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Supplementary Information
Supplementary METHODS
Description of test batteries:
German sample: Spelling was measured using age-appropriate spelling tests (writing to
dictation) which render T scores that are distributed as N(50,100) in unaffected children (1).
The IQ was assessed using the Culture Fair Test, (CFT-1) (2) or CFT-20 (3), depending on
the age of the proband. Families were excluded from the study when either the proband or a
sibling displayed symptoms of attention deficiency/hyperactivity disorder (ADHD), as
determined during a standardized clinical interview with the mother (4). Furthermore,
families were not included if the proband had a history of a bilingual education, an IQ < 85,
an uncorrected disorder of peripheral hearing or vision, a psychiatric or neurological
disorder with a possible impact on the development of reading and spelling ability, or was
above 21 years of age.
To assess mathematical skills, the test batteries were modelled after Butterworth (2003) (5),
as described previously (6). In brief, simple tasks of addition (n=24) and multiplication
(n=24) were presented on a computer screen, e.g. “4+5=9”. The child was asked to press
the left mouse button if the result was correct, and to press the right mouse button if the
result was false. The child was instructed to answer as quickly as possible. In both tests, the
reaction times of correct responses were scored. Addition and multiplication subtests were
combined into one mathematical calculation phenotype (mathematical calculation, MC) by
taking the mean of both measurements. Numerosity judgement (NJ) was assessed by
presenting a random number of dots on one side of the screen, and a numeral on the other
side. The child had to decide whether the number of dots shown on the left was equivalent
to the Arabic symbolic representation given on the right, and to indicate their response by
pressing a button. The reaction time of correct responses was scored.
Munich sample: Exclusion criteria, based on parental reports, were: (i) a multilingual
background; (ii) a history of a specific language disorder; (iii) a history of serious head
trauma; (iv) an uncorrected visual or auditory deficit; or (v) a history of ADHD. Each child
completed a standardized test of reading fluency (7). The arithmetic tests were addition and
multiplication tasks. The child was required to write down as many correct answers as
quickly as possible within a time limit of 2 minutes. Numerosity judgement (NJ) was
measured by mapping the numerosity of objects with numbers, the child was required to
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quickly count or estimate the number of objects within one minute and write down the
Arabic symbolic representation. Number of correct responses within one minute were
scored for NJ.
Austrian sample: Exclusion criteria were: (i) German as a second language, and (ii) a
clinical diagnosis of ADHD. As with the Munich sample, all children completed a
standardized reading test (7). MC was assessed analogously to the Munich sample. For NJ a
dot counting task was applied that required the mapping of a cluster of dots with the
corresponding number word. The child had to state the number of dots (between 1 and 8,
randomly arranged on a computer screen) as quickly as possible. Altogether, 32 dot
displays (four different displays per number) were presented in a fixed pseudo-random
sequence. Incorrect responses were rare and were excluded from the response time analysis.
The total score for NJ was generated by averaging the individual median reaction times for
each dot number.
German/Austrian control sample: The ascertainment process and test batteries were
analogous to those used for the German/Austrian replication-2 sample. However, to be
included as a control, the individual had to have a reading performance not more than 0.85
sd below the age norm.
Twin Early Development Study (TEDS) sample: This sample consisted of 4,401 twin pairs
from the UK. Subjects performed tests of reading, spelling, and mathematical ability at the
ages of 7, 9, and 10 years (8). One individual from each twin pair was selected at random
for our analysis. Assessed phenotypes (for the mathematical tasks as well as for reading and
spelling performance) were measured according to an ordinal scale from 1 to 5, indicating
the level of performance in the corresponding task. Given the genetic continuity of
quantitative traits (9), in our analysis, we used an average of this score across the three age
groups (mathematical abilities MA_UK: mean=0.07 ± 0.83) to render the analysis more
stable.
Structural MRI study. Subjects: For the structural imaging genomics analysis, 100 neuropsychiatrically healthy adult subjects who had been scanned at the Max Planck
Institute
(MPI) of Psychiatry in Munich within the context of an independent genetic study (10)
were investigated. All subjects underwent a semi-structured clinical interview to exclude
any past or present psychiatric disorder or neurological disease. Additionally, MRI-based
exclusion criteria were applied including territorial infarction, obvious structural
developmental anomalies, any pathology requiring further medical consultation, or
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excessive motion artifact. Each subject completed a questionnaire on demographics, family
and individual history, as well as medical history and ethnicity, under the supervision of a
study nurse. MRI acquisition details: High resolution T1-weighted MR images were
acquired on a 1.5 Tesla General Electrics scanner (Signa Excite) using an inversion
recovery spoiled gradient echo sequence with a field of view 22  22 cm2; matrix 256 
256, 124 sagittal slices; whole brain and skull coverage; resulting voxel size 0.9 × 0.9 ×
[1.2−1.4] mm3; TR=10.3 s; TE=3.4 ms; and flip angle=20°.
Image postprocessing and sulcus morphology: Basic image postprocessing and sulcus
morphology procedures were performed using the combined BrainVisa(BV)/Anatomist
software version 3.02 (http://brainvisa.info) on a 64-bit processor Linux workstation.
DICOM raw images were transformed to the ANALYZE format and imported into a BV
database. After manual definition of left/right orientation, the anterior and posterior
commissure, and the interhemispheric line, the full BV sulcal extraction and identification
pipeline was employed, as described elsewhere (11): (1) correction of radio frequency (RF)
field inhomogeneity; (2) histogram analysis of resulting voxel intensities; (3) segmentation
into gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF); (4) definition of
brain mask and masks separating the hemispheric supratentorial compartments from the
infratentorial compartment; (5) extraction of hemispheric spherical GM and WM meshes
from GM/CSF and WM/GM interfaces; (6) reconstruction of sulcal folds between the most
internal point of the sulcal fold to the convex hull of the cortex using a homotopic erosion
technique and a 'crevasse detector' (12;13); and (7) identification of 58 sulcal structures for
each hemisphere on the basis of collaboratively working neural network based pattern
classifiers implemented in BV. The algorithm is based on 26 expertly-classified images
with classification accuracies ranging between 95% for primary and secondary fissures to
70% for the highly variable tertiary sulcal structures (14).
Visualization and extraction of maximal sulcal depth and volume of each of the following
four segmentations of the left and right IPS was performed: (i) the main part of the IPS (ref.
to as IPSmain) which contains the horizontal segment and the superior postcentral part of the
IPS; (ii) the anterior ascending segment of the IPS (also referred to as the inferior
postcentral sulcus); and (iii and iv) two smaller intermediary branches of the posterior
descending segment of the IPS. The hypothesis was selectively directed to the IPS main in
accordance with reports of the functional neuroanatomy of ordinal abilities and pathology
for dyscalculia of genetic origin (15). The bilateral central sulcus (CS) was chosen as a
control structure region. The average sulcus depth (depthavg) and the total sulcus volume
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(SVtotal) of all classified sulci of each hemisphere were calculated as additional markers for
later use as covariates.
Quality control: Definition of a uniform postprocessing pipeline for all cases is essential in
order to prevent biases introduced by, for example, systematic differences in GM surface
extraction. We defined parameters in the BV software that allowed robust processing of
80% of the original 100 cases. In 20 cases, RF field inhomogeneity correction and subsequent histogram analysis failed, leading to underestimation of the GM volume. Although
these cases could be further processed after changing the inhomogeneity correction
parameters, the resulting sulcus depth averaged over both hemispheres was highly distinct
from the remaining cases, suggesting a residual systemic bias. These cases were therefore
excluded from the final analysis. One further case was excluded due to failed genotyping.
In all of the remaining 79 cases, the automated sulcus allocation pipeline generated robust
results that were visually controlled. The demographic details of the final MRI sample are
provided in Supplementary Table 4.
Genotyping of subjects from the MRI sample: Genotypes for rs133885 were extracted from
genome-wide data derived from IlluminaTM HumanHap300k BeadChips, which had been
used for a different project. SNP rs133885 had a genotype call rate of 98.8% and did not
deviate from Hardy-Weinberg-Equilibrium (P=0.269).
Statistical analysis of sulcal parameters: We used analysis of covariance (ANCOVA) to
compare the maximal depth of the right and left IPSmain between carriers of the A-allele
(genotypes AA and AG) and non-carriers of the A-allele (genotype GG) for rs133885, with
the inclusion of age, gender, and depthavg as covariates. This analysis was repeated for the
IPSmain volume, and for the depth and volume of the bilateral central sulcus. For analysis of
sulcal volume, depthavg was replaced by SVtotal in the model. Reported ANCOVA results
imply non-significant result for Levene's test of quality of variance errors (all P > 0.05).
Multiple test correction was performed for 8 tests (2 sulci [IPSmain and CS], 2 measures
[depth and volume], 2 hemispheres). After observing a strong genotypic effect on the depth
of the right IPSmain, we probed regional specificity to reduce the risk of a false positive
finding by expanding the analysis to all 58 non-IPS and non-CS sulci extracted by the BV
algorithm for each hemisphere.
Voxel-based morphometry (VBM). Using the original sample of 79 subjects, we
employed VBM without regional restriction to screen for differences in GM and WM
volume at the voxel level. Preprocessing and statistical analyses were performed on a 64-bit
processor Linux work station, using SPM (http://www.fil.ion.ucl.ac.uk/spm, version SPM8)
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and in-house software written in IDL 6.3 (http://www.creaso.com). Image preprocessing
for voxel-based morphometry (VBM). We employed the diffeomorphic image registration
algorithm (referred to subsequently as DARTEL), which optimizes intersubject alignment
(16). T1-weighted high resolution images were subjected to inhomogeneity correction,
spatial normalization, and segmentation into GM, WM, and CSF using the unified
segmentation algorithm (17) as implemented in SPM5 and prior probability maps of the
standard SPM5 distribution in MNI152 space (resolution 2  2  2 mm3) as based on the
International
Consortium
for
Brain
Mapping
maps
([ICBM],
http://www.loni.ucla.edu/ICBM). After a first affine alignment of the segmented GM and
WM maps to the MNI space, these were iteratively coregistered with six generations of GM
and WM template pairs in MNI space using linear and non-linear deformations. Default
settings were used to specify outer and inner iterations, regularization parameters for each
iteration, and optimization settings. Templates at 1.5  1.5  1.5 mm3 resolution were based
on DARTEL coregistration of independent 550 healthy adults from the IXI-cohort
(http://www.brain-development.org), available in the VBM8 toolbox (http://dbm.neuro.unijena.de/vbm8). The flow fields resulting from DARTEL coregistration were applied to
segmented native GM and WM with Jacobian modulation to preserve local volumes. Prior
to statistical analysis, images were spatially smoothed (Gaussian kernel, full width half
maximum at 8  8  8 mm3). Statistical analysis. Analysis of covariance was performed
within the GLM framework of SPM5, after stratifying into three genotype groups (AA, AG,
and GG) with the covariates total GM (or WM, respectively), age, squared age, and gender.
The main contrast of interest was the comparison between A-carriers (collapsing groups
AA and AG) and GG-carriers in both directions. After collecting clusters at P < 0.005,
cluster P-values were corrected for family-wise error under consideration of non-stationary
smoothness (18), and clusters with Pcluster.FWE < 0.05 were considered significant.
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Supplementary RESULTS
Association analyses. In the present study, dyslexia severity (measured by the difference
between expected and observed spelling score) differed between the German discovery and
replication-1 samples (Supplementary Table 1). BMAF per se was significantly
associated with the degree of dyslexia severity (P = 2.56×10-05 combined German sample).
Thus, two additional analyses were performed to exclude the possibility that association
between rs133885 and the basic mathematical abilities factor (BMAF) is simply due to a
severe spelling impairment.
First, no association was found between rs133885 and severity of dyslexia (P = 0.88
discovery-sample, P = 0.32 replication-sample, allelic model). Second, association results
for rs133885 and BMAF remained significant when the data were corrected for dyslexia
severity (P = 2.91×10-09 discovery-sample, P = 0.012 replication-1 sample, P = 1.61×10-09
combined German sample; all according to the carrier-A model). This analysis strongly
suggests that rs133885 has an influence on mathematical abilities in addition to the given
effect on dyslexia severity.
In the German discovery-sample, BMAF showed a stronger association than its underlying
single measures ‘mathematical calculation’ (MC) and ‘numerosity judgement’ (NJ,
Supplementary Table 6). This suggests that the principal component of both mathematical
test batteries provides more power to detect the genetic association. Accordingly, in each of
the two replication-samples, the combined factor BMAF was also more significantly
associated compared to the single measures. However, MC and NJ also showed at least a
statistical trend towards association (Supplementary Table 6).
Locus-specific analysis. LD structure. In our genome-wide data of the German discoverysample, information on 92 SNPs in MYO18B including rs133885 was available after QC.
With the exception of rs133885, rs3859865 showed the strongest association with
mathematical abilities (P=3.05×10-04, BMAF, genotypic model, P=5.00×10-05 carrier-A
model). However, this association became non-significant when conditioned on rs133885.
Expansion of sulcal analysis to all sulci. We modelled gender as second factor in a 2factorial analysis. We found no gender main effect (P=0.920), and no gender  genotype
interaction (P=0.719). We also excluded the possibility that the non-significant covariates
gender and depthavg, contributed to the observed genotype effect (F1,76=12.787, P=0.0006).
Right hemisphere. Testing of the depth of all remaining 58 right hemispheric sulci revealed
nominal significance for two further sulci. For one sulcus (cuneal sulcus), violation of the
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assumption of equality of variances (Levene's test, P=0.001) was noted, and removal of
three outlier values in the A-allele carrier group after raw value inspection led to a nonsignificant result. The second right hemisphere sulcus to show nominal significance was the
superior temporal sulcus (P=0.014). Although this would support previous findings that
mathematical networks in dyscalculic patients are located to the temporal regions in the
right hemisphere (19), this association was only nominally significant and was not as strong
as the association observed for the right IPS. Overall, the rs133885 genotype effect on the
depth of the right-hemispheric IPSmain proved regionally specific. Left hemisphere. Testing
of the depth of all of the remaining 58 left hemispheric sulci revealed six sulci with nominal
significance (precentral sulcus, P=0.024; paracentral sulcus, P=0.001; medial frontal
sulcus, P=0.045; callosomarginal sulcus, P=0.038; subbranches of the sylvian fissure:
P=0.045 and P=0.023, respectively), suggesting low general effect sizes and low regional
specificity for the left hemispheric effects.
Expansion of right IPS analysis to length and surface area. As additional measures, the
sulcus analysis pipeline provided sulcus length and sulcus area which we analyse to
complete the morphometric characterization. All four sulcus measures were positively
correlated with each other (r=[+0.286;+0.883], p=[<0.001;0.010]). For sulcus length which
was weakly correlated with depth (r=0.286), a weak effect of the rs133885 genotype with
lower length in GG-carriers was detected (p=0.049, corrected for age, gender and average
sulcus length). For surface area that showed a moderate correlation with sulcus depth
(r=0.522), the genotype effect was about equally strong (p=0.045, corrected age, gender
and average sulcus surface area) with smaller surface area in GG-carriers. As a pattern,
these effects argue for a generally more ‘shallow’ shape of the right IPSmain.
MYO18B. Myosins are generally known as actin-based molecular motors and are
ubiquitously expressed in all eukaryotic cells (20;21). In MYO18B, the corresponding actin
binding domains identified to date are located in the head motor region. Its N- and Ctermini only contain unique sequences which, with the exception of a nuclear localization
signal, do not show any similarities with known protein domains (Fig. S3) (22;23).
However, recent evidence has been obtained suggesting the presence of additional actininteraction sites within the MYO18B N-terminus. Firstly, the N-terminus contains the
conserved amino-acids V153L154, which have been identified as being essential for
binding of actin filaments in co-sedimentation experiments in MYO18A (V117L118) (24).
Secondly, it has been suggested that many ligands for F-actin contain proline-rich domains
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(25). Indeed, the presence of a proline-rich sequence between positions 21 and 34 of
MYO18B may be an additional clue that the N-terminus of MYO18B is involved in F-actin
interaction. The G44E variant is located close to this proline-rich region, which may further
suggest an influence on binding properties in the three-dimensional protein structure. It
remains to be clarified whether the interaction of MYO18B and actin occurs via direct
binding or whether it involves additional interacting proteins. HOMER2, a post-synaptic
adapter protein which modulates the Ca2+ signalling pathway in neurons, has recently been
identified as one binding partner candidate (26).
Independent GWAS data of mathematical ability. To the best of our knowledge, the
present study is the first to have identified genetic contributors to mathematical abilities in
children with dyslexia using genome-wide data, and the second to have investigated genetic
susceptibility to mathematical (dis-)ability in the general population (27). In the study by
Docherty et al. (27), ten SNPs with suggestive evidence of association were identified.
None of these SNPs showed an association with any mathematical phenotype in our GWAS
data for the discovery-sample. This might be due to: (i) the small effect sizes, (ii) the lower
number of individuals compared to the study by Docherty et al.; or (iii) the fact that our
sample included individuals with dyslexia. Docherty et al. reported effect sizes of up to
0.6% for single SNPs and 2.9% for the combination of all ten associated SNPs. In the
present study, the effect sizes obtained for rs133885 in the general population were lower
(0.007%), although the genetic contribution to mathematical abilities in individuals with
dyslexia was around 4.87%. This provides further support for the hypothesis that the locus
identified in the present study contributes most strongly to mathematical performance
within the context of low literacy skills, and that homogeneity of the investigated sample
increased power for the detection of risk variants contributing to mathematical
performance.
Mathematical- and dyslexia phenotypes. Despite previous research suggesting that
mathematical and reading abilities may involve similar cognitive factors (28;29), recent
evidence, however, suggests that literacy disabilities aggravate, rather than cause,
arithmetic deficits (30). Notably, children with isolated dyscalculia (defined as the lowest
end of distribution of arithmetic abilities) show age-appropriate performance in tasks
involving verbal abilities and auditory working memory, such as phonological awareness
and rapid automatized naming, which represent the most characteristic cognitive deficits
associated with dyslexia (31;32). Consistently, numerical processing has been identified as
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a cognitive component that is equally deficient in children with isolated dyscalculia and
children with combined dyslexia and dyscalculia, but which is intact in children with
isolated dyslexia (31;33).
It may be important to take environmental factors (such as early remediation in verbal
domains) into account in future genetic investigations. Children carrying the rs133885 risk
genotype who display no symptoms of reading and/or spelling impairment may experience
early problems in numerical processing and mathematics and, accordingly, receive training
and stimulation in these specific areas. In contrast, children with dyslexia who carry the
same rs133885 risk may not receive this intervention, since their problems with reading /
spelling are more prominent. Since widespread public opinion is that mathematical
difficulties in individuals with dyslexia are a consequence of the underlying cognitive
deficits, interventions are aimed at the verbal/phonological domain, and thus neglect the
second deficient domain of numerical processing. This might provide a further explanation
of why the genetic basis of mathematical skills appears to be stronger in dyslexia samples.
Unfortunately, no data are available on preventive- or remediation training for any of the
samples used in the present study. It could be hypothesized that the genetic effect of
rs133885 would be even stronger if such information was included as a covariate in the
analyses.
9
Reference List
(1) Brähler E, Holling V, Leutner D, Pettermann F. Handbuch psychologischer und
pädagogischer Tests. Göttingen: Hofgrefe; 2002.
(2) Weiß R, Osterland J. Grundintelligenz Skala (CFT-1). Göttingen: Hogrefe; 1997.
(3) Weiß R. Grundintelligenz Skala 2 (CFT-20). Göttingen: Hofgrefe; 1998.
(4) Unnewehr S, Schneider S, Margraf J. Kinder-DIPS: diagnostisches Interview bei
psychischen Störungen von Kindern und Jugendlichen. Berlin: Springer; 1998.
(5) Butterworth B. Dyscalculia Screener. London: nfer Nelson Publishing Company
Limited; 2003.
(6) Schulte-Körne G, Ziegler A, Deimel W, Schumacher J, Plume E, Bachmann C, et
al. Interrelationship and familiality of dyslexia related quantitative measures. Ann
Hum Genet 2007;71(2):160-75.
(7) Landerl K, Moll K. Comorbidity of learning disorders: prevalence and familial
transmission. J Child Psychol Psychiatry 2010 Mar;51(3):287-94.
(8) Oliver BR, Plomin R. Twins' Early Development Study (TEDS): a multivariate,
longitudinal genetic investigation of language, cognition and behavior problems
from childhood through adolescence. Twin Res Hum Genet 2007 Feb;10(1):96-105.
(9) Haworth CM, Kovas Y, Petrill SA, Plomin R. Developmental origins of low
mathematics performance and normal variation in twins from 7 to 9 years. Twin Res
Hum Genet 2007 Feb;10(1):106-17.
(10) Inkster B, Nichols TE, Saemann PG, Auer DP, Holsboer F, Muglia P, et al.
Association of GSK3beta polymorphisms with brain structural changes in major
depressive disorder. Arch Gen Psychiatry 2009 Jul;66(7):721-8.
(11) Kochunov P, Mangin JF, Coyle T, Lancaster J, Thompson P, Riviere D, et al. Agerelated morphology trends of cortical sulci. Hum Brain Mapp 2005 Nov;26(3):21020.
(12) Mangin JF, Riviere D, Coulon O, Poupon C, Cachia A, Cointepas Y, et al.
Coordinate-based versus structural approaches to brain image analysis. Artif Intell
Med 2004 Feb;30(2):177-97.
(13) Mangin J, Frouin V, Brannon E, Regis J, Lopez-Krahe J. From 3D magnetic
resonance images to structural representations of the cortex topography using
topology preserving deformations. J Math Imaging Vis 1995;5:297-318.
(14) Riviere D, Mangin JF, Papadopoulos-Orfanos D, Martinez JM, Frouin V, Regis J.
Automatic recognition of cortical sulci of the human brain using a congregation of
neural networks. Med Image Anal 2002 Jun;6(2):77-92.
(15) Molko N, Cachia A, Riviere D, Mangin JF, Bruandet M, Le BD, et al. Functional
and structural alterations of the intraparietal sulcus in a developmental dyscalculia
of genetic origin. Neuron 2003 Nov 13;40(4):847-58.
10
(16) Ashburner J. A fast diffeomorphic image registration algorithm. Neuroimage 2007
Oct 15;38(1):95-113.
(17) Ashburner J, Friston KJ. Unified segmentation. Neuroimage 2005 Jul 1;26(3):83951.
(18) Hayasaka S, Phan KL, Liberzon I, Worsley KJ, Nichols TE. Nonstationary clustersize inference with random field and permutation methods. Neuroimage 2004
Jun;22(2):676-87.
(19) Rykhlevskaia E, Uddin LQ, Kondos L, Menon V. Neuroanatomical correlates of
developmental dyscalculia: combined evidence from morphometry and
tractography. Front Hum Neurosci 2009;3:51.
(20) Hasson T, Mooseker MS. Molecular motors, membrane movements and
physiology: emerging roles for myosins. Curr Opin Cell Biol 1995 Aug;7(4):58794.
(21) Sellers JR. Myosins: a diverse superfamily. Biochim Biophys Acta 2000 Mar
17;1496(1):3-22.
(22) Redowicz MJ. Unconventional myosins in muscle. Eur J Cell Biol 2007
Sep;86(9):549-58.
(23) Salamon M, Millino C, Raffaello A, Mongillo M, Sandri C, Bean C, et al. Human
MYO18B, a novel unconventional myosin heavy chain expressed in striated
muscles moves into the myonuclei upon differentiation. J Mol Biol 2003 Feb
7;326(1):137-49.
(24) Isogawa Y, Kon T, Inoue T, Ohkura R, Yamakawa H, Ohara O, et al. The Nterminal domain of MYO18A has an ATP-insensitive actin-binding site.
Biochemistry 2005 Apr 26;44(16):6190-6.
(25) Witke W. The role of profilin complexes in cell motility and other cellular
processes. Trends Cell Biol 2004 Aug;14(8):461-9.
(26) Ajima R, Kajiya K, Inoue T, Tani M, Shiraishi-Yamaguchi Y, Maeda M, et al.
HOMER2 binds MYO18B and enhances its activity to suppress anchorage
independent growth. Biochem Biophys Res Commun 2007 May 18;356(4):851-6.
(27) Docherty SJ, Davis OS, Kovas Y, Meaburn EL, Dale PS, Petrill SA, et al. A
genome-wide association study identifies multiple loci associated with mathematics
ability and disability. Genes Brain Behav 2010 Mar 1;9(2):234-47.
(28) Geary D, Hoard M. Learning disabilities in basic mathematics: Deficits in memory
and cognition. In: Royer J, editor. Mathematical Cognition.Greenwich: Information
Age Publishing; 2002. p. 93-115.
(29) Hecht SA, Torgesen JK, Wagner RK, Rashotte CA. The relations between
phonological processing abilities and emerging individual differences in
mathematical computation skills: a longitudinal study from second to fifth grades. J
Exp Child Psychol 2001 Jun;79(2):192-227.
11
(30) Jordan NC, Kaplan D, Nabors OL, Locuniak MN. Number sense growth in
kindergarten: a longitudinal investigation of children at risk for mathematics
difficulties. Child Dev 2006 Jan;77(1):153-75.
(31) Landerl K, Fussenegger B, Moll K, Willburger E. Dyslexia and dyscalculia: two
learning disorders with different cognitive profiles. J Exp Child Psychol 2009
Jul;103(3):309-24.
(32) Willburger E, Fussenegger B, Moll K, Wood G, Landerl K. Naming Speed in
dyslexia and dyscalculia. Learning and Individual Differences 2008.
(33) Landerl K, Bevan A, Butterworth B. Developmental dyscalculia and basic
numerical capacities: a study of 8-9-year-old students. Cognition 2004
Sep;93(2):99-125.
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