Site-specific transcription factors (TFs) bind to their target sites on the
DNA, where they regulate the rate at which genes are transcribed. Bacterial TFs
undergo facilitated diffusion (a combination of 3D diffusion around and 1D
random walk on the DNA) when searching for their target sites. Using computer
simulations of this search process, we show that the organisation of the
binding sites, in conjunction with TF copy number and binding site affinity,
plays an important role in determining not only the steady state of promoter
occupancy, but also the order at which TFs bind. These effects can be captured
by facilitated diffusion-based models, but not by standard thermodynamics. We
show that the spacing of binding sites encodes complex logic, which can be
derived from combinations of three basic building blocks: switches, barriers
and clusters, whose response alone and in higher orders of organisation we
characterise in detail. Effective promoter organizations are commonly found in
the E. coli genome and are highly conserved between strains. This will allow
studies of gene regulation at a previously unprecedented level of detail, where
our framework can create testable hypothesis of promoter logic