On the form of the partition function for the helix–coil transition of random copolymers

Abstract The purpose of this paper is to examine and contrast several formulations of the partition function for the helix–coil transition of random‐sequence nucleic acids. In the exact approach, the sequence of bases in a given molecule is fixed, but this leads to expressions which are difficult to evaluate. Another approach is to make a summation over all possible sequences, each weighted by the probability of its occurrence, thereby in effect allowing all sequences to a given molecule. The error in this approach is that it does not guarantee that the average base sequence is random. This difficulty can, in principle, be overcome by applying successively increasing constraints on the system to ensure that all moments of the distribution are equal to the random‐sequence values. It is shown for the particular case of short molecules which melt only from the ends that the convergence of this method to the true solution is poor. The major conclusion is that composition fluctuations which cover a sizeable region of the molecule must be included in an accurate description of the melting transition.