Thermodynamic formulations have been devised to obtain ⌬G°v alues directly from spectroscopic data at a fixed common temperature in nucleic acid duplex-simplex melting curves. In addition, the dependence of melting on salt concentration has been expressed in terms of a stepwise stoichiometric representation, which leads to a specific equation for the partition of the added sodium ions between the different oligonucleotide forms. G enerally the free energy of melting of an oligonucleotide duplex, D, into its constituent complementary single strands, S 1 and S 2 , is obtained from the temperature at the midpoint of the melting curve, T m . To compare the ⌬G°s of a series of duplexes of varying composition, one obtains the respective T m values and adjusts them to a common temperature using data for the ⌬HЊ of the transition.It is also possible to obtain ⌬GЊ for a series of duplexes from absorbance data at only one fixed common temperature in the melting curves. We have explored this alternative mode of treatment with a set of duplexes having oligonucleotide lengths of 10 bp.Melting curves of duplex DNA are very sensitive to salt concentration. The dependence of T m and of ⌬GЊ on Na ϩ molarity has been generally formulated on the basis of the following chemical equation for the oligonucleotide equilibrium,

Equations for the concentration profiles of all species in equilibria in the coupled binding of two ligands to a receptor have been formulated in a compact translucent form convenient for numerical analyses. These have been used to generate graphical presentations of the variation of each profile over a wide range of ligand concentration. New insights into the distribution of species have been obtained.