How many numbers are required to specify sequence-dependent properties of polynucleotides?

There are 10 unique dinucleotides of double-stranded DNA, but only 8 independent nearest-neighbor energies that occur in circular DNA, as shown by D. M. Gray and I. Tinoco (1970) Biopolymers 9, 223-244]. We extend that analysis to include end effects, and show that the number of unique dinucleotide pairs (including ends) is 14, but there are only 12 independent energies. We discuss how these 12 energies (or spectra or any other pairwise additive property) can be measured and displayed, and how they should and should not be compared between experimenters. As an example, we analyzed the recently reported melting curves M.J. Doktycz et al. (1992) Biopolymers, 32, 849-864.] of 16 DNA dumbbells in two different Na+ environments. This analysis reveals a new means for evaluating end effects and the emergence of longer than nearest-neighbor interactions at low salt concentration.