The genetics of spatiotemporal variation in cortical thickness in youth

Abstract

Prior studies have shown strong genetic effects on cortical thickness (CT), structural covariance, and neurodevelopmental trajectories in childhood and adolescence. However, the importance of genetic factors on the induction of spatiotemporal variation during neurodevelopment remains poorly understood. Here, we explore the genetics of maturational coupling by examining 308 MRI-derived regional CT measures in a longitudinal sample of 677 twins and family members. We find dynamic inter-regional genetic covariation in youth, with the emergence of regional subnetworks in late childhood and early adolescence. Three critical neurodevelopmental epochs in genetically-mediated maturational coupling were identified, with dramatic network strengthening near eleven years of age. These changes are associated with statistically-significant (empirical p-value <0.0001) increases in network strength as measured by average clustering coefficient and assortativity. We then identify genes from the Allen Human Brain Atlas with similar co-expression patterns to genetically-mediated structural covariation in children. This set was enriched for genes involved in potassium transport and dendrite formation. Genetically-mediated CT-CT covariance was also strongly correlated with expression patterns for genes located in cells of neuronal origin.

Schmitt et al. studied the genetics of maturational coupling via longitudinal models of cortical thickness in N=677. Genetic correlations were dynamic. Patterns resembled expression of genes associated with potassium channels and dendrite formation.

Introduction

The human cerebral cortex is highly dynamic in youth^1,2. From mid-childhood to early adulthood, maturational changes in cortical volumes are primarily driven by cortical thickness (CT)³. Longitudinal studies using MRI have found rapid increases in CT in the newborn period^4,5, followed by more protracted and generally monotonic decreases in CT over later childhood and adolescence^3,6–8. These global trends are underpinned by considerable spatial variability in rates of change in CT across the cortical sheet. For example, adolescence is a period of accelerated thinning in the lateral frontal lobes, but decelerating thinning in occipital regions³. There is also evidence that peri-Sylvian and peri-calcarine cortex have less pronounced thinning relative to other areas^3,8,9. In general, cortical maturation proceeds along a posterior to anterior gradient, first involving primary sensory cortex, with subsequent maturation of association areas¹⁰.

While longitudinal studies have provided important insights into how CT changes with age, these univariate analyses do not directly consider the complex spatial interactions between brain regions. Multivariate investigations into structural covariance have characterized the cross-region neuroanatomic relationships in cross-sectional samples, finding reproducible and scientifically plausible networks in typically-developing samples across the lifespan^11–14. For example, a study of structural covariance patterns in a series of four distinct child and adolescent cohorts (total age range 4.9–18.0) found that cortical networks are small and initially limited to adjacent structures and contralateral homologs; primary and sensory cortical networks subsequently emerge, followed by higher-order networks¹⁵. While many canonical networks appear to progressively increase in size with age, the spatial extent of many networks (e.g. visual, auditory, and the default mode network) experience their peak near 13 years of age, with subsequent pruning during late adolescence – ultimately resembling networks of young adults.

By examining dynamic changes in cross-regional covariance over time (i.e. combining the longitudinal and multivariate analytic approaches described above), the coordinated spatiotemporal patterns of CT changes over neurodevelopment, i.e. maturational coupling, can be investigated⁹. This work has found that correlational patterns of CT change are weak in neonates and strengthen in toddlerhood¹⁶. Across adolescence, maturational coupling is strongest in the fronto-temporal association cortex, and weakest in primary sensory cortex⁹. Peak network connection strength and nodal density is observed at ~9.5–11.5 years of age, followed by reductions in network strength in late childhood¹⁷. Weakening network strength continues into early adulthood¹⁸. Prior studies have found that patterns of maturational coupling, structural covariance, and functional networks are similar^9,19,20.

In an independent thread of research, prior quantitative genetic analyses using twin samples have found that numerous structural neuroimaging phenotypes are significantly heritable²¹. For example, genetic influences on cerebral gray matter are detectable even in neonates²², and the heritability of cortical gray matter increases in older children²³. Our prior work on NIMH’s Intramural Longitudinal MRI Study of Human Brain Development^24,25 found regionally-specific variation in in the heritability of CT, with stronger genetic effects observed in more evolutionarily-novel regions²⁵. Analysis of CT-CT structural covariance between gyral-level regions of interest (ROIs) in this sample found a strong shared global genetic factor that influences CT throughout the brain, but regionally-specific genetic factors are also critical in local cortical patterning²⁶. When examining CT at high spatial resolution (40,962 vertices), genetically mediated associations with global mean CT were strongest in association cortex, and genetic factors were dominant in explaining the covariance between cerebral hemispheres (e.g. between contralateral homologs)²⁷.

There is emerging evidence that genetic factors also influence the longitudinal trajectories of brain growth^2,28–30. When examining the NIMH longitudinal sample using genetically informative latent growth curve models, we previously found that the genetic influences on CT in youth are highly dynamic². Both genetic and environmental variance decreases with age, while heritability generally increases due to smaller reduction in genetic variance. The areas of greatest change correspond to more evolutionarily novel cortical regions². However, the role of genetics on maturational coupling in youth (i.e. examining genetic, multivariate, and longitudinal information simultaneously) remains relatively unexplored. Cortical thickness is influenced by numerous factors including cellular density, cell size, dendrite formation, synaptogenesis, and cortical myelination^31–35; these are all presumably influenced by genetic effects. Following early neurodevelopment, shared trophic factors and functional activity may induce maturational coupling, subsequently leading to more stable structural covariance patterns following early neurodevelopment. We have previously investigated the genetics of maturational coupling at the lobar-level using genetically informative, multivariate, longitudinal models, finding dynamic changes in CT-CT covariance over childhood and adolescence in 16 large cerebral ROIs³⁶.

The current study expands on this prior work, fusing longitudinal, multivariate, and quantitative genetic models in order to explore the genetics of CT maturational coupling at significantly higher spatial resolution in a large MRI dataset of child and adolescent twins and families. Using these models, we probe several critical questions on the genetics of cortical development. First, we quantify the genetically-mediated patterns of structural covariance between cortical regions in youth. Second, we exploit the longitudinal nature of our data to model trajectories of CT-CT genetic correlations over time, and subsequently explore how age influences brain network cohesion. Third, we identify critical genetically-mediated maturational epochs in CT-CT maturational coupling. Finally, we fuse our results with extant transcriptional data from the Allen Human Brain Atlas (AHBA) in order to identify gene sets with similar expression patterns to the CT-CT genetic correlational patterns we observe in youth.

Results

Dynamic genetic effects on CT variance and maturational coupling

Longitudinal, multivariate quantitative genetic models identified dynamic changes in genetic influences on the thickness of 308 cortical regions (Fig. 1A) over childhood and adolescence. In general, heritabilities (i.e. the proportion of phenotypic variances attributable to additive genetic effects) were highest in the inferior frontal gyri, superior frontal gyri, temporal pole, and insula (Fig. 1B). Regional estimates of CT heritability generally increased over childhood and adolescence. Genetically-mediated structural connectivity also changed substantially over childhood (Fig. 1B and Supplementary Movies). At younger ages (e.g., 5 years), there were already relatively strong regionally-specific (e.g. lobar) genetic correlations, but over time these local relationships tended to strengthen, while associations with more spatially distant ROIs generally weakened. The result was increasingly localized and more tightly coupled networks over the age range, particularly in late childhood and adolescence. In later childhood, strong network hubs emerged in the right parietal and posterior frontal lobes. Spectral clustering revealed the most striking in changes in genetically mediated ROI community membership between 10 and 15 years of age (Fig. S1).

Fig. 1. Genetic influences on cortical thickness in youth.

A Example of the 308 cortical parcellations used to measure regional thickness; color assignments were randomly generated. B Dynamic changes in the influence of genetic factors on cortical thickness. Brain maps display maximum likelihood (univariate) heritability for seven equally-spaced timepoints, while brain graphs display genetic correlations >0.80, with nodes colored by lobe and with node size proportional to its degree. The dynamic changes in genetically mediated maturational coupling can also be appreciated in the supplemental movies. C Statistical significance of additive genetic effects on CT-CT covariation. The matrix on the left plots χ² comparing the full model to one without any genetic effects on CT-CT covariance (df=6), while the matrix on the right displays χ² for genetic change (df=5), while allowing for main effects of genes on total ROI covariance.

The statistical significance of ROI-ROI genetic covariance is shown in Fig. 1C (Supplementary Data). Strong additive-genetic covariances were observed between nearby ROIs, with patterns generally replicating lobar anatomy based on genetic covariances alone (e.g. blocks of high correlations along the main diagonal). There were strong shared genetic effects between contralateral homologs. Genetically-mediated maturational couplings over the age range were, in some ways, similar to absolute genetic effects, with relatively strong coupling between ROIs in the same cerebral lobe. ROIs in the bilateral frontal cortices had relatively strong genetically-mediated changes with many ROIs elsewhere in the brain.

Identification of critical maturational epochs in CT-CT covariance

We then applied non-negative matrix factorization (NMF) to the 3D genetic correlation matrix. NMF is a machine learning technique that can be used cluster timeframes with similar spatial features. Results are summarized in Fig. 2. Three critical maturational epochs were identified near 5, 11, and 18 years of age. Between ages 5 and 11, there was a substantial increase in the number of strong genetic correlations (r_G > 0.8), largely driven by increases network strength in the frontal and parietal lobes (Figs. 2 and S2). The right cerebrum had somewhat stronger genetically mediated structural connectivity relative to the left. There were statistically significant increases in both global clustering coefficient (Δ = 0.10, empirical p-value < 0.0001) and assortativity (Δ = 0.25, empirical p-value <0.0001) between 5 and 11 years of age. Differences between ages 11 and 18 were more subtle, with generally weaker genetic correlations, but focally stronger network hubs in the right parietal lobe. Global clustering coefficient was comparable between ages 11 and 18, but assortativity significantly decreased in late adolescence (Δ = −0.14, empiric two-p-value <0.0001). Similar findings persisted over all levels of network sparsity (Supplementary Figs. S3–S6).

Fig. 2. Identification of neurodevelopmental epochs in cortical thickness patterning using non-negative matrix factorization (NMF).

The 3D genetic correlation matrix was first transformed by vectorizing correlations from each timepoint. The matrix was constrained to be non-negative by dividing the data in to two segments, one with the positive values (zero if the correlation was originally negative), and the second with the absolute value of the negative correlation (zero if originally positive). NMF was then applied to generate matrices containing edge coefficients (W) and the temporal information on the temporal strength of each subgraph (H). The coefficient matrix was then reorganized into 3 subgraphs temporally peaking at ages 5, 11, and 18 years. Graph models of genetically mediated network architecture were then constructed (displayed graphs have density = 1%). Corresponding global network statistics with 95% confidence intervals are also provided (bottom right, see also Figs. S3–S6).

Neuronal gene expression parallels CT genetic correlations in youth

We then used our CT-CT genetic correlation matrix as a probe to identify genes in AHBA with similar co-expression patterns, via supervised principal components analysis (sPCA). Results are provided in Fig. 3. The dominant factor (sPC1) explained over 70% of the total variance in gene expression (Fig. 3C). Embeddings on this component had a strong anterior-posterior gradient, with strongest absolute values found in the occipital cortex, near the temporal poles, and in the anterior cingulate. Co-expression matrices based on those genes with the top and bottom 1% of factor loadings (Supplementary Data 1 and tab Table S1) were strikingly similar to the original CT-CT genetic correlation matrix. When comparing specific spatial gene expression between the top and bottom gene candidates, expression patterns were near mirror images of one another. This finding was confirmed when examining spatial expression patterns for specific genes with the highest (e.g. SCN1B, SEMA7A) and lowest (e.g. PTGER3, SY17) factor loadings.

Fig. 3. Associations between genetically-mediated CT covariance and gene co-expression patterns.

A Co-registration of data from the Allen Human Brain Atlas (AHBA) to 152 left-sided ROIs from our sample. The black dots represent MNI centroids for twin CT data, while the colored dots indicate the location of AHBA samples (colors correspond to individual subjects) and with lines indicating nearest neighbor connections. B Supervised PCA (sPCA) input. C Results from sPCA Scree barplot with dominant component (sPC1) highlighted in red. The embedding map for PC1 is also shown. Gene co-expression correlation matrices for the 2% of genes with the strongest loadings on PC1 are shown, as well as gene expression Z-scores for each ROI separately. Whole-brain expression maps for several genes with the strongest factor loadings (e.g. SCN1B, PTGER3) are also shown. D Gene enrichment and protein-protein interaction networks based on Metascape analysis of the top 2% of genes associated with sPC1.

Gene enrichment analysis (Fig. 3D) found that those genes with strongest factor loadings on sPC1 were significantly enriched for voltage-gated potassium channels (-log p-value = 7.24, q-value = 0.0013), with greater than 11-fold enrichment relative to background, and with our gene set including nearly 25% of all genes in the voltage-gated potassium channel Reactome ontology (Fig. S7). Genes involved in dendrite extension also were significantly enriched (-log p-value 4.15, q-value 0.0199) and included two semaphorins (SEMA7A and SEMA4F), NOTCH1, and monoamine oxidase (MAOB). Protein-protein interaction analyses found significant enrichment in neuronal systems (−log p-value = 12.0, q-value < 0.0001). The largest MCODE subnetworks were involved in potassium ion transport, voltage-gated potassium channels, and midbrain development (Fig. 3D, Supplementary Data 1, and tab Table S2). Post hoc analysis found that spatial patterns of sPC1-derived median gene expression were moderately correlated with both excitatory (r = 0.67) and inhibitory (r = 0.62) neuron gene sets, and were more weakly correlated with gene sets from glial cell types (all r < 0.35) (Fig. S8). ROI-ROI gene co-expression maps for both excitatory and inhibitory neurons were similar to sPCA regional co-expression patterns; out of all cell-derived sets, neuronal sets had the strongest similarities to sPC1 gene co-expression (empirical p-value <0.0001).

Discussion

The current study investigates the genetics of maturational coupling at high spatiotemporal resolution. We find dynamic patterns of CT-CT genetic correlational relationships throughout youth, with general trends towards increased regional specificity and the emergence of strong network hubs in frontoparietal regions in later childhood and adolescence. In early childhood, we find widespread and relatively uniform genetic correlations throughout the cerebral cortex, possibly due to shared global genetic effects influencing the entire cortex early in life (i.e., in the fetal period, or very early childhood). We also found strong genetic correlations between ROIs and their contralateral homologs over the study interval, a finding also observed in multiple samples over the entire lifespan; these correlations appear well-established by age 5 and persist at least into early adulthood. In contrast, we find profound increases in genetically-mediated regional connectivity over this age range. Our findings suggest that not only are the genetic influences on CT highly dynamic in childhood, but the evolving patterns of structural correlations also are highly influenced by changes in shared additive genetic factors.

The importance of genetics on maturational coupling has been previously hypothesized^9,37. Patterns of gene expression in mouse models predict emergent patterns of structural covariance^38,39. In humans, genetic, structural, functional, and maturational covariance maps show clear neuroanatomic similarities with one another^26,20. Neurodevelopmental trajectories in cortical thinning over the lifespan have been shown to predict genetic structural covariance in middle age, and are remarkably similar to patterns of cortical thinning in older adults⁴⁰. Our observed dynamic correlational patterns in youth resemble patterns of spatiotemporal brain dynamics previously reported in childhood and adolescence in postmortem samples⁴¹.

It has been postulated that cortical networks develop through distinct connectivity milestones⁴². Global structural network strength rapidly increases in early childhood, peaking in the beginning of the second decade of life¹⁷, and with subsequent weakening more gradually throughout adolescence¹⁸. We find similar patterns to those reported previously, although our data suggest that these changes in network strength are largely genetically mediated. We additionally report evidence of three distinct neurodevelopmental epochs in youth, based on the observed dynamic genetic correlational patterns, with particular changes in network structure observed late childhood near 11 years of age. Like prior studies, we find that average ROI degree, global clustering coefficient, and assortativity all dramatically increase during this time period. Although many neurodevelopmental processes wane by the second decade of life, late childhood and early adolescence are a period of active synaptic pruning⁴³ and cortical myelination⁴⁴. Our study provides further evidence that many of these changes are driven by shared additive genetic factors influencing spatiotemporal variation in CT-CT neurodevelopmental trajectories. Prior phylogenetic research has found periods of relative genetic convergence during mid embryogenesis, with divergence before and after this timepoint (i.e., the “hourglass” model of development), likely owed to evolutionary constraints at critical neurodevelopmental epochs^45,46. A similar hourglass-shaped transcriptional profile has been observed for gene expression in the brain in human youth during fetal development⁴⁷. These periods of relative genetic constraint could potentially explain some of our observed patterns of genetically-mediated CT-CT covariance in youth. Although temporally preceding the peak age of onset of most childhood psychiatric disorders by a few years⁴⁸, the dramatic changes in structural networks that we observe during this time period may explain the genetic liability to these conditions⁴⁹, as well as to their genetically-mediated comorbidities.

Finally, we identify gene sets with expression profiles that replicate CT genetic correlational patterns in youth. Prior studies have found that cortically-based transcriptional and structural covariance networks have similar properties⁵⁰. Using sPCA to combine these data, we identify a dominant genetic factor with a clear anterior-posterior gene expression gradient. This finding mirrors previous work showing a dominant genetically-mediated anterior-posterior gene expression gradient in the cerebral cortex^51,52, as well as paralleling known patterns of neurodevelopmental changes in the cerebral cortex observed over youth^8,53. We found that the genes with the strongest loadings on this factor all had very strong anterior-posterior expression profiles when examined individually. The spatial co-expression pattern of our AHBA gene set was also remarkably similar to the CT genetic correlation matrix, and was particularly enriched for genes involved in potassium transport. Thus, variation in potassium transport may contribute to individual differences in CT in youth. Cortical thinning during adolescence has been associated with expression patterns of S1 pyramidal cells; these cells in turn have increased expression of potassium channels⁵⁴. Genetic variation in potassium transport may induce spatiotemporal variation intracellular potassium levels, which is associated with apoptosis⁵⁵. Ion channels and transporter gene expression have also been prominently associated with cortical volumes⁵⁶ and resting state functional connectivity^57,58. Genes involved in dendrite extension were also significantly enriched in our analysis. Cortical thickening in adolescence is associated with CA1 pyramidal cell expression profiles, which in turn are enriched in gene ontologies associated with neuroplasticity, particularly dendrite extension⁵⁴. Our observations of strong similarities in regional gene co-expression between CT-associated genetic effects and neuron-expressed gene sets supports this hypothesis.

Limitations

There are several limitations to the current study that must be considered when interpreting these findings. First, the sample size is modest by the standards of quantitative genetic analysis. The presence of multivariate longitudinal data and continuous measures both ameliorate this issue; larger genetically informative longitudinal studies such as the Adolescent Brain Cognitive Development (ABCD) study will likely provide additional insights in the near future⁵⁹. Second, as inherently based on a twin paradigm, our principal analyses inherit all the assumptions of this design, most notably the assumption of an equal shared environment for MZ and DZ twins, at least with respect to non-elicited factors influencing the phenotypes measured (i.e. CT). Additional assumptions include random mating, no non-additive genetic variation, no significant G-E covariance, and no G x E interaction. Third, due to the complex computational nature of these models, we do not explicitly test for shared environmental effects in this study. However, it is noteworthy that we did not find shared environmental influences in our prior work on maturational coupling in a similar sample (albeit using substantially larger ROIs³⁶). Fourth, we exclusively used the CIVET pipeline for image processing, which increases the risk of methodologically specific results; although prior work has shown comparable measurements of CT across common image-processing pipelines, there are some notable pipeline-specific differences, for example in paralimbic and mid-occipital regions using CIVET⁶⁰. However, we would expect these differences to have a relatively small effect on the current study given its focus on longitudinal changes and within-family covariance, rather than absolute measures of CT relative to a gold standard. Temporal changes in scanner settings could also potentially contribute to observed variation over time⁶¹. Fifth, the unusual nature of the NIH longitudinal Twin MRI dataset makes direct replication in independent samples challenging; replication of this work in ABCD and other samples will be important. Sixth, the AHBA data was obtained on adults rather than children, and variations in gene expression over age are not accounted for; this was the principal rationale for examining only spatial (rather than spatiotemporal) correlates with AHBA and our data, although in principle trajectories of genetically-mediated change could also be investigated. The role of environmental influences on gene expression, gene x environment interactions, and the potential differential environmental effects between the NIH and AHBA samples were also not examined. Additionally, by using the entire CT-CT genetic correlation matrix as a probe, our analysis did not investigate potential regionally-specific transcriptional variation in cortical subnetworks; this could represent a potential future research direction.

Methods

Subjects

677 typically developing children, adolescents and young adults from 382 families were recruited at the Child Psychiatry Branch of the National Institute of Mental Health (NIMH), as part of the Longitudinal MRI Study of Human Brain Development⁵³. The sample included pediatric, adolescent, and young adult monozygotic twins (MZ, N = 183), dizygotic twins (DZ, N = 75), siblings of twins (N = 71), and singleton (N = 232) family members (summarized in Table 1, Fig. S9). Parents of prospective participants were interviewed by phone and asked to report their child's health, developmental, and educational history. Subjects were excluded if they had taken psychiatric medications, had been diagnosed with a psychiatric disorder, had undergone brain trauma, or had any condition known to affect gross brain development. Inclusion criteria were a minimum gestational age of 29 weeks and a minimum birth weight of 1500g. Approximately 80% of families responding to the ads met inclusion criteria. For twin subjects, zygosity was determined by DNA analysis of buccal cheek swabs using 9–21 unlinked short tandem repeat loci for a minimum certainty of 99%, by BRT Laboratories and Proactive Genetics. We obtained verbal or written assent from the child and written consent from the parents for their participation in the study. The Combined Neurosciences Institutional Review Board (CNS-IRB) at the National Institutes of Health approved the protocol. All ethical regulations relevant to human relevant to human research participants were followed.

Table 1.

Demographic characteristics of the sample

	MZ	DZ	Siblings of twins	Singletons	Total
Sample size	222	101	84	270	677
Mean age at first scan (years $\mp$ SD)	8.6 (3.7)	7.4 (3.6)	9.7 (4.3)	9.1 (5.2)	8.7 (4.5)
Mean scan interval (years $\mp$SD)	2.3 (0.72)	2.3 (0.60)	2.5 (1.12)	2.9 (1.44)	2.6 (1.2)
Scan age range (years)	5.4 – 27.0	5.3 – 25.6	5.4 – 23.9	3.3 – 34.4	3.3 – 34.4
Gender	119 F (54%) 103 M (46%)	55 F (54%) 46 M (46%)	36 F (43%) 48 M (57%)	144 F (53%) 126 M (47%)	354 F (52%) 323 M (48%)
Handedness	194 R (87%) 15 M (7%) 13 L (6%)	83 R (82%) 10 M (11%) 8 L (8%)	68 R (80%) 7 M (8%) 9 L (11%)	241 R (89%) 18 M (7%) 11 L (4%)	586 R (87%) 50 M (7%) 41 L (6%)
Socioeconomic status (SES) (Hollingshead Index $\mp$ SD)	43.2 (18.0)	41.8 (15.2)	40.7 (17.3)	40.1 (20.1)	41.4 (18.4)

MRI acquisition

All MRI images were acquired on the same General Electric 1.5 Tesla Signa Scanner located at the National Institutes of Health Clinical Center in Bethesda, Maryland. A three-dimensional spoiled gradient recalled echo sequence in the steady state sequence was used to acquire 124 contiguous 1.5-mm thick slices in the axial plane (TE/TR = 5/24 ms; flip angle = 45 degrees, matrix = 256 × 192, NEX = 1, FOV = 24 cm, acquisition time 9.9 min). A Fast Spin Echo/Proton Density weighted imaging sequence was also acquired for clinical evaluation. A total of 1,318 MRI scans were acquired. Up to six MRI scans were performed per individual (specific N by timepoint: timepoint 1 = 300, 2 = 213, 3 = 93, 4 = 46, 5 = 21, 6 = 4), with sibships containing up to five members. The mean interval between scans was 2.4 years. All anatomic images were visually inspected for quality by an expert reviewer using a four-point scale⁶²; only scans with the highest quality rating were included in the current analysis. Given increasing concerns of the role of image quality on measurement^63,64, a more stringent quality control pipeline was used compared to prior work³⁶ resulting in the exclusion of 115 subjects from the current analysis.

Image analysis

All MR images were imported into the CIVET pipeline for automated structural image processing⁶⁵. Briefly, the native MRI scans were registered into standardized stereotaxic space using a linear transformation⁶⁶ and corrected for non-uniformity artifacts⁶⁷. The registered and corrected volumes were segmented into white matter, gray matter, cerebrospinal fluid, and background using a neural net classifier⁶⁸. The gray and white matter surfaces were fitted using deformable surface-mesh models and nonlinearly aligned toward a template surface^69–71. Both surfaces were subsequently resampled into native space. The tissue classification information was combined with a probabilistic atlas to provide volumetric region of interest (ROI) measures⁷². Lobar volumes were included in this analysis for each hemisphere separately. Cortical thickness was measured in native-space using the linked distance between the white and pial surfaces^70,73 and assigned to specific regions using a probabilistic atlas⁷⁴. Each vertex was assigned to one of 308 regional parcellations based on the 68 ROIs of the Desikan-Killany atlas⁷⁵. These canonical parcellations were further divided into ~500mm² sub-ROIs based on a backtracking algorithm⁷⁶. This approach resulted in relatively uniformly-sized ROIs, while also preserving the original boundaries of the Desikan-Killany atlas (Fig. 1A). ROIs were subsequently visually inspected to ensure quality.

Statistics and reproducibility

Latent growth curve modeling

Each subject’s neuroanatomic measures were imported into the R statistical environment for analysis⁷⁷. The data were reformatted such that each record represented family-wise (rather than individual-wise) data. The subsequent dataset contained up to six longitudinal ROI measures per individual, and up to five individuals per family. Genetic modeling was performed in Open Mx, a structural equation modeling package fully integrated into the open source R environment^78,79.

For each pairwise combination of ROIs, a genetically informative bivariate quadratic latent growth curve (LGC) model was constructed^80,81. Genetically informative LGC models for the analysis of neuroimaging data have been described elsewhere^2,36. Compared to other longitudinal methods, LGCs have the advantage that they allow for direct age-based predictions, are robust to missing data cells, and are customizable to unique data structures⁸². A simplified path diagram is provided in Supplementary Fig. S10. Structural equation models decomposed the variances and covariances between the three latent growth curve factors (intercept, linear, and quadratic) into additive genetic (A) and specific environmental (E) components. Quantitative genetic models often include latent factors estimating the role of the shared environment (C); however, since prior studies have shown that shared environmental contributions to CT variance in this age rage are minimal²⁵, shared environmental latent factors were excluded from the model. Because the study design acquired panel rather than cohort longitudinal data, the age at scan was integrated into the model as a dynamic (i.e. definition) variable to individualize growth curve predictions⁸³. ROI CT means were adjusted for sex, age, age, and global mean CT.

Models were fitted by maximum likelihood, which generally yields asymptotically unbiased parameter estimates of the genetic and nongenetic contributions to ROI-ROI CT covariance. In order to test the statistical significance of genetic factors on temporal variability, submodels were constructed which removed the free parameters modeling changes in ROI-ROI covariance (while retaining the main effects); Given certain regularity conditions, differences in log-likelihood between these models asymptotically follow a χ² distribution with degrees of freedom equal to number of parameters removed (9 degrees of freedom for all genetic effects, 6 degrees of freedom for change)^84–86. The statistical significance of all additive genetic influences on CT variability (i.e. both main effects and changes) were quantified similarly. Statistical tests were two-sided.

Visualizing dynamic changes in genetic associations

Using the maximum likelihood parameter estimates from our quadratic models, time-specific genetic covariance matrices were then estimated for 124 equally-spaced intervals over the 5–18 year age range (~0.1 year intervals), which resulted in sufficient temporal resolution to describe the growth curves. Genetic covariance matrices can be conceptualized as that portion of the phenotypic variance-covariance matrix associated with additive genetic effects on the diagonal. ROI-ROI genetic covariances, describing the covariance that two phenotypes share via additive genetic factors, comprise the of-diagonal elements Genetic correlations (r_G) were then calculated for each timepoint by standardizing the genetic covariance matrix, mathematically defined as:

$$r_{x,y}=\frac{A_{xy}}{\sqrt{A_x*A_y}}$$

Where $A_{\left\{xy\right\}}$ is an off-diagonal element of $A$, and $A_x$ and $A_y$ are the corresponding diagonal elements.

Dynamic changes in r_G over time were then visualized by concatenating serial heatmaps to construct a 3D correlation matrix, with 2 spatial dimensions (pairwise ROI-ROI combinations) and 1 temporal dimension (Supplemental Movie S1). As an alternative method of visualization, serial graph theoretical (i.e., network) models of the strongest CT-CT genetic correlations were constructed at multiple timepoints, with each ROI’s position in the graph set to the MNI spatial coordinates of its centroid. Undirected edges were determined by binarizing the 3D correlation matrix based on correlational thresholds (e.g., r_G = 0.8) and the results visualized using serial graph models (e.g., Fig. 1B and Supplemental Movies S2 and S3). Heritability estimates (i.e. the proportion of phenotypic variance attributable to additive genetic effects) for each ROI were also calculated for each timepoint (Fig. 1B). Finally, spatiotemporal variation in community structure were visualized using the PisCES algorithm, a clustering method that incorporates temporal changes in network strength into its algorithm, enabling visualization of how genetically-mediated CT clusters evolve over time (Supplementary Fig. S1)⁸⁷.

Neurodevelopmental epochs in maturational coupling

To identify critical neurodevelopmental periods in genetically-mediated maturational coupling, we applied nonnegative matrix factorization (NMF) to our 3D genetic correlation matrix (Fig. 2A). NMF is an unsupervised data reduction technique similar to latent variable analysis that has been applied to a variety of large datasets including image recognition⁸⁸, gene discovery⁸⁹, structural and functional brain connectivity analysis^90,91, and a broad assortment of other high-dimensional bioinformatics data. NMF has several advantages relative to other dimensionality reduction techniques, including that it allows for overlap of subcomponents and generally leads to better interpretability of parameter estimates. Of particular note, NMF has previously been applied to high-dimensional neuroimaging datasets on temporally-varying endophenotypes^90,92.

Our general analytic framework was modeled after Kao et al., which investigated similarly structured data consisting of a 3D series of dynamic ROI-ROI correlation matrices⁹⁰. The lower triangular ROI-ROI genetic correlation matrix (g=47,278 pairwise elements) for t=31 equally-spaced time points (~0.4 year intervals) from ages 5-18 was vectorized; the choice of 31 timepoints was based on computational limitations. All time-specific correlation vectors were then concatenated into a single g x t matrix. Because NMF requires positive values, positive r_G values were isolated by constructing a matrix in which negative correlations were set to zero. Negative correlations were similarly isolated (with positive values set to zero), and both positive and negative matrices were concatenated into a single V = g x 2t analysis matrix.

NMF was then applied to this matrix using the NMF package in R⁹³. NMF attempts to identify:

$$\mathit{V}\approx \mathit{WH}$$

where W and H are g x r and r x 2t non-negative matrices, respectively. The NMF algorithm initialized W and H parameters using Nonnegative Double Singular Value Decomposition⁹⁴, and then performed iterative optimization of the Kullback-Leibler Divergence^89,95. Choice of factorization rank, r, was determined empirically using the method of Hutchins et al.⁹⁶. Specifically, the residual sum of squares (RSS) for models with r ranging from 2-26 was generated and plotted with 100 randomly-initiated runs per rank; r was selected at the natural inflection point in the RSS curve (Figure S11). For our data, this resulted in a factorization of 6. The output matrix W represents genetically-mediated edge strength between two ROIs for each of 6 subgraphs, and H represents time-varying expression strength of each subgraph. Similar to Kao et al., there was strong temporal correspondence between positive and negative correlation subgraphs; these were combined to generate subgraphs at the 3 critical neurodevelopmental timepoints identified by the NMF algorithm.

The network properties of each subgraph were then explored in igraph⁹⁷. A 308 x 308 unweighted adjacency matrix R was generated that contained pairwise similarity measures for all elements r_ij, resulting in a set of M ROI-ROI connections (i.e. edges). Common global network statistics for three common measures of network strength (degree, clustering coefficient, assortativity)¹² were then calculated for each epoch separately. Briefly:

Degree (D): The degree, or node strength, is simply the total number of connections that a network vertex (in our case, an ROI) has with other vertices. For vertices i and j:

$$D_i=\sum _j{r}_{ij}$$

The more connections an ROI has to other brain regions, the higher the degree. The global measure was simply calculated the mean degree over the entire network.

Clustering Coefficient (C): The global clustering coefficient (also known as transitivity) is the mean proportion of a vertex’s neighbors that are also connected to one another⁹⁸. For a single vertex v in set V, the clustering coefficient C the proportion of all possible connections with neighboring vertices which are realized:

$$C\left(R\right)=\frac{1}{V}\sum _{v\in V}\frac{closedtriplets}{alltriplets}$$

where a “closed triplet” represents a group of three vertices that are all connected, and “all triplets” also includes groups where only two vertices are connected.

Assortatitivity (A): Assortatitivity describes the tendency of vertices connect to other vertices with similar properties⁹⁹. We used the most commonly used measure of assortiativity; degree assortativity. For M total edges in the network, the degree assortativity can be calculated as:

$$A=\frac{M^{-1}{\sum }_k{i}_k{j}_k-{\left[M^{-1}{\sum }_k\frac{1}{2}\left(i_k+j_k\right)\right]}^2}{M^{-1}{\sum }_k\frac{1}{2}\left(i_k^2+j_k^2\right)-{\left[M^{-1}{\sum }_k\frac{1}{2}\left(i_k+j_k\right)\right]}^2}$$

where i_k and j_k are the degrees of the vertices at the ends of the kth edge for k=1 … M¹⁰⁰. Note that although this calculation appears complex, it essentially represents the Pearson correlation of degree between pairs of linked vertices.

Since network density can potentially influence many network statistics¹⁰¹, all global network densities were calculated for multiple network sparsities ranging from 1% to 20%. 95% confidence intervals were obtained via bootstrap, with the null distribution generated by randomly rewiring each graph (while preserving graph degree), with 1000 replicates per bootstrap. The two-sided statistical significance of age-related differences in global network statistics were assessed via permutation of difference scores, also with 1000 replicates per sparsity level.

Cortical thickness and gene transcription

We then compared the observed patterns of CT-CT genetic correlations to the normalized human gene transcriptional profiles provided by the Allen Human Brain Atlas (AHBA). The AHBA includes post-mortem transcriptional measurements for >62,000 probes from 6 individuals aged 24–57 years, sampled at hundreds neuroanatomic locations per subject (364 – 947), all mapped to MNI space¹⁰². Prior to transcriptomic analysis, gene-to-probe reannotation was performed with Re-Annotator¹⁰³. We then excluded AHBA samples derived from noncortical structures (e.g. putamen). Only probes with high expression above background were included; specifically, only probes with a both (1) a mean difference score p-value <0.01, and (2) a standard deviation >2.6 above background levels survived QA¹⁰⁴. Expression values for each sample were subsequently converted to Z-scores.

AHBA samples were then aligned to CT data by nearest neighbor matching, based on MNI coordinates (Fig. 3A). Because only two AHBA subjects had samples from the right cerebral hemisphere, these samples were mirrored onto the left hemisphere by inverting their MNI x coordinates. Following alignment, all but one of the 152 left-sided CT ROIs were matched to at least one sample. The single unmatched ROI (supramarginal gyrus 7) was excluded. Median expression values at each location between all subjects were then calculated. Following all QA, annotation, and alignment steps, expression data for 21,165 probes across 151 ROIs were available. We then used our CT genetic correlation matrix to extract gene sets with similar co-expression patterns. This analysis was accomplished using Seurat, an R package with algorithms designed for multidimensional transcriptomics¹⁰⁵. The left-hemispheric genetic correlation matrix for age = 13 years (151 x 151) was converted to a k=20 weighted nearest neighbor kernel. Age 13 was selected because it was close to the median age of our sample, in the region of densest genetically informative data. Supervised Principal Component Analysis (sPCA) was then performed using this kernel and the genetic transcription matrix as inputs¹⁰⁶. sPCA is similar to routine PCA, except the algorithm ensures that the subsequent components have maximal dependence on the kernel response variables.

The largest component (sPC1) explained nearly 70% of the total variance in the AHBA dataset. We subsequently constructed a candidate gene set associated with sPC1 by extracting genes with the strongest (top and bottom 1%) associations to this latent component, i.e., those genes with the strongest absolute loadings on the dominant factor. Spatial expression patterns for the genes with the strongest factor loadings were visualized by projecting expression Z-scores onto brain models. The total gene set was then input into Metascape for annotation, gene enrichment analysis, and identification of protein-protein interactions¹⁰⁷. To minimize false positives, a custom set of 15,745 brain-expressed genes was used as the background for enrichment analysis¹⁰⁸. Protein interaction analysis was performed with the Molecular Complex Detection (MCODE) algorithm¹⁰⁹ and subsequent functional enrichment in Metascape.

Because of results from gene enrichment analysis, we also compared gene expression patterns from our sPCA-derived set with several cell-specific gene sets, as described in Seidlitz et al.¹¹⁰. Cell-specific sets were based on data from several prior studies^111–114. Median gene expression for each cell-specific gene set was calculated over 151 cortical ROIs. Similar median expression vectors were also calculated for our sPCA gene set (Supplementary Data 1: tab Table S1), all 21,165 AHBA genes surviving QA/QC, and the subset 15,745 of brain-expressed genes also used as background for enrichment analyses¹⁰⁸. Correlations in regional expression patterns between each set were calculated. Additionally, the 151 x 151 ROI-ROI co-expression matrices were compared between sPCA and each cell-specific gene set using the partial Mantel test, after controlling for co-expression patterns in the brain-expressed gene set. 10,000 permutations were used to estimate the null; statistical tests were two-sided.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

Eric Schmitt: conceptualization, statistical design, analysis, visualization, writing-original draft, and editing. Aaron Alexander-Bloch: statistical consultation, software development, writing-review, and editing. Jakob Sleiditz: statistical/genomic consultation, generation of cell-specific expression dataset, writing-review and editing. Armin Raznahan: conceptualization, data acquisition, image processing, writing-review, and editing. Mike Neale: conceptualization, software development, writing-review, and editing.

Peer review

Peer review information

Communications Biology thanks Hervé Lemaître and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Michel Thiebaut de Schotten, Karli Montague-Cardoso and Jasmine Pan.

Data availability

The NIMH Longitudinal Development MRI dataset is available online at: http://nda.nih.gov/edit_collection.html?id=3142. Derived data (e.g. 3D genetic correlations), Supplementary Figs., tables, and movies are available in DataDryad: 10.5061/dryad.7h44j103r¹¹⁵.

Code availability

R code for genetically informative longitudinal structural equation models, NMF, AHBA-NIH sample integration, and sPCA is available from the corresponding author upon request. Gene enrichment analysis tools are freely-available available online.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42003-024-06956-2.