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Notes: Optical melting curves of 22 DNA dumbbells with the 16-base pair duplex sequence 5′-G-C-A-T-C-A-T-C-G-A-T-G-A-T-G-C-3′ linked on both ends by single-strand loops of At or Ct sequences (˛ = 2, 3, 4, 6, 8, 10, 14), Tt sequences (˛ = 2, 3, 4, 6, 8, 10), and Gt sequences (t = 2, 4) were measured in phosphate buffered solvents containing 30, 70, and 120 mM Na+. For dumbbells with loops comprised of at least three nucleotides, stability is inversely proportional to end-loop size. Dumbbells with loops comprised of only two nucleotide bases generally have lower stabilities than dumbbells with three base nucleotide loops. Experimental melting curves were analyzed in terms of the numerically exact (multistate) statistical thermodynamic model of DNA dumbbell melting previously described (T. M. Paner, M. Amaratunga & A. S. Benight (1992), Biopolymers 32, 881). Theoretically calculated melting curves were fitted to experimental curves by simultaneously adjusting model parameters representing statistical weights of intramolecular hairpin loop and single-strand circle states. The systematically determined empirical parameters provided evaluations of the energetics of hairpin loop formation as a function of loop size, sequence, and salt environment. Values of the free energies of hairpin loop formation ΔGloop(n 〉 t) and single-strand circles, ΔGcir(N) as a function of end-loop size, t = 2-14, circle size, N = 32 + 2t, and loop sequence were obtained. These quantities were found to depend on end-loop size but not loop sequence. Their empirically determined values also varied with solvent ionic strength. Analytical expressions for the partition function Q(T) of the dumbbells were evaluated using the empirically evaluated best-fit loop parameters. From Q(T), the melting transition enthalpy ΔH, entropy ΔS, and free energy ΔG, were evaluated for the dumbbells as a function of end-loop size, sequence, and [Na+]. Since the multistate analysis is based on the numerically exact model, and considers a statistically significant number of theoretically possible partially melted states, it does not require prior assumptions regarding the nature of the melting transition, i.e., whether or not it occurs in a two-state manner. For comparison with the multistate analysis, thermodynamic transition parameters were also evaluated directly from experimental melting curves assuming a two-state transition and using the graphical van't Hoff analysis. Comparisons between results of the multistate and two-state analyses suggested dumbbells with loops comprised of six or fewer residues melted in a two-state manner, while the melting processes for dumbbells with larger end-loops deviate from two-state behavior.Dependence of thermodynamic parameters on[Na+] as a function of loop size suggests single-strand end-loops have different counterion binding properties than the melted circle. Results are compared with those obtained in an earlier study of dumbbells with the slightly different stem sequence 5'-G-C-A-T-A-G-A-T-G-A-G-A-A-T-G-C-3' linked on the ends by T loops (˛ = 2,3,4,6,8,10,14).© 1996 John Wiley &Sons, Inc.