The understanding of transcription regulation is a major goal of today's biology. The challenge is to utilize diverse high-throughput data in order to infer mechanistic models of transcription control. We propose a new model which integrates transcription factor-gene affinity, protein abundance, and gene expression profiles. The model provides a detailed, yet computationally tractable description of the relations between transcription factors, their binding sites at gene promoters, and the combinatorial regulation of transcription. At the core, our model manipulates dose-affinity-response functions that associate transcription factor concentrations and transcription factor-DNA affinities to determine the rate of transcription factor-DNA reactions. We study computational problems that arise in optimizing such models and develop polynomial algorithms for certain problems. We show how to assess missing values (notably protein abundance) and describe a novel framework to infer models from currently available data. On budding yeast carbohydrate metabolism data, our results demonstrate the sensitivity and specificity of the approach. They also suggest new active binding sites and a regulation model for the transcription program of the galactose system.