Phase transitions in sequence matches and nucleic acid structure.

Analyses of phase transitions in biopolymers have previously been restricted to studies of average behavior along macromolecules. Extremal properties, such as longest helical region, can now be studied with a new family of probability distributions Arratia, R., Gordon, L. & Waterman, M. S. (1986) Ann. Stat. 14, 971-993. Not only is such extremal behavior analyzed with great precision, but new phase transitions are determined. One phase transition occurs when behavior of the free energy of the longest helical region abruptly changes from proportional to sequence length. The annealing of two single-stranded molecules and the melting of a double helix are both considered. These results, initially suggested by studies of optimal matching of random DNA sequences Smith, T. F., Waterman, M. S. & Burks, C. (1985) Nucleic Acids Res. 13, 645-656, also have importance for significance tests in comparison of nucleic acid or protein sequences.