Analytic binding isotherms describing competitive interactions of a protein ligand with specific and nonspecific sites on the same DNA oligomer

Many studies of specific protein-nucleic acid binding use short oligonucleo tides or restriction fragments, in part to minimize the potential for nonsp ecific binding of the protein. However, when the specificity ratio is low, multiple nonspecifically bound proteins may occupy the region of DNA corres ponding to one specific site; this situation was encountered in our recent calorimetric study of binding of integration host factor (IHF) protein to i ts specific 34-bp H ' DNA site. Here, beginning from the analytical McGhee and von Hippel infinite-lattice nonspecific binding isotherm, we derive a n ovel analytic isotherm for nonspecific binding of a ligand to a finite latt ice. This isotherm is an excellent approximation to the exact factorial-bas ed Epstein finite lattice isotherm even for short lattices and therefore is of great practical significance for analysis of experimental data and for analytic theory. Using this isotherm, we develop an analytic treatment of t he competition between specific and nonspecific binding of a large ligand t o the same finite lattice (i.e., DNA oligomer) containing one specific and multiple overlapping nonspecific binding sites. Analysis of calorimetric da ta for IHF-H ' DNA binding using this treatment yields enthalpies and bindi ng constants for both specific and nonspecific binding and the nonspecific site size. This novel analysis demonstrates the potential contribution of n onspecific binding to the observed thermodynamics of specific binding, even with very short DNA oligomers, and the need for reverse (constant protein) titrations or titrations with nonspecific DNA to resolve specific and nons pecific contributions. The competition treatment is useful in analyzing low -specificity systems, including those where specificity is weakened by muta tions or the absence of specificity factors.