Cooperative and anticooperative effects in binding of the first and second plasmid O(sym) operators to a lad tetramer: Evidence for contributions of non-operator DNA binding by wrapping and looping

The interaction of lac operator DNA with lac repressor (LacI) is a classic example of a genetic regulatory switch. To dissect the role of stoichiometry, subunit association, and effects of DNA length in positioning this switch, we have determined binding isotherms for the interaction of LacI with a high affinity (O(sym)) operator on linearized plasmid (2500 bp) DNA over a wide range of macromolecular concentrations (10^-14 to 10^-8 M). Binding data were analyzed using a thermodynamic model involving four equilibria: dissociation of tetramers (T) into dimers (D), and binding of operator-containing plasmid DNA (O) to dimers and tetramers to form three distinct complexes, DO, TO, and TO₂. Over the range of concentrations of repressor, operator, and salt (0.075 M K⁺ to 0.40 M K⁺) investigated, we find no evidence for any significant thermodynamic effect of LacI dimers. Instead, all isotherms can be interpreted in terms of just two equlibria, involving only T and the TO and TO₂ complexes. As a reference binding equilibrium, which we propose must approximate the DO binding interaction, we compare the plasmid O(sym) results with our extensive studies of the binding of a 40 bp O(sym) DNA fragment to LacI. On this basis, we obtain a lower bound on the LacI dimer-tetramer equilibrium constant and values of the equilibrium constants for formation of TO and TO₂ complexes. At a salt concentration of 0.40 M, the O(sym) plasmid binding data are consistent with a model with two independent and identical binding sites for operator per LacI tetramer, in which the binding to a site on the tetramer is only slightly more favorable than the reference binding interaction. Increasingly large deviations from the independent-site model are observed as the salt concentration is reduced; binding of a second operator to form TO₂ becomes strongly disfavored relative to formation of TO at low salt concentrations (0.075 to 0.125 M). In addition, binding of both the first and second plasmid operator DNA molecules to the tetramer becomes increasingly more favorable than the reference binding interaction as [K⁺] is reduced from 0.40 M to 0.125 M. At 0.075 M K⁺, however, the strength of binding of the second plasmid operator DNA to the LacI tetramer is dramatically reduced; this interaction is much less favorable than binding the first plasmid operator DNA, and becomes much less favorable than the reference binding interaction. We propose that these differences arise from changes in the nature of the TO and TO₂ complexes with decreasing salt concentration. At low salt concentration, we suggest the hypothesis that flanking non-operator sequences bind non-specifically (coulombically) by local wrapping, and that distant regions of non-operator DNA occupy the second operator-binding site by looping. We propose that wrapping stabilizes both 1:1 and 2:1 complexes at low salt concentration, and that looping stabilizes the 1:1 complex but competitively destabilizes the 2:1 TO₂ complex at low salt concentration. These effects must play a role in adjusting the stability and structure of the LacI-lac operator repression complex as the cytoplasmic [K⁺] varies in response to changes in extracellular osmolarity.