5
Proc. Nati. Acad. Sci. USA Vol. 83, pp. 2551-2555, April 1986 Genetics Evidence for an X-linked modifier gene affecting the expression of Tourette syndrome and its relevance to the increased frequency of speech, cognitive, and behavioral disorders in males DAVID E. COMINGS* AND BRENDA G. COMINGSt *Department of Medical Genetics, City of Hope Medical Center, Duarte, CA 91010; and t59 Crestview Court, Duarte, CA 91010 Communicated by Rachmiel Levine, December 5, 1985 ABSTRACT A number of disorders affecting speech, learning, and behavior have a 3:1 or greater male:female ratio. This has usually been explained on the basis of a developmental model postulating a difference in the young male versus female brain. Tourette syndrome is a hereditary neurobehavioral disorder due to a single major autosomal gene. It is associated with learning disorders and attention deficit disorder with hyperactivity and shows a similar predilection for males. Because of the more obvious nature of the tics and vocal noises, it is uniquely suited for examining an alternative hypothesis of an X-linked modifying gene to account for the increased incidence in males. Two alternative models tested were an autosomal modifying gene and the developmental model. Family pedigrees on a series of 430 consecutive cases of Tourette syndrome with 966 age-corrected offspring were used to compare the observed affected and unaffected sons and daughters for nine different phenotype matings with the expected ratios for three different models. The X-linked modifier model provided a better fit to the observed data and accounted for marked differences in the percentage of affected sons and daughters when the father versus the mother trans- mitted the Tourette syndrome gene. A similar model may account for the male predominance in other genetically influ- enced disorders of speech, learning, and behavior. Boys have more problems with speech, school, and behavior than girls. This is a reflection of the fact that there is a significant male preponderance (Table 1) for attention deficit disorder with or without hyperactivity (1), dyslexia (2), stuttering (3), delayed speech (4), conduct disorder (1), anti-social personality disorder (1), autism (1), and Tourette syndrome (TS) (1, 5-7). Combined these affect 10-15% of all males but only 2-5% of females (Table 1). Various types of developmental differences in the brain between young males and females, especially in regard to right-left brain develop- ment, have been suggested as the cause of this sex difference (8-10). TS is a hereditary (11-17) neurobehavioral disorder characterized by motor and vocal tics, a waxing and waning course, and suppressibility of symptoms (1). Studies suggest it is caused by a single major autosomal gene (12, 13). There is evidence for a genetic component to attention deficit disorder (18-26), dyslexia (27, 28), stuttering (3, 29), conduct disorder (18, 25, 30), anti-social personality disorder (31-35), and autism (36, 37). However, the genetic aspects of these disorders are more difficult to study than TS because of their heterogeneity, low penetrance, difficulty in uniform diagnosis and, in some cases, improvement with age. Of all of these disorders TS is most suited to evaluation of the possible role of modifying genes for the following reasons; (i) the diagnosis [ref. 1 (DSM III criteria)] is more clear cut, (it) it appears to be due to a single major gene, (iii) the penetrance Table 1. Sex ratios and prevalences for various central nervous system disorders Approximate Male/female prevalence Disorder ratio per 10,000 Autism 3.8:1 1 TS 3.5:1 50 Delayed speech 4.0:1 60 Stuttering 3.8:1 70 Anti-social personality disorder 3-4:1 300 Development dyslexia 3.5:1 500* Attention deficit disorder 4.0:1 500* Conduct disorder 4-12:1 500* *Not mutually exclusive. is relatively high, especially in males, (iv) the symptoms usually last throughout life, (v) attention deficit disorder (6, 7, 38), dyslexia, and learning disorders (refs. 5 and 39; unpublished observations), stuttering (ref. 39; unpublished observations), and autistic-like behavior (unpublished obser- vations) are more common in patients with TS than the general population, (vi) estimates are available for the gene frequency, sex ratio, and penetrance in males and females, and (vii) a large series of 430 cases with detailed family histories are available for study from our TS clinic. The present study was stimulated by a unique case of a boy with both TS and a rare X-linked disorder, adrenoleuko- dystrophy (40). Often, when two unusual events occur together it is not entirely due to chance. Studies have shown that some males have multiple X-linked recessive diseases due to the deletion of contiguous X-linked genes (41). Since TS is an autosomal disorder this explanation could not apply here. However, a deletion of an adrenoleukodystrophy gene and a contiguous X-linked gene acting as a modifier of the Ts gene, or the mutant adrenoleukodystrophy gene itself acting as a modifier of the Ts gene, was possible. (For convenience we shall refer to the Tourette syndrome gene as Ts, the normal gene as ts, the X-linked dominant modifier gene as Xt, the normal X-linked recessive modifier gene as xt, the normal autosomal recessive modifier gene as am, and the autosomal dominant modifier gene as Am.) This stimulated us to ask the question, is there evidence from our TS pedigrees that an X-linked gene was acting as a modifier of Ts gene expression? METHODS For the diagnosis of TS the following criteria were carefully adhered to: (i) onset between 2 and 15 years of age, (it) the presence of multiple motor tics, (iii) the presence of vocal tics, (iv) a waxing and waning course, (v) suppressibility of symptoms, and (vi) the presence of symptoms for more than Abbreviations: TS, Tourette syndrome; C, carrier; N, normal. 2551 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. Downloaded by guest on February 4, 2021

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Page 1: Evidencefor an X-linked modifier of Tourette ... · with both TS and a rare X-linked disorder, adrenoleuko-dystrophy (40). Often, when two unusual events occur togetherit is notentirelyduetochance

Proc. Nati. Acad. Sci. USAVol. 83, pp. 2551-2555, April 1986Genetics

Evidence for an X-linked modifier gene affecting the expression ofTourette syndrome and its relevance to the increased frequencyof speech, cognitive, and behavioral disorders in malesDAVID E. COMINGS* AND BRENDA G. COMINGSt*Department of Medical Genetics, City of Hope Medical Center, Duarte, CA 91010; and t59 Crestview Court, Duarte, CA 91010

Communicated by Rachmiel Levine, December 5, 1985

ABSTRACT A number of disorders affecting speech,learning, and behavior have a 3:1 or greater male:female ratio.This has usually been explained on the basis of a developmentalmodel postulating a difference in the young male versus femalebrain. Tourette syndrome is a hereditary neurobehavioraldisorder due to a single major autosomal gene. It is associatedwith learning disorders and attention deficit disorder withhyperactivity and shows a similar predilection for males.Because of the more obvious nature of the tics and vocal noises,it is uniquely suited for examining an alternative hypothesis ofan X-linked modifying gene to account for the increasedincidence in males. Two alternative models tested were anautosomal modifying gene and the developmental model.Family pedigrees on a series of 430 consecutive cases ofTourette syndrome with 966 age-corrected offspring were usedto compare the observed affected and unaffected sons anddaughters for nine different phenotype matings with theexpected ratios for three different models. The X-linkedmodifier model provided a better fit to the observed data andaccounted for marked differences in the percentage of affectedsons and daughters when the father versus the mother trans-mitted the Tourette syndrome gene. A similar model mayaccount for the male predominance in other genetically influ-enced disorders of speech, learning, and behavior.

Boys have more problems with speech, school, and behaviorthan girls. This is a reflection of the fact that there is asignificant male preponderance (Table 1) for attention deficitdisorder with or without hyperactivity (1), dyslexia (2),stuttering (3), delayed speech (4), conduct disorder (1),anti-social personality disorder (1), autism (1), and Tourettesyndrome (TS) (1, 5-7). Combined these affect 10-15% of allmales but only 2-5% of females (Table 1). Various types ofdevelopmental differences in the brain between young malesand females, especially in regard to right-left brain develop-ment, have been suggested as the cause of this sex difference(8-10). TS is a hereditary (11-17) neurobehavioral disordercharacterized by motor and vocal tics, a waxing and waningcourse, and suppressibility of symptoms (1). Studies suggestit is caused by a single major autosomal gene (12, 13).There is evidence for a genetic component to attention

deficit disorder (18-26), dyslexia (27, 28), stuttering (3, 29),conduct disorder (18, 25, 30), anti-social personality disorder(31-35), and autism (36, 37). However, the genetic aspects ofthese disorders are more difficult to study than TS because oftheir heterogeneity, low penetrance, difficulty in uniformdiagnosis and, in some cases, improvement with age. Of allof these disorders TS is most suited to evaluation of thepossible role of modifying genes for the following reasons; (i)the diagnosis [ref. 1 (DSM III criteria)] is more clear cut, (it)it appears to be due to a single major gene, (iii) the penetrance

Table 1. Sex ratios and prevalences for various central nervoussystem disorders

ApproximateMale/female prevalence

Disorder ratio per 10,000Autism 3.8:1 1TS 3.5:1 50Delayed speech 4.0:1 60Stuttering 3.8:1 70Anti-social personality disorder 3-4:1 300Development dyslexia 3.5:1 500*Attention deficit disorder 4.0:1 500*Conduct disorder 4-12:1 500*

*Not mutually exclusive.

is relatively high, especially in males, (iv) the symptomsusually last throughout life, (v) attention deficit disorder (6,7, 38), dyslexia, and learning disorders (refs. 5 and 39;unpublished observations), stuttering (ref. 39; unpublishedobservations), and autistic-like behavior (unpublished obser-vations) are more common in patients with TS than thegeneral population, (vi) estimates are available for the genefrequency, sex ratio, and penetrance in males and females,and (vii) a large series of 430 cases with detailed familyhistories are available for study from our TS clinic.The present study was stimulated by a unique case of a boy

with both TS and a rare X-linked disorder, adrenoleuko-dystrophy (40). Often, when two unusual events occurtogether it is not entirely due to chance. Studies have shownthat some males have multiple X-linked recessive diseasesdue to the deletion of contiguous X-linked genes (41). SinceTS is an autosomal disorder this explanation could not applyhere. However, a deletion of an adrenoleukodystrophy geneand a contiguous X-linked gene acting as a modifier of the Tsgene, or the mutant adrenoleukodystrophy gene itself actingas a modifier of the Ts gene, was possible. (For conveniencewe shall refer to the Tourette syndrome gene as Ts, thenormal gene as ts, the X-linked dominant modifier gene as Xt,the normal X-linked recessive modifier gene as xt, the normalautosomal recessive modifier gene as am, and the autosomaldominant modifier gene as Am.) This stimulated us to ask thequestion, is there evidence from our TS pedigrees that anX-linked gene was acting as a modifier of Ts gene expression?

METHODS

For the diagnosis of TS the following criteria were carefullyadhered to: (i) onset between 2 and 15 years of age, (it) thepresence of multiple motor tics, (iii) the presence of vocaltics, (iv) a waxing and waning course, (v) suppressibility ofsymptoms, and (vi) the presence of symptoms for more than

Abbreviations: TS, Tourette syndrome; C, carrier; N, normal.

2551

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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2552 Genetics: Comings and Comings

one year. The diagnosis of chronic motor tics was the sameexcept that ii or iii was missing-i.e., there were either motoror vocal tics, but not both. As shown in prior studies of ours(12) and others (11, 15, 17), TS and motor tics are bothexpressions of the Ts gene and in this paper TS refers to thecombined TS-motor tic trait. Thus, we are not describing theeffects of modifier genes on the expression of the Ts gene asonly motor tic, but consider only the total lack of expressionof the Ts gene as no motor tics and no vocal noises. Othercharacteristics concerning the unselected ascertainment ofthese patients have been described (6, 7, 12). Our study (12)of the first 250 cases of this series provided the followingparameters: p (normal ts gene frequency) = 0.995, q (Ts genefrequency) = 0.005, penetrance of Tsts in males = 0.7,penetrance of Tsts in females = 0.3, penetrance in combinedmales and females = 0.5.The segregation ratios in the observed pedigrees were

determined as follows. In all cases the propositus was

excluded from the counting to prevent ascertainment bias. Aparent was determined to be normal if he or she was

asymptomatic and had no first or second degree relativeswith TS. A parent of aTS child was considered to be a carrierif he or she never had motor or vocal tics but had a sibling,parent, aunt, uncle, or grandparent with TS. The phenotypicand assumed phenotypic mating types were classified ac-cording to whether the father or mother had TS, was a carrier,or was normal. Unaffected children were age corrected basedon the cumulative proportion of individuals with TS showingan onset of symptoms by a given age between 2 and 15 years.

MODELS

Three general models for the variation in sex differences inpenetrance in males and females were used.

Sex-Linked Model. This model assumes the presence of anormal recessive gene, xt, on the X-chromosome that does

not protect individuals from expressing a Ts gene and adominant Xt allele that protects hemizygous Xt males andheterozygous Xtxt and homozygous XtXt females from theeffects of the Ts gene. Since the penetrance of Tsts in malesis 0.7, the frequency of the normal xt gene is assumed to be0.7, and the frequency of the protective modifying gene Xt is0.3. Where the frequency of xt = r and of Xt = s, thefrequency of the various genotypes for females is (e2 + 2pq+ q2)(r2 + 2rs + s2) and for males is (p2 + 2pq + q)(r + s).An example of the method of calculating the expected valuesfor the X-linked model is shown in Table 2. The 54 differentpossible male and female genotype mating frequencies weredivided into the 9 different phenotype matings. TS males X

normal females and normal males x TS females are used asexamples for 10 of the 54, and the population frequency ofthese matings is shown in column A. The relative frequencyof each genotype mating for each phenotype group wasdetermined (column B, A/A total). The risk of TS maleprogeny/total male progeny and of TS female progeny/totalfemale progeny was entered for each genotype mating (col-umn C, male and female). Four examples of this are shownin Fig. 1. This risk was multiplied by the relative contributionof that mating type (B) producing the weighted column B x

C. Summing all entries in this column for a given phenotypemating gave the final expected risk of TS for males andfemales.

In the carrier x normal phenotypic mating, assuming nosporadic cases, most of the presumed carriers would be truecarriers. However, in the TS x carrier class this assumptiondoes not necessarily hold and here possibly some of thepresumed carriers are in fact not carriers, since the childcould have gotten TS from the TS parent. However, therewere such a small number of children in this mating type(1.5%), that this difference between assumption and realitywould not significantly affect the results. This also holds forthe carrier x carrier mating types where in fact only one

Table 2. Examples of calculation of expected males and females

B,A/A C B x CGenotype A, Freq.* Tot.* Males Fem. Males Fem.

X-linked modelTs males x Normal females

Tsts xt tsts XtXt 0.0006206 0.0897744 0.000 0.000 0.0000 0.0000Tsts xt tsts Xtxt 0.0028%1 0.4189474 0.250 0.250 0.1047 0.1047Tsts xt tsts xtxt 0.0033788 0.4887719 0.500 0.500 0.2444 0.2444TsTs xt tsts XtXt 0.0000016 0.0002256 0.000 0.000 0.0000 0.0000TsTs xt tsts Xtxt 0.0000073 0.0010526 0.500 0.500 0.0005 0.0005TsTs xt tsts xtxt 0.0000085 0.0012281 1.000 1.000 0.0012 0.0012

Total 0.0069128 1.0000000 0.3509 0.3509Normal males x TS females

tsts Xt Tsts xtxt 0.0014481 0.2992481 0.500 0.000 0.14% 0.0000tsts xt Tsts xtxt 0.0033788 0.6982456 0.500 0.500 0.3491 0.3491tsts Xt TsTs xtxt 0.0000036 0.0007519 1.000 0.000 0.0008 0.0000tsts xt TsTs xtxt 0.0000085 0.0017544 1.000 1.000 0.0018 0.0018

Total 0.0048390 1.0000000 0.5013 0.3509Autosomal modelTs parent x Normal parent

Tsts amam tsts amam 0.0047303 0.4887719 0.500 0.500 0.2444 0.2444TsTs amam tsts amam 0.0000119 0. 0012281 1.000 1.000 0.0012 0.0012Tsts amam tsts Amam 0.0040546 0.4189474 0.250 0.250 0.1047 0.1047TsTs amam tsts Amam 0.0000102 0.0010526 0.500 0.500 0.0005 0.0005Tsts amam tsts AmAm 0.0008688 0.0897744 0.000 0.000 0.0000 0.0000TsTs amam tsts AmAm 0.0000022 0.0002256 0.000 0.000 0.0000 0.0000

Total 0.0096780 1.000000 0.3509 0.3509

Freq., frequency; Fem., female.*Values calculated with 8 decimal places and rounded to 7 decimal places.

Proc. Natl. Acad. Sci. USA 83 (1986)

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Proc. Natl. Acad. Sci. USA 83 (1986) 2553

TS x N C x N

Tt tt Tt Tt g ttX Xx X X IXX

Eibbb~F66 b~bb 6Tt Tt tt t Tt Tt t tt Tt Ttx x Xx xx xx xxxx x x Xx Xx

25% 25% 50% 0%

N x TS N x C

tt Tt n T TtX XX X Xx X

Tt Ut Tt tt Tt Tt tt Tt Tt tt t

x x Xx Xx x x Xxxx Xxxx

50% 0% 25% 25"%

[3 ( TS [r (1) Carrier O 0 Normal

FIG. 1. A diagrammatic illustration of four specific matingsshowing how an X-linked modifier gene predicts striking differencesin risks to sons and daughters depending upon whether the father orthe mother expresses TS. The risks for percent of affected sons anddaughters are shown under each pedigree. Ts, ts, Xt, and xt havebeen abbreviated to T, t, X, and x, respectively.

parent may be a carrier. However, this group was also small,constituting only 1.8% of the total.The phenotype "normal" x "normal" mating combines

those categories where presumed genotypic carriers werephenotypically normal. Inclusion ofthis group is based on theassumption that genotype normal tsts x tsts matings wouldnot be expected to have TS children and in these cases oneor both parents were actually Ts carriers. This assumes thatthere are no sporadic cases of TS. In the prior studies of asingle gene model the frequency ofsporadic cases (phenocop-ies or new mutations) was estimated at 35% (12) and 1% (13).This subject is covered further in the discussion.Autosomal Modifier Gene Model. This model assumes a

normal autosomal recessive gene am that does not protect anindividual from the expression of a Ts gene and a dominantAm allele that protects heterozygousAmam and homozygousAmAm individuals from the effects of either heterozygousTsts or homozygous TsTs genes. Where the frequency ofam= r and Am = s, only amam individuals would express a Tsgene. Since the combined penetrance of TS in males andfemales is 0.5, r2 = 0.5, r = 0.7 and s = (1 - r) = 0.3. Thefrequency of each mating type was calculated as the poly-nomial expansion of (p2 + 2pq + q2)(r2 + 2rs + S2) and thesegregation ratio for males and females was determined foreach mating type. The expected number of TS males andfemales for phenotypic matings was then determined from theweighted sums (Table 2).Developmental Model. In this model it was assumed that the

predominance of males is not due to modifying genes (exceptin the sense that sex is genetically determined) but is due todifferences in early brain development making any malecarrying the Ts gene more susceptible to expression than

females. Here the phenotype frequency of Tsts, Tsts, and tstsmales was determined by multiplying the genotype frequen-cies by 0.7 for expressing males and by 0.3 for nonexpressingmales. An example for TS x N and N x TS matings areshown in Table 3. The phenotype frequency of females wasdetermined by multiplying the genotype frequency by 0.3 forexpressing females and 0.7 for nonexpressing females. Themating frequencies are given in Table 3. Values in theremainder of the table were determined as for the X-linkedand autosomal models. The phenotype risk figures weredetermined by multiplying the genotype risks by 0.7 for malesand 0.3 for females. Thus, for males the genotype risks of 1,0.75, and 0.5 became 0.7,0.525, and 0.35, and forfemales 0.3,0.225, and 0.15, respectively.

RESULTS AND DISCUSSIONTable 4 shows the observed and expected frequencies for thethree models. Each model gives significantly different ex-pectations. The most striking feature is the significant effectof the presence ofTS or carrier status in the father versus themother in the X-linked model. For example, when the fatheris a carrier (C) and the mother has TS ( C x TS), 75% of sonsare expected to be affected and 0% of the daughters, whilewhen the parental status is reversed (TS x C), 31% of bothsons and daughters are expected to be affected. A similar butless striking disparity is seen for N x C and C x N matings,where N stands for normal. When the father is a carrier andthe mother is normal (C x N), 35% of sons and 0% ofdaughters are expected to be affected. In the reverse situation(N x C), 21% of sons and 14% of daughters are expected tobe affected. In the C x C mating, 31% of sons and 0% ofdaughters are expected to be affected. In the autosomalmodifier model there is no difference in the expected risk ofsons versus daughters. The developmental model does pre-dict a difference in risk for sons and daughters, but this isindependent of the parental phenotype. As seen in Table 4 ofthe observed versus expected data, there is, in fact, asignificant effect on the frequency of TS in sons versusdaughters depending upon whether the father or mother wasof a certain phenotype.The numbers in the TS x C, C x TS, and C x C matings,

are too small to be of significance. By contrast, the TS x N,N x TS, C x N, N x C, and "N" x "N" matings had bothrelatively large numbers of individuals and gave significantlydifferent expectations for the different models. These areoutlined in Table 4. In the TS x N mating, 35% of males andfemales were expected to be affected in both the X-linked andautosomal models, while 35% affected males and 15% affect-ed females were expected in the developmental model. Theobserved was 37% affected males and 30% affected females.This suggests that developmental influences were minimal. Inthe reverse N x TS mating, only the X-linked model predictsa change to 50% affected males and 35% affected females.The observed was 40%o males and 25% females. In the C xN mating the X-linked model predicts 35% affected males and0o affected females, the autosomal model predicts 15.6%

Table 3. Example of calculations for the developmental model

Phenotype Genotype Frequency A, B, C B x CFather Mother Father Mother Father Mother F x M A/A Total Males Females Males FemalesTS N Tsts tsts 0.7 x 2pq P2 0.0068955 0.698246 0.35 0.15 0.2444 0.1047N TS tsts Tsts p2 0.3 x 2pq 0.0029552 0.299248 0.35 0.15 0.1047 0.0449TS N TsTs tsts 0.7 x q2 p2 0.0000173 0.001754 0.70 0.30 0.0005 0.0002N TS tsts TsTs p2 0.3 x q2 0.0000074 0.000752 0.70 0.30 0.0005 0.0002

Total 0.0098755 1.000000 0.3509 0.1504

F, female; M, male; N, normal.*Values are calculated using 8 decimal places and rounded to 7 decimal places.

Genetics: Comings and Comings

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2554 Genetics: Comings and Comings

Table 4. The observed and expected values for the three models

Father x Mother Mating TypesTSxTS TSxC CxTS TSxN NxTS CxC CxN NxC NxN Total

TotalObserved

Sons 24.8 6.0 2.0 86.9 81.3 12.7 51.5 108.3 143.9 517.4Daughters 12.5 9.9 1.0 88.9 60.2 5.4 30.9 90.4 149.5 448.6

Total 37.3 15.9 3.0 175.7 141.5 18.1 82.4 198.7 293.4 966.0Number with TSObserved

Sons 19.0 4.0 0.0 32.0 33.0 1.0 22.0 38.0 18.0 167.0Daughters 6.0 5.0 0.0 27.0 15.0 0.0 1.0 17.0 12.0 83.0

ExpectedX-linkedSons 18.6 1.9 1.5 30.5 40.7 3.9 18.1 22.3 37.4 174.9Daughters 9.4 3.1 0.0 31.2 21.1 0.0 0.0 13.1 13.6 91.5

AutosomalSons 18.6 1.9 0.6 30.5 28.5 1.6 8.0 16.9 22.4 129.0Daughters 9.4 3.1 0.3 31.2 21.1 0.7 4.8 14.1 23.3 108.0

DevelopmentalSons 13.0 2.1 0.7 30.5 28.5 6.7 18.1 38.0 50.6 188.2Daughters 2.8 1.5 0.2 13.4 9.1 1.2 4.6 13.6 22.5 68.9

Percent with TSObserved

Sons 76.7 66.6 0.0 36.8 40.6 7.6 42.7 35.1 12.5Daughters 48.0 50.5 0.0 30.4 24.9 0.0 3.2 18.8 8.0

ExpectedX-linkedSons 75.1 30.9 75.1 35.1 50.1 30.9 35.1 20.6 26.0Daughters 75.1 30.9 0.0 35.1 35.1 0.0 0.0 14.4 9.1

AutosomalSons 75.1 30.9 30.9 35.1 35.1 12.7 15.6 15.6 15.6Daughters 75.1 30.9 30.9 35.1 35.1 12.7 15.6 15.6 15.6

DevelopmentalSons 52.6 35.1 35.1 35.1 35.1 52.6 35.1 35.1 35.1Daughters 22.4 15.0 15.0 15.0 15.0 22.5 15.0 15.0 15.0

affected males and females, and the developmental modelpredicts 35% affected males and 15% affected females. Theobserved was 43% males and 3% females. In the reversesituation again only the X-linked model predicts a change to20.6% affected males and 14.4% affected females. Theobserved was 35% affected males and 19% affected females.These findings are most consistent with the X-linked model.Finally, for the N x N mating the expected values for theautosomal and developmental models are the same as for theC x N and N x C matings. However, the X-linked modelpredicts 26% affected males and 9% affected females. Theobserved was 12.5% males and 8% females. These numbersmay be lower than expected because there are indeed somesporadic cases. This mating type would be most sensitive tothe presence of sporadic cases and contained 30% of the totalprogeny. Since the propositus has been excluded, if all casesin this group were sporadic, no TS siblings would beexpected. For the X-linked model 48% of the expected TS

sons and 88% of the expected daughters were observed. Forthe autosomal model, the figures were 80%o of sons and 51%of daughters, and for the developmental model the figureswere 36% for sons and 53% for daughters. Thus, the observedTS progeny of N x N matings are consistent with 10-26%sporadic cases regardless of the model. However, onlyprecise Ts gene markers would prove if any cases are trulysporadic.These observations indicate that there are in fact signifi-

cant observed differences depending upon whether the moth-er or the father was of a certain phenotype and these aresimilar in dimension to those expected by the X-linked modelwith some sporadic cases. The less than expected number ofdaughters in the TS x TS matings suggests that the devel-opmental model may also be playing some role.Each model was compared to the observed values by the

X2 test. A standard x2 could not be determined because threeof the expected values in the X-linked model were zero. To

Table 5. x2 values for the three models

X-linked Autosomal DevelopmentalModel Values Sons Daughters Total Sons Daughters Total Sons Daughters Total

Main model X2 27.9 7.7 35.6 52.6 13.6 66.2 31.4 35.2 66.6P 0.0005 0.43 <0.0005 <0.0005 0.09 <0.0005 <0.0005 <0.0005 <0.0005Ratio* 1 1 1 1.88 1.77 1.85 1.13 4.57 1.87

Constant penetrance model x2 27.9 7.7 35.6 40.6 16.8 57.3 31.4 26.5 57.9P 0.0005 0.43 <0.0005 <0.0005 0.03 <0.0005 <0.0005 <0.0005 <0.0005Ratio* 1 1 1 1.46 2.18 1.61 1.13 3.44 1.63

*Ratio of x2 of X-linked/X-linked, autosomal and developmental.

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Proc. Natl. Acad. Sci. USA 83 (1986) 2555

alleviate this problem a constant (0.5) was added to each ofthe observed and expected values. The resulting values aregiven in Table 5. For sons, daughters, and sons plus daugh-ters, the X-linked modifier model gave the best fit to the data.Only the female offspring in the X-linked model gave x2indicating the expected was well within random expectationof the observed (P = 0.43). The daughters in the autosomalmodel were also not significantly different from observed, buthere the P was much less (0.09). The failure of any model tocompletely predict the observed is understandable given thecomplexity of the biological system being examined, the factthat the X-linked and developmental model may both play arole, the need for some assumptions about TS carrier statusand number of sporadic cases that might not always be true,and the probability that the male:female ratio is affected byother factors (34).The relative superiority of the X-linked model was not

changed if values greater than 0.5 were added to eachobserved and expected. The sex ratio of the observedprogeny minus the propositi was 167/83 or 2:1, which is lessthan the usual observed of3 or more to 1. This reflects the factthat our observed TS is actually TS plus motor tic, and the sexratio for patients with motor tic only was lower than for TS.In the pure X-linked model, with the frequency of thepermissive gene, r, being 0.7 the expected male:female ratiois rir2 = 0.7/0.49 or 1.43:1. However, as the gene frequencyof r decreases the sex ratio increases (i.e., 0.5, 2:1; 0.4, 2.5:1;0.3, 3.3:1; 0.2, 5:1; 0.1, 10:1).

In this paper we have used r = 0.7 for the gene frequencyof xt or am, and s = 1 - r or 0.3 for the frequency of Xt orAm. To determine if our results critically depended uponthese assumptions we wrote an iterative computer programand demonstrated that the X-linked model gave the best fit tothe data at all values of r from 0.1 to 0.9. We also varied thefrequency of the Ts gene, q, from 0.001 to 0.35. At all valuesof r from 0.1 to 0.9 the X-linked model gave the best fit to thedata.When the penetrance in males for the X-linked model is

0.7, the penetrance for females becomes (0.7)2 or 0.49. Onecould object that since this is different than the penetrance of0.3 used for females in the autosomal and developmentalmodels, the results are simply a reflection of this. Todetermine if this was a factor the expected values wererecalculated using a Penetrance for females of 0.49 for allthree models. The X values for this constant penetrancemodel are also given in Table 5. This resulted in no significantdifference in the results and, if anything, the X-linked modelfaired even better since now the results for daughters in theautosomal model is significantly different from the expected(P = 0.03).

Since these are not nested hypotheses, no precise statis-tical comparison of the models could be made. However, theratio of the x2 values gives a qualitative indication. Theseratios ranged from 1.13 to 3.44 in favor ofthe X-linked model.While the present model was based on the observations in

TS, we think it is not unreasonable that if the X-linkedmodifier model is correct in accounting for much of the malepreponderance in TS, the same (or other) X-linked genes mayaccount for a similar male preponderaence in other disordersshown to have a significant genetic component such asattention deficient disorder, autism, dyslexia, stuttering,conduct disorder, and anti-social personality.

This work was supported in part by the Barton W. WeprinResearch Fellowship.

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