Theory of the helix–coil transition in DNA considered as a copolymer

Abstract The grand‐partition‐function theory of the preceding paper is used to derive expressions for the number of base pairs bonded in DNA with explicit consideration of the copolymeric nature of the DNA. The following features of the DNA molecule are taken into account: ( 1 ) the DNA's from different sources have different ratios of a–t and g–c pairs; ( 2 ) the a–t pair is weaker than the g–c pair; ( 3 ) the nearest‐neighbor frequencies of the two kinds of base pairs are nonrandom; ( 4 ) the stacking energies (nearest‐neighbor energies) of the various combinations of pairs may be different. An ensemble is constructed in which the features ( 1 ) through ( 4 ) are introduced by means of statistical weights on the various pairs and combinations of pairs, and an expression for the corresponding partition function is written. Expressions are derived for the number of bonded base pairs and the number of helical sequences.