(a) Heat-map depiction of the probability-ratio level for a thick chain with two ‘out-of-phase’ protrusions taken at a fixed inter-site distance (s). Inset: chain schematic showing the Z-shaped binding architecture. (b) Cross-section of the heat map at N=152 links, showing oscillations with a 5- to 6-bp periodicity. Protrusion size was taken to be 5.44 nm in diameter. (c) Expression level ratio data for LacI synthetic enhancers with tandem binding sites spaced at 38 bp. (d) Expression level ratio data for synthetic enhancers with tandems of TetR-binding sites that are spaced by half integer (s=27 bp, red line) and integer multiples of the helical repeat (s=32 bp, green line), showing identical regulatory function. Inset: the structural binding model showing a thick chain with two dumbbell-shaped protrusions positioned in-phase (right) and out-of-phase (left), respectively. Error bars correspond to the s.d. from multiple measurements.