Structural and transcriptional signatures of arithmetic abilities in children

The study investigates whether individual differences in children’s arithmetic abilities (subtraction and multiplication) are embedded in distributed patterns of gray matter volume across the brain and whether these structural patterns are associated with specific gene expression profiles. Arithmetic competence is vital for education, employment, and socioeconomic outcomes, while difficulties such as dyscalculia carry broad impacts. Prior neuroimaging work has largely focused on hypothesis-driven regions of interest (e.g., intraparietal sulcus, angular gyrus, MTG/STG), yielding mixed findings potentially due to varying tasks and age ranges. The present work aims to use a data-driven, cross-validated approach to identify brain-wide GMV signatures predictive of arithmetic skills, examine their relationship with working memory, and link these structural signatures to transcriptional profiles using neuroimaging–transcriptome association analyses.

Prior studies have implicated the intraparietal sulcus (IPS) in magnitude representation and procedural strategies during arithmetic, with GMV in left IPS linked to non-symbolic number perception and math performance in some cohorts. MTG/STG have been associated with storage of arithmetic facts in verbal code, and regions such as right fusiform gyrus and left angular gyrus (AG) have been tied to arithmetic fluency and fact retrieval, respectively. However, findings are inconsistent across age groups and measures. Suárez-Pellicioni and colleagues examined ROI-based associations between IPS and left MTG/STG and arithmetic performance, reporting links between left MTG/STG and multiplication and predictive value of left IPS for subtraction growth. Genetic influences on brain development suggest potential genetic bases for arithmetic skills, yet candidate gene studies show small or non-replicated effects, and prior genetic imaging work has focused on predefined parietal regions. Recent advances in neuroimaging–transcriptome analyses enable linking spatial patterns in neuroimaging phenotypes to brain-wide gene expression, but such approaches have not been fully applied to children’s arithmetic abilities.

Dataset: Public longitudinal dataset (OpenNeuro ds001486) of schoolchildren grades 3–8; this study used the first (cross-sectional) session (n=130 after quality control; mean age 11.26 years, 62 males). All were right-handed, native English speakers without neurological disorders; IQ ≥85. Behavioral measures: CMAT subtraction (23 items; single-/multi-digit, decimals, fractions) and CMAT multiplication (26 items; single-/multi-digit, decimals, fractions), both untimed and administered outside the scanner. Working memory (WM): AWMA-Short Form subtests—verbal WM (Digit Recall, Listening Recall) and visuospatial WM (Dot Matrix, Spatial Recall); standardized scores used. MRI acquisition: Siemens 3T TIM Trio, high-resolution T1-weighted (TR=2300 ms, TE=3.36 ms, 1 mm isotropic). Preprocessing with FreeSurfer (recon-all): intensity normalization, skull stripping, MNI transform, tissue segmentation, surface reconstruction and smoothing. Cortical parcellation with the Destrieux atlas into 148 ROIs; GMV computed for each ROI. Visual QC; 2 participants excluded for surface errors. GMV-based predictive modeling: Inspired by connectome-based predictive modeling (CPM), separate models for subtraction and multiplication using leave-one-out cross-validation (LOOCV). In each training fold, partial correlations were computed between each ROI’s GMV and the target arithmetic score, controlling covariates (age, gender, estimated total intracranial volume [eTIV] and, to isolate ability-specific effects, the other arithmetic score—multiplication controlled in subtraction model and vice versa). ROIs with significant associations (P<0.01) in the training set were selected as features. A multivariate GLM related selected ROIs’ GMVs to the target score with age, gender, eTIV as covariates; predictions were generated for the left-out participant. Predictive power was assessed by Pearson correlation between observed and predicted scores across all participants. Reliability was evaluated by two permutation schemes: (1) shuffling observed scores 10,000 times relative to fixed predictions to build null correlations, and (2) shuffling observations and fully reconstructing the LOOCV models 1,000 times to build null distributions. Identification of involved regions: Brain areas contributing to prediction were those with non-zero model weights across LOOCV models. Additional control analyses reconstructed models without controlling the alternate arithmetic skill to examine inclusion of canonical regions (e.g., IPS, AG) and overlap between subtraction and multiplication. Working memory analyses: Correlated predicted arithmetic scores (model outputs) with AWMA-S subtests (Digit Recall, Listening Recall, Dot Matrix, Spatial Recall). Constructed an analogous GMV-based predictive model for visuospatial WM (Spatial Recall) using the same LOOCV pipeline (covariates: age, gender, eTIV), and examined overlapping ROIs between WM and arithmetic models. Neuroimaging–transcriptome linkage: Used Allen Human Brain Atlas adult post-mortem microarray data (two whole-brain donors). Preprocessing included removal of brainstem/cerebellum samples, probe re-annotation, intensity-based filtering, robust sigmoid normalization, and mapping samples to Destrieux ROIs via nearest-point in MNI space, then averaging within donor and across donors to yield ROI-level expression for 15,745 genes. Structural patterns for each arithmetic skill (and visuospatial WM) were defined as vectors of partial correlation coefficients (between the target ability and GMV for ROIs involved in the predictive model, controlling age, gender, eTIV; for subtraction/multiplication, without re-controlling the alternate skill at this step). For each gene, spatial similarity to the structural pattern was computed by Pearson correlation across involved ROIs; genes with significant positive correlation (r>0, P<0.05) were retained. Functional enrichment of these gene sets was performed using ToppGene Suite with multiple-comparison correction (FDR or Bonferroni as reported).

• Predictive performance: GMV-based models significantly predicted arithmetic scores in LOOCV.
  • Subtraction: r = 0.3506; reported P values include 4.32 × 10^-5 (figure) and 4.32 × 10^-10 (text). Permutation tests: P_perm = 0.0001 (shuffle observed vs fixed predictions), P_perm = 0.001 (full model rebuild with shuffled observations).
  • Multiplication: r = 0.2824; P = 0.0011. Permutation tests: P_perm = 0.0006 and P_perm = 0.025.
• Involved brain regions (non-zero model weights):
  • Subtraction: cingulate cortex (left ventral cingulate gyrus; right posterior cingulate gyrus and sulcus; right marginal branch of cingulate sulcus), temporal cortex (bilateral inferior temporal gyrus; right anterior transverse collateral sulcus; right transverse temporal sulcus), motor cortex (right paracentral lobule and sulcus).
  • Multiplication: motor cortex (left precentral gyrus; left inferior part of precentral sulcus), occipital cortex (left superior occipital sulcus; transverse occipital sulcus), frontal cortex (left orbital sulci; right suborbital sulcus), temporal cortex (bilateral superior temporal gyrus; right transverse temporal sulcus), parietal cortex (right subparietal sulcus).
• Control models without including the other arithmetic skill as a covariate remained significant and brought in canonical regions:
  • Subtraction model: r = 0.3231; P_perm = 0.0001 (shuffle observed), P_perm = 0.007 (rebuild); included left IPS.
  • Multiplication model: r = 0.3304; P_perm = 0.0001 (shuffle observed), P_perm = 0.006 (rebuild); included right angular gyrus (AG). The two control models shared 9 regions.
• Relationship to working memory:
  • Subtraction predicted scores correlated with visuospatial WM: Dot Matrix r = 0.2178, P = 0.0155; Spatial Recall r = 0.3100, P = 0.0005; no significant correlations with verbal WM.
  • Multiplication predicted scores correlated with visuospatial WM: Dot Matrix r = 0.3216, P = 0.0002; Spatial Recall r = 0.3664, P = 3.067 × 10^-5; also a modest correlation with Digit Recall (verbal WM): r = 0.1932, P = 0.0323; not significant for Listening Recall.
  • Visuospatial WM predictive model (Spatial Recall): r = 0.3435; P_perm = 0.0001 (shuffle observed), P_perm = 0.001 (rebuild). Overlap in ROIs between WM and arithmetic models was observed (e.g., bilateral superior temporal sulcus; left superior/transverse occipital sulci; right transverse temporal sulcus for multiplication; right inferior temporal gyrus, right marginal cingulate sulcus, right transverse temporal sulcus for subtraction).
• Gene expression associations:
  • Subtraction structural pattern: 570 genes positively correlated (P<0.05, r>0); enriched biological processes primarily in transmembrane transport (e.g., inorganic ion transmembrane transport, cation transmembrane transport, regulation of transmembrane transport).
  • Multiplication structural pattern: 212 genes positively correlated; enriched biological processes in synaptic signaling.
  • Visuospatial WM structural pattern: 240 genes positively correlated; enriched processes in histone modification (e.g., histone H4-K16 acetylation; positive regulation of histone methylation).

The study demonstrates that distributed GMV patterns across widespread cortical regions reliably predict individual differences in subtraction and multiplication abilities in children and adolescents within a cross-validated framework, addressing limitations of prior ROI-focused, hypothesis-driven approaches. The predictive models’ robustness, supported by permutation testing, indicates viable neuroimaging-based biomarkers. Differences in involved regions align with known strategy distinctions: subtraction relates more to quantity-based, procedural operations and mental number line processes (involving inferior temporal and cingulate regions), while multiplication relies more on fact retrieval and verbal memory (involving superior temporal and frontal/occipital regions). When not controlling the alternate arithmetic skill, canonical regions emerge (left IPS for subtraction; right AG for multiplication), consistent with literature. The significant associations between model outputs and visuospatial working memory—and overlap among predictive model regions—suggest a shared neural substrate between arithmetic and visuospatial WM, with multiplication also showing some linkage to verbal memory (Digit Recall). Neuroimaging–transcriptome analyses indicate that structural patterns underlying subtraction align with genes involved in ion transmembrane transport (supporting neural signaling and synaptic plasticity), and multiplication with synaptic signaling genes (critical for circuit formation and cognitive function). Visuospatial WM structural patterns relate to histone modifications implicated in memory formation. Together, these results integrate structural neuroimaging with transcriptional signatures to clarify neural and genetic mechanisms of children’s arithmetic abilities.

This work introduces cross-validated, GMV-based predictive models that serve as neuromarkers for children’s subtraction and multiplication abilities and reveals shared structural bases with visuospatial working memory. It further links arithmetic-related structural patterns to gene sets enriched for transmembrane transport (subtraction) and synaptic signaling (multiplication), and WM-related patterns to histone modification processes. The study advances understanding of neural and genetic substrates of arithmetic skills and provides practical predictors of performance. Future research should validate these models in clinical populations (e.g., dyscalculia), employ child-specific transcriptomic data when available, and use tasks with controlled strategy demands (e.g., single-digit operations) to refine specificity and generalizability.

• Gene expression data were from adult post-mortem brains; although spatial expression patterns are thought to be relatively stable postnatally, child-specific data would better validate developmental inferences.
• Arithmetic assessments were out-of-scanner, untimed, and included multi-digit, decimals, and fractions, potentially reducing strategy differentiation between subtraction and multiplication despite controlling the alternate skill in modeling.
• Cross-sectional analysis of the first session (n=130) limits developmental trajectory inferences; external validation on independent samples and clinical cohorts (e.g., dyscalculia) is needed.
• While permutation tests support reliability, generalization beyond the sample awaits prospective validation; ROI selection variability across LOOCV iterations may affect feature stability.