Proc. NatI. Acad. Sci. USA Vol. 89, pp. 4215-4217, May 1992 Medical Sciences
Population genetics of the fragile-X syndrome: Multiallelic model for the FMRI locus (FRAXA/mental retardation)
N. E. MORTON*t AND J. N. MACPHERSONt *Cancer Research Campaign Research Group in Genetic Epidemiology, University of Southampton, South Academic Block, Southampton General Hospital, Southampton S09 4XY, United Kingdom; and *Wessex Regional Genetics Laboratory, Salisbury District Hospital, Odstock, Salisbury SP2 8BJ, United Kingdom
Contributed by N. E. Morton, January 8, 1992
the cryptic allele Z. Furthermore, to explain the Sherman paradox (1), it is necessary to postulate different conversion probabilities in the two sexes. The most parsimonious hypothesis is that this differential is limited to the conversion of Z to L, and there is no reversion from S to N, from Z to S, or from L to Z:
A model is developed to account for recent ABSTRACT molecular observations. It postulates four alleles: normal (N), small rather stable insert (S), larger, unstable insert (Z), and large insert (L). The last-named allele causes the fragile-X phenotype, inactivation of the FMRI locus by methylation, and mental impairment; the FMRI locus (for fragile-X mental retardation locus 1) resides in the FRAXA region. When this model is fit to pre-molecular data, the Z allele appears to be no more frequent than L, while the S allele is polymorphic. Predictions of the model are in reasonable agreement with observation and suggest much more powerful tests of molecular data, including the Laird hypothesis that conversion of Z to L does not occur in active X chromosomes.
0 u k N-*S-Z L, 9 u k y
where u, k, and y are rates of conversion and zero indicates no conversion. It is understood that each step symbolized by an arrow denotes a gametic generation, and so the model (Table 1) may be expressed in words as follows. (i) A male who receives the S allele from his mother transmits it unchanged to his daughters with probability 1 - k and as a Z allele otherwise. (ii) A male who receives a Z allele from his mother transmits it unchanged to his daughters. (iii) A female who receives an S allele from either parent transmits it unchanged to her children with probability 1 - k and as a Z allele otherwise. (iv) A female who receives a Z allele from either parent transmits it unchanged to her children with probability 1 - y and as an L allele otherwise. (v) The rate of conversion from N to S is u, and the selection coefficient against NIL females is g. Gene frequencies are denoted by q in males and p in females. In this model somatic mutations are neglected. For the equilibrium theory, we denote gene frequencies in the previous generation by a prime. Then the following relations hold, neglecting products of small gene frequencies.
The premolecular era of fragile-X syndrome research established regularities in recurrence risk that implied a two-stage mutation (1). This led to ingenious models involving gene recombination (2), a sex-influenced autosomal modifier gene (3), and failure of chromosome X reactivation in the female germ line (4), which could not be confirmed or disproven so long as transmitting and expressing phenotypes were defined on the bases of chromosomal fragility, mental impairment, and clinical features. Recent progress in the molecular genetics of the fragile-X syndrome, brilliant but still undigested, allows replacement of the transmitting vs. expressing dichotomy by more objective criteria based on the presence and size of a DNA insert. There is no proven model for the inheritance of these differences, but an attempt to model them must be made to guide population studies that will provide critical tests. The Model
qs = p'(l - k) + p?4u
The classical fragile-X syndrome is determined by a large insertion [>600 base pairs (bp)] at the fragile-X locus (5-8), which we denote as the L allele of the FMRI locus (for fragile-X mental retardation locus 1), which resides in the FRAXA region. Present evidence indicates that this allele is stably transmitted at least in females (there are no observations yet on transmission in males, who are severely retarded). For simplicity we neglect the possibility of reversion. The origin of the L allele is complex. Molecular observations show that it arises with high frequency from a small insert of 150-400 bp, which family studies suggest exists in two states that can be represented as alleles S and Z, differing in the likelihood of conversion to L (9). Our present inability to separate S and Z reliably by molecular techniques makes the theory and its application rather difficult, although much clearer than the former dichotomy between transmission and expression for which there was no molecular support. We suppose that S cannot convert to L without passing through
qz=p'k+pz(
-y)
qL = PLW -g) + PZY
2Ps = (Ps + q')(1 - k) + (PN + q')u 2pz = (p' + qs)k + pz(l - y) + qz 2PL = PLW -g) + pzy
=
qL
Therefore, this model predicts the same frequency of the L genotype in males and females. By rearranging the last equation to give PL, the equilibrium frequency of L in males is qL = 2pzy/(l + g) = 2PL.
The remaining frequencies at equilibrium may be derived by equating gains and losses. For the Z allele, the gain is (2ps + qs)k, and the loss is 2pzy. For the S allele, the gain is (2PN
The 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.
tTo whom reprint requests should be addressed.
4215
Medical Sciences: Morton and Macpherson
4216
Proc. Natl. Acad. Sci. USA 89
(1992)
Table 1. Postulated alleles at the FMRI locus Allele
Characteristic Insertion, bp Male gene frequency Female gene frequency Male fitness NIX female fitness Fragile X in males, % Fragile X in females, % IQ in males IQ in NIX females Megatestes in males Dysmorphic facies in males Conversion rate NET+S S -Zinmales So Zin females Z L in males Z L in females
N 0
g) (y)
21-
1
2
2)
qs
qz
qL
Ps
Pz
1 1
Population genetics of the fragile-X syndrome: Multiallelic model for the FMRI locus (FRAXA/mental retardation)
N. E. MORTON*t AND J. N. MACPHERSONt *Cancer Research Campaign Research Group in Genetic Epidemiology, University of Southampton, South Academic Block, Southampton General Hospital, Southampton S09 4XY, United Kingdom; and *Wessex Regional Genetics Laboratory, Salisbury District Hospital, Odstock, Salisbury SP2 8BJ, United Kingdom
Contributed by N. E. Morton, January 8, 1992
the cryptic allele Z. Furthermore, to explain the Sherman paradox (1), it is necessary to postulate different conversion probabilities in the two sexes. The most parsimonious hypothesis is that this differential is limited to the conversion of Z to L, and there is no reversion from S to N, from Z to S, or from L to Z:
A model is developed to account for recent ABSTRACT molecular observations. It postulates four alleles: normal (N), small rather stable insert (S), larger, unstable insert (Z), and large insert (L). The last-named allele causes the fragile-X phenotype, inactivation of the FMRI locus by methylation, and mental impairment; the FMRI locus (for fragile-X mental retardation locus 1) resides in the FRAXA region. When this model is fit to pre-molecular data, the Z allele appears to be no more frequent than L, while the S allele is polymorphic. Predictions of the model are in reasonable agreement with observation and suggest much more powerful tests of molecular data, including the Laird hypothesis that conversion of Z to L does not occur in active X chromosomes.
0 u k N-*S-Z L, 9 u k y
where u, k, and y are rates of conversion and zero indicates no conversion. It is understood that each step symbolized by an arrow denotes a gametic generation, and so the model (Table 1) may be expressed in words as follows. (i) A male who receives the S allele from his mother transmits it unchanged to his daughters with probability 1 - k and as a Z allele otherwise. (ii) A male who receives a Z allele from his mother transmits it unchanged to his daughters. (iii) A female who receives an S allele from either parent transmits it unchanged to her children with probability 1 - k and as a Z allele otherwise. (iv) A female who receives a Z allele from either parent transmits it unchanged to her children with probability 1 - y and as an L allele otherwise. (v) The rate of conversion from N to S is u, and the selection coefficient against NIL females is g. Gene frequencies are denoted by q in males and p in females. In this model somatic mutations are neglected. For the equilibrium theory, we denote gene frequencies in the previous generation by a prime. Then the following relations hold, neglecting products of small gene frequencies.
The premolecular era of fragile-X syndrome research established regularities in recurrence risk that implied a two-stage mutation (1). This led to ingenious models involving gene recombination (2), a sex-influenced autosomal modifier gene (3), and failure of chromosome X reactivation in the female germ line (4), which could not be confirmed or disproven so long as transmitting and expressing phenotypes were defined on the bases of chromosomal fragility, mental impairment, and clinical features. Recent progress in the molecular genetics of the fragile-X syndrome, brilliant but still undigested, allows replacement of the transmitting vs. expressing dichotomy by more objective criteria based on the presence and size of a DNA insert. There is no proven model for the inheritance of these differences, but an attempt to model them must be made to guide population studies that will provide critical tests. The Model
qs = p'(l - k) + p?4u
The classical fragile-X syndrome is determined by a large insertion [>600 base pairs (bp)] at the fragile-X locus (5-8), which we denote as the L allele of the FMRI locus (for fragile-X mental retardation locus 1), which resides in the FRAXA region. Present evidence indicates that this allele is stably transmitted at least in females (there are no observations yet on transmission in males, who are severely retarded). For simplicity we neglect the possibility of reversion. The origin of the L allele is complex. Molecular observations show that it arises with high frequency from a small insert of 150-400 bp, which family studies suggest exists in two states that can be represented as alleles S and Z, differing in the likelihood of conversion to L (9). Our present inability to separate S and Z reliably by molecular techniques makes the theory and its application rather difficult, although much clearer than the former dichotomy between transmission and expression for which there was no molecular support. We suppose that S cannot convert to L without passing through
qz=p'k+pz(
-y)
qL = PLW -g) + PZY
2Ps = (Ps + q')(1 - k) + (PN + q')u 2pz = (p' + qs)k + pz(l - y) + qz 2PL = PLW -g) + pzy
=
qL
Therefore, this model predicts the same frequency of the L genotype in males and females. By rearranging the last equation to give PL, the equilibrium frequency of L in males is qL = 2pzy/(l + g) = 2PL.
The remaining frequencies at equilibrium may be derived by equating gains and losses. For the Z allele, the gain is (2ps + qs)k, and the loss is 2pzy. For the S allele, the gain is (2PN
The 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.
tTo whom reprint requests should be addressed.
4215
Medical Sciences: Morton and Macpherson
4216
Proc. Natl. Acad. Sci. USA 89
(1992)
Table 1. Postulated alleles at the FMRI locus Allele
Characteristic Insertion, bp Male gene frequency Female gene frequency Male fitness NIX female fitness Fragile X in males, % Fragile X in females, % IQ in males IQ in NIX females Megatestes in males Dysmorphic facies in males Conversion rate NET+S S -Zinmales So Zin females Z L in males Z L in females
N 0
g) (y)
21-
1
2
2)
qs
qz
qL
Ps
Pz
1 1
