11
PHENOTYPIC VARIATION AND FMRP LEVELS IN FRAGILE X Danuta Z. Loesch, 1 * * Richard M. Huggins, 2 and Randi J. Hagerman 3 1 School of Psychological Science, La Trobe University, Melbourne, Australia 2 Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia 3 M.I.N.D. Institute, and Department of Pediatrics, University of California, Davis, Sacramento, California Data on the relationships between cognitive and physical pheno- types, and a deficit of fragile X mental retardation 1 (FMR1) gene-specific protein product, FMRP, are presented and discussed in context with earlier findings. The previously unpublished results obtained, using standard pro- cedures of regression and correlations, showed highly significant associa- tions in males between FMRP levels and the Wechsler summary and subtest scores and in females between these levels and the full-scale intelligence quotient (FSIQ), verbal and performance IQ, and some Wechsler subtest scores. The published results based on data from 144 extended families with fragile X, recruited from Australia and the United States within a collaborative NIH-supported project, were obtained using robust modifica- tion of maximum likelihood in pedigrees. The results indicated that process- ing speed, short-term memory, and the ability to control attention, espe- cially in the context of regulating goal-directed behavior, may be primarily affected by the FMRP depletion. The effect of this depletion on physical phenotype was also demonstrated, especially on body and head height and extensibility of finger joints. It is recommended that further studies should rely on more accurate measures of FMRP levels, and use of larger samples, to overcome extensive variability in the data. © 2004 Wiley-Liss, Inc. MRDD Research Reviews 2004;10:31– 41. Key Words: FMRP; IQ; anthropomorphic measures; fragile X; neurocog- nitive testing; physical phenotype; pedigree analysis INTRODUCTION F ragile X syndrome is caused by an unstable mutation in the FMR1 gene located on the X chromosome [Verkerk et al., 1991]. This mutation involves the expansion of trinu- cleotide (CGG) repeats in the promoter region of this gene. Small expansions, ranging from 50 to 200 CGG repeats (pre- mutation), cause no obvious developmental delay, but they tend to expand into a “full mutation” (200 CGG repeats) if trans- mitted through a female. This usually leads to an inactivation of the FMR1 gene and gross deficit of the protein gene product, FMRP [Pieretti et al., 1991]. Evidence indicates that FMRP is involved in normal brain development [Irwin et al., 2002]. A higher expression of FMRP has been documented in the human brain compared with other tissues [Hinds et al., 1993], especially in neuron-rich areas [Devys et al., 1993]. Moreover, the more recent studies using mouse brains have shown that FMRP is involved in synaptogenesis, especially in the cerebral cortex, cerebellum, and hippocampus [Willemsen et al., 1995; Irwin et al., 2002; Mineur et al., 2002] and in modifying synaptic struc- ture in response to environmental stimulation [Weiler et al., 1997; Weiler and Greenough 1999; Beckel-Mitchener and Greenough, this volume). The assumption is therefore justified that cognitive impairment, which is a core deficit in the fragile X syndrome, is primarily caused by the deficit of FMRP. The phenotype of individuals with the full mutation as- sociated with depletion of FMRP is characterized, apart from a global intellectual impairment, by the presence of distinctive neurocognitive deficits that are not always proportional to the global impairment (reviewed in Bennetto and Pennington 2002). In males, these deficits concern visuospatial ability, the processing of sequential information, and attentional skills [Crowe and Hay 1990; Freund and Reiss 1991; Munir et al., 2000; Loesch et al., 2002a] and a deviant speech pattern [Sudhal- ter et al., 1992]. In females, specific neurocognitive impairments include attention and concentration skills [Mazzocco et al., 1993] and visuospatial abilities [Mazzocco et al., 1993; Cornish et al., 1998], especially on tasks involving a visuoconstructive component [Cornish et al., 1999]. Many of these deficits are related to higher control processes of attention such as executive functioning [Barkley 1997], which involves cognitive flexibility, planning, initiation, behavioral and attentional regulation, feed- back utilization, and self-perception. There is strong evidence for executive function deficits in both males and females with the full mutation [Mazzocco et al., 1993; Sobesky et al., 1996; Munir et al., 1998; Loesch et al., 2003b]. Studies of individual constructs of attention in boys with fragile X demonstrated deficits at higher levels of attention function/executive func- tioning, especially in the ability to inhibit or delay responding and divide or switch attention [Munir et al., 2000; Cornish et al., 2001]. Females are usually less affected than males because of the presence of a second unaffected X chromosome. Between 50% and 71% of females demonstrate a significant cognitive deficit Grant sponsor: NICHD; Grant number: HD36071; Grant sponsor: General Clinical Research Centers Program, National Center for Research Resources, NIH; Grant number: 5MO1RR00069; Grant sponsor: Mental Retardation Research Center at the University of Colorado Health Sciences Center, NICHD; Grant number: HD04024. *Correspondence to: Danuta Z. Loesch, School of Psychological Science, La Trobe University, 3083 Bundoora, Victoria, Australia. E-mail:[email protected] Received 10 April 2003; Accepted 11 June 2003 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/mrdd.10084 MENTAL RETARDATION AND DEVELOPMENTAL DISABILITIES RESEARCH REVIEWS 10: 31– 41 (2004) © 2004 Wiley-Liss, Inc.

PHENOTYPIC VARIATION AND FMRP L FRAGILE X · PHENOTYPIC VARIATION AND FMRP LEVELS IN FRAGILE X Danuta Z. Loesch,1** Richard M. Huggins,2 and Randi J. Hagerman3 1School of Psychological

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Page 1: PHENOTYPIC VARIATION AND FMRP L FRAGILE X · PHENOTYPIC VARIATION AND FMRP LEVELS IN FRAGILE X Danuta Z. Loesch,1** Richard M. Huggins,2 and Randi J. Hagerman3 1School of Psychological

PHENOTYPIC VARIATION AND FMRP LEVELSIN FRAGILE X

Danuta Z. Loesch,1** Richard M. Huggins,2 and Randi J. Hagerman3

1School of Psychological Science, La Trobe University, Melbourne, Australia2Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia

3M.I.N.D. Institute, and Department of Pediatrics, University of California, Davis, Sacramento, California

Data on the relationships between cognitive and physical pheno-types, and a deficit of fragile X mental retardation 1 (FMR1) gene-specificprotein product, FMRP, are presented and discussed in context with earlierfindings. The previously unpublished results obtained, using standard pro-cedures of regression and correlations, showed highly significant associa-tions in males between FMRP levels and the Wechsler summary and subtestscores and in females between these levels and the full-scale intelligencequotient (FSIQ), verbal and performance IQ, and some Wechsler subtestscores. The published results based on data from 144 extended familieswith fragile X, recruited from Australia and the United States within acollaborative NIH-supported project, were obtained using robust modifica-tion of maximum likelihood in pedigrees. The results indicated that process-ing speed, short-term memory, and the ability to control attention, espe-cially in the context of regulating goal-directed behavior, may be primarilyaffected by the FMRP depletion. The effect of this depletion on physicalphenotype was also demonstrated, especially on body and head height andextensibility of finger joints. It is recommended that further studies shouldrely on more accurate measures of FMRP levels, and use of larger samples,to overcome extensive variability in the data. © 2004 Wiley-Liss, Inc.MRDD Research Reviews 2004;10:31–41.

Key Words: FMRP; IQ; anthropomorphic measures; fragile X; neurocog-nitive testing; physical phenotype; pedigree analysis

INTRODUCTION

Fragile X syndrome is caused by an unstable mutation in theFMR1 gene located on the X chromosome [Verkerk etal., 1991]. This mutation involves the expansion of trinu-

cleotide (CGG) repeats in the promoter region of this gene.Small expansions, ranging from 50 to 200 CGG repeats (pre-mutation), cause no obvious developmental delay, but they tendto expand into a “full mutation” (�200 CGG repeats) if trans-mitted through a female. This usually leads to an inactivation ofthe FMR1 gene and gross deficit of the protein gene product,FMRP [Pieretti et al., 1991]. Evidence indicates that FMRP isinvolved in normal brain development [Irwin et al., 2002]. Ahigher expression of FMRP has been documented in the humanbrain compared with other tissues [Hinds et al., 1993], especiallyin neuron-rich areas [Devys et al., 1993]. Moreover, the morerecent studies using mouse brains have shown that FMRP isinvolved in synaptogenesis, especially in the cerebral cortex,cerebellum, and hippocampus [Willemsen et al., 1995; Irwin etal., 2002; Mineur et al., 2002] and in modifying synaptic struc-ture in response to environmental stimulation [Weiler et al.,

1997; Weiler and Greenough 1999; Beckel-Mitchener andGreenough, this volume). The assumption is therefore justifiedthat cognitive impairment, which is a core deficit in the fragileX syndrome, is primarily caused by the deficit of FMRP.

The phenotype of individuals with the full mutation as-sociated with depletion of FMRP is characterized, apart from aglobal intellectual impairment, by the presence of distinctiveneurocognitive deficits that are not always proportional to theglobal impairment (reviewed in Bennetto and Pennington2002). In males, these deficits concern visuospatial ability, theprocessing of sequential information, and attentional skills[Crowe and Hay 1990; Freund and Reiss 1991; Munir et al.,2000; Loesch et al., 2002a] and a deviant speech pattern [Sudhal-ter et al., 1992]. In females, specific neurocognitive impairmentsinclude attention and concentration skills [Mazzocco et al.,1993] and visuospatial abilities [Mazzocco et al., 1993; Cornishet al., 1998], especially on tasks involving a visuoconstructivecomponent [Cornish et al., 1999]. Many of these deficits arerelated to higher control processes of attention such as executivefunctioning [Barkley 1997], which involves cognitive flexibility,planning, initiation, behavioral and attentional regulation, feed-back utilization, and self-perception. There is strong evidencefor executive function deficits in both males and females withthe full mutation [Mazzocco et al., 1993; Sobesky et al., 1996;Munir et al., 1998; Loesch et al., 2003b]. Studies of individualconstructs of attention in boys with fragile X demonstrateddeficits at higher levels of attention function/executive func-tioning, especially in the ability to inhibit or delay respondingand divide or switch attention [Munir et al., 2000; Cornish etal., 2001].

Females are usually less affected than males because of thepresence of a second unaffected X chromosome. Between 50%and 71% of females demonstrate a significant cognitive deficit

Grant sponsor: NICHD; Grant number: HD36071; Grant sponsor: General ClinicalResearch Centers Program, National Center for Research Resources, NIH; Grantnumber: 5MO1RR00069; Grant sponsor: Mental Retardation Research Center at theUniversity of Colorado Health Sciences Center, NICHD; Grant number: HD04024.*Correspondence to: Danuta Z. Loesch, School of Psychological Science, La TrobeUniversity, 3083 Bundoora, Victoria, Australia. E-mail:[email protected] 10 April 2003; Accepted 11 June 2003Published online in Wiley InterScience (www.interscience.wiley.com).DOI: 10.1002/mrdd.10084

MENTAL RETARDATION AND DEVELOPMENTAL DISABILITIESRESEARCH REVIEWS 10: 31–41 (2004)

© 2004 Wiley-Liss, Inc.

Page 2: PHENOTYPIC VARIATION AND FMRP L FRAGILE X · PHENOTYPIC VARIATION AND FMRP LEVELS IN FRAGILE X Danuta Z. Loesch,1** Richard M. Huggins,2 and Randi J. Hagerman3 1School of Psychological

[de Vries et al., 1996], as the unaffected Xchromosome still produces normal levelsof FMRP. It was demonstrated that, infull-mutation females, the spectrum ofcognitive impairments, especially in Per-formance IQ, was related to the X-acti-vation ratio, which represents the per-centage of cells that have the normal X asthe active X [Abrams et al., 1994; deVries et al., 1996; Riddle et al., 1998;Tassone et al., 1999]. Consistently withthese findings, our own data from a largesample of full-mutation females showedthat this ratio was highly correlated withthe FMRP levels (Loesch, unpublished),with a Spearman correlation equal to0.94 (P � 0.0001).

The more direct evidence of theprimary involvement of FMRP deple-tion in developmental delay is obtainedby relating this depletion to cognitivedeficits and physical anomalies in indi-viduals with fragile X. Since the intro-duction of the FMRP diagnosticmethod, it has been shown, using stan-dard regression, that the global intellec-tual impairment (assessed by cognitive ordevelopmental measures) is highly corre-lated with a deficit of FMRP in bloodlymphocytes, in both full-mutation malesand females [Kaufmann et al., 1999; Tas-sone et al., 1999; Bailey et al., 2001b;Dyer-Friedman et al., 2002] and in hairfollicles in females [Willemsen et al.,2003]. Functional MRI (fMRI) studieshave also demonstrated positive correla-tions between FMRP and brain meta-bolic activity in females with the fullmutation during a visuospatial workingmemory task [Kwon et al., 2001; Menonet al., 2002] and during arithmetic pro-cessing [Rivera et al., 2002]. On theother hand, FMRP has not correlatedwith behavior problems in boys, includ-ing the degree of autism [Bailey et al.,2001a; Hessl et al., 2001]; however, thiscould be related to the limited range ofFMRP in these studies. FMRP has cor-related with internalizing problems ingirls, including withdrawn and anxious/depressed behavior [Hessl et al., 2001].

Most of the FMRP studies havebeen done on small numbers of patientswithout a detailed look at the relation-ship between FMRP and broader neuro-psychologic measures. This gap has beenfilled by the 2000–2002 US–Australiancollaborative genotype–phenotype rela-tionship series of studies supported byNICHD, where the effects of FMRPdeficits on the wide range of specificcognitive and executive functioning def-icits, as well as on global intellectual im-pairment, have been investigated [Loeschet al., 2002a, 2003a, 2003b]. The rela-

tionships between FMRP levels andphysical measures have also been re-ported [Loesch et al., 2003c]. In all thesestudies, pedigree models were fitted tothe data collected from fragile X subjectsand their relatives, which allowed us toaccount for the effect of the backgroundheritable variation, thereby explainingsome of the variability of the traits ofinterest and increasing the power of thetests. Some of these studies’ results arepresented in the section titled Applica-tions of Pedigree Analysis in FMRP—Phenotype Relationship Studies throughthat titled Heritabilities, and our unpub-lished data on the relationship betweenFMRP and cognitive deficits based onstandard regression and correlations isoutlined under Correlations betweenFMRP Levels and Cognitive (Wechsler)Scores.

The data for our series of studieswere collected from a combined sampleof 144 families recruited from Australiaand United States. The Australian partic-ipants diagnosed with fragile X syn-drome, and their non-fragile X relatives,were ascertained through the registry ofpatients attending Genetic Health Ser-vices at the Royal Children’s Hospital inMelbourne. The American participantswere recruited through the Child Devel-opment Unit at the Children’s Hospitalin Denver, Colorado. There were 287individuals from 66 extended families forwhom the data on FSIQ were availablein the Australian sample and 216 individ-uals from 78 families in the Americansample. However, sample sizes weresmaller for data on specific cognitive orexecutive functioning scores, physicalmeasures, or FMRP levels. The ages ofthe participants ranged from 4 to 76years.

Fragile X status in participants fromboth investigative sites was establishedusing a specific DNA test [Taylor et al.,1994] carried out at Kimball Genetics(Denver, CO). The DNA results wereused as a diagnostic tool to classify indi-viduals into premutation, full-mutation,and non-fragile X status categories. Thesample considered in this presentationconsisted of 87 male and 58 female full-mutation subjects, 32 male and 142 fe-male premutation subjects, and 114 maleand 57 female non-fragile X relatives,although the numbers may be less forindividual traits. Because of low num-bers, two gray-zone individuals (40 to 49CGG repeats) have been included in thenormal category. Premutation/full-mu-tation mosaics, as well as unmethylatedfull mutations (approximately 20% of theaffected males), have been included in

the full-mutation category. The data onage distribution among different fragile Xstatus categories and the two investigativesites were given in Loesch et al. [2003b],where the method used to adjust for as-certainment bias was also discussed.

The cognitive testing used thestandard Wechsler scales (as in [Loesch etal., 2002a]). Executive function tests ap-plied were as described in Loesch et al.[2003b] and included the WisconsinCard Sorting Test (WCST) [Heaton etal., 1993] to assess working memory,planning, and flexibility in changing sit-uations; the Rey Complex Figure Test(RCFT) [Meyers and Meyers, 1995] toassess visuospatial memory and visuospa-tial constructional ability; and the Behav-ioural Dyscontrol Scale (BDS), whichconsists of nine items designed to test formotor planning, inhibition, and workingmemory [Grigsby and Kaye, 1996].Physical (anthropometric) traits includedstandard measures of the head, face, trunkand limbs as previously described [Loeschet al., 1988, 2003c].

FMRP VARIATIONFMRP assays were conducted on

blood smears, which were made within24 h of blood draw as previously de-scribed in Willemsen et al. [1995]; Tas-sone et al. [1999], and Loesch et al.[2002b]. FMRP level is expressed as thepercentage of lymphocytes that are posi-tive in staining for FMRP using immu-nocytochemical techniques [Tassone etal., 1999].

The composition of the sampleswas such that the largest number of maleindividuals were in the full-mutation cat-egory, with FMRP levels �10%, and thelargest number of female individualswere in the premutation category, withFMRP levels � 85%. Sixteen individualswith partially methylated/unmethylatedfull-mutation or premutation/full-muta-tion mosaicism provided intermediateFMRP levels in the male sample, whichwas important in achieving an adequatecontinuity of distribution of this measure.

CORRELATIONS BETWEENFMRP LEVELS AND COGNITIVE(WECHSLER) SCORES

Simple correlation and regressionmethods (that ignore familial depen-dence) were used in exploratory analysesto examine trends in the data. Scatter-plots and curvilinear (males) and linear(females) regression lines shown in Figure1 were obtained by using the best fittingregression models to describe the rela-tionship between FSIQ score and FMRPlevels in the sample of 117 fragile X males

32 MRDD RESEARCH REVIEWS ● PHENOTYPIC VARIATION AND FMRP LEVELS ● LOESCH ET AL.

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(a) and 173 fragile X females (b), with thepremutation and full-mutation categoriescombined.

There are too few observations ofmales with FMRP levels between 20%and 60% (Fig. 1a), and there is a consid-erable variation around the fitted regres-sion line in females, especially for FMRPvalues �40 (Fig. 1b). Outliers are appar-ent in both the male and female samples,but there is also some reduction in thevariability for FMRP levels (�60% inmales and �40% in females). The regres-sion of FSIQ on FMRP in males fits boththe linear and curvilinear models, al-though the latter shows a slightly betterfit (see R2 in legend for Fig 1a). Thisregression in females fits a linear model,where, consistently with earlier predic-tions [Reiss et al., 1995], FMRP changesaccount for only a small percentage ofvariance in FSIQ, because of a modifyingeffect of the second normal X chromo-some of a pair. The sample of premuta-tion females is sufficiently large to showthat the FMRP level of �80% marks thecessation of an association between theintellectual impairment and protein def-icits. Beyond this threshold there is awide spread of FSIQ scores, which areapproximately normally distributed, asshould be expected from the combinedeffect of background genes and smooth-ing environmental effects. A similar trendas shown for FSIQ was evident for bothPerformance and Verbal IQ. But for thesubtests scores the variation around thefitted line was usually larger; Digit Spanshowed the smallest and Object Assem-bly, Picture Completion and Similaritiesshowed the greatest variation.

The results of a simple regression/correlation in the full-mutation males(Table 1a) show that the contribution ofFMRP deficit to the total variance of therespective summary and subtest scores(R2) varies from a high of 59% (for Pro-cessing Speed and Digit Span) to a low of19% (for Object Assembly). In the full-mutation females (Table 1b), the contri-bution of FMRP to the variance of cog-nitive scores is predictably lower, withR2 not exceeding 16.5%. A linear regres-sion was applied in both male and femalesamples as the most appropriate model todescribe relationships between FMRPlevels and cognitive scores. Because ofextensive variability characteristic of frag-ile X data, we have also used Spearmancorrelations that, unlike simple regres-sion, are resistant to outliers. For exam-ple, in Table 1a the regression for ObjectAssembly in males was significant, butthe Spearman correlation was not, whichmay reflect the relatively lowest internal

consistency and reliability of this testamong the WAIS-III subtests. Thegreater variability of the scores for ObjectAssembly may also account for the lowR2 value shown in the same table. Butthe majority of results of regression listedin Table 1a and 1b are consistent with thevalues of the Spearman correlations.

It was of interest to determinewhether the effect of FMRP on the var-ious summary and subtest of scores wasdue to factors beyond the decline inFSIQ. After we adjusted the individualsummary and subtest scores in males forFSIQ, as well as for FMRP, in simpleregressions, the FMRP levels were notsignificantly related to any of thesescores, except Digit Span and SymbolSearch (results not shown).

APPLICATION OF PEDIGREEANALYSIS INFMRP–PHENOTYPERELATIONSHIP STUDIES

Why Use Pedigree Analysis?The variability of both phenotypic

expression and FMRP levels betweenfragile X individuals is caused by the un-stable nature of the mutation in theFMR1 gene and the background herita-ble variation of the phenotypic traits.However, common statistical proceduresbased on unrelated samples do not ac-count for this latter source of variation. Amore efficient maximum-likelihoodanalysis in pedigrees, where the meansand covariance structure are simulta-neously estimated from pedigree data,

Fig. 1. Scatterplots of FSIQ on FMRP levels for fragile X premutation and full-mutation males (a)and females (b). For females, both regression parameters were highly significant (P � 0.001 andR2 � 28.8%). For males, both parameters were highly significant in linear regression (P � 0.001),and in polynomial regression, all except the second parameter in the regression model above weresignificant (P � 0.01), but R2 was slightly higher (73.0% for linear compared with 74.6%, forpolynomial model).

33MRDD RESEARCH REVIEWS ● PHENOTYPIC VARIATION AND FMRP LEVELS ● LOESCH ET AL.

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was used in our first study of genotype–phenotype relationships in fragile X[Loesch et al., 1993]. This approach,originally developed by Lange, Westlake,and Spence [Lange et al., 1976], allowsone to control for the normal heritablevariation in any phenotypic measure andthus to reduce the unexplained trait vari-ability.

Another advantage of this ap-proach is that it addresses the problem ofascertainment bias. There were differ-ences between the American and Austra-lian samples in the ratio of the premuta-tion to full-mutation subjects in both

sexes, with a greater number of premu-tation to full mutation subjects andsmaller family size in the former com-pared with the latter sample. This reflectsdifferences in the follow-up of ascer-tained families between the two samples,with more extensive cascade testing con-ducted in Australia. However, the pro-bands were selected for this studythrough clinical admissions based ontheir overall neurocognitive impairment(FSIQ), so that the other traits underinvestigation were not directly relevantto ascertainment. To adjust for the ascer-tainment bias we conditioned on the

FSIQ score by including FSIQ as an ex-planatory variable in the pedigree models[Thompson, 1993]. Moreover, each in-dividual’s IQ was conditioned on thismeasure in this individual’s relatives.These procedures served as an adjustmentnot only for ascertainment bias but alsofor the differences in ascertainment be-tween the Australian and American sam-ples.

However, an important drawbackof the maximum-likelihood approachwas that it did not fully address the prob-lem of extreme (outlying) observationsoccurring because of the highly variable

Table 1. Results of Simple Linear Regression of the Wechsler Summary and Subtest Scores onFMRP Levels, and Non-parametric Spearman Correlation Coefficients between These Scores and

FMRP in the Combined Sample of Full Mutation Males and Females

Wechsler variables

Males

n Intercept (P-value) Gradient (P-value) R2 Spearman (P-value)

Full Scale IQ 68 44.99 (�0.001) 0.528 (�0.001) 0.522 0.509 (�0.001)Perceptual Organization 61 53.39 (�0.001) 0.450 (�0.001) 0.414 0.476 (�0.001)Processing Speed 56 50.71 (�0.001) 0.487 (�0.001) 0.587 0.606 (�0.001)Verbal Comprehension 61 53.42 (�0.001) 0.376 (�0.001) 0.264 0.396 (0.002)Performance IQ 68 49.52 (�0.001) 0.477 (�0.001) 0.499 0.474 (�0.001)Block Design 67 1.444 (�0.001) 0.091 (�0.001) 0.385 0.322 (0.008)Coding 55 0.772 (0.001) 0.067 (�0.001) 0.561 0.596 (�0.001)Object Assembly 61 2.507 (�0.001) 0.072 (�0.001) 0.189 0.244 (0.058)Picture Arrangement 61 1.468 (�0.001) 0.076 (�0.001) 0.433 0.408 (0.001)Picture Completion 67 2.120 (�0.001) 0.075 (�0.001) 0.244 0.307 (0.012)Symbol Search 56 0.777 (0.007) 0.078 (�0.001) 0.531 0.586 (�0.001)Verbal IQ 69 48.85 (�0.001) 0.501 (�0.001) 0.511 0.480 (�0.001)Arithmetic 67 0.578 (0.019) 0.074 (�0.001) 0.494 0.440 (�0.001)Comprehension 67 1.441 (�0.001) 0.092 (�0.001) 0.395 0.466 (�0.001)Digit Span 60 0.836 (0.001) 0.082 (�0.001) 0.586 0.589 (�0.001)Information 67 1.945 (�0.001) 0.083 (�0.001) 0.315 0.318 (0.009)Letter Number Sequencing 31 0.338 (0.464) 0.090 (�0.001) 0.571 0.692 (�0.001)Matrix Reasoning 33 2.017 (�0.001) 0.087 (�0.001) 0.497 0.444 (0.010)Similarities 67 1.371 (�0.001) 0.063 (�0.001) 0.236 0.408 (0.001)Vocabulary 64 1.594 (�0.001) 0.073 (�0.001) 0.389 0.523 (�0.001)

Wechsler variables

Females

n Intercept (P-value) Gradient (P-value) R2 Spearman (P-value)

Full Scale IQ 56 56.92 (�0.001) 0.319 (0.008) 0.123 0.311 (0.020)Perceptual Organization 49 57.00 (�0.001) 0.339 (0.004) 0.160 0.462 (0.001)Processing Speed 47 68.86 (�0.001) 0.162 (0.221) 0.033 0.171 (0.251)Verbal Comprehension 49 61.63 (�0.001) 0.286 (0.031) 0.095 0.266 (0.064)Performance IQ 56 61.86 (�0.001) 0.270 (0.014) 0.107 0.349 (0.008)Block Design 54 2.740 (0.041) 0.057 (0.007) 0.132 0.319 (0.019)Coding 43 4.770 (0.005) 0.028 (0.264) 0.030 0.166 (0.289)Object Assembly 50 3.831 (0.004) 0.044 (0.027) 0.098 0.282 (0.047)Picture Arrangement 50 1.958 (0.161) 0.064 (0.003) 0.165 0.423 (0.002)Picture Completion 54 3.881 (0.015) 0.058 (0.017) 0.105 0.273 (0.045)Symbol Search 47 3.058 (0.100) 0.038 (0.162) 0.043 0.162 (0.277)Verbal IQ 56 58.90 (�0.001) 0.311 (0.012) 0.112 0.258 (0.055)Arithmetic 54 1.605 (0.286) 0.052 (0.028) 0.090 0.297 (0.029)Comprehension 54 2.377 (0.163) 0.072 (0.007) 0.130 0.269 (0.049)Digit Span 50 2.984 (0.061) 0.055 (0.025) 0.101 0.272 (0.056)Information 54 3.661 (0.010) 0.053 (0.015) 0.109 0.253 (0.065)Letter Number Sequencing 32 5.823 (0.187) 0.016 (0.794) 0.002 0.042 (0.820)Matrix Reasoning 33 7.518 (0.023) �0.014 (0.756) 0.003 0.053 (0.770)Similarities 54 3.725 (0.033) 0.035 (0.187) 0.033 0.132 (0.340)Vocabulary 51 2.433 (0.155) 0.061 (0.021) 0.104 0.257 (0.068)

34 MRDD RESEARCH REVIEWS ● PHENOTYPIC VARIATION AND FMRP LEVELS ● LOESCH ET AL.

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expression of the fragile X disorder andmeasurement errors. To overcome thisproblem, a (robust) modification of themultivariate normal maximum-likeli-hood approach was developed [Huggins1993], which allowed the objectivedown-weighting of outliers and thusconcentrated on modeling the centralsymmetrical portion of the data. Thismodification was applied in all recentlypublished studies concerning theFMRP—phenotype relationships in frag-ile X based on pedigree data [Loesch etal., 2002a, 2002b, 2003a, 2003b, 2003c],and the results of these studies are dis-cussed in the following sections of thisarticle.

EFFECTS OF FMRP DEFICITSON PSYCHOLOGICALPHENOTYPE ASSESSED BYPEDIGREE ANALYSIS

Wechsler ScaleThe results presented in this sec-

tion were obtained in our earlier studies[Loesch et al., 2002a, 2002b], where themodels for the means and covariancestructure were defined, and the methodsof testing for significance of parametersestimated from pedigree data that repre-sent effects of FMRP deficit on individ-ual traits (P values) have been described.The P values for these parameters forFSIQ, as well as for unadjusted summaryand subtest scores, are shown in Table 2.These data are comparable with the Pvalues for the regression slope based onstandard regression presented in Table 1,because simple linear regression was con-sidered in the mean model in pedigreeanalysis, where within- and between-family variation was also accounted for inthe concurrent models for the covariancestructure. The results for males (Table 2a)show a very close similarity to the corre-sponding P values in Table 1a in that theeffect of FMRP on all summary andsubtest Wechsler scores is highly signifi-cant. The results for females confirm thesignificance of FMRP effects as shown bystandard regression in Table 1b. How-ever, the P values for the parameters forthe FMRP effect on individual scores infemales obtained from pedigree analysisare higher, and, in contrast with the datain Table 1b, this effect is significant forProcessing Speed as well. This exampleillustrates a greater power of pedigreeanalysis to detect the relationships be-tween the measures due to reduced vari-ability in the data.

After adjustment for participants’own FSIQ in pedigree analysis, the effectwas highly significant in males only for

Digit Span and Symbol Search and infemales only for Picture Arrangement[Loesch et al., 2002a]. This effect on Ob-ject Assembly and Similarities was alsosignificant in both sexes, and on Infor-mation in males only, but after a conser-vative Bonferroni-type correction formultiple comparisons, the P values were�0.05 (ibid).

The direction of the effects ofFMRP levels is best demonstrated graph-ically by using the parameters estimatedfrom pedigree models. To demonstratethe magnitude and direction of the effectsof FMRP deficits on phenotypic mea-sures adjusted for FSIQ or another ex-planatory variable, these effects werestandardized for various levels of FMRPto be the percentage deviation from theestimated mean for a normal sample, asdescribed in Loesch et al. [2002a], andthe FMRP levels considered were 10%to 90%, in increments of 40%. Thesedeviations are illustrated for FSIQ-ad-justed summary scores in Figure 2 formales (a) and females (b) and for thesubtest scores in Figure 3 for males (a)and females (b). It is remarkable that,among the summary scores, the greatesteffect of progressive FMRP deficit inboth sexes is on Processing Speed (Fig.3). Among the subtest scores, the greatesteffect is in Symbol Search in both sexes,particularly in females, in Digit Span inmales, and in Picture Arrangement infemales.

EXECUTIVE FUNCTIONINGThe scores from the three major

tests for executive functioning (WCST,RCFT, and BDS) were all significantlyaffected by the levels of FMRP [Loeschet al., 2003b]. However, for the FSIQ-adjusted measures, the effect of FMRPdepletion was significant only in lower-ing the total BDS score. When nine in-dividual BDS items’ scores adjusted forFSIQ (and age if appropriate) were ex-amined using standard logistic regression(pedigree analysis was not applicable toindividual BDS items because of categor-ical scoring), the effect of FMRP deficitwas significant in lowering performanceon items 2–7. These items are involvedin working memory, attentional control,and motor control and are represented bytapping (2 and 4) and Go-No go (3) tasksand the tests for motor procedural learn-ing (5 and 6), and echopraxia (7).

The discrepancy between the re-sults from three executive function testsmight be attributed to the finding, in thesame study [Loesch et al., 2003b], thatthe BDS score was relatively independentof FSIQ, whereas the scores from theremaining two tests (WCST, RCFT)were found to be closely correlated withthe level of the overall cognitive impair-ment. Another reason may be that only alimited number of individuals in oursample could be tested on WCST andRCFT, because of low IQ (�50), oryoung age, whereas at least 90% of fragile

Table 2. Significance of the Effects of FMRP Deficits inWechsler Summary and Subtest Scores, in Full Mutation Malesand Females, Estimated from Pedigree Analysis, with Simple

Linear Regression Considered in the Mean Model

Wechsler variables Males Females

Full Scale IQ �0.0001 0.0009Perceptual Organization �0.0001 �0.0001Processing Speed �0.0001 0.0499Verbal Comprehension �0.0001 0.0056Performance IQ �0.0001 �0.0001Block Design 0.0001 0.0002Coding �0.0001 0.1435Object Assembly �0.0001 0.0375Picture Arrangement 0.0001 �0.0001Picture Completion �0.0001 0.0190Symbol Search �0.0001 0.1147Verbal IQ �0.0001 0.0185Arithmetic �0.0001 0.0216Comprehension 0.0003 0.0093Digit Span �0.0001 0.0058Information �0.0001 0.0480Letter Number Sequencing 0.0019 0.3827Matrix Reasoning 0.0006 0.8217Similarities 0.0012 0.1234Vocabulary �0.0001 0.0037

P-values were determined using the Wald test to simultaneously test hypotheses about these effects for males or females separately, asexplained in Loesch et al. (2003b). The Wald test adjusts for the covariance between the estimates, and a chi-square distribution is used todetermine the P-values.

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X subjects were successfully tested on theBDS [Loesch et al., 2003b].

EFFECTS OF FMRP DEFICITSON PHYSICAL PHENOTYPEASSESSED BY PEDIGREEANALYSIS

The earliest study of the effect ofFMRP levels on physical phenotype as-sessed using the robust modification ofthe maximum likelihood approach basedon pedigree data concerned two der-matoglyphic measures, ridge count andridge breadth [Loesch et al., 2002b]. Inthe more recent study, a series of headand facial measurements, weight, height,2 trunk measures and 3 limb measureswere related to the FMRP deficits[Loesch et al., 2003c]. The relationshipof a gradual decrement of FMRP with

these measures encountered in the abovestudy is illustrated in Fig. 4, where theeffects of this decrement were standard-ized for various FMRP levels to becomepercentage deviation from the estimatedmeans for a normal sample, as describedin [Loesch et al., 2003c]. The parametersestimated from pedigree models, repre-senting effect of FMRP deficits, weresignificant for the majority of the mea-sures included for the two samples com-bined, with more variables affected bythese deficits in males than in females.The most evident effect in both sexes wastoward decreased body height and in-creased head height (Figs. 4a–4d) andincreased extensibility of the middle fin-ger (data shown in Loesch et al., 2003c).Moreover, in males, a significant effect ofFMRP deficit was toward decreased fa-

cial widths (represented by bizygomaticand bigonial measures) and increased earsize (height and width) and weight,whereas in females, a unique effect wastoward increased ear prominence andjaw length. Although the magnitude ofthe effect of FMRP was greater in malesthan in females, the trend illustrated inFigure 4 is very similar in both sexes andacross age groups.

HERITABILITIESThe heritability (H) is estimated as

the proportion of the genetic variance tothe total variance in a trait, and the resultswere given in our earlier publications forcognitive [Loesch et al., 2002a, 2003a,2003b] and physical [Loesch et al.,2002b, 2003c] measures.

Heritabilities of individual traits es-timated from the models considering theregression of traits on FMRP were gen-erally lower than those estimated fromother models. Predictably, the highestvalues of genetic variance/heritabilitywere for the physical measures, rangingfrom 80% to 90% for body height andlimb length, 60% to 80% for most trunkand head measures, and some facial mea-sures, with a low of 16% for the earheight [Loesch et al., 2003c]. Heritabili-ties for dermatoglyphic measures of ridgecount and ridge breadth calculated fromthe same model were 65% and 60%, re-spectively [Loesch et al., 2002b]. Forcognitive (Wechsler) scores, heritabilitesfor FSIQ, Verbal and Performance IQ,Perceptual Organization, and ProcessingSpeed were only �30%, but genetic vari-ance was significant for all the abovemeasures; for the Wechsler subtests her-itabilities were �30%, and genetic vari-ance was not significant except for Infor-mation and Vocabulary [Loesch et al.,2002a]. A similar value was obtained fora majority of executive function scores,with only two RCFT items approaching40% [Loesch et al., 2003b]. Possible rea-sons for a discrepancy between these re-sults for physical and psychological scoresinclude greater measurement error in ob-taining psychological measures comparedto physical measures, which increases thevalue of (individual) environmental vari-ance; the complex nature of psychologicalscores; and a greater contribution of non-genetic components generally. The effectof FMRP variation on covariance betweenrelatives (which has not been investigated)may also affect heritability estimates. Un-like individual environment, common en-vironmental component, which must con-siderably affect psychological scores, couldnot be separated from genetic variance inour analyses because of an insufficient

Fig. 2. Standardized percentage change in the mean values of the FSIQ-adjusted Wechslersummary scores due to FMRP deficit for various FMRP levels (10%, 50%, and 90%) in fragile X(full-mutation) male (a) and female (b) samples. The percentage change was standardized at theestimated FSIQ mean for the nonfragile relatives of fragile X subjects in our sample (from Loesch etal. J Dev Behav Pediat 2002, 23 p. 420, Fig. 1). [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

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number of distant relatives and the relativesmallness of the family sample.

SUMMARY AND IMPLICATIONSFOR FUTURE RESEARCH

The results based on standard re-gression have demonstrated a strong re-lationship of FMRP depletion in fragileX full-mutation subjects with overallcognitive deficit, as well as specific cog-nitive skills and executive functioning.Our data on FSIQ from the Australian–U.S. collaborative NIH study were con-sistent with the earlier findings of a strongrelationship between cognitive testingand FMRP levels [Kaufmann et al., 1999;Tassone et al., 1999; Bailey et al., 2001a;Dyer-Friedman et al., 2002]. Moreover,our results showed that in males all theWechsler subtests (unadjusted for FSIQ)were significantly correlated withFMRP, but in females only a few weresignificantly correlated. The earlier find-ing that arithmetic processing was signif-icantly correlated with FMRP in full-mutation fragile X females [Rivera et al.,2002] is consistent with our data forArithmetic. On the other hand, thesedata have shown that the contribution ofFMRP to the total variance of this trait infemales is only 9%, and it does not exceed16.5% for the remaining subtests.Whereas in males, this contribution is49% for Arithmetic and ranges from 19%for Object Assembly to the 59% for Pro-cessing Speed and Digit Span. A very lowcontribution of FMRP to the variance ofObject Assembly may be largely attrib-uted to the low reliability of this subtestin WAIS-III. But after adjustment ofsummary and subtest (Wechsler) scoresfor FSIQ, a deficit of FMRP no longermade significant contribution to the vari-ance of the subtests in females exceptPicture Arrangement and only for DigitSpan and Symbol Search in males.

However, as noted above, thereare some important drawbacks in usingstandard statistical analysis in genotype–phenotype relationship studies. These arerelated to ascertainment bias caused byrecruiting families through clinical ad-missions or combining the data collectedin different investigative sites, as well asto the effects of confounding factors andof interaction between these factors, inaddition to small sample sizes. Therefore,in the series of studies of the relationshipbetween the phenotype and FMRP infragile X [Loesch et al., 2002a, 2002b,2003a, 2003b, 2003c], we applied themore powerful approach based on pedi-gree data, which overcomes some of theflaws and biases of standard correlation/regression approaches. This method al-

lowed us to control for the effect of thebackground heritable variation and totest (and adjust when appropriate) forpossible confounding variables and forinteraction between these variables (suchas between FSIQ and FMRP). Althoughthe interaction between confoundingvariables is a universal problem, it is fur-ther complicated in disorders caused bydynamic mutations, where measures rep-resenting the severity of a condition mayalso interact with age. This results fromanticipation, whereby the younger gen-erations are usually more affected andhave bigger FMRP/FSIQ deficits thanthe older generations. Apart from thebenefits of the maximum likelihood ap-proach in controlling for confoundedvariables and the interactions, a robustmodification applied in our series of

studies has enabled us to objectivelydown-weight the outliers and thus toconcentrate on the analysis of the generaltrend in the data.

The results on the effect of FMRPdeficit on global intellectual impairment(FSIQ) obtained from pedigree modelsare not inconsistent either with our ownresults (in 3) or with the earlier publisheddata based on standard correlations[Kaufmann et al., 1999; Tassone et al.,1999; Bailey et al., 2001a; Dyer-Fried-man et al., 2002]. However, pedigreeanalysis is more reliable in investigatingphenotype–genotype relationships andflexible enough to test the range of hy-potheses around the confounding effects.A highly significant effect of FMRP def-icit on all the summary and subtest scoresin males and on a number of these scores

Fig. 3. Standardized percentage change in the mean values of the FSIQ-adjusted Wechslersubtest scores at serial FMRP levels in fragile X (full-mutation) male (a) and female (b) samples. Thepercentage change was standardized at the estimated FSIQ mean for the nonfragile relatives offragile X subjects in our sample (from Loesch et al. J Dev Behav Pediat 2002a, 23 p.420, Fig. 2).[Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

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in females as demonstrated by pedigreeanalysis is not unexpected, because ofstrong relationships between these scoresand FSIQ. But this approach is far moreimportant in assessing this effect on theFSIQ-adjusted scores to identify specificdeficits/strengths in fragile X, related toFMRP levels, but occurring indepen-dently of the level of an overall cognitiveimpairment.

We have identified Digit Span andSymbol Search in both sexes and PictureArrangement in females as outstandingexamples of such deficits specifically af-fected by FMRP depletion, and amongthe summary scores, Processing Speed

was also significantly impaired [Loesch etal., 2002a]. These findings suggest thatthe brain processes, which may be pri-marily affected by a deficit of FMRP,especially in males, are processing speed,short-term memory, and attention. Inour data Processing Speed (which iscomposed of Symbol Search and Cod-ing) was affected by FMRP deficit irre-spective of the overall IQ, along withSymbol Search and Coding, and short-term memory was mainly involved inSymbol Search and Digit Span tasks [Sat-tler 1992; Guerreiro et al., 1998]. Atten-tion is also involved in performance onthese tasks, as well as on Picture Arrange-

ment, which was specifically affected byFMRP deficits. Decrements in process-ing of sequential information and atten-tion skills have been found in previousstudies of full-mutation males [Freundand Reiss 1991; Munir et al., 2000]. Ourfindings on the effect of FMRP on ex-ecutive function tests are not inconsistentwith the argument that attention may beone of the processes primarily affected bya deficit of FMRP. A progressive FMRPdepletion significantly reduced theFSIQ-adjusted total BDS score, as well asa number of individual item scores[Loesch et al., 2003b], which mainly testfor the ability of controlling attention,especially in the context of regulatinggoal-directed behavior. On the otherhand, the claim that processing speed,memory, and attention are primarily af-fected by FMRP deficit is not incompat-ible with experimental evidence of theinvolvement of this protein in develop-ing and shaping up brain synapses[Weiler et al., 1997; Weiler andGreenough 1999; Irwin et al., 2002].

Although the gender differences inseverity of the effect of FMRP depletionon both summary and subtest IQ scoresare evident from the data presented, thedifferences in the degree of impairmenton certain subtest scores are difficult tointerpret, because we have conducted nocomparative analyses of cognitive profilesaffected by FMRP deficit in either sex.The results so far indicate the effect ofFMRP depletion is predominantly onprocessing speed, memory, and attentionin both sexes but that visuospatial defectsmay be more strongly manifested in fe-males than in the males irrespective oftheir overall IQ levels.

The above conclusions refer to theresults from a sample of full-mutationsubjects. However, in the most recentstudy [Loesch et al., 2003a] a significanteffect of FMRP deficit on a number ofCognitive (Wechsler) scores, includingFSIQ, and Performance and Verbal IQwas demonstrated in premutation males,which supports rare findings of a subtlereduction of FMRP levels in these carri-ers [Tassone et al., 2000a; Tassone et al.,2000b; Hagerman et al., 2001; Kennesonet al., 2001]. In addition to the impact ofalleged FMRP deficit on cognitive de-velopment, there may be other mecha-nisms in fragile X premutation carrierscontributing to some specific cognitivedeficits, such as in arithmetic skills [Loe-sch et al., 2003a]. The elevated mRNAlevels in those with the premutation mayhave a toxic gain-of-function effect onthe brain [Tassone et al., 2000a; Hager-

Fig. 4. Effect sizes representing the percentage change due to FMRP for various FMRP levels(10%, 50%, and 90%) for the age-adjusted physical measures (threshold model) in the fragile Xsample of males (a and b) and females (c and d). These effects were estimated at the threshold agefor each trait. The values are standardized and plotted separately for the “young” subjects locatedbelow the estimated individual threshold values for males (a) and females (c), and for “adult”subjects above the threshold values for males (b) and females (d). (from Loesch et al. Am J MedGenet 2003, Fig. 2). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

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man and Hagerman 2002; Jacquemont etal., 2003].

Although the impairment in over-all cognitive functioning, as well as somespecific skills, can be explained simply bythe detrimental effect of FMRP deple-tion on brain development, the underly-ing mechanisms leading to a physical de-fect in fragile X full mutation is morecomplex and difficult to interpret in con-text with FMRP deficit. Demonstrationof (linear) effects of progressively reducedlevels of FMRP in fragile X subjects on anumber of physical measurements,mainly of trunk, limbs, and head, whichwas in a direction consistent with thefragile X physical phenotype, has been animportant step toward understandingthese mechanisms. It has been suggested[Loesch et al., 2003c] that they may berelevant to hypothalamic dysfunctioncaused by reduced synaptic contacts be-cause of immaturity of dendritic spines[Comery et al., 1997; Weiler andGreenough 1999]. Earlier data on thegrowth pattern in fragile X [Loesch et al.,1995] imply that this dysfunction maycause premature increase in the pulsatilesecretion of GnRH, followed by prema-ture secretion of high doses of estrogen,thus leading to earlier epiphyseal matura-tion. The FMRP-related increase in headheight might reflect an increased brainsize, which is most prominent in thefrontal lobe and also relevant to synapticdysmorphology [Reiss et al., 2000].

An important finding in the Loeschet al. [2003c] study concerned a signifi-cant effect of FMRP deficit in extensi-bility of finger joints, which may indicatea direct association of this protein with aconnective tissue disorder in fragile X[Opitz et al., 1984; Riddle et al., 1998].Because FMRP is known to play a rolein mRNA transport and translation[Corbin et al., 1997], it was postulated[Loesch et al., 2003c] that the deficit orabsence of this protein during develop-ment may cause a cascade alterationtranslation of different mRNAs, such asthe ones involved in the connective tis-sue morphology and function.

Although using advanced analyticalmethods and large samples allows impor-tant information on the effects of FMRPdecrement on both psychological andphysical phenotype to be obtained, theanalysis is most effective in full-mutationsubjects, where the FMRP levels aredrastically reduced, and the relationshipsof this deficit with the phenotype arestrong. But the results of the analysis aremore difficult to interpret if the FMRPdeficit is small or controversial, such as inthe premutation carriers [Tassone et al.,

2000b; Kenneson et al., 2001]. This ispartly because inferences concerning def-icits of this protein in the brain have beenmade from the data from peripheralblood lymphocytes, irrespective of thesuggested differences in FMR1 muta-tional patterns across different tissues(e.g., [Taylor et al., 1994; AllinghamHawkins et al., 1996; Dobkin et al.,1996; Maddalena et al., 1996]). Indeed,the recent study [Willemsen et al., 2003]that related the IQ score to FMRP levelsin hair root cells (originating from thesame germ layer as brain tissue) in fragileX females reported a higher correlationbetween these traits (r � 0.61) than thiscorrelation obtained from our data (r �0.31 in Table 2). However, the IQ scoreswere not directly comparable betweenthese two studies, and the scatterplot pre-sented in Willemsen et al. [2003] showsgreater variability, including the presenceof outliers, which may have affected theircorrelation results. Irrespective of thechoice of biopsy tissue, the FMRP scorerepresents the level assessed only at onetime point, and thus provides no data onthis level during development. But mostimportantly, the existing method doesnot constitute an assessment of the actuallevel of this protein in each cell, but onlyscores the proportion of FMRP-express-ing lymphocytes among all lymphocytescounted. Therefore, this assay is not sen-sitive to mild deficits of FMRP and maynot recognize all the isoforms of FMRP.Clearly, a test that permits the rapid, ex-tremely sensitive, and specific measure-

ment of FMRP levels, and that recog-nizes small level changes, needs to bedeveloped; such a test and would thus bemore appropriate to assess the effect of asmall deficit of this protein on the phe-notype of individuals carrying smallerCGG expansions.

The lack of FMRP data over thewhole 0–100 range and the floor effect inthe IQ scores are sources of difficulty instatistical modeling. To overcome thisproblem, the sample sizes should be fur-ther increased and the most seriously af-fected individuals should be scored usingtests that are better able to discriminateamong low-functioning individuals. Thiswill enable various curvilinear andthreshold models to be fitted, and a largernumber of explanatory variables to beincluded, to assess the effect of FMRPdeficits on individual traits more accu-rately. Nonparametric methods that al-low more flexible models without theneed to specify a particular parametricform are becoming common in manyareas of statistics. There is clearly a needfor the development of robust nonpara-metric approach that extend the clustereddata methods of Lin and Carroll [2000] topedigree data. For example, some pre-liminary results concerning the nonpara-metric estimation of the FMRP/FSIQrelationship in males and females aregiven in Figure 5. The nonparametricestimate is consistent with the curvilinearmodel for males shown in Figure 1, butfor females the modifying effect of thesecond chromosome (which introduces

Fig. 5. Separate plots of the mean functions for males and females (full-mutation, premutationand non-fragile X relatives combined) using nonparametric estimates of the mean function.

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heterogeneity) is revealed as a distur-bance in the 40–60 FMRP range. Thisinteraction between the development ofstate-of-the-art statistical procedures andthe new data arising in molecular genet-ics in general and genotype–phenotyperelationships in particular, following fromthe previous developments of pedigreeand robust methods, is an exciting andpromising area of multidisciplinary re-search. f

ACKNOWLEDGMENTSWe extend special thanks to Dr.

Annette Taylor, who conducted allDNA and FMRP testing, and to Dr.Jennifer Epstein, Dr. Rebecca Wilson,and Emma Butler, who performed psy-chological assessment in the subjects in-cluded in our studies. We also thank allthe families participating in this study.

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