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Slow relaxational processes in the melting of linear biopolymers: A theory and its application to nucleic acids

We treat the problem of the mean time of complete separation of complementary chains of a duplex containing N base pairs. A combination of analytical and computer methods is used to obtain the exact solution in the form of a compact expression. This expression is used to analyze the limits of application of the equilibrium theory of helix–coil transition in oligo‐ and polynucleotides. It also allows the melting behavior of a biopolymer to be predicted when its melting is nonequilibrium. In the case of oligonucleotides for which the equilibrium melting takes place at a high value of the stability constant s, the general expression turns into the equation of Craig, Crothers, and Doty, used by them to determine the rate constant kf of the growth of a helical region from temperature‐jump experiments. For the case of fragmented DNA with N ∼ 102, the melting process is shown to be completely nonequilibrium, and as a result, the observed melting temperature should be higher than that for the equilibrium. A simple equation is obtained that makes possible calculation of the real, “kinetic” melting temperature Tk. As N increases, the observed melting temperature should approach the equilibrium value, Tm. This analysis has explained quantitatively the peculiar chain‐length dependence of the experimentally observed shift in the DNA melting temperature during fragmentation. A thorough analysis is given of the nonequilibrium effects in the melting process of long DNA molecules (N ≳ 103). The main conclusion is that even in the presence of profound hysteresis phenomena, the melting profile observed on heating may differ only slightly from the equilibrium profile.