Theoretical calculations of the helix–coil transition of DNA in the presence of large, cooperatively binding ligands

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Abstract
Theoretical calculations are conducted on the helix–coil transition of DNA, in the presence of large, cooperatively binding ligands modeled after the DNA‐binding proteins of current biological interest. The ligands are allowed to bind both to helx and to coil, to cover up any number of bases or base pairs in the complex, and to interact cooperatively with their nearest neighbors. The DNA is treated in the infinite homogeneous Ising model approximation, and all calculations are done by Lifson's method of sequence‐generating functions. DNA melting curves are calculated by computer in order to expolore the effects on the transition of ligand size, binding constant, free activity, and ligand–ligand cooperativity. The calculations indicate that (1) at the same intrinsic free energy change per base pair of the complexes, small ligands, for purely entropic reasons, are more effective than are large ligands in shifting the DNA melting temperature; (2) the response of the DNA melting temperature to increased ligand binding constant K and/or free ligand activity L is adequately represented at high values of KL (but not at low KL) by a simple independent site model; (3) if curves are calculated with the total amount of added ligand remaining constant and the free ligand activity allowed to vary throughout the transition, biphasic melting curves can be obtained in the complete absence of ligand–ligand cooperativity. In an Appendix, the denaturation of poly[d(A‐T)] in the presence of the drug, netropsin, is used to verify some features of the theory and to illustrate how the theory can be used to obtain numerical estimates of the ligand binding parameters from the experimental melting curves.