On the Statistical Ensemble for the Theory of Helix-Coil Transition of Copolymeric DNA

Helix-coil transition of copolymeric DNA molecule is investigated hy calculating the partition functions averaged over two kinds of ensembles of 'random sequences of base pairs, namely, the Bernoulli ensemble and permutation ensemble. Then it can be shown that the ensemble over which the partition function is averaged plays an important role to discuss the melting process of random copolymers. The treatment based on the Bernoulli ensemble leads to the arithmetic mean approximation for the statistical weight of bonded base pair and it fails to give the reasonable separate contributions of G-C and A-T base pairs to the melting process. On the other hand the treatment by the permutation ensemble gives a plausible result for the separate contributions of two kinds of base pairs and it is shown that in this case the partition function generally lies somewhere between the ariilimetic mean approximation and the geometric mean approxinw1 ion.