Transcription regulation typically involves the binding of proteins over long distances on multiple DNA sites that are brought close to each other by the formation of DNA loops. The inherent complexity of the assembly of regulatory complexes on looped DNA challenges the understanding of even the simplest genetic systems, including the prototypical lac operon. Here we implement a scalable quantitative computational approach to analyze systems regulated through multiple DNA sites with looping. Our approach applied to the lac operon accurately predicts the transcription rate over five orders of magnitude for wild type and seven mutants accounting for all the combinations of deletions of the three operators. A quantitative analysis of the model reveals that the presence of three operators provides a mechanism to combine robust repression with sensitive induction, two seemingly mutually exclusive properties that are required for optimal functioning of metabolic switches.
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