Evolution of the Friedreich’s ataxia trinucleotide repeat expansion: Founder effect and premutations

Friedreich’s ataxia, the most frequent inherited ataxia, is caused, in the vast majority of cases, by large GAA repeat expansions in the first intron of the frataxin gene. The normal sequence corresponds to a moderately polymorphic trinucleotide repeat with bimodal size distribution. Small normal alleles have approximately eight to nine repeats whereas a more heterogeneous mode of large normal alleles ranges from 16 to 34 GAA. The latter class accounts for ≈17% of normal alleles. To identify the origin of the expansion mutation, we analyzed linkage disequilibrium between expansion mutations or normal alleles and a haplotype of five polymorphic markers within or close to the frataxin gene; 51% of the expansions were associated with a single haplotype, and the other expansions were associated with haplotypes that could be related to the major one by mutation at a polymorphic marker or by ancient recombination. Of interest, the major haplotype associated with expansion is also the major haplotype associated with the larger alleles in the normal size range and was almost never found associated with the smaller normal alleles. The results indicate that most if not all large normal alleles derive from a single founder chromosome and that they represent a reservoir for larger expansion events, possibly through “premutation” intermediates. Indeed, we found two such alleles (42 and 60 GAA) that underwent cataclysmic expansion to pathological range in a single generation. This stepwise evolution to large trinucleotide expansions already was suggested for myotonic dystrophy and fragile X syndrome and may relate to a common mutational mechanism, despite sequence motif differences.

An endogenous rate of time preference, the Penrose effect, and dynamic optimality of environmental quality.

In the present paper, the endogenous theory of time preference is extended to analyze those processes of capital accumulation and changes in environmental quality that are dynamically optimum with respect to the intertemporal preference ordering of the representative individual of the society in question. The analysis is carried out within the conceptual framework of the dynamic analysis of environmental quality, as has been developed by a number of economists for specific cases of the fisheries and forestry commons. The duality principles on intertemporal preference ordering and capital accumulation are extended to the situation where processes of capital accumulation are subject to the Penrose effect, which exhibit the marginal decrease in the effect of investment in private and social overhead capital upon the rate at which capital is accumulated. The dynamically optimum time-path of economic activities is characterized by the proportionality of two systems of imputed, or efficient, prices, one associated with the given intertemporal ordering and another associated with processes of accumulation of private and social overhead capital. It is particularly shown that the dynamically optimality of the processes of capital accumulation involving both private and social overhead capital is characterized by the conditions that are identical with those involving private capital, with the role of social overhead capital only indirectly exhibited.