Polynucleotides. XI. Thermodynamics of (A) N ·2(U) ∞ from the dependence of T m N on oligomer length

The variation in the helix‐coil transition temperature, T m N , with oligomer length, N , for the system (I)\documentclass{article}\pagestyle{empty}\begin{document}$$ \left( {\rm A} \right)_N \cdot 2\left( {\rm U} \right)_\infty \mathop \to \limits_\Delta \left( {\rm A} \right)_N + 2\left( {\rm U} \right)_\infty $$\end{document} has been examined. The results for N = 4‐13, measured in 0.2 M Na+, have been analyzed in terms of the expression of Blake (1972): (II)\documentclass{article}\pagestyle{empty}\begin{document}$$ 1/T_{m^N } \, - \,\,(1\, - \,0.67/3N)/T_{m^\infty } \, = \,(R/N\,\Delta H_r )\,\ln \,(c_m NV_{r^{\rm f} } )\,({\rm II}) $$\end{document} where c m is the free oligomer concentration at T m N , and V r f is the thermodynamic free volume available to a helical base‐triplet residue. The correlation coefficient for the fit to expression (II) of data obtained over a 50° temperature range is 0.997 when Δ H r = −12.6 kcal/mole of base‐triplets (independent of oligomer length (N ⪖ 4) or temperature), the value previously obtained from both calorimetry of (A) ∞ ·2(U) ∞ and (A) 4 concentration dependence of T m . It is found that V r f = 8.0 × 10 −4 1/mole (± 30%) or 1.33 Å 3 per helical base‐triplet, and is constant with temperature. A maximum value for V r f of 21.0 × 10 −4 1/M (± 1.3%), equivalent to 3.54 Å 3 per helical basetriplet is obtained by the same treatment of the helix‐coil transition data for the three‐stranded helix formed by adenosine ( N = 1) and 2(U) ∞ obtained by Davies and Davidson (1971).