Triplet repeat instability and DNA topology: an expansion model based on statistical mechanics.

The variance of writhe, the contribution of writhe to supercoiling, and the free energies of supercoiling were calculated for (CTG.CAG)n and (CGG.CCG)n triplet repeat sequences (TRS) by statistical mechanics from the bending and torsional moduli previously determined. Expansions of these sequences are inherited by non-mendelian transmission and are linked with several hereditary neuromuscular diseases. The variance of writhe was greater for the TRS than for random B-DNA. For random B-DNA, (CGG)n, and (CTG)n, the contribution of writhe to supercoiling was 70, 78, and 79%, whereas the free energy of supercoiling at a length of 10 kilobase pairs was 1040.RT, 760.RT, and 685.RT, respectively. These data indicate that the TRS are preferential sites for the partitioning of supercoiling. Calculations of the differences in free energy of supercoiling between the TRS and random B-DNA revealed a local minimum at approximately 520 base pairs. Human medical genetic studies have shown that individuals carrying up to 180-200 copies of TRS (540-600 base pairs, premutations) in the fragile X or myotonic dystrophy gene loci are usually asymptomatic, whereas large expansions (>200 repeats, full mutations), which lead to disease, are observed in their offspring. Therefore, the length corresponding to the local minimum in free energy of supercoiling correlates with the genetic breakpoint between premutation and full mutation. We propose that (a) TRS instability is mediated by DNA mispairing caused by the accumulation of supercoiling within the repeats, and (b) the expansions that take place at the premutation to full mutation threshold are associated with increased mispairing caused by the optimal partitioning of writhe within the TRS at this length.