An n-allele model for progressive amplification in the FMR1 locus.

Abstract

An n-allele model is developed for the FMR1 locus, which causes the fragile X syndrome, where n is the number of triplet repeats in the first exon. Frequencies in the general population and in index families are used to generate an n to n + 8 transition matrix that predicts specific risks in satisfactory agreement with observation. However, until sequencing distinguishes between stable and unstable alleles with the same value ofn, it is premature to infer whether allelic frequencies at the FMRI locus are at equilibrium or, as some have suggested, are evolving toward higher frequencies of the pathogenic allele.The fragile X syndrome [Fra(X)] of mental retardation is the commonest disease of progressive amplification, inf which an increasing insert leads to failure of gene expression. A fourallele model accounts for major features of Fra(X) (including gene frequencies, mutation rates, and genetic risks) in terms of triplet repeats in the FMR1 locus (1). The N allele seldom has more than 40 repeats and is stable except for rare mutation to allele S, which has more than 40 repeats and converts to an unstable allele Z at the rate of about 0.01 per generation. The Z allele converts at the rate of 74% in the female germ line to the "full mutation" allele L characterized by methylation, late replication, loss of expression of the FMRI gene, and the Fra(X) phenotype. This conversion of the maternal X chromosome may occur in the early zygote, and L alleles are somatically unstable (2, 3). The Z allele typically has more than 60 repeats, while the L allele usually has more than 200 ( Fig. 1). Poor distinction between Z "premutations" with a high risk for Fra(X) offspring and "intermediate" S alleles with infinitesimal risk is troublesome in clinical genetics. Although (CGG), sequences are more unstable than less monotonous repeats of the same length (4-6), too little sequencing has yet been done to model these qualitative effects. We are concerned here with frequencies and quasicontinuous effects of repeat length. MATERIALS AND METHODSFrom data on fragment lengths in normal populations we estimate frequencies of large values of n, assuming a monotonic discrete distribution. Risks for unstable transmission are assumed to have a logistic distribution dependent on fragment size. Parameters were estimated by maximum likelihood (ML), using Newton-Raphson iteration with exact derivatives. Because of evidence that the conventional molecular standard underestimates length of (CGG)n by one repeat and that the mode of n is 30, we added 1 to each value of n in samples with the mode at 29 (7). RESULTS Frequencies in the General Population. A sample of T chromosomes from the general population is expected to haveThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. a frequency Qs = u/k for allele S, where the mutation rate from N to S has been estimated as u = 24.7 x 10-5 p...

The FMR1 CGG repeat and linked microsatellite markers in two Basque valleys

“…The gray zone frequencies in Markina were comparable with those of Morris et al (1995) and were slightly lower than those of the general sample from Biscay. Of note was the finding of 12.07% of chromosomes in the gray zone in Arratia.…”

“…The estimated frequencies of gray zone alleles in the general population were 2.50% (Morris et al, 1995). The gray zone frequencies in Markina were comparable with those of Morris et al (1995) and were slightly lower than those of the general sample from Biscay.…”

A Maximum-Likelihood Approach to Fitting Equilibrium Models of Microsatellite Evolution

“…Models of the evolutionary processes that produced allelic frequency distributions have mostly been based on or developed from Moran's (1975) analysis of random-walk models and are known collectively as stepwise-mutation models because alleles are assumed to mutate upward or downward in ''steps'' consisting (usually) of one repeat. Recent examples that do not assume that the mutation step is one repeat include those of Fu and Chakraborty (1998) and Morris et al (1995). In the early versions of these models, there were no evolutionary processes restricting the excursions of the random walks.…”

Why do fragile X carrier frequencies differ between Asian and non-Asian populations?

“…Earlier models were constructed to estimate the values of parameters that shape allele and genotype frequencies at FMR1 (Vogel, 1984;Ashley and Sherman, 1995;Morris et al, 1995;Morton and Macpherson, 1992;Kolehmainen, 1994;Pembrey et al, 1985;Sherman et al, 1985;Sved and Laird, 1990). All of these models provide opportunities to infer values for key parameters, including mutation rates and fitness values.…”