  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.
