Energetics of protein–DNA interactions: An exact calculation for binding of ligands to a lattice of overlapping sites

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Abstract
Exact equal ions are developed for analyzing the binding of ligands to a linear lattice of overlapping sites in which occupied–unoccupied as well as occupied–occupied interactions are included for the analysis of the binding isotherms. We demonstrate that positive cooperativity on the binding of ligands to multiple sites may derive from either occupied–unoccupied or occupied–occupied interactions. When the binding of proteins to linear polynucleotides and DNA has exhibited positive cooperativity protein–protein (occupied–occupied), interactions have heretofore been invoked as the sole energetic source in determining the cooperative effect. Models and equations developed previously for the analysis of these binding isotherms have included only the protein–protein interactions (usually characterized with the symbol ω). The exact equations of this paper are capable of analyzing binding data in a manner to evaluate the relative importance of both occupied–unoccupied and occupied–occupied interactionsRelations derived here are employed to analyze some existing data, and the resulting parameter values are compared to those developed with equations employing only the protein–protein (occupied–occupied) interactions. The resulting parameter values are qualitatively different. Values of the binding constants differ by about three orders of magnitude. When only protein–protein interactions are taken into account, the resulting free energy of interaction is negative, indicating attractive forces between bound protein molecules; when both occupied–unoccupied and occupied–occupied interactions are applied, the resulting free energies of interaction are positive, indicating destabilizing forces acting primarily on the polynucleotide lattice. © 1995 John Wiley & Sons, Inc.