Am. J. Hum. Genet. 50:960-967, 1992

Germinal Mosaicism and Risk Calculation

in

X-linked Diseases

Marc Jeanpierre INSERM Unit6 129 and Service de Biochimie Genetique, Institut Cochin de Gen6tique Moleculaire, Paris

Summary Germinal mosaicism is a major problem in risk estimation for an X-linked disease. A mutation can happen anytime in germ cell development, and the proportion of germ cells bearing the mutated gene is twice the probability of recurrence of the mutation. This proportion could be either very low in late mutations or very high in germinal and somatic mosaicism. When this heterogeneity is taken into consideration, the distribution of the recurrence risk is conveniently represented as a set of discrete classes that may be derived either from models of gametogenesis or from empirical data. A computer program taking into account germinal mosaicism has been devised to calculate the probability of a possible carrier belonging to any of these classes, in order to settle the origin of the mutation of a given family. Germinal mosaicism increases the probability of inheriting the mutation, but this effect is always lowered by the possibility of heterogeneity. When the mother of a possible carrier is not herself a carrier, the risk of her daughter being a carrier is approximately halved, even under the assumption of a high recurrence risk from mosaicism.

Introduction Germinal mosaicism has been demonstrated in inbred animals with both an abnormal color pattern and an unequal progeny segregation (Bridge 1919; Muller 1920; Wright and Eaton 1926). From these early studies of rodents and of Drosophila, it appeared that a significant proportion of mutations was embryonic, showing either as a germinal or somatic mosaicism with a recurrence risk from as high as 50% to as low as a few percent. By contrast, germinal mosaicism has only been documented in some human dominant diseases such as achondroplasia (Bowen 1974; Fryns et al. 1983; Reiser et al. 1984; Philip et al. 1988). With the advent of direct mutation detection, germinal mosaicism has been demonstrated in most severe dominant

diseases, including osteogenesis imperfecta (Constantinou et al. 1990; Sykes 1990; Wallis et al. 1990), or in X-linked diseases, such as hemophilia A (GitschReceived June 17, 1991; final revision received December 4, 1991.

Address for correspondence and reprints: Dr. Marc Jeanpierre, INSERM Unite 129, Institut Cochin de Genetique Moleculaire, 24 rue du Faubourg Saint-Jacques, 75014 Paris, France. i 1992 by The American Society of Human Genetics. All rights reserved. 0002-9297/ 92/5005-0009$02.00

960

ier 1988; Higuchi et al. 1988; Brocker-Vriends et al. 1990), hemophilia B (Taylor et al. 1991), ornithine transcarbamylase deficiency (Maddalena et al. 1988), X-linked agammaglobulinemia (Hendriks et al. 1989), and Duchenne muscular dystrophy (DMD) (Bakker et al. 1987; Darras and Francke 1987; Lanman et al. 1987; Monaco et al. 1987; Wood and McGillivray 1988; Boileau and Junien 1989; Claustres et al. 1990; Lebo et al. 1990). Mutations of the dystrophin gene, which are the cause of DMD, are especially suitable for mosaicism studies since this not uncommon disease is severe (and consequently has a high proportion of new mutations) and since mutations can be easily detected in about 60% of the cases. The recurrence risk for germinal mosaicism has been estimated recently from a panel of families in which the parental origin of the new deletion or duplication could be determined (Bakker et al. 1989; van Essen et al. 1992). From these analyses, we determined that the mutation was transmitted more than once by a parent in whom it was absent in lymphocytes, leading to a recurrence risk of 15%-20% for the at-risk haplotype. Mosaicism is the result of the occurrence of a mutation during development; the proportion of gametes that carry the mutation corresponds to the time of

Germinal Mosaicism and Risk Calculation development of the mutation. The proportion of early and late mutations could be derived either from empirical data (Bakker et al. 1989; van Essen et al. 1992) or from models of gametogenesis (Hartl 1971; Edwards 1989; Wijsman 1991). The distribution of recurrence risks in families with both a new mutation and only one affected child is here assumed to be known and will be referred to as the "prior distribution." The probability of a possible carrier being a mosaic of a given class will be shifted toward either higher or lower recurrence risk, according to pedigree structure. The present paper focuses on a method for computerized calculation of the most likely distribution of mosaicism in possible carriers of an X-linked mutation. Methods Genetic Heterogeneity of Mosaicism The first step in risk calculation is the definition of a model. The framework of risk calculation from an early model of germinal mosaicism is the simple hypothesis of a dichotomous germinal proliferation and the assumption of a constant mutation rate per cell generation (Hartl 1971). This model, which assumes that cells are dividing as bacterial cells do in a culture flask, is closely related to the famous model for the accumulation of mutations in a bacterial population (Luria and Delbruck 1943). The recurrence risk of germinal mosaicism after the birth of an affected child is close to 1 /n, with n being the number of germ cell divisions. The recurrence risk in families with two affected sibs is not dependent on the number of cell generations, and is 1/3 (Hartl 1971; Edwards 1989; Wijsman 1991). The recurrence risk in DMD was shown to be higher than 1 /n (Bakker et al. 1989; van Essen et al. 1992). This high recurrence risk could be explained by a model of germ cell development that takes into account the possibility of mutations between conception and choice of the progenitor germ cells, as described by Wijsman (1991). Since the publication of the very first papers on germinal mosaicism (Bridges 1919; Muller 1920; Wright and Eaton 1926), the risk of recurrence of a dominant or X-linked recessive mutation has been known to be variable: it may be close to 50% in somatic and germinal mosaicism or much lower in late embryonic mutations. For Drosophila, this was illustrated by the finding of two males with a tiny-wing mutation among 153 sons of a particular female, and six males with the cut mutation among 131 sons of another female (Bridges 1919). The recurrence risk attached to the

961 mutated haplotype is half the proportion of germ cells that have the mutated gene. The distribution of these probabilities is an indirect estimation of the distribution of the mutations during embryogenesis. It may be convenient to represent the distribution of the recurrence risk by using a limited set of discrete classes of risk. A set of n risk classes could be defined if there are n cell divisions in gametogenesis. It is, however, not always necessary to consider a large number of classes if the computation is grounded only in empirical data. The probability distribution function is now replaced by a discrete distribution. Each of these classes is characterized by a recurrence probability (the proportion of germinal cells bearing the mutation) and an occurrence probability (the frequency of this class). The distribution of the recurrence risk in a population of potential carriers is the prior distribution and is assumed to be known. When a putative carrier has several children, the probability of the mother being a mosaic of a given class will be shifted toward either higher or lower recurrence risk; this estimated distribution is referred to as "posterior distribution" for this person. Recently, Grimm et al. (1990) have reported a model based on the assumption of mutation-selection equilibrium, which assumes equal mutation rates in males and females, and on use of a mean proportion of mutations leading to germinal mosaicism. From this model it could be calculated that one-third of the affected males inherit the mutation from a germ-line mosaic mother or a noncarrier female, which is reminiscent of the proportion of one-third of affected males born from noncarrier females in the simple situation of a lethal X-linked disease with equal mutation rates in males and females (Haldane 1935). This paper will be constructed on the same assumption of mutation-selection equilibrium. The prior proportion of new cases will first be computed in the general case where fitness is not null, as in Becker muscular dystrophy, and where there are distinct male and female mutation rates. A mutated gene resulting from germinal mosaicism could mimic an inherited mutation. Here, for the sake of simplicity, a "carrier" is defined as a heterozygote female or a hemizygote. The term "mutation" encompasses both isolated mutation without recurrence and germ-line mosaicism with a recurrence risk. Prior Probabilities

Let xc be the probability of inheriting the gene from a heterozygote female and letfy, be the probability of

Jeanpierre

962

inheriting the gene from a hemizygote male of fitness f. If i and kg stand for the probabilities of inheriting the mutated gene from a female or a male, respectively, who has not him- or herself inherited this mutation, then k is the ratio of the male mutation rate to the female mutation rate (Edwards 1986). We have P (heterozygote) = xc + g +fy, + kg P (hemizygote) = x, + [ .

Since x, is half the probability of having a heterozygous mother and since yc is the probability of having an hemizygous father, we have X =

/k+ 1 +

1(

At

)

and the proportion of affected males who have inherited the mutated gene from a carrier mother is p_

xc

_ k+ 1 +f

Table I Origin of Mutation in Female Carrier

Hypothesis Maternal mutation

........

Paternal mutation

..........

Inherited from mother

....

Inherited from father

......

Absolute Probability

Probabilitya

kg

Ro 2 kRo

Relative

2 1 2

k +1 +f

1-f 11

(k + 2)f 2(k+ 1 +f)

(k + 2)f 1 -f

Total ..................2.k. + 1 +f

1-f

=

2tL Ro

1.0000

a Marginal probability is represented as a function of prior odds, here dubbed Ro. Note that, for the mother of a carrier, the prior probability of being a carrier is always .5, which is the figure derived from the simple model of mutation equilibrium (Haldane 1935). The phenotype of the father must be taken into account in a nonlethal mutation when f > 0.

xC-+ k+2 These probabilities represent the prior probabilities for a nuclear family with a single affected son. The prior probability that a mother of a carrier is herself a carrier could also be derived from the same expressions. The prior odds for an affected son (new mutation:inherited mutation) is defined as Ro. Table 1 summarizes the probabilities relative to the parents of a carrier. Risk Computation

Let us begin with the simple case of a nuclear family. The possibility of mutation is a composite hypothesis that could be calculated as for compound probabilities, from a prior distribution of risk and a set of likelihood factors. If one mutation case among n distinct classes of mutation is notated Ni, then the distribution of the prior probabilities belonging to a given class Ni follows the relation n

i P(N1) = 1 . i=1

The likelihood of each hypothesis is the probability, given this hypothesis, of observing the set of data and could be derived for each alternative. If the inherited case is notated F and if "data" is an abbreviation of pedigree data, then the expression of the posterior odds in a nuclear family is described as

P(carrier) =n

P(data F)P(F) P(data F)P(F) + RoEP(data Ni)P(N1) i=l

where Ro is the prior odds (new mutation:inherited mutation). The nuclear family problem is an oversimplification of a typical problem of genetic counseling. Let us consider now the family depicted in figure 1. The computation of the likelihood of three unaffected uncles is inherently more difficult, and two alternative strategies could be followed: an extensive strategy, consisting in the enumeration of distinct events and their likelihood, and an analytical strategy, consisting in the integration of separate elements into a common term. The first of these procedures is simple but gives birth to large tables with an exponentially growing number of lines. This strategy is, however, a convenient way of checking an analytical procedure. Within an analytical procedure, only the possibility of A being a carrier is reduced by the information from B. If the possibility of two distinct mutations in the family is neglected, then the risk that a given pedigree member is a carrier of a recessive X-linked disease can be described as a chain of linked probabilities, from the distant individual (B) to the most proximal possible carrier (A): P(B carrier) = P(B carrier A carrier) P(A carrier)

.

963

Germinal Mosaicism and Risk Calculation

Figure I Example of pedigree depicting relatives of boy with X-linked mutation. Results from a two-allele locus analysis (alleles 1 and 2) and possible carriers (A-D) are indicated.

If RB stands for the likelihood ratio of B being the origin of a mutation rather than being a carrier, then the likelihood of A is altered by a factor RA which could be computed from the relative probabilities of mutation and familial transmission (table 1). Let subscripts F and N represent heterozygosity and new mutation, respectively. Then,

P(data AN)

P(data AN)

P(data AF)

P(data BN)P(BN) + P(data BF)P(BF)

RA ==

2RB

1

1+ CmRB

Cm

1

2

2RB

with Cm being a function of the likelihood that a mutation had occurred either in B or in the father of A. Let the probability of one in m classes of paternal mosaicism be Mi for i = 1,2, . . . , m. We have n

m

Cm = ZP(data I N) + kZP(data M,) Ro. The conditional probability of B being a carrier, given that A is a carrier, could be derived from the same rationale as applies in the general situation (Jeanpierre 1988). This expression is the denominator of the likelihood ratio: P(B carrier A carrier) =

1 +CmRB

When, after DNA analysis, B is shown not to be a carrier, RB is a very large ratio, since a mutation is likely, and the likelihood of A not being a carrier is altered by a factor 2 / Cmo, where Cmo represents the minimum value of Cm. An estimation of this minimum value relies on the precise determination of the distribution of the risk of recurrence, which is not the aim of this paper. However, this minimum value should

not be very low: paternal mosaicism is so rare that the description of a single case still deserves publication (Darras and Francke 1987; Hendriks et al. 1989; Claustres et al. 1990; Lebo et al. 1990; Taylor et al. 1991), indicating that most of the paternal mutations are isolated, which puts Cmo between 1 and 2. When the mother of a possible carrier is shown not to be a carrier, this demonstration has little effect on the carrier risk for the daughter and gives a likelihood ratio close to 2, which could, at most, halve the risk that the daughter is a carrier. A computer program has been formulated in the Pascal programming language (TurboPascal for IBM PC and ThinkPascal for an Apple Macintosh computer). This computer program provides, for each at-risk family member, an estimation of the probability of being a carrier or belonging to one class of mosaicism. Results

Models of Gametogenesis The prior distribution of recurrence risks may be drawn either from empirical data or from models of

germ cell development. Under the assumption that mosaic classes have an exponential distribution (Hartl 1971), the probabilities of recurrence from mosaicism have been found to be 1/n, 1/3, 3/7, and 7/15 in nuclear families with one, two, three, and four affected children, respectively (n here being the number of cell divisions). These recurrence risks are identical to those obtained for a fully penetrant dominant disorder (Hartl 1971; Edwards 1989). The mother of an affected boy with a lethal X-linked recessive disorder could be either a heterozygote or a mosaic, and the mother of two affected boys is indeed more likely to be a carrier than to be a mosaic. If, after the birth of a first affected boy, the mean probability of recurrence from mosaicism is r, then the birth of a second affected boy shifts the odds (mosaic:carrier) by a factor rI.5. The probability that the mother had inherited the mutation becomes 1 P(carrier) = 2r 1+k

The probability r could be either derived from a model of gametogenesis (Hartl 1971; Edwards 1989; Wijsman 1991) or obtained through empirical studies (Bakker et al. 1989; van Essen et al. 1992). The spe-

964

Jeanpierre Table 2 Risks for Possible Carriers in Figure 1, under Four Models

PROBABILITIES OF RISK UNDER

POSSIBLE CARRIERS A B C D

.....

..... ..... .....

Model 1: without Mosaicism

Model 2: Uniform Risk of Recurrence

Model 3: Two Classes

Model 4: 20 Classes

.50906 .01811 .48945 .00036

.36445 .02345 .46709 .06146

.44117 .02062 .52900 .01018

.44343 .02053 .53083 .00887

NOTE.-The probability of recombination between the mutation and the two-allele locus is .02. Occurrence of a second mutation is neglected here. The affection is lethal (I = 0) with an equal mutation rate in males and females (k = 1).

cific recurrence risk from mosaicism may be identical in autosomal dominant and recessive X-linked diseases, but, where this risk is the only risk in dominant diseases, it is only a component of an overall risk. For purposes of illustration, in the simple situation of Hartl's (1971) model where r = 1 / n, the probability that the mother of two affected boys will have another affected child in the next pregnancy is

1/V21/ In 1+2 1+ k

V3

+ 1/

1 + 1+k

2/

If k = 1, then we haveP = (12+V3)/(1+n). Example

Consider the pedigree in figure 1; the risks assigned to individuals of this family are listed in table 2. Calculations were made either without assuming germinal mosaicism (model 1) or with three distinct distributions of mutation that share a mean risk of .20 for the at-risk haplotype, which is close to the risk estimation in DMDs (Bakker et al. 1989; van Essen et al. 1992). In model 2 a single class of mosaic is assumed (r = .20); in model 3 two classes are postulated-the recurrence risk for the at-risk allele is .025 (80% of mosaic) in one and is .90 (20%) in the other. The risk distribution of model 3 is intended to represent the possibility of mosaicism being a combination of both (1) rare somatic cases with a very high recurrence risk and (2) frequent germinal cases with a low recurrence risk. These figures are not directly drawn from experimental data and are given solely as an illustration of computation. Model 4 has been derived from the model of Wijsman (1991): the recurrence risk varies from 1 /2(n-1) to 1, and the prior frequency of the higher-risk

class, representing mutations between conception and choice of the progenitor germ cells, has been adjusted in order to give a mean recurrence risk that is exactly .20, following the birth of an affected boy. If the mean risk is kept constant, then the posterior risk is weakly dependent on n if n > 12 (data not shown). In model 4, n = 20 and the prior frequency of the higher-risk class has been multiplied by 3.5 in order to give a mean risk of .20. The probability of recombination between the DNA marker and the mutation is assumed to be .02. This example shows that taking mosaicism into account has some effect on the risk for individual D, whose mother is unlikely to be a carrier, and does not alter the risk of individual C, who is the offspring of a person with a high probability of being a carrier. Models 2-4, with the same mean recurrence risk, have a variable influence on the risk for D: the hypothesis of a uniform recurrence risk increases the estimation of the risk, and it can be demonstrated that the selection of a model with a single class of recurrence risk gives the higher estimation of the risk (not shown). A lower estimation of risk is observed in heterogeneous models, where both very low and very high recurrence probabilities are possible. This gives an upper and lower limit to the risk. From a practical point of view, since the computation of the mean recurrence risk in families with both a single affected child and a new mutation is less difficult than the estimation of the prior distribution (van Essen et al. 1992), the rapid determination of the limits of the risk may be useful. Parental Origin of New Mutations In the absence of any information to the contrary, it is reasonable to assume that k is not much greater or less than 1, but this does not mean that it is equal to 1. Estimation of k is not simple (Karel et al. 1986;

96S

Germinal Mosaicism and Risk Calculation Table 3 Risks for Individual D in Figure I, at Different Male-to-Female Mutation Rates

k

Model 1: without Mosaicism

Model 2: Uniform Risk of Recurrence

Model 3: Two Classes

Model 4: 20 Classes

4 ...... 2 ...... 1 ...... 1/2 ...... 1/4 ......

.00086 .00053 .00036 .00027 .00023

.05782 .06022 .06146 .06210 .06243

.01014 .01017 .01018 .01019 .01019

.00892 .00889 .00887 .00886 .00886

NOTE.-The probability of recombination between the mutation and the two-allele locus is .02. Occurrence of a second mutation is neglected here.

Muller and Grimm 1986). Table 3 gives probabilities that individual D in figure 1 is a carrier for distinct values of k from 4 to 1 / 4 according to the three models of mutation in Table 2. Without mosaicism, the frequency of familial cases increases with k (Edwards 1986). When germinal mosaicism is assumed, the probability of B being a carrier also increases with k, but now the probability of D being a carrier is a function of the relative probabilities of inheritance and mosaicism. Since the determination of the phase is highly sensitive to the possibility of mosaicism, the overall risk for D often decreases when k increases. Recent mutations are less frequent in nonlethal recessive X-linked diseases. Table 4 shows that the risk for D is only mildly affected by the estimation of the fitness of a male with a given mutation. Discussion

Germ-line mosaicism is demonstrable in most X-linked diseases and should be a parameter of risk calculation. This aim could be attained with an extension of Haldane's (1935) model of mutation equilibrium. A mutation can happen at any time in term cell development: a late mutation gives a low recurrence risk, and an early mutation gives approximately the

risk of an inherited case. It might be desirable to introduce this heterogeneity of risk into the calculation. The distribution of the different classes of mosaicism is likely to be highly asymmetric, since it is a combination of both (1) frequent mutations with a low recurrence rate and (2) rare mutations with a high recurrence rate.The mean recurrence risk should therefore be used cautiously. The procedure described in this paper does not take into account the possibility of a second mutation: the resulting figure is the risk for having the same mutation as the affected boy, not the probability of having a mutated gene. The difference is small, close to 10-4, and appears only in very-low-risk cases. When the risk is expressed as the probability of having the same mutation as the affected boy, this result can be conveniently scaled by the comparison between this figure and the mean risk in a person from the general population. Germinal mosaicism should be considered only where a recent mutation is likely to have occurred, which is not an infrequent situation, since one-third of the mothers of DMD boys, and two-thirds of the grandmothers, have not inherited a defective gene. In these families, a practical question is the weight of the information from ancestors. Since the odds for not being a carrier are increased by a factor which could

Table 4 Risks for Individual D in Figure 1, as Function of f

f .00 .30 .50 .70

..... .....

..... .....

NOTE.-f

=

Model 1: Without Mosaicism

Model 2: Uniform Risk of Recurrence

Model 3: Two Classes

Model 4: 20 Classes

.00036 .00059 .00088 .00153

.06146 .06084 .06005 .05832

.01018 .01031 .01047 .01084

.00887 .00902 .00920 .00962

fitness of affected males, when k = 1

966

not be much larger than 2, analysis of the grandparental generation might not always be necessary. Phase determination may be difficult in families with evidence of a recent mutation. The prior probability of belonging to one class of mosaicism must be derived from population studies, and the posterior distribution must be computed from the pedigree and other genetic data for a given family. According to this posterior distribution, the probability that a transmitted allele is associated with the mutation is a composite term, reflecting the heterogeneity of the recurrence risk. This figure is important in prenatal diagnosis when both alleles may have the same likelihood of being linked to the mutation. In this situation, DNA analysis of fetal DNA is meaningless, since the risk to the fetus is not affected by the outcome of the test, even in a fully informative family: whatever the result of the DNA analysis, the risk to this fetus will be close to half the risk in the mother. Computation of phase is needed in order to detect this unusual but troublesome situation.

Acknowledgments Financial support was provided by the Association Francaise contre les Myopathies. I wish to thank J. C. Kaplan, C. Boileau and A. Strickland for their helpful and critical comments on the manuscript.

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Brocker-Vriends AHJT, Briet E, Dreesen JCFM, Bakker B, Reitsma P, Pannehoek H, Van de Kamp JJP, et al (1990) Somatic origin of inherited haemophilia A. Hum Genet 85:288-292

Jeanpierre Claustres M, Kjellberg P, Desgeorges M, Bellet H, Demaille J (1990) Germinal mosaicism from grandpaternal origin in a family with Duchenne muscular dystrophy. Hum Genet 86:241-243 Constantinou CD, Pack M, Young SB, Prockop DJ (1990) Phenotypic heterogeneity in osteogenesis imperfecta: the mildly affected mother of a proband with a lethal variant has the same mutation substituting cysteine for al-glycine 904 in a type I procollagen gene (COLlA1). Am J Hum Genet 47:670-679 Darras BT, Francke U (1987) A partial deletion of the muscular dystrophy gene transmitted twice by an unaffected male. Nature 329:556-558 Edwards JH (1986) The population genetics of Duchenne: natural and artificial selection in Duchenne muscular dystrophy. J Med Genet 23:521-530 (1989) Familiarity, recessivity and germline mosaicism. Ann Hum Genet 53:33-47 Fryns JP, Kleczkowska A, Verresen H, van den Berghe H (1983) Germinal mosaicism in achondroplasia: a family with 3 affected siblings of normal parents. Clin Genet 24: 156-158 Gitschier J (1988) Maternal duplication associated with gene deletion in sporadic hemophilia. Am J Hum Genet 43:274-279 Grimm T. Muller B, Muller CR, Janka M (1990) Theoretical considerations on germline mosaicism in Duchenne muscular dystrophy. J Med Genet 27:683-687 Haldane JBS (1935) The rate of spontaneous mutation for a human gene. J Genet 31:317-326 Hartl DL (1971) Recurrence risks for germinal mosaics. Am J Hum Genet 24:124-134 Hendriks RW, Mensink EJBM, Kraakman MEM, Thomson A, Schuurman RKB (1989) Evidence for male X chromosomal mosaicism in X-linked agammaglobulinemia. Hum Genet 83:267-270 Higuchi M, Kochhan L, Olek K (1988) A somatic mosaic for haemophilia A detected at the DNA level. Mol Biol Med 5:23-27 Jeanpierre M (1988) A simple method for calculating risks before DNA analysis. J Med Genet 25:663-668 Karel ER, te Meerman GJ, Ten Kate (1986) On the power to detect differences between male and female mutation rates for Duchenne muscular dystrophy, using classical segregation analysis and restriction fragment length polymorphisms. Am J Hum Genet 38:827-840 Lanman JT Jr, Pericak-Vance MA, Bartlett RJ, Chen JC, Yamaoka L, KohJ, Speer MC, et al (1987) Familial inheritance of a DXS 164 deletion mutation from a heterozygous female. Am J Hum Genet 41:138-144 Lebo RV, Olney RK, Golbus MS (1990) Somatic mosaicism at the Duchenne locus. Am J Med Genet 37:187-190 Luria SE, Delbruck M (1943) Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28:491-511 Maddalena A, Sosnoski DM, Berry GT, Nussbaum RL

Germinal Mosaicism and Risk Calculation (1988) Mosaicism for an intragenic deletion in a boy with mild ornithine transcarbamylase deficiency. N Engl J Med 319:999-1003 Monaco AP, Bertelson CJ, Colletti-Feener C, Kunkel LM (1987) Localization and cloning of Xp deletion breakpoints involved in muscular dystrophy. Hum Genet 75: 221-227 Muller CR, Grimm T (1968) Estimation of the male to female ratio of mutation rates from the segregation of X-chromosomal DNA haplotypes in Duchenne muscular dystrophy families. Hum Genet 74:181-183 Muller HJ (1920) Further changes in the white-eye series of Drosophila and their bearing on the manner of occurrence of mutation. J Exp Zool 31:443-472 Philip N, Auger M, Mattei JF, Giraud F (1988) Achondroplasia in sibs of normal parents. J Med Genet 25:857-859 Reiser CA, Pauli RM, Hall JG (1984) Achondroplasia: unexpected familial recurrence. Am J Med Genet 19:245250 Sykes B (1990) Bone disease cracks genetics. Nature 348: 18-20

967 Taylor SAM, Deugau KV, Lillicrap DP (1991) Somatic mosaicism and female-to-female transmission in a kindred with hemophilia B (factor IX deficiency). Proc Natl Acad Sci 88:39-42 van Essen AJ, Abbs S, Baiget M, Bakker E, Boileau C, Broeckoven C, Bushby K, et al (1992) Parental origin and germline mosaicism of deletions and duplications of the dystrophin gene: a European study. Hum Genet 88:249257 Wallis GA, Starman BJ, Zinn AB, Byers PH (1990) Variable expression of osteogenesis imperfecta in a nuclear family is explained by somatic mosaicism for a lethal point mutation in the al(I) gene (COLlAl) of type I collagen in a parent. Am J Hum Genet 46:1034-1040 Wijsman EM (1991) Recurrence risk of a new dominant mutation in children of unaffected parents. Am J Hum Genet 48:654-661 Wood S, McGillivray B (1988) Germinal mosaicism in Duchenne muscular dystrophy. Hum Genet 78:282-284 Wright S, Eaton ON (1926) Mutational mosaic coat patterns of the guinea pig. Genetics 11:333-351

Germinal mosaicism and risk calculation in X-linked diseases.

Germinal mosaicism is a major problem in risk estimation for an X-linked disease. A mutation can happen anytime in germ cell development, and the prop...
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