Thermodynamics of oligo(A) N ·2poly(U) ∞ from the dependence of the temperature of the helix–coil transition on oligomer concentration

Abstract On the basis of elementary two‐state, ideal solution thermocynamics, a modified expression for the melting of oligo. polynucleotide helices is derived which is applicable to variations in T m N and/or oligomer concentration, C m with oligomer length, N : (I)\documentclass{article}\pagestyle{empty}\begin{document}$$ \{ 1/T_m{}^N - [1 - 0.67/(n + 1)N]/T_m{} ^\infty \} = (R/N \cdot \Delta H_{\rm r} )\,{\rm ln}\ (c_m \cdot N \cdot V_{\rm r} ^{\rm f} ) $$ \end{document} Δ H r is the enthalpy per helix residue, i.e., per base‐pair or base‐triplet, V r f is the thermodynamic “available” or “reaction” volume, in liters/mole of helical residues; and n is the number of poly nucleotide strands, e.g., n = 2 for oligo (A) N ·2 poly(U)∞. Some earlier treatments have engendered confusion in the interpretation of the “reaction volume,” but with the derivation herein, the entropic origin and physical significance of V r f is unequivocal. The following approximation was arrived at for the reduction expected in the configurational entropy, Δ S r conf, ∞ , for (A)∞·2(U)∞, when the poly(A), strand is substituted for by an equivalent strand of contiguous oligo(A) N ,′s: (II)\documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta S_{\rm r}{}^{{\rm conf,}N} =(1 - 0.67/3N)\Delta S_{\rm r}{}^{{\rm conf,}\infty} $$\end{document} This adjustment of Δ S r conf, ∞ represents the source of the coefficient to 1/ T m ∞ in expression (I). The expectation that Δ S r conf, N < Δ S r conf, ∞ is due to the effect of releasing normal internucleotide configurational restrictions every N th residue in one‐third of the strands of the (A) N ·2(U)∞ helix. Although the reduction in Δ S r conf, ∞ (II) may seem small (i.e., only 5.5% for the tetramer), its effect on the magnitude of V r f in expression (I) is exponential. Thus, without these considerations the quantitative applicability of earlier expressions is questionable. By examining the variation in T m N with c m for a single N , all assumptions, required for evaluating V r f or the entropic effects of discontinuities in the (A) N strand are avoided in the determination of a reliable enthalpy. We have therefore examined the system (III)\documentclass{article}\pagestyle{empty}\begin{document}$$ \left( {\rm A} \right)_4 \cdot 2\left( {\rm U} \right)_\infty \rightleftharpoons {\rm tetra}\left({\rm A} \right)_4 + 2{\rm poly}\left( {\rm U} \right)_\infty $$\end{document} and obtained a Δ H r = 12.58 ± 0.08 kcal per mole (A)·2(U) base‐triplets between 5 and 2.5°C. That this value for Δ H r is in such excellent agreement with all calorimetric values reported for (A)∞·2(U)∞ suggests that the enthalpy for reaction(III) is not significantly affected by disconnections in the backbone of (A) 4 ·2(U)∞. From (I), V r f = 6.0 × 10 −4 1/mole or 1 Å 3 per helical residue. Δ H r °, corrected for residual single‐strand stacking in (A) 4 , is in excellent agreement with that found earlier for (A) 1 ·2(U)∞. A residual heat capacity of 90 kcal(±20) per mole (A)·2(U) base‐triplets per °C is deduced from the decrease of Δ H r ° with temperature.