On the application of polyelectrolyte limiting laws to the helix–coil transition of DNA. III. Dependence of helix stability on excess univalent salt and on polynucleotide phosphate concentration for variable equivalent ratios of divalent metal ion to phosphate

Abstract Using the free energy difference between double‐helix and random‐coil forms of DNA as a measure of the stability of the double helix, we calculate the dependence of the stability on excess univalent cation concentration and on polynucleotide phosphate concentration, both as functions of the equivalent ratio r of divalent cation‐to‐phosphate concentrations. The theoretical tool is merely to compare the free energy of one polyelectrolyte solution, characterized by the polyelectrolyte linear charge density, with the free energy of another, characterized by a different value of the charge density. It is assumed only that the charge density of the double helix is greater than that of the coil form. The calculation represents the only molecular theory given to date (for r ≠ O) for these aspects of helix stability. We find that, as excess univalent cation concentration increases, the helix stability increases if r is small but decreases if r is large (i.e., of the order of unity). Moreover, as the concentration of nucleotide phosphate increases, the helix stability does not change for small values of r but increases for large values. For both effects, a continuous transition as a function of r bridges the low‐ r and high‐ r behaviour.