The variance of writhe, the contribution of writhe to supercoiling, and the free energies of supercoiling were calculated for (CTG⅐CAG) n and (CGG⅐CCG) n triplet repeat sequences (TRS) by statistical mechanics from the bending and torsional moduli previously determined. Expansions of these sequences are inherited by nonmendelian 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 1040⅐RT, 760⅐RT, and 685⅐RT, 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 ϳ520 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.Several human loci associated with neurodegenerative disorders have been shown to carry a new form of mutation, i.e. the expansion of a DNA triplet repeat sequence (TRS) 1 with composition (CTG⅐CAG) n , (CGG⅐CCG) n , or (GAA⅐TTC) n , referred to as (CTG) n , (CGG) n , and (GAA) n , respectively (reviewed in Refs. 1-4). These diseases fall into two categories (1).The first, which includes spinal and bulbar muscular atrophy, Huntington's disease, spinocerebellar ataxia type 1, dentatorubral-pallidoluysian atrophy, and Machado-Joseph disease, is characterized by small expansions of a (CTG) n repeat from the ϳ10 -40 in the normal population to ϳ40 -120 units in diseased individuals that encode a polyglutamine tract in the corresponding gene products. This mutation may impart a gain of function to the mature polypeptides that is deleterious to neuronal activity (1-3).The second, which includes the myotonic dystrophy (dystrophia myotonica (DM)) and the fragile X and E (FRAXA and FRAXE) genes, is characterized by much larger expansions of either a (CTG) n or (CGG) n repeat, respectively, in the untranslated region of the genes. The mechanisms by which these expansions lead to disease are not fully understood (5, 6). The number of repeats is polymorphic in the normal population and ranges from 6 to 5...