Higher-Order Phase Transitions in Two-Stranded Macromolecules

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Abstract
A model for infinitely long two‐stranded macromolecules, previously shown to exhibit phase transitions in association with the helix–coil equilibrium, is examined further. It is found that phase transitions of all orders from one to infinity are formally possible, depending on the value of a , which is defined by the fact that the probability of loop closure for a random flight of k steps is proportional to k −a . Defining h = a − 1 for the “matching case” and h = a − 2 for the “mismatching case,” a phase transition of order m (m = 2, 3,···,) is predicted if 1 / m ≤ h < 1 / (m − 1) . The transition is of infinite order if h ≤ 0 and of first order if h > 1 . From calculated transition curves it is found that the apparent order may be lower than the true order if the stacking parameter b is sufficiently small. The maximum slope of the transition curve is found to vary as b −1/(1−h) for b ≪ 1, h ≤ 1 2 , in agreement with previous studies of certain special cases. An examination of mean sequence lengths shows that, for phase transitions of low order, the mean length of a helical sequence remains near a critical minimum value over a considerable range of the degree of bonding, while the mean loop size varies greatly over the same range. Experiments on the helix–coil equilibrium in two‐stranded polyriboadenylic acid are reported, demonstrating the existence of a true equilibrium under certain conditions, and confirming the occurrence of an apparent second‐order phase transition under these conditions. Attempts to fit the experimental data to the theory lead to the conclusion that a is in the range 2.3–2.5 if the mismatching model is correct but that a would be lower if some bias exists toward the matching condition.