Vol. 16 nº 1 - Jan/Feb/Mar de 2022
Original Article Pages 105 to 114

Working memory and arithmetic impairments in children with FMR1 premutation and gray zone alleles
Dificuldades na memória de trabalho e na aritmética em escolares com pré-mutações ou alelos da zona cinzenta do gene FMR1

Authors: Aline Aparecida Silva Martins1,2; Giulia Moreira Paiva3,4; Carolina Guimarães Ramos Matosinho1,2; Elisângela Monteiro Coser5; Pablo Augusto de Souza Fonseca1,2; Vitor Geraldi Haase3,4,6,7,8; Maria Raquel Santos Carvalho1,2


Descriptors: Learning; Dyscalculia; Working Memory, FMR1.
Aprendizagem; Discalculia; Memória de Trabalho; FMR1.

Expansive mutations in familial mental retardation 1 (FMR1) gene have been associated with different phenotypes. Full mutations are associated with intellectual disability and autism spectrum disorder; premutations are associated with math learning difficulties and working memory impairments. In gray zone, neuropsychological development has not yet been described.
OBJECTIVES: This study aimed to describe the frequency of FMR1 premutation and gray zone alleles in a school population sample representing a broad spectrum of variation in math achievement and detail school achievement and cognitive performance in the children identified with FMR1 premutation or gray zone alleles.
METHODS: We described a two-phase study. In the first phase, 2,195 school-age children were screened for math achievement. In the second phase, 378 children with normal intelligence were neuropsychologically assessed and genotyped for FMR1. Of these, 121 children (61 girls) performed below percentile 25 in mathematics (MD group) and 257 children (146 girls) performed above percentile 25 (control group).
RESULTS: Four pupils presented expanded alleles, one premutation and three gray zone alleles. The girl with the premutation and one boy with a gray zone allele presented impairments in working memory and arithmetic performance below percentile 6, compatible with the diagnosis of developmental dyscalculia. These children�?Ts difficulties were not associated with inaccuracy of nonsymbolic number representations or literacy impairments. Dyscalculia in these children seems to be associated mainly with working memory impairments.
CONCLUSIONS: FMR1 expansions in the gray zone may contribute to dyscalculia in otherwise healthy and normally intelligent children.

Mutações expansivas no gene FMR1 têm sido associadas a diferentes fenótipos. Mutações completas estão associadas a deficiência intelectual e transtorno do espectro do autismo; pré-mutações, com dificuldades de aprendizagem de matemática e comprometimentos de memória de trabalho. Na zona cinzenta o desenvolvimento neuropsicológico ainda não foi descrito.
OBJETIVOS: Descrever a frequência de alelos pré-mutados e zona cinzenta em uma amostra escolar que representa amplo espectro de variação do desempenho em Matemática e detalhar o desempenho escolar e cognitivo em crianças identificadas com alelos pré-mutados ou zona cinzenta.
M�%TODOS: Aqui, descrevemos um estudo de duas fases. Na primeira fase, 2.195 crianças em idade escolar foram selecionadas para desempenho em Matemática. Na segunda fase, 378 crianças com inteligência normal foram avaliadas neuropsicologicamente e, em seguida, por genotipagem FMR1.
RESULTADOS: Tiveram desempenho abaixo do percentil 25 em Matemática (grupo DM) 121 crianças (61 meninas), e tiveram desempenho acima do percentil 25 (grupo controle) 257 crianças (146 meninas). Quatro alunos apresentaram alelos expandidos, sendo uma pré-mutação e três alelos da zona cinza. A menina com a pré-mutação e um menino com o alelo da zona cinza apresentaram prejuízos na memória de trabalho e desempenho aritmético abaixo do percentil 6, compatíveis com o diagnóstico de discalculia do desenvolvimento. As dificuldades dessas crianças não foram associadas à imprecisão de representações não simbólicas de números ou deficiências de alfabetização. A discalculia nessas crianças parece estar associada principalmente a deficiências da memória de trabalho.
CONCLUS�ES: Em conclusão, expansões na zona cinzenta do FMR1 podem contribuir para a discalculia em crianças saudáveis com inteligência normal.


Difficulties with math learning are associated with poor psychosocial outcomes, such as lower wages, unemployment, and externalizing and internalizing psychopathology1. Problems with math learning are characterized as dyscalculia, when the performance in standardized tests is below the percentile rank 5 (PR5), and as Math difficulties (MD) when the performance is below PR252. Prevalence rates correspond to the cutoff scores used3. Evidence for a genetic component in dyscalculia and MD stems from familial aggregation and twin studies indicating heritability in the 40â?"60% range, as well as from associated molecular-genetic markers4. In addition, dyscalculia is part of the phenotype of some genetic conditions, including typical and atypical 22q11.2DS, Williams-Beuren and Turner syndromes, and neurofibromatosis type 15.

Dyscalculia was also described in clinical samples of persons having a premutation in the familial mental retardation 1 (FMR1) gene6. Normally, this gene contains a CGG repetitive element on its 5ʹ-untranslated region (5â?T-UTR). This CGG repeat is polymorphic, and according to the number of CGGs, the FMR1 gene presents four allelic classes: normal (6â?"44 CGG), gray zone (45â?"54 CGG), premutation (55â?"199 CGG), and full mutation alleles (>200 CGG)7. In some studies, the range between 41 and 54 CGG repeats was considered an expanded gray zone8.

FMR1 mutations have been associated with several phenotypes. FMR1 full mutations cause the fragile X syndrome (FXS), which is characterized by intellectual disability and working memory (WM) deficits in boys, and borderline to normal IQ and autism associated with obesity from the second decade of life on in girls9. FMR1 premutations have been associated with FXTAS, premature ovarian failure (POF), and Parkinsonâ?Ts disease10. Individuals with premutation may have deficits in cognitive functions such as processing speed, WM, executive functions, phonological, visuospatial processing, numerical magnitude comparison, long-term memory, and learning deficits11-16. Boys with premutation present higher rates of attention deficit/hyperactivity disorder, autism spectrum disorder, and intellectual disability17. Girls with a premutation allele may also have difficulties in basic numeric processing and arithmetic such as enumeration, numerical transcoding, and calculation, similar to those observed in dyscalculia6,18,19. Additionally, adults may have psychiatric problems, such as anxiety and depression20. Individuals with gray zone alleles are usually asymptomatic, but may present impairments in short-term memory and WM. In addition, dyslexia has been reported in two males with gray zone alleles in a family study21. However, to the best of our knowledge, there are no data in the literature associating gray zone alleles with developmental dyscalculia or MD.

Typically, studies reporting learning difficulties in children with premutations and gray zone alleles are based on clinical samples. Such studies tend to capture most prominent phenotypes and may not represent the spectrum of phenotypic variations present in the general population. School samples are less prone to such biases. However, no study has investigated the contribution of FMR1 premutation or gray zone alleles to dyscalculia in population samples of school-age children using a detailed neuropsychological assessment. Here, we described the frequency of FMR1 premutation and gray zone alleles in a school population sample representing a broad spectrum of variation in math achievement. The school achievement and cognitive performance was further detailed in the children identified with FMR1 premutation or gray zone alleles.


Bioethical approach

The study complied with the Helsinki guidelines for research with human participants and was previously approved by the ethics board of the Universidade Federal de Minas Gerais (COEP-UFMG). Informed consent was obtained in written form from parents/guardians and orally from children.


Data were obtained from a demographically based sample of children from 6 to 14 years attending public schools in Belo Horizonte, Brazil. Initially, 2,195 children participated in a screening phase, responding to group-administered tests of intelligence and school achievement (Table 1). Children with intelligence above PR15 were invited to participate in a second phase of individual neuropsychological assessment, using the following exclusion criteria: gemelarity, chronic diseases (e.g., diabetes, sickle cell anemia, and epilepsy), autism spectrum disorder, monogenic or chromosomal genetic syndromes, and maternal alcohol/drug use during pregnancy. A total of 378 pupils participated in the second phase of the study and were genotyped for the FMR1 CGG repeat.

Performance in the Arithmetic subscale of the Brazilian School Achievement Test (TDE)22 allowed to classify participants into a group of broadly defined MD with performance below PR25 and a control group with performance at above PR25. In the second phase, stricter diagnostic criteria (PR<6â?"7) informed by the individual neuropsychological assessment were applied to classify math achievement.

A total of 378 children completed both phases of the neuropsychological evaluation, 121 children (61 girls) were identified as having MD. To the control group were assigned 257 children (146 girls).


Neuropsychological testing was conducted at the schools by specially trained psychology research assistants. Tests were applied in groups in the first phase and individually in the second phase. The neuropsychological protocol is shown in Table 2. A few additional tasks were applied in individuals with FMR1 expanded alleles.

FMR1 genotyping

Genomic DNA was extracted from peripheral blood or saliva samples, using a salting out protocol29. Genotyping of the FMR1 CGG repeats was performed using the AmplideX FMR1 PCR Reagents RUO Kit (Asuragen, EUA). This method allows accurate identification of expanded FMR1 alleles30,31. Polymerase chain reaction (PCR) products were separated using an ABI 3730 DNA Analyser (Thermo Fisher Scientific, USA). Profiles were evaluated using the GeneMarker version 2.6.2 software (SoftGenetics, USA). FMR1 genotyping was repeated to confirm results, when gray zone, premutation, or full mutation alleles were detected.

Statistical analyses

Frequencies of gray zone and premutation alleles in the MD and control groups were compared using the Fisherâ?Ts exact test. Neuropsychological results of each individual with expanded FMR1 alleles were compared to those of subgroups of controls, referred to as comparison groups, controlling for sex, age, school grade, and socioeconomic status. The z metric was chosen for comparisons, with a cutoff of normality at z=-1.5 (PR6â?"PR7)32.


FMR1 genotypes

The results of the FMR1 genotyping for the 378 participants on the individual neuropsychological assessment are shown in Table 3.

One premutation allele was detected in a girl from the MD group (1:61 considering only girls and 1:121 considering boys and girls). Three children presented alleles in the gray zone: one boy and one girl in the control group (1:111 and 1:146, respectively) and one boy in the MD group (1:60 considering boys and 1:121 considering boys and girls). In addition, four children in the control group (4:146) presented alleles with 41â?"44 CGG, which belong to the expanded gray zone range (Table 3). These four children have normal results in the neuropsychological assessment and will not be further discussed. The most frequent allele had 30 CGG repeats, except for the boys in the MD group for whom the 31 CGG repeat allele was the most frequent (Supplementary Figures 1â?"4). As expected, considering the inclusion criteria of intelligence above PR15, no FMR1 full mutations were observed.

Neuropsychological performance of children with expanded FMR1 alleles

Quantitative results of the neuropsychological performance of each child with a premutation or a gray zone expanded FMR1 allele are presented in Figure 1. Table 4 presents descriptions of the neuropsychological phenotypes for each child.

Figure 1. Neuropsychological performance of the children with FMR1 premutation and gray zone alleles. (A) Child 1 (premutation); (B) Child 2; (C) Child 3; (D) Child 4. Deficits in individual tests were assumed when scores < or = -1.5 SD (PR6â?"PR7).
w: internal Weber fraction in nonsymbolic number comparisons; Raven CPM: Ravenâ?Ts Coloured Progressive Matrices.


The investigated hypothesis was that dyscalculia is a phenotype associated with expanded FMR1 alleles in demographically recruited school-age children. In a sample of 378 children with normal intelligence and no chronic disease and/or neurodevelopmental disorder, 4 children were identified as having expanded FMR1 alleles. Here, we compared the observed frequencies of the premutation and gray zone alleles with those described in the literature and describe the neuropsychological profiles of these children.

Frequency of FMR1 premutation or gray zone alleles in the sample

Our first question was whether the frequency of premutation or gray zone alleles was similar to that described in the literature. In samples of persons with intellectual disability, the contribution of FMR1 full mutations has been estimated to be 1â?"6%33,34. The frequency of FMR1 full mutations was estimated to be approximately 1:5000 in a screening sample composed of over 36,000 newborn males35. Therefore, having an FMR1 full mutation entails a risk for intellectual disability that is 50â?"300 times higher than the risk in the general population. Considering the exclusion criteria implemented here and the sample size, we did not expect to identify any FMR1 full mutations in the current sample.

Our focus was on the contribution of FMR1 premutation or gray zone alleles for learning difficulties and related phenotypes. In the literature, the frequency of premutation and gray zone alleles was investigated in a sample composed of approximately 20,000 male and female adults representing the general population36. According to this study, the frequency of premutation in females was 1:148 and that in males was 1:290; the frequency of gray zone alleles (45â?"54 repeats) was 1:33 females and 1:62 males; and the frequency of “expanded” gray zone alleles (here defined as 41â?"54 CGG repeats) was 1:14 females and 1:22 males. In the current sample, the frequency of premutation, gray zone, and expanded gray zone alleles did not statistically differ from these values (results not shown).

Neuropsychological impairments in demographically sampled cases of FMR1 premutation and gray zone alleles

The second question was whether children sampled from the general population and identified with premutation, gray zone, or expanded gray zone alleles also have a neuropsychological profile resembling that described for some children from families in which FXS segregates, having similar alleles19. Two individuals were identified with performance below the PR6â?"PR7 in WM and arithmetic tasks. One child had a premutation and the another a gray zone allele. Both had normal intelligence and normal written language processing as assessed by word spelling, which excluded concomitant intellectual disability or a literacy acquisition disorder. In Child 1, phonological WM (Digit span backward) was below the cutoff score and spatial WM (Corsi blocks span backward) was in the lower normal range (1 SD below the average). The performance of Child 2 was at or below the cutoff in both phonological and spatial WM.

Both children also presented impairments in arithmetic abilities. Child 1 performed below the cutoff score in single-digit subtraction and more than 1 SD below the average in the other calculation tasks. Child 2 performed below the cutoff score for all single-digit operations. It is remarkable that these children presented difficulties with very basic arithmetic skills acquired in the first 3 years of schooling. It is also noteworthy that both the accuracy of nonsymbolic numerical representations (w) and number reading and writing were normal in these two children. This indicates impaired calculation together with spared number processing.

Math learning difficulties of varying degrees of severity have been reported in persons having premutations in families with FXS19. However, clinical samples tend to include more severe cases and to overestimate both the frequency and the impact of the difficulties. A possible solution to avoid such biases is to identify cases among the school population. Two studies have investigated the frequency of FMR1 premutations and gray zone alleles in school-age children37,38. In the study by Murray and colleagues37, boys were identified in the schools by teachers or principals due to learning disability and no specific neuropsychological evaluation was conducted. In the study by Mazzocco and colleagues38, children who were identified in pediatric or developmental neuropsychology facilities as having normal intelligence and learning disabilities were screened for FMR1 premutations and gray zone alleles. Neither of these screening studies specifically assessed WM and numerical/arithmetic abilities. Both studies may have included individuals with borderline intelligence or intellectual disability.

Diagnosis of developmental dyscalculia

In both participants with expanded FMR1 alleles (Child 1 and Child 2), performance in the single-digit calculation tasks was below the PR6â?"PR7. Both children also presented clinical evidence of impairments in very basic math-related school abilities. Qualitatively, both children had difficulty in understanding the concepts underlying the operations and used immature strategies, such as finger counting, to solve the most basic single-digit calculations. Thus, a diagnosis of developmental dyscalculia is justifiable according to the current nosological standard3.

Cognitive mechanisms underlying math learning difficulties

Five main cognitive mechanisms have been proposed to explain difficulties in learning math in cases of developmental dyscalculia: (a) inaccurate nonsymbolic numerical magnitude representations in an approximate number system (ANS); (b) deficits in the access to nonsymbolic numerical representations from symbolic ones; (c) phonological processing deficits associated with developmental dyslexia; (d) visuospatial/visuoconstructional processing deficits associated with nonverbal learning disability; and (e) working memory/executive function impairments5. These cognitive mechanisms may be interpreted as endophenotypes in different combinations in children with dyscalculia, a heterogeneous condition, often occurring with developmental dyscalculia, attention deficit disorder, and other conditions5.

In this present study, neuropsychological results excluded impairments in written language and phonological processing in the two children with expanded FMR1 alleles and dyscalculia. None of these two children presented difficulties with the accuracy of or access to nonsymbolic numerical representations. These results exclude a role for phonological and nonsymbolic numerical processing in their difficulties. Their difficulties were otherwise associated with impairments of both verbal and visuospatial WM.

The literature on females with FXS has disclosed an uneven cognitive profile of assets (verbal memory and analytic visual perception) and deficits (visuospatial and executive function)39. Other evidence indicates spared number reading/writing and rote counting abilities with deficits in magnitude judgments, mental number line judgments, understanding of counting principles, and basic addition in FXS girls40,41.

There are reports of individuals with FMR1 premutation presenting deficits in cognitive functions such as WM, executive function, visuospatial perception, phonological processing, and reaction time16,42,43. Females with a premutation allele may present difficulties in basic numerical comprehension and numerical transcoding of mathematical questions and calculations6,18,19. It is remarkable, however, that the impairments described in premutation alleles are usually of lesser severity than required for the diagnosis of developmental dyscalculia.

Considering this literature, our neuropsychological results suggest that (a) WM impairments in individuals having FMR1 expansions may play a role in difficulties learning math, as it has been previously reported; (b) accuracy of nonsymbolic numerical representations is normal in at least a subgroup of individuals with FMR1 mutations; and (c) neuropsychological impairments are observed not only in FXS and premutation alleles but also, as described here, in individuals with gray zone alleles.

Our results must be cautiously interpreted. One limitation is the number of individuals having FMR1 abnormal alleles detected. From the 2,195 children taking part in the initial population screening phase, 328 concluded the second phase of the study and, among these, only 4 had FMR1 alleles in the abnormal range. These numbers seem small, reflecting the complexities underlying a population design necessary to detect FMR1 expansions (due to their low frequency) and dyscalculia (due to the wide range of tests needed to diagnose it). However, it is important to highlight that the neuropsychological profile presented by these two children is typically seen in association with FMR1 premutations, suggesting that the presence of developmental dyscalculia is not a fortuitous finding. The exclusion of low and borderline intelligence may have removed children with full mutations from the sample. However, the focus here was actually to ascertain children with normal intelligence and MD.

Child 1, a girl with a 57 CGG premutation, was the single individual identified with an FMR1 premutation in our sample and she also presented developmental dyscalculia. According to the literature, these math difficulties should be expected only in individuals with more than 100 CGG repeats11,18,44. However, Lachiewicz and colleagues6 reported that girls with premutation alleles around 80â?"88 CGG repeats have lower arithmetic performance than women with alleles greater than 100 CGG repeats. The findings from Lachiewicz and coworkers and this study suggest that the typical neuropsychological profile may be present in the premutation range, independent of the number of CGG repeats.

Child 2, a boy with a 46 CGG gray zone allele was identified as having developmental dyscalculia. The other two children with gray zone alleles, as well as the four children with alleles in the 41â?"44 CGG range, had typical neuropsychological performance. Although other studies have investigated the contribution of FMR1 full mutation and premutation alleles to MD, this is the first study to investigate their contribution in a sample of school-age children undergoing a detailed neuropsychological and cognitive-numerical assessment. We provided evidence that gray zone alleles may occur in individuals with normal neuropsychological profiles; whereas other individuals with gray zone or premutation alleles display specific neuropsychological deficits, characterized by low performance in WM and low math achievement, corresponding to a diagnosis of developmental dyscalculia. This suggests that other factors, in addition to the gray zone alleles, must be present to cause the developmental difficulties in learning math for these children.

The finding that two out of four children with an FMR1 premutation and gray zone allele presented developmental dyscalculia associated with WM impairments suggests this is an important phenotype in FMR1 expansions. In contrast, the frequency observed in this study, two children with abnormal FMR1 alleles out of 121 children with MD, suggests that this gene makes an important contribution to MD and developmental dyscalculia. As impairments in WM were the most salient finding, it also suggests that WM impairment is an important endophenotype of developmental dyscalculia. Indeed, FMR1 provides one of the larger contributions of a single gene to the dyscalculia phenotype reported so far. Similar findings have been previously reported38. A genetic contribution to MD has also been reported for 22q11.2 deletion syndromes45,46. Most importantly, our data suggest that even minor alterations of the FMR1 gene may contribute to developmental dyscalculia.

This is the second study from our group to investigate the genetic basis of developmental dyscalculia. In the same sample, a child has already been identified with a 22q11.2(LCR4â?"LCR5) deletion syndrome46. Therefore, we found three children with a genetic condition out of 121 children with MD. None of these children had severe congenital malformations or even a funny face that would refer them for a genetic investigation. These findings are preliminary, but raise the question whether and when a genetic investigation should be considered in otherwise healthy children with MD.


The authors thank the children and their parents and also the schools, for taking part in this project. They also thank Prof. Peter Laspina, from Viamundi School of Language and Translations for reviewing language. The authors thank the Program for Technological Development in Tools for Health-PDTIS/FIOCRUZ for use of its facilities.

Authorsâ?T contributions. AASM, GMP: contributed equally to this study; AASM: formal analysis, investigation, project administration, and writing â?" original draft. GMP: data curation, formal analysis, investigation, project administration, and writing â?" original draft. CGRM, PASF, and EMC: investigation. VGH and MRSC: conceptualization, funding acquisition, methodology, project administration, supervision, writing â?" original draft, and writing-review & editing.


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This study was conducted by the Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil.

1. Universidade Federal de Minas Gerais, Intituto de Ciências Biológicas, Departamento de Genética, Ecologia e Evolução, Postgraduate Program em Genética, Belo Horizonte MG, Brazil
2. Universidade Federal de Minas Gerais, Intituto de Ciências Biológicas, Departamento de Genética, Ecologia e Evolução, Belo Horizonte MG, Brazil
3. Universidade Federal de Minas Gerais, Faculdade de Filosofia e Ciências Humanas, Departamento de Psicologia, Belo Horizonte MG, Brazil
4. Universidade Federal de Minas Gerais, Instituto de Ciências Biológicas, Programa de Pós-Graduação em Neurociências, Belo Horizonte MG, Brazil
5. Fundação Oswaldo Cruz, Instituto René Rachou, Departamento de Informática de Biossistemas e Genômica, Belo Horizonte MG, Brazil
6. Universidade Federal de Minas Gerais, Faculdade de Medicina, Postgraduate Program em Saúde da Criança e do Adolescente, Belo Horizonte MG, Brazil
7. Universidade Federal de Minas Gerais, Faculdade de Filosofia e Ciências Humanas, Departamento de Psicologia, Postgraduate Program em Psicologia, Belo Horizonte MG, Brazil
8. Instituto Nacional de Ciência e Tecnologia em Cognição, Comportamento e Ensino, São Carlos SP, Brazil


Maria Raquel Santos Carvalho
Emails: ma.raquel.carvalho@gmail.com; mraquel-carvalho@ufmg.br

Received on April 22, 2021
Accepted in final form on October 3, 2021

Disclosure: The authors report no conflicts of interest

Funding: AASM, GMP, CGRM, and PASF are supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) fellowships. VGH is supported by the CNPq excellence in research fellowship (308157/2011-7 and 308267/2014-1). This project was partially supported by a grant from CAPES/DAAD (PROBRAL). MRSC was awarded a fellowship from the Brazilian National Research Council (Conselho Nacional de Pesquisa, CNPq, grant number 312068/2015-8) and is also supported by grants from the Fundação de Amparo à Pesquisa de Minas Gerais (FAPEMIG, APQ-01093-15, APQ-02003-15, and APQ-01377-17)


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