit complex spatiotemporal expression patterns in liver. Cytochrome P450 1A1 (CYP1A1), for example, is restricted to the pericentral region of liver lobules in response to the interplay between aryl hydrocarbon receptor (AhR) and Wnt/β-catenin signaling pathways. However, the mechanisms by which the two pathways orchestrate gene expression are still poorly understood. With the help of 29 mutant constructs of the human CYP1A1 promoter and a mathematical model that combines Wnt/β-catenin and AhR signaling with the statistical mechanics of the promoter, we systematically quantified the regulatory influence of different transcription factor binding sites on gene induction within the promoter. The model unveils how different binding sites cooperate and how they establish the promoter logic; it quantitatively predicts two-dimensional stimulus-response curves. Furthermore, it shows that crosstalk between Wnt/β-catenin and AhR signaling is crucial to understand the complex zonated expression patterns found in liver lobules. This study exemplifies how statistical mechanical modeling together with combinatorial reporter assays has the capacity to disentangle the promoter logic that establishes physiological gene expression patterns.