Abstract
The expansion of DNA triplet repeats has been shown to be responsible for about a dozen hereditary diseases. In this paper we are concerned with a computer model of such expansion, applied to the fragile X syndrome and Huntington's disease, for which enough quantitative data have been collected. The nucleotide sequence associated with the fragile X consists of CGG repeats and is located inside theFMR1 gene. In normal individuals there is a variable number of triplet repeats less than 60; in asymptomatic carriers the number of repeats is 60–200 (premutation). From the premutation range, the number of triplet repeats can increase within one generation to more than 200 producing affected individuals. In Huntington's disease the CAG repeats are located inside theHDgene. In normal individuals the number of repeats varies from around 11, up to 34. In the intermediate range (34–37 repeats), the mutability is increased, frequently leading to alleles of more than 37 repeats, and the disease phenotype. The rapid increase of the number of triplet repeats in affected individuals has been proposed to be due to the formation of folded DNA structures (hairpins) and their repair or misrepair. In order to determine if this proposed mechanism is adequate to account for the rapid increase of repeats and the large number of repeats in affected individuals we developed a mathematical model that includes the known mechanisms of hairpin formation, and strand synthesis and repair. Simulations based on the model using realistic probabilities of hairpin formation produced results that corresponded with the observed range of repeats and transition probabilities from normal to affected individuals. Similar modelling has been published for the Huntington's disease data. However, in this paper we demonstrate that a uniform approach works for fragile X and Huntington's disease, although the detailed assumptions of the model have to be different. These difference provide insight into the mechanisms of expansion in both cases. Among these insights is that an apparent threshold in the number of repeats for rapid expansion, and the preference for expansion over contraction, may be accounted for by relative probabilities of hairpin formation, replication, slippage and repair.