Brain functional-structural gradient coupling reflects development, behavior and genetic influences

Domain: neuroscience
Published: 2026-04-09
Editorial outcome: major_revision

Abstract
Gradients provide low-dimensional representations of macroscale brain organization, yet how structural-functional gradient coupling develops and relates to behavioral and molecular features remains unclear. Here, we studied structural-functional gradient coupling across multiple metrics and spatial scales using high-resolution structural and functional connectivity from 5,343 children in the Adolescent Brain Cognitive Development study and 875 adults from the Human Connectome Project. We find that gradient coupling shows developmental refinement from childhood to adulthood and distinct sex-specific patterns. Gradient coupling metrics are significantly associated with cognitive and mental health measures and enable robust out-of-sample prediction. Heritability analyses reveal that gradient coupling is strongly influenced by genetic factors. Transcriptomic analyses further demonstrate that highly heritable coupling patterns are enriched for genes expressed in deep-layer excitatory neurons. Together, our findings establish structural-functional gradient coupling as a biologically meaningful feature of brain organization that bridges macroscale connectivity, cognition, behavior, and molecular architecture.

Introduction
Understanding how the anatomical architecture of the brain supports its functional activity is a central question in neuroscience. Structural and functional connectivity (SC and FC) provide complementary, network-level characterizations of the brain structural and functional organization, where SC captures physical pathways of white matter tracts while FC characterizes temporal synchronization of activity between regions across the whole brain. The relationship between SC and FC, known as structure-function (SF) network coupling, reflects how closely brain functional patterns are shaped by anatomical constraints at a large-scale network level [1, 2]. Prior work on SF coupling spans infant [3], youth [4], and adult cohorts [5, 6, 7, 8].

Importantly, developmental studies also show that SF network coupling increases with age in several cortical territories and follows nonuniform maturational trajectories across the cortex [4, 9, 10]. Together, these observations suggest that the SC-FC relationship is neither spatially homogeneous nor developmentally static, but instead varies systematically along cortical hierarchies.

Concurrently, recent advances in gradient-based approaches have deepened our understanding of large-scale brain organizations. Rather than characterizing the brain as a set of discrete networks, gradient-based approaches reduce high-dimensional connectivity data into a few continuous axes that capture gradual transitions in the brain organization [11]. Functional connectivity gradients (FCGs) describe smooth spatial variation in FC, revealing continuous transitions from sensory-motor regions toward association cortex, as well as additional axes reflecting other large-scale functional distinctions [12]. Structural connectivity gradients (SCGs) characterize analogous patterns in SC, delineating axes such as somatosensory-medial prefrontal and ventral-dorsal visual transitions [13]. Building on these ideas, we focus on structural-functional gradient coupling (SFGC): the spatial alignment between SCGs and FCGs, which provides a complementary and more hierarchical perspective on SF coupling. Unlike traditional node-wise SF coupling, which quantifies how similar each region’s SC and FC profiles are, SFGC captures how structural and functional hierarchies correspond across the cortex. This distinction is particularly important for neurodevelopment because gradients index large-scale hierarchical organization, whereas node-wise SF coupling reflects only local SC-FC correspondence. Divergent findings between SFGC and node-wise SF coupling, therefore, could highlight distinct multiscale mechanisms of SF organization that cannot be inferred from connectome-level measures alone. Despite its promise, SFGC remains largely understudied. Most research has focused on gradients within a single modality, often limited to FCGs [12], while the cross-modal correspondence between SCGs and FCGs has received limited attention. Prior work has shown that microstructural gradients and FCGs are increasingly dissociated in transmodal cortex [7, 14] and that SC–FC correspondence decreases along the functional principal gradient during development [10]; however, no studies have directly examined how SFGC develops over time to our best knowledge. Moreover, the behavioral and genetic relevance of individual differences in SFGC, and whether these relationships differ across development, remain unclear. Filling these gaps could offer critical insight into how the brain integrates structure and function over neurodevelopment, how these interactions support cognition and mental health, and how they are shaped by molecular architectures.

While prior research has suggested that SF coupling may support cognitive performance and clinical outcomes [1, 6], the relationship between SFGC and individual differences in cognition or mental health has been underexplored. In particular, the potential of SFGC as a predictive feature for behavioral traits has not been investigated. It remains unclear whether variation in the alignment of structural and functional hierarchies can explain altered cognition and behavior, and if so, which coupling patterns are most informative. Addressing this gap is critical for advancing our understanding of how macroscale brain organization supports complex traits and for identifying potential neuromarkers to inform neurodevelopmental and psychiatric conditions.

Furthermore, both SC and FC are known to be heritable [15, 16], and emerging evidence also suggests that SF coupling is shaped by genetic factors [17]. However, it remains unclear whether the alignment between SCGs and FCGs is heritable, which brain systems are most susceptible to genetic influence, or how such effects vary across cortical hierarchies or developmental stages. Meanwhile, transcriptomic atlases such as the Allen Human Brain Atlas (AHBA) now enable researchers to examine whether neuroimaging-derived phenotypes reflect underlying cell-type-specific gene expression patterns [18]. If spatial variations in SFGC correspond to distinct molecular signatures, it would help provide crucial biological context for interpreting this emerging marker for brain organization.

To address these gaps, in this work, leveraging multi-dimensional data from 5,343 children in the Adolescent Brain Cognitive Development (ABCD) study and 875 young adults from the Human Connectome Project (HCP), we construct brain SFGC under various metrics and spatial scales across development stages, and comprehensively uncover its correspondence with cognitive and behavioral domains, as well as genetics and molecular architectures. Our findings suggest age-associated changes in SFGC, with observable differences between male and female groups. We further demonstrate that SFGC robustly predicts a wide range of cognitive and mental health traits across cohorts and methods, establishing it as a behaviorally meaningful neuromarker. Extending beyond phenotype, we show that brain SFGC is highly heritable, exhibiting a developmental specificity where genetic influence targets unimodal and transmodal networks in childhood and shifts to preferentially constrain transmodal hubs in adulthood. Finally, we perform imaging transcriptomic analyses to characterize the spatial correspondence between regional heritability maps and cortical gene expression profiles, revealing that heritable SFGC patterns show distinct molecular associations across development: in adults, regions with stronger genetic influence spatially overlap with genes enriched in superficial and intermediate-layer excitatory neurons, whereas in children they exhibit significant correspondence with endothelial and microglial signatures. Together, these findings position SFGC as a biologically grounded, developmentally refined, and behaviorally relevant feature of human brain organization.

Results
Leveraging multimodal neuroimaging data from two independent cohorts, including children from the ABCD study and young adults from the HCP cohort, we constructed SC and FC for each subject from T1-weighted, diffusion, and functional magnetic resonance imaging (MRI) data. We then derived individual-level cortical SCGs and FCGs, and constructed both macroscale-level and subnetwork-level SFGCs as illustrated in Fig. 1. The detailed data processing, data harmonization and metrics construction procedures are described in the Methods section.

To investigate SFGC and its developmental dynamics, we first examined the architectures of SCGs and FCGs separately. The averaged SC and FC matrices displayed clear network-level structure (Supplementary Fig. 1a), forming the connectivity framework for subsequent gradient and coupling analyses. Applying diffusion embedding to the connectivity affinity matrices yielded a small number of principal gradient axes that summarize large-scale patterns in SC and FC. Visualization of the first two gradients across cohorts was provided in Fig. 2a, b, g, h, illustrating how their spatial layout differed with age. In addition, heatmaps of the False Discovery Rate (FDR)-adjusted p-value (p) from 10,000 spin permutations further confirmed that the spatial correspondence between children and adults differed significantly across multiple SCGs and FCGs (Supplementary Fig. 1b, c). In children, the first FCG predominantly captured a sensorimotor-to-visual axis, reflecting the early organization of primary systems. Their second FCG showed strong similarity to the adult primary axis (r = 0.84, spin permutation test adjusted p = 0.03), indicating the emergence of transmodal association networks. In contrast, adults exhibited a well-defined first FCG extending from primary sensorimotor areas to transmodal hubs, consistent with the mature hierarchical organization of the cortex. SCGs also showed pronounced developmental differences. In children, the first SCG separated the Visual and Somatomotor Networks (VIN and SMN) and the second SCG displayed strong asymmetry in networks across hemispheres (paired t-test p = 1 \times 10^{-10}). In adults, the first SCG similarly separated VIN and SMN, while the second SCG did not exhibit significant hemispheric asymmetry (paired t-test p=0.52), displaying a bilaterally symmetric spatial pattern.

The spatial correspondence between SCGs and FCGs reflected a core principle of SF association across cortical hierarchies. To quantify this correspondence, we computed pairwise cosine similarity between the cohort-level SCGCs and FCGs, resulting in macroscale SFGC matrices (Fig. 2c, i). Throughout this article, we denoted SFGC between the the ith FCG and the jth SCG as FCGi:SCGj. Inspection of the SFGC matrices showed distinct correspondence patterns across gradient pairs. In children, a relatively strong coupling (magnitude of SFGC c = 0.59) was observed between the first FCG and SCG, suggesting that early functional organization, particularly along the sensorimotor-to-visual axis, remains closely aligned with the underlying structural scaffold. In contrast, the same gradient pair in adults showed much weaker coupling (c = 0.08, two-sample Welch’s t-test adjusted p < 10^{-6}). To formally characterize differences between children and adults, we constructed a heatmap of FDR-corrected p-values for SFGC across all structural–functional gradient combinations, which revealed that most pairs exhibited significant cohort differences (Supplementary Fig. 1d).

Having established the macroscale SFGC strength across different gradient pairs and development stages, we next examined how SFGC patterns manifested within individual functional systems, as defined by the Yeo-7 canonical subnetworks [19]. We observed substantial heterogeneity in the gradient alignment at the subnetwork level: some networks exhibited strong coupling even when global alignment was weak, whereas others displayed decoupling despite strong global coupling. To illustrate this coupling heterogeneity, we focused on a representative gradient pair, FCG1:SCG1, which showed relatively high alignment in children but weak alignment in adults (Fig. 2c, i). Notably, strong coupling was consistently observed in primary sensory and motor networks, whereas association networks such as Default Mode Networks (DMN) showed greater decoupling (Fig. 2d, j). To further assess these network-specific patterns, we visualized coupling strength across networks in each hemisphere using radar plots (Fig. 2e, k). The results highlighted relatively high and consistent gradient alignment in unimodal systems across developmental stages, in contrast to more variable couplings observed in other networks. Specifically, the Ventral Attention Network (VAN) was more pronounced in children, while Frontoparietal Network (FPN) was relatively high in adults. Together, these findings established that both macroscale- and subnetwork-level SFGC represent meaningful levels of organization, and that examining both scales provide a more complete characterization of SF correspondence. We therefore included both metrics in downstream analyses to assess their associations with behavioral, demographic, and genetic factors.

Associations between SFGC and a broad range of behavioral and demographic outcomes were assessed at both macroscale and subnetwork levels. To ensure robust and generalizable estimates, we implemented two predictive modeling approaches: kernel ridge regression (KRR) [20] and multilayer perceptrons (MLP) [21], with 100 random train-test splits. Detailed procedures for model fitting and evaluation are provided in the Methods section.

We examined associations between SFGC and mental health outcomes, motivated by prior evidence linking SF coupling to psychiatric vulnerability [22]. Our results revealed modest average out-of-sample associations between SFGC and mental health outcomes. In particular, the association between SFGC and mental health outcomes varied by spatial scale and age cohort: in children, macroscale-/subnetwork-level SFGC yielded average r = 0.09/0.11 with mental health outcomes; whereas in adults, SFGC exhibited a slightly weaker association with average r = 0.04/0.11 (Fig. 3a). Furthermore, in both cohorts, the strongest association was observed for rule-breaking (RuleBreak) symptoms with subnetwork SFGC (r=0.145 in children, r = 0.144 in adults). The FDR-corrected paired t-tests of the difference between macroscale- and subnetwork-level SFGC in Fig. 3a demonstrated overall subnetwork SFGC’s stronger association with mental health outcomes, e.g., aggressive (Aggressive), withdrawn/depressed (With/Dep), RuleBreak, and externalizing (External) symptoms. This divergence suggested that the spatial scale at which SFGC was behaviorally relevant may shift across development. Beyond mental health, SFGC also showed predictive utility for sex classification, with area under the curve (AUC) values of 0.77/0.83 in children and 0.79/0.87 in adults (Fig. 3a) for macroscale-/subnetwork-level SFGC. Visual inspection of SFGC topographies revealed distinct spatial patterns between males and females (FCG1:SCG1, Fig. 2f, l). Specifically, sex differences were more pronounced in unimodal regions in adults, whereas in children, they appeared in a different cortical pattern, suggesting that SFGC may capture a sex-dimorphic dimension of brain architecture.

To formally assess cohort-related differences, we conducted FDR-corrected two-sample Welch’s t-tests comparing SFGC-behavior association strengths between children and adults. As shown in Fig. 3b, SFGC was more strongly associated with sex and age in adults, while SFGC was in general more associated with mental health outcomes (Aggressive, External) in children (adjusted p < 0.01). Given that SFGC underwent extensive harmonization, the persistence of this pattern likely reflected genuine developmental shifts in brain architecture.

To explore how these sex and cohort effects interact in shaping the mental health relevance of SFGC, we further stratified the cohorts by sex and re-estimated SFGC-outcome associations (Fig. 3c). In children, males showed greater associations for External, internalizing (Internal), Aggressive, and anxiety/depression (Anx/Dep) for FDR-corrected Welch t-tests. In adults, however, females exhibited a stronger association of subnetwork SFGC with Aggressive, while males maintained the stronger macroscale SFGC association with Externel, RuleBreak and Internal. These findings suggested the mental health correlates of SFGC were modulated by both development and sex.

Previous studies reported significantly altered SC and FC between hippocampal subregions, implicated in cognition and emotion, and cortical areas in individuals with cognitive impairment [23, 24]. Furthermore, while SF coupling was found to be largely preserved at the whole-brain level in mild cognitive impairment, it was selectively increased in the Dorsal Attention Network (DAN) and decreased in the VAN [25]. These findings suggest that SFGC may reflect compensatory or pathological reorganization and could serve as a predictor of cognitive outcomes.

Building on this, we evaluated the relationship between SFGC and cognitive function across development. SFGC showed broadly similar association patterns, with subnetwork-level coupling showing slightly stronger associations with most cognitive outcomes (Fig. 3a). Specifically, the FDR-corrected paired t-tests for the difference between macroscale- and subnetwork-level SFGC in their association with cognition demonstrated that subnetwork-level SFGC associated with multiple outcomes better than macroscale-level SFGC in both cohorts (adjusted p < 0.001), such as Picture Sequence Memory (PicSeq), Picture Vocabulary (PicVocab), and Total Cognition Composite (CogTotal). Overall, this showcased the additional information embedded in subnetwork SFGC and its significance in downstream analysis.

In addition, the strength of the association between SFGC and cognitive performance was greater in children on average (macroscale/subnetwork: r = 0.26/0.30), particularly for integrative cognitive scores such as CogTotal (macroscale/subnetwork: r = 0.38/0.44). Lower association between cognitive outcomes and SFGC was observed in the adult cohort (macroscale/subnetwork: r = 0.18/0.23), among them the highest association was observed for Crystallized Composite score (CogCrystal, macroscale/subnetwork: r = 0.28/0.38). The two-sample Welch’s t-tests in Fig. 3b further confirmed that SFGC was more predictive of cognitive outcomes in children, including List Sorting Working Memory (ListSort), Fluid Cognition Composite (CogFluid), Dimensional Change Card Sort (CardSCort), CogTotal, PicVocab, and CogCrystal (adjusted p < 0.001), underscoring the greater behavioral relevance of gradient alignment during this critical developmental stage.

Having observed sex differences in the associations between SFGC and mental health, we next examined whether similar sex-dependent patterns exist for cognitive outcomes across development. As shown in Fig. 3c, in children, females exhibited stronger SFGC-cognition associations for PicSeq, and males showed stronger association Flanker Inhibitory Control and Attention (Flanker) and CardSort (adjusted p < 0.001). In contrast, in adults, females showed stronger association with Flanker and CardSort (adjusted p < 0.05), while males showed stronger associations with PicSeq (macroscale: adjusted p < 0.001). In both cohorts, Oral Reading Recognition (ReadEng) remained more strongly linked to SFGC in females; and CogFluid and Pattern Comparison (ProcSpeed) were more strongly linked to SFGC in males. This developmental reversal for PicSeq, Flanker and CardSort may reflect sex-specific patterns of brain maturation. Together, these findings pointed to a dynamic interaction between SFGC and cognitive functions, shaped by both developmental stage and sex.

To identify the neural circuits underlying associations between SFGC and behavioral and demographic outcomes, we analyzed the feature importance of subnetwork-level SFGC measures, defined as normalized primal coefficients for KRR and normalized saliency maps for MLP, see details in Methods section. We report the maximum feature importance (FI) within each subnetwork in the following. A clear cohort-related redistribution of SFGC emerged in associations with sex (Fig. 3f, j). In children, predictive SFGC features for sex were primarily localized in the SMN and DAN (FI = 0.94, 0.95), whereas in adults, these features shifted toward the FPN and VAN (FI = 0.91, 0.96), suggesting a maturation-related transition from sensory-driven (unimodal) to integrative (transmodal) functional systems.

For cognitive outcomes (Fig. 3d, h), we also observed a shift in the spatial distribution of predictive subnetwork features. In children, predictive SFGC located primarily in VAN and VIN (FI = 0.70, 0.62). In contrast, adults showed numerically decreased involvement of VAN (FI = 0.51). For SFGC-age association (Fig. 3g, k), children appeared to rely more heavily on the DMN, FPN and VAN (FI = 0.99, 0.74, 0.71), while in adults, predictive contributions tend to come increasingly from the SMN, DAN and VAN (FI = 0.72, 0.72, 0.72). Additionally, for SFGC-mental health association (Fig. 3e, i), we observed a numerically higher involvement of SMN in adults (FI = 0.71) than in children (FI = 0.56), while a numerically lower involvement of VIN was observed in adult (FI = 0.44) than in children (FI = 0.53).

Moreover, a clear developmental distinction emerged in Fig. 3a, where SFGC-behavior associations showed lower inter-individual variability in children than in adults across all behavioral domains. Taken as a whole, these results suggested that SFGC became increasingly differentiated and individualized with age, offering a potential neural substrate for behavioral diversity in adulthood. Additionally, as shown in Supplementary Fig. 3, we observed consistent overall patterns in the FI maps, supporting the robustness of our analysis and the reliability of the proposed FI metrics.

We further investigated how genetic factors shape SFGC across developmental stages by estimating the heritability of each coupling metric. Specifically, we computed SFGC heritability using both the Yeo-7 canonical subnetworks and the D–K atlas [26] at a finer resolution, with the latter enabling a more precise characterization of the spatial distribution of heritability across the brain and a direct comparison of these patterns with the spatial organization of SFGC itself. As shown in Fig. 4a, b, j, k, the average SFGC strength matrices for both children and adults exhibited a clear hierarchical organization across gradient orders: couplings involving the principal (lower-order) SCGs and FCGs showed the strongest alignment, whereas those involving higher-order gradients were markedly weaker. Following this same hierarchy, the heritability of these SFGC metrics revealed an even more explicit and systematic decline across gradient orders in both cohorts and parcellation schemes (Fig. 4c, d, l, m). Couplings anchored on the principal gradients showed the strongest genetic influence, whereas couplings involving progressively higher-order gradients showed substantially lower heritability. This pattern was particularly pronounced under the D-K atlas, likely due to its finer spatial resolution that enhanced the capture of localized, region-specific genetic signals. Importantly, this hierarchical decline in heritability was not simply a byproduct of weaker coupling strength at higher gradient orders. Rather, it reflected an underlying gradient-based genetic hierarchy, suggesting that lower-order SFGCs, presumed to capture core axes of SF brain organization, were more strongly constrained by genetic factors.

The magnitude of SFGC heritability was broadly consistent across parcellations and cohorts, with slightly higher averages in children (Yeo-7: h2 = 18.32% versus 19.45%; D-K: h2 = 16.48% versus 17.42%). The highest heritability estimates for individual subnetwork-level SFGC reached 61.99% in adults and 60.02% in children. At the macroscale-level SFGC, the mean heritability increased further to 24.13%, with maximum values up to 61.56%. To contextualize these estimates, we compared them to the heritability of unimodal gradients (Supplementary Fig. 4). While FCGs and SCGs showed moderate to strong heritability, SFGC exhibited mean heritability comparable to these unimodal gradients but reached higher maximal values. Notably, paired comparisons after multiplicity correction (Supplementary Table 1) revealed that SFGC displayed significantly higher heritability than corresponding FCGs in both cohorts, and significantly higher heritability than SCGs in children but lower heritability than SCGs in adults. These findings indicated that SFGC captures highly heritable multimodal axes of cortical organization whose genetic influence differs systematically from unimodal gradients and shifts across development.

Building on the hierarchical heritability patterns across gradient indices, we further examined the spatial topography of SFGC heritability across the cortex. We systematically quantified heritability for all 400 coupling pairs, characterizing both global average patterns and the subnetwork-level distribution of genetic influence. In the following, we highlight the FCG1:SCG1 coupling as a representative example, as it consistently exhibited strong heritability in both children and adults. At the Yeo-7 subnetwork level (Fig. 4e, n, g, p), the spatial pattern of FCG1:SCG1 heritability closely matched the generalized heritability distributions. In adults, both the surface map of FCG1:SCG1 heritability and the subnetwork-level heritability distributions highlighted the DMN and FPN as heritability hotspots, with significantly higher values in the left hemisphere (LH; DMN: adjusted p = 0.006; FPN: adjusted p = 0.010), suggesting strong and lateralized genetic constraint on transmodal systems during maturity. In children, peak heritability was localized primarily within the VIN and DMN. Only the VAN showed significant hemispheric asymmetry (adjusted p = 0.037), again favoring the LH. Across cohorts, the VIN and DMN consistently showed high median heritability, while the Limbic Network ranked lowest. These findings collectively indicated a developmental progression from broad genetic constraints in unimodal and attentional systems in childhood to strongly lateralized transmodal hubs in adulthood.

Regional analyses using the D-K atlas (Fig. 4f, o, i, r) refined these patterns. In adults, FCG1:SCG1 heritability was highest in the superior frontal gyrus, precuneus, and inferior parietal cortex, and the full distribution across coupling traits confirmed peak densities in bilateral precuneus, a pivotal DMN hub, alongside the LH inferior parietal and right middle temporal cortices. In children, heritability was strongest in occipital regions and the precuneus, with the bilateral precuneus, right hemisphere (RH) lingual gyrus, and LH lateral occipital cortex showing maximal density. These findings revealed a shift from occipital-precuneus dominance in children to precuneus-frontoparietal dominance in adults, with the precuneus emerging as a developmentally stable genetic hotspot.

Finally, hemispheric correlations in regional heritability (Fig. 4h, q) showed strong bilateral similarity in adults (r = 0.69, p = 6.97 \times 10^{-6}) and moderate similarity in children (r = 0.56, p = 5.77 \times 10^{-4}). Global lateralization was nonsignificant in both cohorts (adults: p = 0.798; children: p = 0.672), yet regional asymmetries were evident. In children, higher RH heritability appeared in the superior frontal and posterior cingulate gyri; in adults, the LH superior frontal and RH isthmus cingulate showed prominent asymmetry. Thus, while overall genetic constraint remained bilaterally balanced, region-specific asymmetries shifted developmentally, highlighting dynamic and genetically regulated functional lateralization across development.

To investigate whether regional variation in SFGC heritability exhibits a structured spatial correspondence with cortical gene expression patterns, we performed imaging transcriptomic analyses by integrating regional heritability estimates with developmentally matched bulk and single-cell gene expression datasets (Fig. 5a, b). Using spatially adjusted gene-heritability correlations and cell-type-specific gene set enrichment, we identified distinct transcriptomic profiles associated with the representative FCG1:SCG1 coupling across development (Fig. 5d, e).

In adults, regional SFGC heritability showed significant positive spatial correspondence with gene sets associated with excitatory neurons enriched in superficial and intermediate cortical layers (Excitatory neuron 3: adjusted p = 0.009; Excitatory neuron 4: adjusted p = 0.042; Excitatory neuron 5: adjusted p = 0.022; Excitatory neuron 8: adjusted p = 0.047). These excitatory classes are crucial for intracortical communication and long-range integration, properties consistent with the transmodal regions exhibiting the strongest heritability. Conversely, significant negative correspondence was observed with Microglia (adjusted p = 0.015) and Astrocytes (adjusted p = 0.046). In children, SFGC heritability showed significant positive spatial correspondence with gene sets associated with Endothelial (adjusted p = 0.015) and Microglia (adjusted p = 0.0004), pointing to a stronger contribution of vascular and immune-related pathways during earlier developmental stages. Together, these findings indicated developmentally distinct molecular patterns underlying the spatial distribution of SFGC heritability.

We also examined individual genes exhibiting both high cell-type specificity and consistent spatial association with SFGC heritability across cohorts. We focused on coding genes corresponding to two excitatory neuron-preferential RNA-binding proteins, CPEB3 and NOVA1 (Fig. 5c), known master regulators of synaptic function. In adults, both CPEB3 (r = 0.33, adjusted p = 0.0345) and NOVA1 (r = 0.33, adjusted p = 0.0267) showed significant positive correlations with the regional heritability of SFGC (Fig. 5g). Similar associations were observed in children (Fig. 5f; CPEB3: r = 0.55, adjusted p = 0.0347; NOVA1: r = 0.53, adjusted p = 0.0492). While broader excitatory gene sets were not enriched in children, these genes provided isolated examples of spatial correspondence that is conserved across development.

Methods
All research described in this study complies with all relevant ethical regulations. This study involves the secondary analysis of data from the ABCD Study and the HCP. The original ABCD Study protocols were approved by a centralized Institutional Review Board (IRB) at the University of California, San Diego, as well as the local IRBs at each of the 21 data collection sites. The HCP study protocols were approved by the IRB at Washington University in St. Louis. All participants or their legal guardians provided written informed consent at the time of original data collection. This study was conducted in accordance with the data use agreements of the ABCD Study and the HCP.

The ABCD Study, funded by the National Institutes of Health, is a large-scale longitudinal research initiative investigating brain development and child health in approximately 11,880 children, recruited at ages 9–10 from 21 sites across the United States [33]. Employing comprehensive assessments, including advanced neuroimaging, genetic analysis, cognitive testing, mental health evaluations, and detailed environmental measures, the study tracks participants from childhood through adolescence into young adulthood. Its primary goals are to understand developmental trajectories, examine how genetic, behavioral, and environmental factors influence cognitive, emotional, social, and physical growth, and identify early indicators of mental health conditions to inform effective intervention strategies.

The neuroimaging and behavioral data used in this study were obtained from the NIMH Data Archive (NDA, https://nda.nih.gov/abcd). After rigorous quality control and preprocessing of the neuroimaging data, and exclusion of participants with incomplete covariate information, the final analytic sample consisted of 5,343 subjects (age: mean = 9.97 years, range = 9.00–10.92 years; sex: 48.1% male). For the heritability analyses, we restricted the sample to 975 subjects drawn from 483 families contributing related pairs, which includes 120 monozygotic (MZ) twin pairs, 176 dizygotic (DZ) twin pairs, and 223 full sibling pairs.

The HCP is a major initiative aimed at comprehensively mapping neural pathways to elucidate the brain’s complex wiring architecture. A key component of this effort is the HCP Young Adult (HCP-YA) cohort (https://www.humanconnectome.org/study/hcp-young-adult/data-releases), which focuses on individuals aged 22 to 35. This life stage is characterized by relative brain maturity and stability, making it ideal for investigating normative brain structure and function. Furthermore, we utilized the HCP-D cohort (https://www.humanconnectome.org/study/hcp-lifespan-development/overview), part of the Lifespan HCP consortia, as a strategic bridge to facilitate harmonization between the childhood and adult cohorts. The HCP has established rigorous standards for data acquisition and preprocessing, providing an unprecedented view of structural and functional connectivity. Beyond neuroimaging, participants complete a battery of behavioral and cognitive assessments, enabling the exploration of brain-behavior relationships. Neuroimaging data and most behavioral measures are publicly available at https://db.humanconnectome.org, subject to the HCP Open Access Data Use Terms.

Following quality control and data aggregation, our final analytic HCP-YA sample comprised 875 participants (age: mean = 28.62 years, range = 22–37 years; sex: 46.74% male) from 407 families, including 104 MZ twin pairs, 54 DZ twin pairs, 478 full sibling pairs, 25 half sibling pairs, and 106 singletons. The final analytic sample for HCP-D involved 93 subjects (age: mean = 10.01 years, range = 9.00–10.92 years; sex: 38.7% male).

For both children and young adults, we included the NIH Toolbox Cognition Battery, a standardized and developmentally appropriate assessment recommended for individuals aged 7 and older [48]. This battery spanned multiple cognitive domains, including executive function, episodic memory, language, working memory, processing speed, and sustained attention. It also included composite indices such as the Total, Fluid, and Crystallized Cognition scores, which provided aggregate measures of global, reasoning-based, and knowledge-based abilities, respectively. In our analyses, we included all seven individual task scores and the three composite scores to comprehensively assess the association between cognitive performance and the proposed coupling metric.

For mental health, we used instruments from the Achenbach System of Empirically Based Assessment: the Child Behavior Checklist (CBCL) for children and adolescents (ages 6-18), and the Adult Self-Report (ASR) for adults (ages 18-59). These parallel tools offered dimensional measures of behavioral and emotional functioning based on caregiver report (CBCL) and self-report (ASR), respectively. Specifically, we examined the broadband internalizing and externalizing scores, as well as key syndrome subscales including anxious/depressed, withdrawn/depressed, rule-breaking behavior, and aggressive behavior. A complete list of all cognitive and mental health measures used in our analyses, along with their corresponding variable codes, is provided in Supplementary Table 2. In addition, we summarized demographic variables as well as cognitive and mental health measures stratified by sex and cohort in the Supplementary Table 3.

The ABCD scan session followed a fixed sequence, beginning with a brief localizer for head alignment, followed by the acquisition of high-resolution 3D T1-weighted structural images, two runs of eyes-open resting-state fMRI, diffusion-weighted imaging, and 3D T2-weighted structural scans [33]. Depending on real-time motion monitoring, one or two additional resting-state fMRI runs were acquired to optimize data quality. The session concluded with task-based fMRI paradigms, including the Monetary Incentive Delay, Stop-Signal, and emotional n-back tasks, which probed reward processing, inhibitory control, and working memory. All data were collected using harmonized protocols across Siemens Prisma, GE 750, and Philips platforms at 21 U.S. sites, and underwent centralized quality control and Brain Imaging Data Structure-compliant preprocessing. Quality control (QC) encompassed both automated and manual processes. Automated QC quantified modality-specific metrics including SNR, temporal SNR, head motion (mean FD), and dMRI-specific artifacts such as dark slices identified via tensor-fit residuals. Trained technicians then visually inspected all modalities and derived images using standardized montages, with datasets showing severe motion or imaging artifacts flagged and excluded from further processing. Furthermore, structural, diffusion, and functional MRI data were preprocessed using the standardized ABCD pipeline. For structural T1w/T2w images, preprocessing included gradient nonlinearity correction, cross-modal registration using mutual information, and advanced bias-field correction to mitigate steep receive-coil intensity variations that can affect cortical surface reconstruction. Diffusion MRI data underwent iterative model-based eddy current correction with robust dark-slice censoring, rigid-body motion correction with rotation-adjusted gradient tables, B0 distortion correction using reversed phase-encode b=0 pairs, gradient nonlinearity correction, and registration to T1w space before resampling to 1.7-mm isotropic resolution. Functional MRI preprocessing included AFNI-based head-motion correction, B0 distortion correction using spin-echo field maps, gradient nonlinearity correction, between-scan rigid alignment to a mid-session reference scan, and registration to structural images, with final data retained in native space at 2.4-mm isotropic resolution. More details can be found elsewhere [49].

The HCP-YA protocol was distributed across four approximately 1-hour sessions over two days, each beginning with a rapid localizer to ensure precise head positioning. Day 1 combined ultra-high-resolution structural imaging (T1- and T2-weighted) with alternating blocks of resting-state and task-evoked fMRI. Day 2 emphasized multi-shell diffusion acquisitions and included additional resting-state and task fMRI runs to enhance test-retest reliability [50]. All scans were performed on a customized Siemens Connectome Skyra with enhanced gradients and multiband EPI sequences. Data were processed through six of the HCP Minimal Preprocessing Pipelines, which included three structural pipelines (PreFreeSurfer, FreeSurfer, PostFreeSurfer), two functional pipelines (fMRIVolume and fMRISurface), and a diffusion pipeline [51]. The structural pipelines corrected spatial distortions, aligned T1w and T2w images, performed bias field correction, reconstructed cortical surfaces, and registered data to both an undistorted subject native space and the Conte69 standard surface. The functional pipelines removed spatial distortions, corrected motion, registered fMRI data to the structural images, and projected timeseries into the standardized CIFTI grayordinate space (91,282 cortical and subcortical grayordinates). Diffusion preprocessing normalized B0 intensities, corrected susceptibility, eddy current and motion artifacts, applied gradient nonlinearity correction, aligned diffusion data to the structural images, and resampled them to 1.25 mm resolution. Together, these pipelines produced harmonized surface-based multimodal data optimized for cross-subject analyses. QC combined automated metrics with visual inspection at several stages. Automated QC evaluated raw data and intermediate outputs using measures such as framewise displacement, head motion, and changes in global signal, and included checks for protocol conformance and correct frame counts. Trained technicians also visually inspected structural, functional, and diffusion images, as well as surface reconstructions and registration outputs, to identify artifacts or processing failures.

To accommodate the lower tolerance of younger participants for long scanning durations, the HCP-D protocol was condensed into two 1-hour sessions [52]. All acquisitions were performed on standard Siemens 3T Prisma scanners equipped with 80 mT/m gradients and 32-channel head coils. Structural imaging (T1w and T2w) was acquired at 0.8mm isotropic resolution. Notably, the HCP-D protocol utilized multi-echo MPRAGE and embedded volumetric navigators for real-time prospective motion correction and selective reacquisition of motion-corrupted k-space lines. Functional scans (resting-state and task) maintained 2.0mm isotropic resolution with a TR of 800ms, utilizing AP/PA phase encoding to optimize performance on the Prisma platform. Diffusion imaging was shortened to 21 minutes using a two-shell protocol (b=1,500 and 3,000 s/mm2) at 1.5mm resolution, with an increased multiband factor (MB=4) and a shortened TR (3.23s) to maintain high q-space sampling efficiency. Data were processed using the HCP Minimal Preprocessing Pipelines, ensuring harmonized CIFTI grayordinate outputs (91,282 grayordinates) consistent with the HCP-YA workflow. QA was enhanced by real-time motion monitoring (FIRMM) during BOLD acquisitions, complemented by automated metrics (e.g., framewise displacement) and rigorous visual inspection of surface reconstructions and registrations.

Following these preprocessing steps, we constructed individual-level FC and SC matrices using the Surface-Based Connectivity Integration pipeline, a surface-based, atlas-free approach [53]. This approach uses the white surface (the interface between white and gray matter) to construct connectivity matrices without being constrained by predefined brain parcellations. In this framework, FC was obtained from resting-state fMRI by mapping blood oxygen level-dependent time series continuously onto each vertex of the reconstructed white-gray matter boundary in an atlas-free framework [53]. Pairwise Pearson correlations between all vertex-wise time courses were computed and Fisher-z transformed to yield a dense, vertex-wise FC map that captured fine-grained synchrony across the cortical surface without reliance on pre-specified parcellations. By treating FC as a continuous field on the white surface, this approach preserved the full topographic detail of functional network organization and facilitated direct, high-resolution comparisons with SC.

Building upon this continuous FC representation, SC was derived from diffusion MRI by estimating fiber orientation distributions via multi-tissue constrained spherical deconvolution and performing surface-enhanced tractography with seeds placed directly on the white-matter surface mesh [53]. Each streamline’s endpoints were projected onto cortical vertices to construct a continuous density function of white matter connections, which was then smoothed and normalized to form a probabilistic, vertex-wise SC matrix perfectly aligned with the FC topology. This continuous SC map provided an anatomical scaffold that could be integrated seamlessly with the FC field for SF coupling analyses.

Throughout our analyses, cross-cohort comparisons of SFGC between children (ABCD) and young adults (HCP-YA) were central for revealing developmental differences in gradient coupling. Because such comparisons can be confounded by differences in study protocols, scanners, and sites, we implemented a comprehensive harmonization procedure to align SFGC measures across cohorts. This approach was designed to minimize pipeline- and site-related biases, so that the differences we reported more specifically reflected inherent developmental differences rather than technical artifacts.

It is important to note that directly aligning ABCD and HCP-YA could obscure true cross-cohort differences in the SFGC, because such a procedure cannot distinguish between differences arising from processing pipelines and genuine SFGC differences between the two cohorts. Therefore, we included the HCP-D dataset [54], a companion study to HCP-YA that extends the HCP framework to participants aged 5–21 years. HCP-D uses imaging protocols and processing pipelines closely aligned with those of HCP-YA and samples an age range that overlaps with ABCD. For these reasons, HCP-D served as a bridging dataset between ABCD and HCP-YA. Our procedure thus involved (i) a harmonization step within each cohort to correct for scanner and site effects, and (ii) an alignment step between ABCD and HCP-YA through HCP-D to correct for study and pipeline effects.

First, we applied strict motion quality control by excluding participants with large mean framewise displacement (mean FD > 0.3mm), yielding final samples of 5343 ABCD, 93 HCP-D, and 875 HCP-YA participants. Second, we harmonized data within cohorts using ComBat [55] as implemented in the R package sva [56]. For ABCD, we modeled scanner and site as batch variables; for HCP-D, which was collected on a single scanner, we modeled site only. Consistent with standard ComBat practice, age and sex were included as biological covariates so that their effects were preserved while scanner and site effects were removed. HCP-YA was collected on a single scanner at a single site and therefore did not require scanner/site harmonization. Lastly, we corrected for the remaining effect that are caused by study pipeline differences between ABCD and HCP-D. To achieve this goal, we performed an additional ComBat harmonization treating study (ABCD or HCP-D) as batch effect and again included age and sex as covariates. This would enable us to estimate the mean study effect difference between ABCD and HCP-D, denoted as \Delta_{ABCD-HCP}. Then we added the mean study effect \Delta_{ABCD-HCP} to each HCP-YA subject, thereby placing ABCD and HCP-YA in a comparable SFGC space while preserving inherent developmental differences rather than pipeline artifacts.

For consistency, we applied this harmonization procedure before using gradients, macroscale SFGC, or subnetwork SFGC in all downstream analyses reported in this paper. As shown in Supplementary Fig. 5, this strategy substantially improved harmonization quality, particularly by mitigating pronounced motion- and scanner-related effects in the ABCD cohort.

Cortical gradients were extracted to capture macroscale organizational principles of structural and functional connectivity using the BrainSpace toolbox [57]. Following previous gradient-based imaging studies [27, 36], we applied proportional thresholding at the subject level: for each individual-level SC and FC matrix, we ranked all non-diagonal connection weights and retained the strongest 10% of edges, setting the remaining 90% to zero. This procedure controls network sparsity and reduces the influence of weak or noisy edges while maintaining comparability across participants and modalities. We then transformed these sparsified matrices into cosine similarity affinity matrices for gradient estimation. Gradients were then derived via diffusion mapping, a nonlinear dimensionality reduction technique known for its robustness to noise. In short, diffusion map embedding constructs a Markov operator P(\alpha) = (\Gamma(\alpha))^{-1}W(\alpha), where \Gamma(\alpha) is a diagonal matrix with \Gamma_{i,i}(\alpha) = \sum_{j} W_{i,j}(\alpha), W(\alpha) = \Gamma^{-1/\alpha}A\Gamma^{-1/\alpha} is the affinity matrix A reweighted by the anisotropic diffusion parameter \alpha, and \Gamma is the degree matrix of A. One then solves P_{\alpha} \phi_{\ell} = \lambda_{\ell} \phi_{\ell}, and defines the m-dimensional embedding at diffusion time t (the number of virtual steps in the random walk) as G_{DM}(i) = (\lambda_{1}^{t} \phi_{1}(i), \lambda_{2}^{t} \phi_{2}(i), ..., \lambda_{D}^{t} \phi_{D}(i)), omitting the trivial \lambda_{0} = 1 eigenvector. Raising each eigenvalue to the tth power downweights modes that decay quickly. This yields gradients that capture both local and global connectivity structure with built-in noise robustness. In our implementation, we set \alpha = 0.5 to balance the influence of sampling density, ensuring that neither dense nor sparse regions dominate the embedding. We used t=0 to preserve the full spectrum of connectivity detail.

To enable group-wise comparisons, we aligned individual gradients to a cohort-level template, thereby minimizing inter-subject geometric variability. Following this pipeline, we retained the first 200 gradients per modality, which together explained over 99% of the variance in connectivity structure. For subject i, the resulting functional gradients G^{f}_{i} and structural gradients G^{s}_{i} were matrices of dimension V \times D, where V denotes the number of cortical vertices and D = 20 is the number of retained diffusion components, selected according to the highest eigenvalues in descending order. The resulting principal gradients in both the ABCD and HCP cohorts closely resembled previously reported macroscale gradient topographies [57, 36, 58, 59]. In the cohort-level maps (Fig. 2a, g), the first two functional gradients accounted for 39% of variance in adults and 43% in children. In contrast, the first two structural gradients explained 49% of variance in adults but only 22% in children. While most information was captured by the first few components, variance explained declined gradually across higher-order gradients—dropping by less than 10% per gradient, and less than 5% beyond the fifth. To balance interpretability with information retention, we retained gradients that collectively explained at least 70% of the total variance. Specifically, in adults, the top 20 gradients accounted on average for 74% of structural and 92% of functional connectivity variance. In children, the corresponding figures were 83% for structural and 70% for functional connectivity. Note that the specific topographical ordering of sub-dominant gradients (e.g., FCG2 in adults) can be sensitive to the spatial representation of the connectome and the close proximity of eigenvalues, which is consistent with perturbation theory for eigenspace stability.

For gradient analyses, we performed two sets of statistical tests. First, to assess cross-cohort spatial correspondence of cohort-level gradients, we conducted spin-rotation permutation tests (10,000 permutations) separately for FCGs and SCGs. For each gradient pair (e.g. FCGi in adults and FCGj in children), we evaluated the spatial correspondence between gradients from the two cohorts and assessed its significance against a spatially constrained null distribution generated by spin permutations, with p-values corrected for multiple comparisons using FDR. Second, to assess hemispheric asymmetry in structural gradients, we performed two-sided paired t-tests for each SCG within each cohort.

To quantify the alignment between SC and FC, we introduced SFGC, based on the gradients derived from each modality. We evaluated this coupling at two levels: (i) macroscale, capturing whole-brain gradient alignment, and (ii) subnetwork, assessing regional specificity (see Fig. 1 for illustration).

At the macroscale level, for each subject i, we computed the SFGC \Psi_{idd'} as the cosine similarity between the dth column of the functional gradient matrix G^{f}_{i} and the d'th column of the structural gradient matrix G^{s}_{i}, defined as: \Psi_{idd'} = \frac{\langle G^{f}_{i, \cdot d}, G^{s}_{i, \cdot d'} \rangle}{\| G^{f}_{i, \cdot d} \| \cdot \| G^{s}_{i, \cdot d'} \|}, (2) where G^{f}_{i, \cdot d} \in R^{V} is the dth functional gradient for all V vertices; G^{s}_{i, \cdot d'} \in R^{V} is the d'th structural gradient for all V vertices; V is the number of vertices in the whole brain; \langle \cdot, \cdot \rangle denotes inner product of two vectors; and \| \cdot \| denotes the standard Euclidean norm of vectors. The resulting covariate vector \Psi_{i} = (\Psi_{i11}, ..., \Psi_{iDD}) is of length D^2, representing individual-specific SF gradient alignment. For example, selecting the top D = 20 gradients from each modality yields a coupling vector of length 400. Furthermore, we evaluated differences in absolute SFGC between cohorts for each gradient pair using two-sample Welch’s t-tests, with p-values adjusted using the FDR approach.

To capture regional variation, we also constructed subnetwork-level SFGC, parcellating coupling signals according to two atlases: the Yeo 7-network functional parcellation [19] and the D-K structural atlas [26]. Specifically, the gradients G^{f}_{i} and G^{s}_{i} were first partitioned into J sub-vectors corresponding to the J predefined regions of interest (ROIs), denoted as G^{s}_{i,jd} \in R^{Vj} and G^{f}_{i,jd'} \in R^{Vj}, 1 \le j \le J, 1 \le d, d' \le D, respectively. Here, Vj is the number of vertices within the jth ROI. Then the subnetwork-level SFGC \Psi_{ijdd'} was calculated as the cosine similarity between each pair of functional and structural gradients within each of the J ROIs, defined as \Psi_{ijdd'} = \frac{\langle G^{f}_{i,jd'}, G^{s}_{i,jd} \rangle}{\| G^{f}_{i,jd'} \| \cdot \| G^{s}_{i,jd} \|}. (3) This yielded a subnetwork-level SFGC of dimension d_{sf} = J \times D^2. For example, using the Yeo 7-network with J = 14 and D = 20 results in a d_{sf} = 5,600-dimensional vector per subject. It is important to note that the association studies for different subnetworks were jointly performed. These subnetwork couplings captured localized SF alignment within canonical brain systems.

To examine associations between SFGC and behavioral outcomes, KRR and MLP models were applied independently to each SFGC-outcome pair, using either the macroscale or subnetwork-level SFGC vectors as input features.

In the KRR model [20], for each subject i, we denoted the SFGC vector as x_{i} \in R^{dsf}, and the outcome variable as y_{i}. Note that x_{i} was a vector of macroscale SFGC with dimension 400 or Yeo-7 subnetwork SFGC with dimension 5,600, and was standardized element-wisely for model stability. The model minimized the regularized squared loss: \frac{1}{n} \| y - \psi w \|^2 + \lambda \| w \|^2, where n was the number of subjects; \psi \in R^{n \times n} was a matrix with linear kernel basis of the form \psi(x_{i}, x_{j}) = x^{T}_{i} x_{j}, 1 \le i, j \le n; w \in R^{n} were the coefficients to be estimated; \lambda was a regularization parameter selected via cross-validation from the set {0.01, 0.1, 0.5, 1, 5, 10, 50, 10^2, 10^3, 10^4, 10^5}. Note that a higher \lambda would inflate the penalty term \lambda \| w \| and lead to a more sparse model.

For MLP, we first introduced the concept of neural networks. A neural network is a computational model inspired by the human brain’s structure, designed to recognize patterns, learn from data, and make predictions. It consists of layers of interconnected nodes or “neurons,” including an input layer that receives data, hidden layers that process it, and an output layer that delivers the final results. Each connection has associated weights and biases, which the network adjusts during training to optimize performance. Using activation functions, neural networks introduce non-linearity, enabling them to model complex relationships. The learning process involves forward propagation, where data flows through the network to produce an output, and back propagation, where errors are used to update weights via optimization algorithms like gradient descent. In our analysis, we implemented MLPs with three fully connected layers for the prediction tasks. The input layer consisted of the macroscale or subnetwork-level SFGC. The hidden dimension was set to 128, with a dropout rate of p = 0.5 to mitigate overfitting, and leaky ReLU activation with a negative slope of 0.2 was applied to the first two layers. For sex prediction, an additional Sigmoid function was included to map the outputs to the range [0,1]. The number of training epochs was selected via cross-validation, with a maximum of 50. In the main text, we focused on the KRR results, and presented the MLP results in Supplementary Fig. 2 as a robustness check, which shows strong consistency.

We evaluated the model performance by comparing each observed behavioral outcome and the predicted behavioral outcome using SFGC. Specifically, for continuous outcomes of interest (e.g., CogTotal), we computed the out-of-sample Pearson correlation coefficient (r) between observed and SFGC-predicted outcome variable for each of 100 splitting replicates. For binary outcomes (e.g., sex), we computed the area under the receiver operating characteristic curve (AUC) using observed labels and SFGC-predicted label probabilities for each of the 100 splitting replicates. The resulting 100 correlation coefficients or AUCs for each coupling-outcome correspondence were averaged or used for two-sample paired t-tests and Welch’s t-tests in SFGC-outcome association studies in the Results section. This procedure of utilizing 100 splitting replicates and computing out-of-sample correlation coefficients and AUCs reinforced the robustness of the discovered association between the SFGC and outcomes of interest.

To assess feature relevance, we computed attribution scores for each model. For KRR, raw feature importance was computed as the primal coefficients, i.e. the correlation coefficients with respect to SFGC, denoted as: FI_{0} = x^{T} w \in R^{dsf}, where w was the learned weights of the kernel functions \psi; x = (x_{1}, ..., x_{n}) \in R^{n \times dsf} was the concatenated SFGC from all subjects; d_{sf} was the dimension of SFGC features, d_{sf} = 400 when macroscale SFGCs were used, d_{sf} = 5,600 when subnetwork-level SFGCs under Yeo-7 network were used. For MLP, we used a saliency map [60], defined as the average gradient of the output with respect to the input features: FI_{0} = \frac{1}{n} \sum_{i=1}^{n} \nabla_{x_{i}} f(x_{i}) \in R^{dsf}, where \nabla_{x_{i}} f(x_{i}) indicated the partial derivative vector of the outcome of interest f(x_{i}) with respect to SFGC x_{i}. Then feature importance (FI) was defined as min-max normalized raw importance: FI = \frac{|FI_{0}| - min(|FI_{0}|)}{max(|FI_{0}|) - min(|FI_{0}|)} \in [0,1]^{dsf}. (4) Higher normalized values indicated stronger predictive contributions of the corresponding features. It is important to note that we concatenated the subnetwork SFGC from all subnetworks, i.e., we use features of a dimension 5,600 = 400 SFGCs \times 14 subnetworks in the Yeo-7 atlas. The feature importance from different subnetworks was extracted from a joint model fitting and was thus comparable.

We estimated the heritability of functional and structural gradients, as well as SFGC, using the classical ACE model based on twin and sibling data from the HCP and ABCD cohorts. The phenotype for each subject was modeled as: y = X\beta + g + c + e, (5) where y \in R^{N} was the phenotype vector for N individuals, X \in R^{N \times Q} denoted the design matrix of fixed covariates (including age and sex), and \beta \in R^{Q} represented the corresponding fixed effects. The random effects included the additive genetic effect g \sim N(0, \sigma^{2}_{A} K), the shared environmental effect c \sim N(0, \sigma^{2}_{C} \Lambda), and the unique environmental effect e \sim N(0, \sigma^{2}_{E} I). Here, K was the genetic relatedness matrix and \Lambda represented the shared environment matrix, both constructed from zygosity and parental identifiers. Heritability was defined as the proportion of phenotypic variance attributable to additive genetic effects: h^{2} = \frac{\sigma^{2}_{A}}{\sigma^{2}_{A} + \sigma^{2}_{C} + \sigma^{2}_{E}}. (6) We used maximum likelihood estimation to fit the ACE model, where the variance components \sigma^{2}_{A}, \sigma^{2}_{C}, and \sigma^{2}_{E} were estimated from the residuals of the fixed-effect model after regressing out the effects of age and sex. The ACE model was applied vertex-wise for functional and structural gradients, and region-wise for SFGC at both subnetwork (Yeo-7) and regional (D-K atlas) levels, given that the D-K atlas enabled a more precise characterization of the spatial distribution of heritability and allowed for direct alignment with transcriptomic data. For the young adult cohort, we used the full sample, which includes MZ and DZ twins, full non-twin siblings, and extended family structures sufficient for estimating genetic and environmental variance components. In contrast, for the children cohort, we restricted the heritability analyses to a genetically informative subset consisting of siblings only (n=975), rather than using the full sample of over 5,000 participants. This restriction was motivated by the extremely sparse genetic and shared environment matrices derived from the full sample, which would hinder the identifiability and stable estimation of variance components. By focusing on siblings with known zygosity, we ensured that the model assumptions were satisfied and that heritability could be robustly estimated.

We evaluated the statistical power to detect nonzero narrow-sense heritability using simulations tailored to each cohort’s observed covariate matrix X and relatedness structures K and \Lambda. Phenotypes were simulated under the model y \sim N(X\beta, \sigma^{2}_{A} K + \sigma^{2}_{C} \Lambda + \sigma^{2}_{E} I) with total variance normalized to one, for a grid of assumed true heritabilities (h^{2} = 0.01 - 0.80) and varying proportions of shared environmental variance (\frac{\sigma^{2}_{C}}{\sigma^{2}_{C} + \sigma^{2}_{E}} = 0, 0.3, 0.5, 0.8). For each parameter combination, we fitted both the full ACE model and a reduced model with \sigma^{2}_{A} = 0 on 5,000 simulated datasets, and calculated likelihood-ratio statistics using the standard 50:50 mixture of \chi^{2}_{1} distributions appropriate for boundary-limited variance components. Power was defined as the fraction of simulations yielding p < 0.05. Power curves summarizing these results were provided in Supplementary Fig. 6.

To enable direct statistical comparison across modalities, unimodal FC and SC gradients were summarized at the same subnetwork resolution used for SFGC (Yeo-7 and D-K). For each participant, we extracted subnetwork-level gradient values by averaging vertex-wise gradient scores within each subnetwork. SFGC values were naturally defined at this same resolution. We computed the heritability of each subnetwork-level phenotype and compared SFGC to its matched FC or SC gradient using two-sided paired t-tests across subnetworks. Because FC, SC, and SFGC were all summarized to the same subnetwork resolution, each subnetwork provided a matched phenotype across modalities, enabling valid paired-sample comparisons. Two comparison schemes were implemented: (i) a global metric aggregating the first 20 unimodal gradients and (ii) principal gradient-specific comparisons (the first three gradients). All paired t-test p-values were corrected for multiple comparisons using the Bonferroni procedure (reported in Supplementary Table 1).

To further investigate the biological mechanisms underlying the observed heritability patterns in SFGC, we performed imaging transcriptomic analyses that integrated regional heritability estimates with gene expression profiles. Analyses focused on the SFGC between the first FCG and SCG (FCG1:SCG1), which represented the principal axes of cortical organization and relatively high heritability. For the young adult cohort, we utilized adult gene expressions from AHBA [61], which contained 15,633 genes across 66 cortical ROIs (two ROIs with missing gene data were excluded), and adult cortical single-cell transcriptomics data [62]. Following the established imaging transcriptomics workflow [63], we extracted region-wise gene expression profiles from the AHBA using the abagen toolbox [64], mapped to the D-K atlas [26]. Gene expression values were normalized within each region to a total count of 10,000. For the children cohort, we used adolescent gene expression data from the BrainSpan atlas [65] (21,315 normalized genes across 11 ROIs) and corresponding adolescent single-cell transcriptomic data [66]. We computed Spearman’s rank correlations between the heritability values and gene expressions across ROIs, and ranked genes in descending order based on their correlation with the phenotype-specific heritability pattern.

To account for spatial autocorrelation in both the gene-level correlations and subsequent enrichment analyses, we generated 10,000 spin-rotation permutations of the regional heritability map. Observed statistics were compared against the corresponding null distributions derived from these permutations to obtain spatially adjusted p-values (Supplementary Table 4). All gene–heritability correlations and GSEA enrichment statistics were evaluated relative to the empirical null from these spin permutations, yielding spatially adjusted significance values.

To assess cell-type specificity, we performed GSEA using the GSEApy library [67]. Cell-type-specific gene sets were derived from scRNA-seq data, where the top 200 differentially expressed genes for each cell type were identified using t-tests implemented via the SCANPY pipeline [68]. GSEA was applied to calculate enrichment scores based on the ranked gene list for each phenotype (e.g., heritability of the first functional gradient or SFGC).

For robustness evaluation, we generated 100 replicates of the data splits; within each replicate, model performance was assessed using 10-fold cross-validation. Family structure was accounted for by assigning participants from the same family to the same cross-validation fold. Since we obtained 100 realizations of SFGC-outcome associations and 100 normalized feature importance scores for each SFGC-outcome pair, these replications enabled us to perform two-sample paired t-tests for comparing SFGC-outcome association difference between macroscale SFGC and subnetwork SFGC; and Welch’s t-test for comparing SFGC-behavior association difference between cohorts and between sex in downstream analyses. This procedure ensured the robustness of the SFGC-outcome correspondence and mitigated potential issues of overfitting and sampling bias.

The two predictive modeling approaches, KRR and MLP, demonstrated strong concordance. We presented the association results based on MLP in Supplementary Fig. 2, which were highly comparable association patterns to Fig. 3a produced by KRR. In addition, the overall Pearson’s r between KRR and MLP in the SFGC-behavior association was 0.75 for macroscale SGFC, and 0.80 for subnetwork SGFC, highlighting the robustness of the associations we identified. Furthermore, KRR and MLP exhibited similar patterns of feature importance, where the most important SFGC features identified by the two models shared similar patterns for both macroscale SFGC (Supplementary Fig. 3a) and subnetwork SFGC (Supplementary Fig. 3b). The averaged feature importance values, computed across both methods, were reported in the Results section.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The study by Gao et al., examines how the brain structural-functional (S-F) gradient differs between two age-stratified\ncohorts (i.e., ABCD and HCP-YA cohorts). The results showed cohort and sex-specific differences in SF coupling,\nassociations between SF gradient coupling and cognitive and mental health metrics, spatial overlap between SF gradient\ncoupling and gene expression profiles from AHBA indicating enrichment for genes expressed in deep-layer excitatory\nneurons, and provide regional heritability estimates for the gradient coupling metrics.\nThe question of how structural functional gradient coupling evolves during development and relates to behavioral,\ngenetic\nand molecular features is important and somewhat understudied, to my knowledge. As such, strengths of the study are its\ncomprehensiveness and utilization of multimodal MRI across two well-characterized, large datasets of different ages. The\npaper is, in general, clearly written. However, there are some major substantive concerns, as well as several minor\nconcerns, regarding the literature review, claims and interpretation of the findings and some of the analyses, which diminish\nenthusiasm for the manuscript in its current form:\n1. A more comprehensive description of the previous literature should be included in the introduction and discussion.\nDespite methodological differences, the S-F coupling gradient has been characterized and examined across several papers\npreviously, which also include replication datasets. E.g., Development of S-F coupling gradient using cross-sectional and\nlongitudinal data, as well as examining associations to cognitive performance (Baum et al., 2019, PNAS, doi:\n10.1073/pnas.1912034117); S-F coupling gradient in young adults, with HCP as a replication dataset (Vazquez-Rodriguez\net al., 2019, PNAS, doi: 10.1073/pnas.1903403116); age-related differences S-F coupling assessed across the lifespan\n(Esfahlani et al., 2022, Nat Com, doi: 10.1038/s41467-022-29770-y); characterization of the S-F coupling gradient with\nreplication dataset (Popp et al., 2024, NeuroImage, https://doi.org/10.1016/j.neuroimage.2024.120563); S-F coupling, age-\nrelated differences and spatial overlap with gene expression (Feng et al., 2024, eLife, https://doi.org/10.7554/eLife.93325.2);\ndiscussed in a review article (Suarez et al., 2020, Trends in Cognitive Sciences, doi: 10.1016/j.tics.2020.01.008). While\nthese articles are cited, the characterization in the introduction of the novelty of this study should be revised. Furthermore,\nthe SNP based heritability of the S-F coupling also has been examined previously by some of the same authors using the\nsame datasets as the current paper (Dai et al., 2024, Imaging Neuroscience, https://doi.org/10.1162/imag_a_00346). Some\nof these papers also examined S-F coupling changes in sensory and associations areas across childhood and adolescence\n(i.e., Feng) and across the lifespan (i.e., Esfahlani), which do not fit with the authors claims in the introduction (i.e., “no study\nhas yet tested how SF gradient coupling evolves from late childhood through early adulthood”). Thus, it would be of\nimportance to properly put these findings in the context of previous studies.\n2. Although I find most of the analyses to be appropriate, some of the claims seem broader than what the results justify. As\nacknowledged by the authors, any differences between the two cohorts can also be attributed to other characteristics than\nage, such as sample characteristics (e.g., socioeconomic status, ethnicity, scanner effects, image quality). Thus, the paper\nwould benefit from rephrasing words like “trajectories” and “evolved”, which gives the impression of a longitudinal analysis\nand causality.\n3. As a related point, the results are often presented in a ‘big picture’ summary style (e.g. , p5, ‘Their second functional\ngradient began to resemble the adult principal axis, indicating…”) This statement is easy to understand, but what particular\nanalysis supported this conclusion? Likewise, on p 6 there is a statistic for SF gradient coupling in children, and a lower C-\nvalue for adults, but from what I can tell, there was no direct statistical comparison conducted. There is more quantitative\ninformation presented in the figures and the supplements , but even there there is a fair amount of un-evenness in the level\nof detail provided about what is being depicted (e.g, what conclusions should be drawn from Supp Figures 1 and 3?). More\ndetailed, quantitative information for each of the results and figures would be helpful in evaluating the strength of the claims\nmade.\n4. In relation to cohort differences, it would be helpful if the authors addressed the within sample correlations in more depth,\nas within-cohort variability may influence the brain-behavior relationships within each cohort. For instance, is there more\nvariance in the cognitive and mental health metrics in the ABCD vs HCP-YA? If so, could the authors elaborate on the\npotential impact of range restrictions on the brain-behavior associations?\n5. The authors state that ‘the potential of SF gradient coupling as a predictive\nfeature for behavioral traits has not been investigated ‘; to that end they employ two predictive modeling approaches to\nexamine relationships to mental health symptoms and cognition, but from what I can tell they only utilized cross-sectional\nABCD data. Why not utilize the longitudinal data to conduct an actual predictive analysis?\n6. The ABCD dataset includes MRI data across >20 sites, and it is unclear to me how the authors addressed potential\ndifferences across scanner sites. Examination of how SF coupling may differ across the scanner sites can provide important\ninsight into the potential confounding variables within the ABCD cohort. In addition, younger children also tend to move\nmore in the scanner, which can also influence data quality. Thus, it would be helpful if the authors compared the image\nquality between the two cohorts (e.g., through Euler number/SNR/tSNR/framewise displacement) to rule out the potential\nimpact of image quality on SF coupling.\n7. How did the authors address potential type 1 errors due to spatial autocorrelation between the brain maps and\ntranscriptomic maps? The wording of the transcriptomics analyses reflects a reverse inference logic, i.e. “Transcriptomic\nanalyses further demonstrated that highly heritable coupling patterns are enriched for genes expressed in deep-layer excitatory\nneurons” “Transcriptomic signatures highlight the cellular basis of SF gradient\ncoupling heritability”, “To identify specific molecular contributors”, “To explore the cellular basis of heritability variation in SF\ngradient coupling”, “transcriptomic analyses revealed that the\nheritability of gradient coupling was enriched for excitatory neuronal signatures” this type of phrasing could be perceived as\ntoo strong given the data; a more neutral tone might be more appropriate (e.g.,\nemphasizing the spatial overlap with gene expression maps that are enriched for genes that are highly expressed in deep\nlayer neurons). In addition, since the gene expression values derived from AHBA are based on post-mortem data from\nadults, it is unclear to me how this would be an appropriate analysis to perform on brain maps derived from children. In\naddition, this section suffers from the same issues noted above regarding broad statements and lack of precision, e.g. “\nParticularly strong signals were observed for excitatory neurons 3 and 4..” What is considered the threshold for ‘particularly\nstrong”? was that determined a priori ?\nMinor:\n8. The study lacks information about the power analyses for the heritability estimates, which will be important given the\nsample size differences in the two cohorts.\n9. The authors state that they performed two-sample t-tests, but it is unclear if they are assuming equal or unequal variance\nbetween the groups.\n10. It would be helpful if the authors provide the age-range of the final analytic samples and a demographic table stratified by\nsex.\n11. “Our approaches and results revealed that SF gradient coupling undergoes systematic neurobiological refinement from\nlate childhood to early adulthood with distinct sex-specific trajectories.”\nThis statement could benefit from more careful wording as it gives the impression of causality and longitudinal analyses.\n12. ‘Finally, we integrated transcriptomic data from the AHBA to reveal that heritable gradient coupling patterns are enriched\nfor genes expressed in deep-layer excitatory neurons’\nThe authors should clarify that these analyses examine the spatial overlap between brain and transcriptomic maps.\n13. ‘Rather than characterizing the brain as a set of discrete networks, gradient-based approaches project connectivity\npatterns into low-dimensional manifolds that reveal continuous axes of organization.’\nIt is not clear to me what the authors mean by ‘low-dimensional manifolds’, I suggest rephrasing for clarity.\n14. ‘Even fewer studies have examined how gradient coupling develops over time or varies across individuals.’\nIt would be helpful if the authors provided references to these studies. See major comment.\n15. ‘Although many aspects of brain development unfold gradually across childhood and adolescence,\nmost studies of SF coupling have focused on either mature adult brains or aggregated developmental trajectories.’\nCould the authors clarify on what they mean by “aggregated developmental trajectories”? It is also hard to evaluate this\nclaim without references.\n16. ‘Specifically, we first thresholded the SC and FC matrices to retain the top 10% of connections, then\ntransformed them into cosine similarity affinity matrices.’\nCould the authors elaborate on how they define the top 10% connections?\n17. ‘We further observed that the SF gradient coupling strength between the principal functional gradient and the second\nstructural gradient (FCG1:SCG2) increased from near-zero levels in children to a robust level in adults’\nIt would be helpful if the authors provide references to the figure or table that support this claim.\n18. ‘Furthermore, the association between SF gradient coupling and outcomes varied by scale and age cohort: in adults,\nsubnetwork-level SF gradient coupling showed stronger association with psychiatric symptoms than macroscale gradient\ncoupling, whereas in children, macroscale SF gradient coupling yielded exhibited associations.’\nIt would be helpful if the authors provided a reference to a figure or numbers that supports this claim. It is also unclear to me\nwhich statistical test and results that was used to support the claim of a ‘stronger association’. Also, it is unclear to me what\nis meant by “yielded exhibited associations” ?\n19. For SF gradient coupling and cognitive performance scores, the authors state that associations get weaker in adults, but\nI struggle to find the statistical test was performed to support this claim other than a numerically lower correlation. In addition,\nthe wording gives the impression that differences in correlations are due to age (e.g., “became weaker in adults”) – if there is\na significant difference, a more accurate description would be “lower in the adult cohort”.\n20. ‘After rigorous quality control and preprocessing of the neuroimaging data, and exclusion of participants with incomplete\ncovariate information, the final analytic sample consisted of 7,025 subjects (mean age = 9.9 years; 48.8% male).’\n‘Following quality control and data aggregation, our final analytic sample comprised 913 participants (mean age = 28.7\nyears; 46.55% male) from 414 families, including 111 MZ twin pairs, 59\nDZ twin pairs, 511 full sibling pairs, and 95 singletons.’\nIt would be helpful if the authors could elaborate on the quality control procedures performed on each cohort.\n21. Will the authors provide the regional values for the SF coupling gradients? This could be further used by other\nresearchers to examine the spatial overlap with SF coupling with other cortical maps.\n22. The GitHub link doesn’t work. It would be helpful if the authors could open the link for review.\n23. p. 3- ‘when brain organizations are more stable and specialized”- change to ‘when brain organization IS more stable and\nspecialized’", "reviewer_2": "This paper measures the similarity of functional and structural gradients (SF gradient coupling) in a cohort of children (9-10\nyears old, ABCD dataset) vs adults (22-35 years old, HCP dataset). The authors assess cohort-level differences in each\ngradient modality and their coupling across cohorts, with coupling evaluated across all regions (“macroscale”) and stratified\nwithin specific subnetworks. They show different SF coupling patterns between children and adults spanning several\nsubnetworks. A series of within cohort analyses link SF coupling patterns to mental health and cognitive measures,\nidentifying different magnitude and patterns of associations across cohorts and additionally uncovering sex-specific effects.\nMore specifically, SF coupling and cognitive measure associations were generally stronger in children, while mental health\nrelationships were stronger in adults. Heritability analyses across modality-specific and SF coupling gradients captured\noverall similar patterns in both groups, with slightly higher heritability estimates in children, particularly for the SF coupling\nassessment. Transcriptomic decoding of SF coupling heritability estimates showed associations with the expression of\nexcitatory neurons subtypes.\nThe paper includes an impressive breadth of analyses. However, I have several major concerns, notably regarding the\nmotivation of the study, the way developmental comparisons were implemented, and note that several interpretations and\nconclusions are not supported by adequate statistical tests.\n1 - The introduction lacks a clear rationale for why gradients and SF gradient coupling are used and important for\nneurodevelopmental inquiry. Currently, the paper is framed as if the primary motivation for looking at SF gradient coupling is\nthat it has not been done before, and therefore behavioural and genetic associations of SF coupling are unknown. What\ninsights can SF gradient coupling bring beyond previously used measures of FC-SC coupling? What would diverging\nresults from connectome-level measures indicate? Without this justification, it is difficult to contextualize the importance or\nnew insights brought by the multitude of analyses performed here.\n2 - The authors perform group-level comparisons of children (9-10) vs young adults (22-35) cohorts. First, as data are not\nharmonized across sites with methods such as Combat, it is unclear if reported effects are attributable to differences in age\nor general site/scanner differences. Second, and as the authors know, both white matter and functional networks change\nthroughout the lifespan, and derivative metrics from these networks peak at different ages for different subnetworks.\nChildhood is a developmental window of rapid change, and even in the adult time window investigated here, FC and SC are\nnot static (Yeatman et al., 2014, Nat Comms; Fjell et al., 2017, HBM; Betzel et al., 2014, NIMG). Most developmental studies\nmodel age effects continuously for this reason. As a result, I am not convinced that a cohort-level comparison performed on\nunharmonized data is appropriate.\n3 - Several analytical choices are not adequately justified. For example, some analyses focus only on G1 and G2, the\ncoupling of FCG1 and SCG1 or FCG1 and SCG2, and the heritability analyses look at 20 distinct gradients. It is hard to\nmake sense of these analytical variations and interpret findings coherently. For example, would we expect different\ndownstream findings from measuring SF gradient coupling using FCG1:SCG1 vs FCG1:SCG2?\n4 - Many claims in the paper are not statistically supported. For example, differences between young and adult cohorts on\nFC and SC gradients are not quantified, only described qualitatively. As a result, the effect of modality-specific differences\non SF gradient coupling differences cannot be assessed (i.e. are the effects driven by one modality over the other). On\npages 6-8, the authors claim “Together, these findings established macroscale and subnetwork-level SF gradient coupling\nas two equally informative metrics for quantifying correspondence between brain structural and functional organization.” Yet,\nno quantitative comparison of the two approaches is performed – how can they be qualified as equally informative? In\nthe heritability analyses, the authors report “These findings suggested that SF gradient coupling captured highly heritable\nmultimodal axes of brain organization that were not fully explained by either modality alone.”. They support these claims by\nsimply reporting heritability metrics FC, SC and SF coupling gradients, yet there are no models implemented to assess\nunique variance explained or direct statistical comparisons of these heritability metrics.\n5 - The HCP and ABCD gradients were aligned to a “cohort-level” template. By aligning each cohort to distinct templates,\ndoes this procedure not run the risk of spuriously inflating group effects?\n6 - The use of causally-ambiguous language in describing transcriptomic findings is unwarranted for a correlation approach\nsuch as the one applied here.\n7 - The Discussion is overall very short and provides little to no contextualization of results with the literature, focusing on a\nsummary of the findings.\n8 - The link provided to reproduce the original analyses in this paper is not functional (https://github.com/Naomi-Ding/SF-\nGradient-Coupling – 404 not found). It is thus not possible to evaluate or review the code used to produce these findings.\n9 - As a minor point, the figures are generally quite dense, making the text and smaller figure panels difficult to parse. Also,\nthe magnitude and topography of group differences are difficult to evaluate when adult and child effects are not presented on\nthe same scale (e.g., Fig 1d-j; f-l, but the point holds throughout the manuscript).", "reviewer_3": "This study introduces and characterizes a novel neuroimaging metric, structural-functional (SF) gradient coupling, which\nquantifies the alignment between structural and functional gradients both globally and within distinct brain networks. The\nauthors examine how this coupling varies across developmental stages, differs by sex, relates to behavior and mental\nhealth, and reflects genetic and transcriptomic influences.\nGiven that the gradients are derived separately for functional and structural modalities, and thereby their rank order does not\nnecessarily correspond across modalities, the authors opted to explore all possible gradient pairings to capture the full\ncoupling pattern. This is an innovative contribution, as structural-functional coupling has rarely been investigated across\nmultiple dimensions. Below, I outline several concerns that should be addressed.\n1. The manuscript claims that “structural gradients primarily reflected the topology of long-range white matter pathways.”\nHowever, this claim is not directly supported by any figure. The authors should clarify how this interpretation is derived from\ntheir results or cite relevant references to support the statement. It would also be helpful to provide validation using existing\nstructural (non-functional) atlases (such as the Desikan-Killiany atlas, which is already used in this paper) by comparing\nFCG1 and SCG1 scores across anatomical parcellations. For instance, Figure 2b shows that SCG1 exhibits much greater\nvariability across subjects within each functional network compared to FCG1, suggesting that FCG1 is more\nconsistent across individuals within these networks. If SCG1 scores show lower variance within anatomical parcellations, this would\nlend support to the interpretation that structural gradients reflect stable topological features of brain anatomy.\n2. In Figure 2, the authors describe the adult structural gradients as exhibiting greater bilateral symmetry and spatial\nprecision compared to the child group, which is supported by the visualizations. However, the boxplots for adult SCG1 and\nSCG2 in Figure 2b suggest greater inter-subject variability in gradient scores compared to those in the child group (Figure\n2h). This apparent dissociation between spatial refinement and increased variability is intriguing from a developmental\nperspective. I recommend that the authors include a brief discussion of this point, as it would strengthen the interpretation of\nage-related changes in structural gradient organization. Additionally, please provide details about the boxplots. For\nexample, do the boxes represent subjects, and what do the centerline and box boundaries indicate?\n3. In several instances, the manuscript blends discussions with descriptions of results. Here are two examples: “This pattern\nwas consistent with prior findings of reduced structure-function correspondence in transmodal regions [21]” and “This\naligned with previous findings of sex-related differences in SF coupling patterns [26].” For clarity, I recommend separating\nthe presentation of results from their discussion.\n4. In the behavioral prediction model, it remains unclear what the input features were, specifically, whether the subnetwork-\nlevel coupling features were used jointly in a multivariate prediction model or entered independently for each subnetwork. The\nkernel ridge regression (KRR) method is described using a single feature vector xᵢ, but the manuscript does not clarify\nwhether this xᵢ represents a concatenated 400×7 feature vector (aggregating coupling features across all seven\nsubnetworks) or whether each subnetwork was modeled separately. While Figures 3d–g display network-specific feature\nimportance bars, suggesting that predictions may have been conducted separately for each subnetwork, Figure 3a includes\nonly one orange box to represent prediction performance for seven networks, which is confusing. I recommend that the\nauthors clarify how the input features were constructed and how the prediction model was implemented for both macro- and\nsubnetwork-level coupling.\n5. The sentence in the results stating that \"heritability estimates decreased monotonically with increasing gradient coupling\"\nappears inconsistent with the directionality shown in Figures 4a and 4b (and related panels). Specifically, the “average\nabsolute values” in both 4a and 4b exhibit a decreasing trend as coupling weakens, suggesting that stronger coupling is\nassociated with higher heritability estimates, not lower. I'm not sure if I may have missed something, so I kindly ask the\nauthors to clarify this point.\n6. The manuscript states that “individual gradients were aligned by constructing a cohort-level template and applying\nProcrustes rotation.” I assume the correction has been done within each cohort. However, it is unclear whether gradients\nwere aligned across the child and adult groups prior to comparison. Since gradient directions can arbitrarily flip across\ngroups in diffusion embedding, direct group comparisons may be confounded without proper alignment.\n7. While the study compares findings across the ABCD and HCP datasets, which differ in both age range and data source,\nthe scanning protocols and preprocessing pipelines were not consistent between the two. Although the ABCD data\nunderwent harmonization, there is no indication that the data were harmonized across cohorts. If not, this should be\nacknowledged and discussed as a potential limitation. Additionally, the preprocessing procedures (particularly for the ABCD\ndataset) are not described in sufficient detail. I recommend that the authors provide greater methodological transparency\nregarding the imaging protocols and preprocessing steps.\n8. In the main text, the authors refer to \"psychiatric symptoms\" when describing associations with subnetwork-level coupling,\nwhereas Figure 3a labels this category as \"Mental Health.\" For consistency and clarity, I recommend using the same\nterminology throughout the manuscript.\n9. Throughout the manuscript, the authors primarily focus on the coupling between the first gradients (FCG1 vs. SCG1).\nHowever, no explicit rationale is provided for prioritizing these gradients over higher-order ones. The authors do mention\n(p.7): “To illustrate this coupling heterogeneity, we focused on two representative gradient pairs, FCG1:SCG1 and\nFCG1:SCG2, each showing strong alignment in one age group but weak alignment in the other.” It would be informative to\nalso report heritability and transcriptomics analyses based on FCG1:SCG2 coupling.\n10. When evaluating “gradient coupling strength across different developmental stages,” the authors compare children\n(ABCD) and adults (HCP) as two broad groups. It may be beneficial to further divide the child cohort into narrower age\nbands to better capture the developmental evolution of SF gradient coupling across childhood and adolescence. Although\nthis may be constrained by the limited age range of the current ABCD dataset (a point that could be acknowledged as a\nlimitation), future work could address this using the HCP Development dataset. Such an approach would offer a more fine-\ngrained view of developmental trajectories and could also help mitigate cross-cohort harmonization concerns raised earlier.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "Authors’ Response to Reviewers’ Comments:\n“Brain Functional-Structural Gradient Coupling Reflects\nDevelopment, Behavior and Genetic Influences”\nWesincerelythankallthereviewersfortheircommentsandsuggestions,whichhelpedsubstantiallyinimproving\nthemanuscript. Wehavethoroughlyaddressedallthecommentsandprovideddetailedpoint-by-pointresponses\nin this letter. To facilitate the reading of the revised manuscript, we have also highlighted major changes to the\noriginalmanuscriptinbluecolorwheneverapplicable.\nReviewer 1\nThe study by Gao et al., examines how the brain structural-functional (S-F) gradient differs between two age-\nstratified cohorts (i.e., ABCD and HCP-YA cohorts). The results showed cohort and sex-specific differences\nin SF coupling, associations between SF gradient coupling and cognitive and mental health metrics, spatial\noverlapbetweenSFgradientcouplingandgeneexpressionprofilesfromAHBAindicatingenrichmentforgenes\nexpressedindeep-layerexcitatoryneurons,andprovideregionalheritabilityestimatesforthegradientcoupling\nmetrics. Thequestionofhowstructuralfunctionalgradientcouplingevolvesduringdevelopmentandrelatesto\nbehavioral,geneticandmolecularfeaturesisimportantandsomewhatunderstudied,tomyknowledge. Assuch,\nstrengthsofthestudyareitscomprehensivenessandutilizationofmultimodalMRIacrosstwowell-characterized,\nlarge datasets of different ages. The paper is, in general, clearly written. However, there are some major\nsubstantiveconcerns,aswellasseveralminorconcerns,regardingtheliteraturereview,claimsandinterpretation\nofthefindingsandsomeoftheanalyses,whichdiminishenthusiasmforthemanuscriptinitscurrentform.\nResponse: We sincerely appreciate Reviewer 1 for the thoughtful review of our work and for offering encour-\naging and constructive feedback. In this revision, we have thoroughly considered all comments and provided a\ndetailed,point-by-pointresponsebelow.\n1. A more comprehensive description of the previous literature should be included in the introduction and\ndiscussion. Despite methodological differences, the S-F coupling gradient has been characterized and\nexamined across several papers previously, which also include replication datasets. E.g., Development\nof S-F coupling gradient using cross-sectional and longitudinal data, as well as examining associations\nto cognitive performance (Baum et al., 2019, PNAS, doi: 10.1073/pnas.1912034117); S-F coupling gra-\ndient in young adults, with HCP as a replication dataset (Vazquez-Rodr´ıguezetal.,2019,PNAS,doi:\n10.1073/pnas.1903403116); age-related differences S-F coupling assessed across the lifespan (Esfahlani\net al., 2022, Nat Com, doi: 10.1038/s41467-022-29770-y); characterization of the S-F coupling gra-\ndient with replication dataset (Popp et al., 2024, NeuroImage, https://doi.org/10.1016/j.\nneuroimage.2024.120563); S-F coupling, age-related differences and spatial overlap with gene\n1\nexpression(Fengetal.,2024,eLife,https://doi.org/10.7554/eLife.93325.2);discussedin\nareviewarticle(Suarezetal.,2020,TrendsinCognitiveSciences,doi: 10.1016/j.tics.2020.01.008). While\nthese articles are cited, the characterization in the introduction of the novelty of this study should be re-\nvised. Furthermore, theSNPbasedheritabilityoftheS-Fcouplingalsohasbeenexaminedpreviouslyby\nsome ofthe same authors usingthe same datasetsas the currentpaper (Dai et al., 2024, Imaging Neuro-\nscience, https://doi.org/10.1162/imag_a_00346). Some of these papers also examined S-F\ncoupling changes in sensory and associations areas across childhood and adolescence (i.e., Feng) and\nacross the lifespan (i.e., Esfahlani), which do not fit with the authors claims in the introduction (i.e., “no\nstudy has yet tested how SF gradient coupling evolves from late childhood through early adulthood”).\nThus,itwouldbeofimportancetoproperlyputthesefindingsinthecontextofpreviousstudies.\nResponse: We thank the reviewer for pointing out these important prior studies. We have now expanded\nboth the Introduction (lines 30–35, 55–60, 63-65) and Discussion (lines 355–358) sections to provide a\nmore comprehensive overview of the literature on structure-function (SF) coupling. Specifically, we now\nsummarizekeyfindingsfromworkcharacterizingSFcouplinganditsdevelopmentalorlifespanvariation\n(Baumetal.,2020;Fengetal.,2024;Poppetal.,2024;Va´zquez-Rodr´ıguezetal.,2019;ZamaniEsfahlani\netal.,2022),aswellasthebroaderconceptualreviewbySua´rezetal.,2020andtheSNP-basedheritability\nanalysis of SF coupling by Dai et al., 2024. We have also revised our description of the novelty of the\npresentstudytoexplicitlyacknowledgethesepriorcontributions.\nWhile these studies have significantly advanced our understanding of how structural and functional con-\nnectivityarealignedacrossthecortexandacrossdevelopment,theyhaveprimarilyfocusedonnode-wise\ncouplingorglobalcouplingindices. Incontrast,ourstudyinvestigatesthegradient-levelcouplingbetween\nstructural and functional topographies, thereby characterizing SF relationships within a continuous, hier-\narchicalgradientspaceandacrossmultiplespatialscalesintwodevelopmentalcohorts. Wenowclarifyin\ntheIntroductionsection(lines37-52,84-95)thatourstudyextendsthisliteratureby(i)formallydefining\nand quantifying structural-functional gradient coupling (SFGC) as a gradient-level endophenotype across\nmacroscale and subnetwork resolutions, (ii) demonstrating that SFGC shows developmental differences\nand predicts individual variation in cognitive performance and mental health-related traits, and (iii) link-\ning SFGC to its genetic and transcriptomic underpinnings through family-based heritability and spatially\nconstrained imaging-transcriptomic analyses. Together, these revisions more accurately situate our work\nwithintheSFcouplingliteraturewhileclearlydelineatingitsadded,gradient-levelcontributions.\n2. Although I find most of the analyses to be appropriate, some of the claims seem broader than what the\nresults justify. As acknowledged by the authors, any differences between the two cohorts can also be\nattributed to other characteristics than age, such as sample characteristics (e.g., socioeconomic status,\nethnicity, scanner effects, image quality). Thus, the paper would benefit from rephrasing words like “tra-\njectories”and“evolved”,whichgivestheimpressionofalongitudinalanalysisandcausality.\nResponse: We sincerely thank the Reviewer for the valuable suggestion. In the revised manuscript, we\nhave removed or rephrased any wording that could be interpreted as implying longitudinal analysis or\ncausalrelationships,andnowpresenttheseresultsstrictlyasdescriptiveandassociationalfindings.\n3. Asarelatedpoint,theresultsareoftenpresentedina‘bigpicture’summarystyle(e.g. ,p5,‘Theirsecond\nfunctional gradient began to resemble the adult principal axis, indicating...”) This statement is easy to\nunderstand, but what particular analysis supported this conclusion? Likewise, on p 6 there is a statistic\n2\nfor SF gradient coupling in children, and a lower C-value for adults, but from what I can tell, there was\nnodirectstatisticalcomparisonconducted. Thereismorequantitativeinformationpresentedinthefigures\nand the supplements , but even there there is a fair amount of un-evenness in the level of detail provided\naboutwhatisbeingdepicted(e.g, whatconclusionsshouldbedrawnfromSuppFigures1and3?). More\ndetailed, quantitative information for each of the results and figures would be helpful in evaluating the\nstrengthoftheclaimsmade.\nResponse:\nWe thank the Reviewer for highlighting the need for additional quantitative support beyond qualitative\ndescriptions. Intherevisedmanuscript,wehaveconductedadditionalstatisticaltestsandhypothesistests\nthroughout our manuscript. All findings and discussions regarding these tests are revised and updated in\ntheResultsandDiscussionsections. Thesetestsinclude:\n(a) Pairwise spin-rotation permutation tests to quantify cross-cohort correspondence for all FC and SC\ngradients(FCG1∼FCG20andSCG1∼SCG20;SupplementaryFig. 1b,c);\n(b) Welch’st-testswithunequalvarianceonthemacroscale-levelcouplingvaluestocomparestructural-\nfunctionalgradientcouplingbetweencohort(SupplementaryFig. 1d);\n(c) Pairedt-teststoassesstheasymmetryofgroup-levelgradientsacrosshemisphereswithineachcohort;\n(d) Pairedt-teststocompareSFGC-outcomeassociationdifferencebetweenmacroscaleSFGCandsub-\nnetworkSFGC(Fig. 2a);\n(e) Welch’s t-tests with unequal variance to compare SFGC-behavior association difference between\ncohortsandbetweensex(Fig. 2b,c);\n(f) Pairedt-teststocomparetheheritabilitymetricsbetweenleftandrighthemispheres(Fig. 4g,p);\n(g) Paired t-tests to compare the heritability metrics between SFGC and individual gradients (Supple-\nmentaryTable1);\n(h) Poweranalysestoassessthedetectabilityofheritabilityestimatesgiveneachcohort’sfamilystructure\n(SupplementaryFig. 6);\n(i) Spin-rotation permutation tests to adjust for the spatial autocorrelation in imaging-transcriptomic\nanalyses(SupplementaryTable4).\nThese statistical tests provide statistical evidence for the statements such as “Their second FCG showed\nstrongsimilaritytotheadultprimaryaxis...” (lines117-119). Inaddition,wehaveprovidedclearerquanti-\ntativeinterpretationtotheresultsandfigures. Specifically,forSupplementaryFig.1a,wenowexplicitly\ndescribe that the structural and functional connectivity matrices, averaged across subjects, exhibit pro-\nnouncednetwork-levelmodularity(lines107-109). Therevisedmanuscripttextnowreads: “Theaveraged\nSCandFCmatricesexhibitedpronouncednetwork-levelmodularity,providingtheorganizationalscaffold\nthat underlies subsequent gradient and coupling analyses (Supplementary Fig. 1a).” For Supplemen-\ntary Fig. 3, we now clarify that these figures illustrate the consistency of the feature importance maps\nobtained using two distinct prediction models (kernel ridge regression and multilayer perceptrons; lines\n256-258). As stated in the Analysis robustness and stability subsection of the Methods section, these\nfiguresdemonstratethatthespatialpatternsoffeatureimportancearehighlysimilaracrossmethods,with\nan overall Pearson correlation of 0.75 ∼ 0.80. This supports the robustness of the behavioral association\nresultsandthereliabilityoftheproposedfeatureimportancemetrics(lines817-822). Wealsoprovidethe\nsubnetworkSFGCimportancebrainmapsinSupplementaryFig.3toimprovereadability.\n3\n4. Inrelationtocohortdifferences,itwouldbehelpfuliftheauthorsaddressedthewithinsamplecorrelations\nin more depth, as within-cohort variability may influence the brain-behavior relationships within each\ncohort. For instance, is there more variance in the cognitive and mental health metrics in the ABCD vs\nHCP-YA? If so, could the authors elaborate on the potential impact of range restrictions on the brain-\nbehaviorassociations?\nResponse: We appreciate the Reviewer’s suggestion to examine within-cohort variability. We therefore\nhave computed the sample standard deviation (SD) of each cognitive and mental health measure in the\nchildren(ABCD)andadult(HCP-YA)cohortsasshowninFigure1below. Overall,thesampleSDsunder\neachmetricwereofsimilarmagnitudeacrosscohorts. Forthecognitivemeasures,childrenshowedmod-\nestly higher SDs for most metrics (children/adults SD ratios ≈1.0-1.2), although some composites (e.g.,\nCogFluid,CogTotal)showedverysimilarorslightlyhigherSDinadults. Forthementalhealthmeasures,\nthe pattern was mixed: adults exhibited slightly higher SDs for Anx/Dep, With/Dep, RuleBreak, and In-\nternal, whereas children showed somewhat higher SDs for Aggressive and External, with all differences\nmodest.\nThus, we do not observe strong or systematic range restriction in one cohort relative to the other. In\naddition, our primary predictive metric is the cross-validated Pearson correlation between observed and\npredicted scores, which is invariant to linear rescaling of the outcome and therefore not trivially driven\nby differences in raw variance. Notably, predictive performance is higher in children than adults even for\nmentalhealthmeasureswhereadultshaveequalorgreatervariance,indicatingthatthestrongerprediction\ninthechildcohortcannotbeexplainedbysimpledifferencesinoutcomevariability. Instead,weinterpret\nthese findings as suggesting that SFGC features account for a larger proportion of observable individual\ndifferencesincognitionandmentalhealthduringchildhoodthaninyoungadulthood.\nFigure1: Linechartforthesamplestandarddeviationsofcognitiveandmentalhealthmetricsacrosscohorts.\n5. Theauthorsstatethat‘thepotentialofSFgradientcouplingasapredictivefeatureforbehavioraltraitshas\nnot been investigated’; to that end they employ two predictive modeling approaches to examine relation-\n4\nships to mental health symptoms and cognition, but from what I can tell they only utilized cross-sectional\nABCDdata. Whynotutilizethelongitudinaldatatoconductanactualpredictiveanalysis?\nResponse: We appreciate the Reviewer’s thoughtful comment. Our primary aim in the present study was\ntocharacterizehowSFGCrelatestocognitionandmentalhealthacrossdevelopmentalstages,ratherthan\nto model within-individual change over time. To address this question in a principled and comparable\nway, wefocusedontheABCDbaselinewave, whichcloselymatchesthecross-sectionalHCP-YAcohort\nin data structure. This allowed us to implement parallel cross-sectional predictive pipelines in children\nand adults and to directly compare the strength of brain-to-behavior associations between developmental\nperiods. Although ABCD has a longitudinal design, leveraging follow-up waves to perform prospective\npredictionwouldrequireadifferentanalyticframeworkandadistinctsetofmodelingchoices. Inaddition,\nthenumberofparticipantswithhigh-qualityimagingandbehavioraldataatlaterABCDwavesiscurrently\nsubstantiallysmallerandlessbalancedthanatbaseline,whichwouldreducepowerandfurthercomplicate\ndirectcomparisonwiththeadultHCP-YAcohort.\nWefullyagreethattestingwhetherbaselineSFGCprospectivelypredictssubsequentcognitiveandmental\nhealth trajectories represents an important and complementary next step. We view the current work as\na necessary first step in establishing cross-sectional predictive validity and developmental differences in\nSFGC-to-behaviorassociations,andweplantoextendthisframeworktolongitudinalpredictioninfuture\nwork once sufficiently large and well-characterized multi-wave samples are available under a common\nprocessingandQCscheme. WehaverecognizedthisasafutureextensionintheDiscussionsection(lines\n441-446).\n6. The ABCD dataset includes MRI data across >20 sites, and it is unclear to me how the authors addressed\npotentialdifferencesacrossscannersites. ExaminationofhowSFcouplingmaydifferacrosthescanner\nsites can provide important insight into the potential confounding variables within the ABCD cohort. In\naddition, younger children also tend to move more in the scanner, which can also influence data quality.\nThus,itwouldbehelpfuliftheauthorscomparedtheimagequalitybetweenthetwocohorts(e.g.,through\nEulernumber/SNR/tSNR/framewisedisplacement)toruleoutthepotentialimpactofimagequalityonSF\ncoupling.\nResponse: WeappreciatetheReviewerforraisingtheseimportantconcernsregardingscanner/siteeffects\nandpotentialimage-qualityconfounds. Intherevisedmanuscript,wehaveimplementedacomprehensive\nquality-controlandharmonizationpipelineforbothgradientsandSFGCbeforeperforminganyanalysis.\nSpecifically, because direct comparisons between ABCD and HCP-YA can be confounded by differences\nin acquisition protocols, preprocessing pipelines, and multi-site versus single-site sampling, we first in-\ntroduced the Human Connectome Project-Development (HCP-D) dataset (Somerville et al., 2018) as a\nbridgingcohort. HCP-DisacompanionstudytoHCP-YAthatextendstheHCPframeworktoparticipants\naged 5-21 years, uses imaging protocols and processing pipelines closely aligned with those of HCP-YA,\nandsamplesanagerangethatoverlapswithABCD.Forthesereasons,HCP-Dprovidesaprincipledbridge\nthatallowsustoseparatestudy-andpipeline-relatedeffectsfromgenuinedevelopmentaldifferenceswhen\ncomparingABCDandHCP-YA.\nOnthisbasis,ourharmonizationprocedureproceedsintwostages. First,weappliedstrictmotionquality\ncontrolbyexcludingparticipantswithlargemeanframewisedisplacement(mean FD> 0.3mm),yielding\nfinalsamplesof5343ABCD,93HCP-D,and875HCP-YAparticipants. Second,weperformedComBat-\nbased harmonization (Johnson, Li, and Rabinovic, 2007) using the sva R package (Leek et al., 2012).\nmonized for site effects only; no scanner or site harmonization was required for the single-site HCP-YA\ncohort. Inallcases,scanner/siteweremodeledasbatchvariablesandageandsexwereincludedascovari-\nates,therebypreservingage-andsex-relatedvariationwhileremovingscannerandsitedifferences.\nToaddressremainingstudy-andpipeline-relateddifferencesbetweenABCDandHCP-YA,wethenaligned\nABCD to HCP-YA through HCP-D. Specifically, we performed ComBat harmonization with study indi-\ncator (ABCD vs. HCP-D) as the batch effect and age and sex as covariates, which allowed us to estimate\nthe mean study-effect difference between ABCD and HCP-D, denoted as ∆ . We then applied\nABCD−HCP\nthismeanstudyeffect∆ toeachindividualsubjectfromHCP-YA,therebyplacingABCDand\nABCD−HCP\nHCP-YA in a comparable SFGC space while preserving inherent developmental differences rather than\npipelineartifacts. AsshowninSupplementaryFig.5,thisstrategysubstantiallyimprovesharmonization\nquality,particularlybymitigatingpronouncedmotion-andscanner-relatedeffectsintheABCDcohort.\nFor consistency, we applied this harmonization procedure before using gradients, macroscale SFGC, or\nsubnetworkSFGCinanydownstreamanalyses,andwereranallanalyseswiththeseharmonizedmeasures,\nwithupdatedresultsreportedintherevisedmanuscript. Themainfindingsremainrobust: SFGCcontinues\ntoemergeasapredictiveandheritableendophenotypethatreflectsdevelopmental,behavioral,andgenetic\ninfluences, and the key cross-cohort differences are not explained by scanner, site, or motion effects. All\nofthesequality-controlandharmonizationsteps,togetherwithmoreexplicitdescriptionsofpreprocessing\nandmotionexclusioncriteria,arenowincludedintheImagingprocessingandconnectivityconstruction\nandDataharmonizationsubsectionsoftheMethodssection.\n7. Howdidtheauthorsaddresspotentialtype1errorsduetospatialautocorrelationbetweenthebrainmaps\nand transcriptomic maps? The wording of the transcriptomics analyses reflects a reverse inference logic,\ni.e. “Transcriptomic analyses further demonstrated that highly heritable coupling patterns are enriched\nfor genes expressed in deep-layer excitatory neurons” “Transcriptomic signatures highlight the cellular\nbasisofSFgradientcouplingheritability”,“Toidentifyspecificmolecularcontributors”,“Toexplorethe\ncellular basis of heritability variation in SF gradient coupling”, “transcriptomic analyses revealed that\ntheheritabilityofgradientcouplingwasenrichedforexcitatoryneuronalsignatures”thistypeofphrasing\ncould be perceived as too strong given the data; a more neutral tone might be more appropriate (e.g.,\nemphasizing the spatial overlap with gene expression maps that are enriched for genes that are highly\nexpressed in deep layer neurons). In addition, since the gene expression values derived from AHBA are\nbased on post-mortem data from adults, it is unclear to me how this would be an appropriate analysis to\nperformonbrainmapsderivedfromchildren. Inaddition, thissectionsuffersfromthesameissuesnoted\nabove regarding broad statements and lack of precision, e.g. “ Particularly strong signals were observed\nfor excitatory neurons 3 and 4..” What is considered the threshold for ‘particularly strong”? was that\ndeterminedapriori?\nResponse: We thank the Reviewer for these thoughtful comments regarding our imaging transcriptomic\nanalyses. In the revised manuscript, we have made the following targeted changes to address all these\nconcernsthoroughly.\nFirst, to control type I error due to spatial autocorrelation, we now explicitly evaluate all imaging tran-\nscriptomic associations against spatially constrained null models. Specifically, for each regional SFGC\nheritabilitymapwegenerate10,000spin-rotationpermutations(Va´sˇaetal.,2018)andrecompute(i)gene-\nheritability correlations and (ii) cell-type enrichment scores under these spatially matched nulls. From\nthesenulldistributions,wederivespatiallyadjustedp-valuesforbothindividualgenesandcell-typegene\n6\nsets. All significance claims in the transcriptomic section now refer to these spatially adjusted p-values\n(reported in Supplementary Table 4), and we define enrichment formally as spatially adjusted p < 0.05\n(lines794-799).\nSecond,wehaverevisedtheimaging-transcriptomicanalysesrelatedtotheABCDcohorttousedevelop-\nmentally appropriate gene-expression resources. We agree that applying adult AHBA data to children is\nsuboptimal. Intherevisedanalyses,AHBAisnowusedonlyfortheadult(HCP-YA)cohort. Forthechild\ncohort,weinsteadusedevelopmentallymatchedadolescentgene-expressiondatafromtheBrainSpanatlas\ntogetherwithage-appropriateadolescentsingle-cellreferences. Thischangedirectlyaddressestheconcern\naboutthesuitabilityoftranscriptomicdataforpediatricimagingmaps.\nFinally, we have systematically softened and clarified the wording of the transcriptomic results to avoid\nreverse inference or mechanistic interpretations. We now describe our findings in terms of spatial corre-\nspondence between regional SFGC heritability maps and gene-expression patterns that are enriched for\nspecific cell-type-specific gene sets, and we support these statements with explicit spatially adjusted p-\nvaluesratherthanpurelyqualitativedescriptions.\n8. Thestudylacksinformationaboutthepoweranalysesfortheheritabilityestimates,whichwillbeimportant\ngiventhesamplesizedifferencesinthetwocohorts.\nResponse: WethanktheReviewerforthisimportantsuggestion. Wehavenowperformedapoweranalysis\nto evaluate the detectability of heritability under varying true heritability levels and proportions of shared\nenvironmentaleffects,giventherelatednessstructureofourcohort. Specifically,wesimulatedphenotypes\nwithagridofassumedtrueheritabilityvaluesh2 = 0.01−0.80andvaryingproportionsofsharedenviron-\nmentalvariance(0,0.3,0.5,0.8),usingthesamerelatednessmatrixandfamilystructureasintheempirical\ndata. Foreachsetting,weestimatedheritabilityusingthesameACEmodelandassessedpowerasthepro-\nportionof5,000simulationswhereheritabilitywasdetectedatp < 0.05. Theresults(SupplementaryFig.\n6) show that, given our current sample size and family structure, the power to detect heritability exceeds\n0.8 when the true h2 ≥ 0.2, particularly when the proportion of shared environment is moderate to high.\nWe focused on varying h2 while holding the sample size fixed, as subsampling would reduce the number\nofinformativetwinpairsandthusdistortthefamilystructure,leadingtoanunrealisticestimateofpower.\nThese results provide a realistic characterization of our detectable effect sizes under the available cohort\nstructure, and we have now included this power analysis in the Heritability estimation using the ACE\nmodelsubsectionoftheMethodssection.\n9. The authors state that they performed two-sample t-tests, but it is unclear if they are assuming equal or\nunequalvariancebetweenthegroups.\nResponse: We appreciate the Reviewer’s request for clarification. For all comparisons between indepen-\ndent groups, we used Welch’s two-sample t-test, which assumes unequal variances and does not impose\nhomogeneityofvarianceacrossgroups. ThisisthetestweappliedwhencomparingmacroscaleSFGCbe-\ntweencohortsandwhenassessingdifferencesinSFGC-behaviorassociationsacrosscohortsandbetween\nsexes. In contrast, for within-subject or within-region comparisons, including comparing SFGC-outcome\nassociationsbetweenmacroscaleandsubnetworkSFGC,comparingheritabilityestimatesbetweenleftand\nright hemispheres and comparing heritability estimates between SFGC and individual gradients (SGC or\nFGC), we used paired t-tests, which doesn’t assume equal variances. In the revised manuscript, we have\nnowexplicitlyspecifiedtheexacttypeoft-testusedineachcomparisonanditsvarianceassumptions.\n7\n10. It would be helpful if the authors provide the age-range of the final analytic samples and a demographic\ntablestratifiedbysex.\nResponse: We thankthereviewerforthis helpfulsuggestion. We havenowreportedthe agerangeofthe\nfinal analytic samples in the Methods section (lines 467-468, 484) and added Supplementary Table 3,\nwhichsummarizesdemographicvariablesaswellascognitiveandmentalhealthmeasuresstratifiedbysex\nandcohort.\n11. “Our approaches and results revealed that SF gradient coupling undergoes systematic neurobiological\nrefinement from late childhood to early adulthood with distinct sex-specific trajectories.” This statement\ncouldbenefitfrommorecarefulwordingasitgivestheimpressionofcausalityandlongitudinalanalyses.\nResponse: Thank you for this comment. To avoid potential confusion, we have revised the statement to:\n“Our findings suggest age-associated changes in SFGC, with observable differences between male and\nfemalegroups.” (lines84-85).\n12. ‘Finally,weintegratedtranscriptomicdatafromtheAHBAtorevealthatheritablegradientcouplingpat-\nterns are enriched for genes expressed in deep-layer excitatory neurons’ The authors should clarify that\ntheseanalysesexaminethespatialoverlapbetweenbrainandtranscriptomicmaps.\nResponse: Thankyouforthisinsightfulcomment. Wehaverevisedthestatementandupdatedtherelevant\nsections of the Introduction, Results and Methods sections to clarify that our imaging transcriptomic\nanalyses assess the spatial overlap between regional heritability patterns of SFGC and age-appropriate\ntranscriptomicmaps.\n13. ‘Rather than characterizing the brain as a set of discrete networks, gradient-based approaches project\nconnectivitypatternsintolow-dimensionalmanifoldsthatrevealcontinuousaxesoforganization.’ Itisnot\ncleartomewhattheauthorsmeanby‘low-dimensionalmanifolds’,Isuggestrephrasingforclarity.\nResponse: We thank the Reviewer for this helpful suggestion. To improve clarity, we have revised the\nsentence to avoid technical terminology. The updated text now reads: “Rather than characterizing the\nbrain as a set of discrete networks, gradient-based approaches reduce high-dimensional connectivity data\ninto a few continuous axes that capture gradual transitions in the brain organization (Tian et al., 2020).”\n(lines37-39).\n14. ‘Evenfewerstudieshaveexaminedhowgradientcouplingdevelopsovertimeorvariesacrossindividuals.’\nItwouldbehelpfuliftheauthorsprovidedreferencestothesestudies. Seemajorcomment.\nResponse: Thank you for this suggestion. As responded in Question 1, we have now expanded both\nthe Introduction and Discussion sections to provide a more comprehensive overview of the literature on\nstructure-function(SF)couplingwithpropercitations. Wehavealsorevisedourdescriptionofthenovelty\nofthepresentstudytoexplicitlyacknowledgethesepriorcontributions.\n8\n15. ‘Although many aspects of brain development unfold gradually across childhood and adolescence,\nmost studies of SF coupling have focused on either mature adult brains or aggregated developmental trajecto-\nries.’ Couldtheauthorsclarifyonwhattheymeanby“aggregateddevelopmentaltrajectories”? Itisalso\nhardtoevaluatethisclaimwithoutreferences.\nResponse: WethanktheReviewerforthishelpfulcomment. Intherevisedmanuscript,wehaveremoved\nthe ambiguous phrase “aggregated developmental trajectories” and replaced it with a clearer and more\naccurate summary of prior work on SF coupling across different developmental cohorts. Specifically, we\nnow cite and summarize studies spanning adult cohorts, infant cohorts, youth cohorts, and broader devel-\nopmental samples, including those that have explicitly examined age-related differences in SF coupling\n(lines30–35, 55–60). Theserevisionsprovideprecisereferencesandeliminateterminologythatcouldbe\ninterpretedasimplyinglongitudinalchange.\n16. ‘Specifically, we first thresholded the SC and FC matrices to retain the top 10% of connections, then\ntransformedthemintocosinesimilarityaffinitymatrices.’ Couldtheauthorselaborateonhowtheydefine\nthetop10%connections?\nResponse: We thank the Reviewer for this question. Following previous gradient-based imaging studies\n(Dong, Margulies, et al., 2021; Dong, X.-H. Zhang, et al., 2024; Katsumi et al., 2023; Margulies et al.,\n2016; Vos de Wael et al., 2020; Yeo et al., 2011), we applied proportional thresholding at the subject\nlevel: foreachindividualSCandFCmatrix,werankedallnon-diagonalconnectionweightsandretained\nthe strongest 10% of edges, setting the remaining 90% to zero. This procedure controls network sparsity\nand reduces the influence of weak or noisy edges while maintaining comparability across participants\nand modalities. We then transformed these sparsified matrices into cosine similarity affinity matrices for\ngradient estimation. The resulting principal gradients in both the ABCD and HCP-YA cohorts closely\nresemblepreviouslyreportedmacroscalegradienttopographies(Dong,X.-H.Zhang,etal.,2024;Y.Hong\netal.,2025;Paquolaetal.,2019;VosdeWaeletal.,2020),supportingthatourfindingsreflectrobustlarge-\nscaleorganizationalpatterns. WehaveclarifiedthisthresholdingprocedureintherevisedFunctionaland\nstructuralgradientconstructionsubsection(lines615-621)oftheMethodssection.\n17. ‘WefurtherobservedthattheSFgradientcouplingstrengthbetweentheprincipalfunctionalgradientand\nthesecondstructuralgradient(FCG1:SCG2)increasedfromnear-zerolevelsinchildrentoarobustlevel\ninadults’Itwouldbehelpfuliftheauthorsprovidereferencestothefigureortablethatsupportthisclaim.\nResponse: WethanktheReviewerforthishelpfulcomment. Afterperformingadditionaldataharmoniza-\ntion during the revision, the previously observed increase in SFGC strength between the first functional\ngradient and the second structural gradient (FCG1:SCG2) was no longer evident. We have therefore re-\nmoved this statement from the revised manuscript to ensure that the description accurately reflects the\nupdatedresults.\n18. ‘Furthermore,theassociationbetweenSFgradientcouplingandoutcomesvariedbyscaleandagecohort:\nin adults, subnetwork-level SF gradient coupling showed stronger association with psychiatric symptoms\nthan macroscale gradient coupling, whereas in children, macroscale SF gradient coupling yielded exhib-\nited associations.’ It would be helpful if the authors provided a reference to a figure or numbers that\n9\nsupportsthisclaim. Itisalsouncleartomewhichstatisticaltestandresultsthatwasusedtosupportthe\nclaim of a ‘stronger association’. Also, it is unclear to me what is meant by “yielded exhibited associa-\ntions”?\nResponse: Wethankthereviewerforpointingouttheseissues. Wenowreporttheaveragedout-of-sample\nassociationbetweeneachobservedbehavioraloutcomeandtheSFGC-predictedbehavioraloutcomeacross\n100 data-splitting replicates, as summarized in Figure 3a, to quantify the strength of these associations.\nThedetaileddefinitionsofout-of-sampleassociationsmeasuredbythePearsoncorrelationcoefficient(r)\nforcontinuousoutcomevariablesandtheareaunderthereceiveroperatingcharacteristiccurve(AUC)for\nbinaryoutcomevariableshavebeenaddedtotheModelperformanceandfeatureimportancesubsection\nof the Method section. In children, macroscale-/subnetwork-level SFGC shows average correlations of\nr = 0.09/0.11 with mental health outcomes, whereas in young adults the corresponding associations\nare slightly weaker (average r = 0.04/0.11). For cognitive outcomes, SFGC-cognition associations are\nalsostrongerinchildrenonaverage(macroscale/subnetwork: r = 0.26/0.30), particularlyforintegrative\nscoressuchasCogTotal(macroscale/subnetwork: r = 0.38/0.44).\nIn addition, we now provide FDR-corrected paired t-tests comparing macroscale- and subnetwork-level\nSFGCcorrelationsforeachoutcome,alsoshowninFigure3a,toformallysupporttheclaimthatsubnetwork-\nlevelSFGCoftenshowsstrongerassociationsthanmacroscaleSFGC.\nFinally, we have removed the unclear phrase “yielded exhibited associations” and rephrased the relevant\nsentencestoreferexplicitlytothesecorrelationestimatesandstatisticaltests.\n19. ForSFgradientcouplingandcognitiveperformancescores,theauthorsstatethatassociationsgetweaker\nin adults, but I struggle to find the statistical test was performed to support this claim other than a nu-\nmericallylowercorrelation. Inaddition,thewordinggivestheimpressionthatdifferencesincorrelations\nare due to age (e.g., “became weaker in adults”) - if there is a significant difference, a more accurate\ndescriptionwouldbe“lowerintheadultcohort”.\nResponse: WeappreciatetheReviewerraisingthesepoints. Intherevisedmanuscript, wenowexplicitly\nstate that cohort differences in SFGC-outcome associations are tested using two-sample Welch’s t-tests\nwithFDR-correctedp-valuesreportedintheResultssectionandFigure3. Wehavealsorevisedtheword-\ningtoavoidimplyinglongitudinalchange;thetextnowstatesthat“SFGCwasingeneralmoreassociated\nwithmentalhealthoutcomes(Aggressive,External)inchildren(adjustedp < 0.01).”\n20. ‘Afterrigorousqualitycontrolandpreprocessingoftheneuroimagingdata,andexclusionofparticipants\nwith incomplete covariate information, the final analytic sample consisted of 7,025 subjects (mean age\n= 9.9 years; 48.8% male).’ ‘Following quality control and data aggregation, our final analytic sample\ncomprised 913 participants (mean age = 28.7 years; 46.55% male) from 414 families, including 111 MZ\ntwin pairs, 59 DZ twin pairs, 511 full sibling pairs, and 95 singletons.’ It would be helpful if the authors\ncouldelaborateonthequalitycontrolproceduresperformedoneachcohort.\nResponse: WethanktheReviewerforthishelpfulcomment. Thedetailedquality-controlandharmoniza-\ntionstepsforeachcohortarenowincludedintheImagingprocessingandconnectivityconstructionand\nDataharmonizationsubsectionsoftheMethodssection.\n10\n21. WilltheauthorsprovidetheregionalvaluesfortheSFcouplinggradients? Thiscouldbefurtherusedby\notherresearcherstoexaminethespatialoverlapwithSFcouplingwithothercorticalmaps.\nResponse: Thanks for this helpful suggestion. We have now provided the individual-level subnetwork\nSFGCforbothcohortsonourGitHubrepositorytofacilitatefurtherspatialanalysesbyotherresearchers.\nPleasecheckourfullcodebase(https://github.com/Zhao-team/SF-Gradient-Coupling).\n22. TheGitHublinkdoesn’twork. Itwouldbehelpfuliftheauthorscouldopenthelinkforreview.\nResponse: WethanktheReviewerforflaggingthis. Wehavecorrectedthelinkandmadeourfullcodebase\npubliclyavailableonGitHub(https://github.com/Zhao-team/SF-Gradient-Coupling).\n23. p. 3-‘whenbrainorganizationsaremorestableandspecialized”-change to‘whenbrainorganizationIS\nmorestableandspecialized’\nResponse: Thanks for the suggestion. The relevant paragraph has now been rewritten in the revised\nmanuscript,andthespecificwordingnotednolongerappears.\nReferences\nBaum, Graham L. et al. (2020). “Development of structure–function coupling in human brain networks during\nyouth”.In:ProceedingsoftheNationalAcademyofSciences117.1,pp.771–778.\nDai,Weietal.(2024).“Heritabilityandgeneticcontributionanalysisofstructural-functionalcouplinginhuman\nbrain”.In:ImagingNeuroscience2,pp.1–19.\nDong,Hao-Ming,DanielSMargulies,etal.(2021).“Shiftinggradientsofmacroscalecorticalorganizationmark\nthetransitionfromchildhoodtoadolescence”.In:ProceedingsoftheNationalAcademyofSciences118.28,\ne2024448118.\nDong,Hao-Ming,Xi-HanZhang,etal.(2024).“Ventralattentionnetworkconnectivityislinkedtocorticalmat-\nurationandcognitiveabilityinchildhood”.In:NatureNeuroscience,pp.1–12.\nFeng,Guozhengetal.(2024).“Spatialandtemporalpatternofstructure–functioncouplingofhumanbraincon-\nnectomewithdevelopment”.In:eLife13,RP93325.\nHong, Yoonmi et al. (2025). “Structural connectome gradients and their relationship to IQ in childhood”. In:\nFrontiersinHumanNeuroscience19.\nJohnson,WEvan,ChengLi,andArielRabinovic(2007).“Adjustingbatcheffectsinmicroarrayexpressiondata\nusingempiricalBayesmethods”.In:Biostatistics8.1,pp.118–127.\nKatsumi,Yutaetal.(2023).“Correspondenceoffunctionalconnectivitygradientsacrosshumanisocortex,cere-\nbellum,andhippocampus”.In:CommunicationsBiology6.1,p.401.\nLeek,JeffreyTetal.(2012).“Thesvapackageforremovingbatcheffectsandotherunwantedvariationinhigh-\nthroughputexperiments”.In:Bioinformatics28.6,pp.882–883.\nMargulies,DanielSetal.(2016).“Situatingthedefault-modenetworkalongaprincipalgradientofmacroscale\ncorticalorganization”.In:ProceedingsoftheNationalAcademyofSciences113.44,pp.12574–12579.\nPaquola,Caseyetal.(2019).“Microstructuralandfunctionalgradientsareincreasinglydissociatedintransmodal\ncortices”.In:PLoSBiology17.5,e3000284.\nIn:NeuroImage290,p.120563.\nSomerville, Leah H et al. (2018). “The Lifespan Human Connectome Project in Development: A large-scale\nstudyofbrainconnectivitydevelopmentin5–21yearolds”.In:Neuroimage183,pp.456–468.\nSua´rez, Laura E et al. (2020). “Linking structure and function in macroscale brain networks”. In: Trends in\nCognitiveSciences24.4,pp.302–315.\nTian, Ye et al. (2020). “Topographic organization of the human subcortex unveiled with functional connectivity\ngradients”.In:NatureNeuroscience23.11,pp.1421–1432.\nVa´sˇa, Frantisˇek et al. (2018). “Adolescent tuning of association cortex in human structural brain networks”. In:\nCerebralCortex28.1,pp.281–294.\nVa´zquez-Rodr´ıguez,Berthaetal.(2019).“Gradientsofstructure–functiontetheringacrossneocortex”.In:Pro-\nceedingsoftheNationalAcademyofSciences116.42,pp.21219–21227.\nVos de Wael, Reinder et al. (Mar. 2020). “BrainSpace: a Toolbox for the Analysis of Macroscale Gradients in\nNeuroimaging and Connectomics Datasets”. In: Communications Biology 3.1, pp. 1–10. ISSN: 2399-3642.\nDOI:10.1038/s42003-020-0794-7.(Visitedon05/02/2023).\nYeo,BTThomasetal.(2011).“Theorganizationofthehumancerebralcortexestimatedbyintrinsicfunctional\nconnectivity”.In:JournalofNeurophysiology.\nZamani Esfahlani, Farnaz et al. (2022). “Local structure-function relationships in human brain networks across\nthelifespan”.In:NatureCommunications13.1,p.2053.\nThis paper measures the similarity of functional and structural gradients (SF gradient coupling) in a cohort of\nchildren (9-10 years old, ABCD dataset) vs adults (22-35 years old, HCP dataset). The authors assess cohort-\nlevel differences in each gradient modality and their coupling across cohorts, with coupling evaluated across\nallregions(“macroscale”)andstratifiedwithinspecificsubnetworks. TheyshowdifferentSFcouplingpatterns\nbetweenchildrenandadultsspanningseveralsubnetworks. AseriesofwithincohortanalyseslinkSFcoupling\npatterns to mental health and cognitive measures, identifying different magnitude and patterns of associations\nacross cohorts and additionally uncovering sex-specific effects. More specifically, SF coupling and cognitive\nmeasure associations were generally stronger in children, while mental health relationships were stronger in\nadults. Heritability analyses across modality-specific and SF coupling gradients captured overall similar pat-\nterns in both groups, with slightly higher heritability estimates in children, particularly for the SF coupling\nassessment. TranscriptomicdecodingofSFcouplingheritabilityestimatesshowedassociationswiththeexpres-\nsion of excitatory neurons subtypes. The paper includes an impressive breadth of analyses. However, I have\nseveralmajorconcerns,notablyregardingthemotivationofthestudy,thewaydevelopmentalcomparisonswere\nimplemented, and note that several interpretations and conclusions are not supported by adequate statistical\ntests.\nResponse: We appreciate Reviewer 2’s positive feedback and insightful suggestions. We have carefully ad-\ndressed all the comments in the revised manuscript. Our detailed, point-by-point responses are provided below.\n1. The introduction lacks a clear rationale for why gradients and SF gradient coupling are used and im-\nportant for neurodevelopmental inquiry. Currently, the paper is framed as if the primary motivation for\nlookingatSFgradientcouplingisthatithasnotbeendonebefore,andthereforebehaviouralandgenetic\nassociations of SF coupling are unknown. What insights can SF gradient coupling bring beyond previ-\nously used measures of FC-SC coupling? What would diverging results from connectome-level measures\nindicate? Without this justification, it is difficult to contextualize the importance or new insights brought\nbythemultitudeofanalysesperformedhere.\nResponse: WethanktheReviewerforthisinsightfulcomment. IntherevisedIntroductionsection(lines\n37-52), we have substantially clarified why we use gradients and structural-functional gradient coupling\n(SFGC),andwhattheyaddbeyondmoreconventionalSFcouplingmeasures.\nFirst,wenowmoreclearlyexplainwhatgradientsareandwhytheyarerelevantfordevelopment: gradient-\nbased representations summarize whole-brain organization along a small number of continuous axes (for\nexample, from sensory/motor regions toward association cortex). This provides a compact description of\nlarge-scaleorganizationthatiswellsuitedforstudyinghowbrainorganizationchangeswithage.\nSecond, we explicitly clarify how SFGC differs from traditional SF coupling measures. Node-wise or\nedge-wise SF coupling focuses on how similar structural and functional connectivity are for each region\nor connection. In contrast, SFGC measures how structural and functional gradients align with each other\nacross the cortex, at both macroscale and subnetwork levels. In the revised text, we state that SFGC\nthereforecapturesthecorrespondencebetweenstructuralandfunctionalhierarchies,ratherthanonlylocal\nSC-FCsimilarity.\nThird, we now briefly explain what it would mean if results based on SFGC differ from those based on\nnode-wiseorconnectome-levelSFcoupling. IfSFGCshowsageorbehavioraleffectswherenode-wiseSF\ncouplingdoesnot,thispointstochangesinthealignmentoflarge-scalehierarchiesratherthanchangesin\n13\nlocalcouplingalone. Iftheoppositepatternoccurs,thiswouldsuggestmorelocalreconfigurationwithout\nmajor changes in the global gradient structure. We highlight that this is the main reason we complement\nexistingSFcouplingmeasureswithagradient-levelcouplingmeasure.\nThese additions make the rationale for using SFGC explicit and connect it directly to the questions about\ndevelopment,behavior,andgeneticsthatweaddressintheremainderofthepaper.\n2. The authors perform group-level comparisons of children (9-10) vs young adults (22-35) cohorts. First,\nasdataarenotharmonizedacrosssiteswithmethodssuchasCombat,itisunclearifreportedeffectsare\nattributabletodifferencesinageorgeneralsite/scannerdifferences. Second,andastheauthorsknow,both\nwhite matter and functional networks change throughout the lifespan, and derivative metrics from these\nnetworks peak atdifferent ages for differentsubnetworks. Childhoodis a developmental windowof rapid\nchange, and even in the adult time window investigated here, FC and SC are not static (Yeatman et al.,\n2014,NatComms;Fjelletal.,2017,HBM;Betzeletal.,2014,NIMG).Mostdevelopmentalstudiesmodel\nage effects continuously for this reason. As a result, I am not convinced that a cohort-level comparison\nperformedonunharmonizeddataisappropriate.\nResponse: We truly appreciate the Reviewer for these important comments. In the revised manuscript,\nwehaveperformedacomprehensivedataharmonizationproceduretostrengthenthevalidityofourcross-\ncohortcomparisonsandclarifiedourdevelopmentalframing.\nFirst, regarding harmonization, we have implemented a ComBat-based harmonization pipeline for both\ngradients and SFGC and rerun all analyses using the harmonized measures. Briefly, we (i) applied strict\nmotionqualitycontrol(excludingparticipantswithmeanframewisedisplacement> 0.3mm),(ii)harmo-\nnizedABCDforscannerandsiteeffectsandHCP-Development(HCP-D)forsiteeffects(withageandsex\\ascovariates),and(iii)usedHCP-Dasabridgetoestimateandcorrectstudy/pipelinedifferencesbetween\nABCD and HCP-YA, thereby placing the cohorts in a comparable SFGC space while preserving age-\nrelatedvariation. AsshowninSupplementaryFig.5,thisproceduresubstantiallyreducesscanner-,site-,\nandmotion-relatedstructure, particularlyinABCD,whileretainingthecohortandagepatternscentralto\nour developmental contrasts. These procedures are now described in detail in the Data harmonization\nsubsection of the Methods section, and all cross-cohort results in the revised manuscript are based on\nthe harmonized data. The updated analyses continue to support our original conclusions that SFGC is a\npredictiveandheritableendophenotypereflectingdevelopmental,behavioral,andgeneticinfluences.\nSecond, regarding the developmental framing, we fully agree that white-matter and functional networks\nchange continuously across the lifespan and that neither childhood nor adulthood is static. Our design\nusestwocross-sectionalcohorts(childreninABCDandyoungadultsinHCP-YA),andwenowstatemore\nclearly that our comparisons provide broad contrasts between late childhood/early adolescence and early\nadulthood,ratherthanadetailedcontinuoustrajectory. Intherevisedtext,we(i)adjustedthelanguagein\nthe Introduction and Discussion sections to avoid implying longitudinal “trajectories”, (ii) clarified that\nageismodeledwithincohortstoaccountforwithin-groupagevariability,and(iii)explicitlyacknowledged\nin the Discussion section that our cross-sectional, two-cohort design cannot capture nonlinear or region-\nspecificageeffectsacrossthefulllifespan,andthatareliablecharacterizationofsucheffectswillrequire\ndenselysampledlongitudinaldata.\nTogether,thesechangesensurethatourcross-cohortcomparisonsarebasedonharmonized,site-corrected\nSFGC measures and that our developmental interpretations are framed as broad cross-sectional contrasts\nwithexplicitacknowledgmentofthelimitsofourdesign.\n14\n3. Several analytical choices are not adequately justified. For example, some analyses focus only on G1\nand G2, the coupling of FCG1 and SCG1 or FCG1 and SCG2, and the heritability analyses look at 20\ndistinctgradients. Itishardtomakesenseoftheseanalyticalvariationsandinterpretfindingscoherently.\nFor example, would we expect different downstream findings from measuring SF gradient coupling using\nFCG1:SCG1vsFCG1:SCG2?\nResponse: We thank the Reviewer for raising this important point. In the revised manuscript, we now\nmakeitexplicitthatallprimaryanalyses,includingcross-cohortcomparisons,behavioralassociations,and\nheritabilityanalyses,arebasedonSFGCindicesderivedfromthefullsetof20×20functional-structural\ngradientcombinationsratherthanonanysinglegradientpair. Theplaceweintroduceanindividualpairas\nademonstrationiswhenillustratinghowSFGCmanifestswithinYeo-7andDesikan-Killianysubnetworks.\nInthatcontext,wefocusonarepresentativepair,FCG1:SCG1,becausetheprincipalgradientsexplainthe\nlargest proportion of variance and show different patterns in the canonical somatomotor-visual hierarchy\nacrosscohorts,makingthemthemostinterpretablefordemonstratingheterogeneityacrossnetworks. This\nexampleisusedtoshowthatsomesubnetworks(e.g.,sensory/motor)remainstronglycoupledwhileothers\n(e.g.,DMN,controlnetworks)aremoredecoupled,inlinewithpriorwork. Itdoesnotdefineorconstrain\ntheSFGCmeasuresusedindownstreamanalyses.\nRegardingthespecificquestionofFCG1:SCG1vs.FCG1:SCG2,differentgradientpairscanindeedshow\ndifferent child-to-adult contrasts at the pairwise level, because they reflect different axes of organization.\nHowever, our conclusions about behavioral associations and heritability across cohorts are drawn from\nSFGC measures computed from the full gradient set, not from any single pair. We have clarified this\ndistinctionintheMethodssectionandintherelevantfigureandtextintherevisedmanuscript.\n4. Many claims in the paper are not statistically supported. For example, differences between young and\nadult cohorts on FC and SC gradients are not quantified, only described qualitatively. As a result, the\neffectofmodality-specificdifferencesonSFgradientcouplingdifferencescannotbeassessed(i.e. arethe\neffects driven by one modality over the other). On pages 6-8, the authors claim “Together, these findings\nestablishedmacroscaleandsubnetwork-levelSFgradientcouplingastwoequallyinformativemetricsfor\nquantifying correspondence between brain structural and functional organization.” Yet, no quantitative\ncomparison of the two approaches is performed - how can they be qualified as equally informative? In\ntheheritabilityanalyses,theauthorsreport“ThesefindingssuggestedthatSFgradientcouplingcaptured\nhighly heritable multimodal axes of brain organization that were not fully explained by either modal-\nity alone.”. They support these claims by simply reporting heritability metrics FC, SC and SF coupling\ngradients, yet there are no models implemented to assess unique variance explained or direct statistical\ncomparisonsoftheseheritabilitymetrics.\nResponse: We appreciate the Reviewer’s comment. In the revised manuscript, we have conducted addi-\ntionalstatisticaltestsandhypothesisteststhroughoutourmanuscript. Allfindingsanddiscussionsregard-\ningthesetestsarerevisedandupdatedintheResultsandDiscussionsections. Thesetestsinclude:\n(a) Pairwise spin-rotation permutation tests to quantify cross-cohort correspondence for all FC and SC\ngradients(FCG1∼FCG20andSCG1∼SCG20;SupplementaryFig. 1b,c);\n(b) Welch’st-testswithunequalvarianceonthemacroscale-levelcouplingvaluestocomparestructural-\nfunctionalgradientcouplingbetweencohort(SupplementaryFig. 1d);\n(c) Pairedt-teststoassesstheasymmetryofgroup-levelgradientsacrosshemisphereswithineachcohort;\n15\n(d) Pairedt-teststocompareSFGC-outcomeassociationdifferencebetweenmacroscaleSFGCandsub-\nnetworkSFGC(Fig. 2a);\n(e) Welch’s t-tests with unequal variance to compare SFGC-behavior association difference between\ncohortsandbetweensex(Fig. 2b,c);\n(f) Pairedt-teststocomparetheheritabilitymetricsbetweenleftandrighthemispheres(Fig. 4g,p);\n(g) Paired t-tests to compare the heritability metrics between SFGC and individual gradients (Supple-\nmentaryTable1);\n(h) Poweranalysestoassessthedetectabilityofheritabilityestimatesgiveneachcohort’sfamilystructure\n(SupplementaryFig. 6);\n(i) Spin-rotation permutation tests to adjust for the spatial autocorrelation in imaging-transcriptomic\nanalyses(SupplementaryTable4).\nSpecifically,fordifferencesinFCandSCgradientsacrosscohorts,wenowperformpairwisespinpermu-\ntationtests(10,000permutations)onharmonizedgradientsfromABCDandHCP-YA.Beforecomparison,\ngradient signs were aligned to a common reference to remove orientation ambiguity. For each ABCD\ngradient (FCG1∼FCG20; SCG1∼SCG20), we computed its spatial correlation with all 20 correspond-\ning gradients in HCP and evaluated significance using the spin test, with FDR correction applied across\nthe 20×20 comparisons. The resulting FDR-corrected p-value heatmaps are shown in Supplementary\nFig.1b,candprovideaformalbasisforthequalitativedescriptionsinthemaintext.\nRegarding the statement that “macroscale and subnetwork-level SFGC are two equally informative met-\nrics,”ourintentionwasnottoclaimformalequivalencebuttoemphasizethatbothscalesofSFGCrepresent\nmeaningfullevelsoforganizationthatprovideusefulinformationaboutstructure-functioncorrespondence.\nWe have revised the manuscript to clarify this wording, and the sentence reads: “Together, these findings\nestablished that both macroscale- and subnetwork-level SFGC represent meaningful levels of organiza-\ntion, and that examining both scales provides a more complete characterization of SF correspondence.”\nWe now have also reported FDR-corrected paired t-tests comparing macroscale vs. subnetwork SFGC in\ntheirassociationswitheachoutcome,asshowninFigure3aanddescribedintheResultssection.\nFor the heritability analyese, to statistically compare the metric under SFGC with those under unimodal\ngradients, we have added a dedicated analysis at matched subnetwork resolution. Because SFGC was\ndefinedattheYeo-7/Desikan-Killianysubnetworklevel,wehavefurthersummarizedvertex-wiseFCand\nSCgradients atthe sameresolution, estimatedheritability foreach subnetwork-levelphenotype usingthe\nsameACEmodel,andconductedtwo-sidedpairedt-testscomparingSFGCwithitscorrespondingFCand\nSCgradientsaspresentedinSupplementaryTable1withBonferronicorrectedp-values. Thisframework\nallowsexplicitstatisticalcomparisonofheritabilityacrossmodalities.\n5. HCPandABCDgradientswerealignedtoa“cohort-level”template. Byaligningeachcohorttodistinct\ntemplates,doesthisprocedurenotruntheriskofspuriouslyinflatinggroupeffects?\nResponse: We appreciate the Reviewer’s thoughtful question. In our analysis, Procrustes alignment was\nperformed only within each cohort: for ABCD and HCP-YA separately, each subject’s gradients were\naligned to that cohort’s empirical mean gradient. This “template” is simply the within-cohort average of\nsubject-levelembeddingsinacommonanatomicalspace. Itisnotsharedacrosscohortsandisnotderived\nfrom any external reference. The Procrustes step applied an orthogonal transformation in the gradient\nspace to resolve the arbitrary sign and orientation of the diffusion embedding. It does not change the\n16\nspatial pattern of gradient values on the cortical surface or their variance, nor does it move one cohort\ntowardtheother.\nBecausetheABCDandHCP-YAtemplateswereestimatedindependentlyandalignmentwasrestrictedto\nwithin-cohortrotations,thisprocedureisexpectedtoreducewithin-cohortnoiseratherthancreateorinflate\nbetween-cohortdifferences. Infact,theriskofusingasinglejointtemplateacrosscohortswouldposethe\noppositerisk,byforcingthecohortsintoanartificiallysimilarembedding. Moreover,allkeycross-cohort\ncomparisons in the revised manuscript are based on harmonized gradients and SFGC measures after our\nComBat-basedharmonizationprocedurecorrectionforscanner,site,andstudy/pipelineeffects,asdetailed\nintheDataharmonizationsubsectionintheMethodssection. Thedevelopmentaldifferenceswereport\narethereforeobservedafterbothwithin-cohortorientationalignmentandacross-cohortharmonization.\n6. Theuseofcausally-ambiguouslanguageindescribingtranscriptomicfindingsisunwarrantedforacorre-\nlationapproachsuchastheoneappliedhere.\nResponse: WeappreciatetheReviewerforraisingthiscomment. WehavethoroughlyrevisedtheResults\nand Methods sections to remove causally suggestive terminology. We now describe the findings through\nourcorrelation-basedanalysesstrictlyasspatialassociationsorcorrespondencebetweenheritabilitymaps\nandgeneexpressionpatterns.\n7. TheDiscussionisoverallveryshortandprovideslittletonocontextualizationofresultswiththeliterature,\nfocusingonasummaryofthefindings.\nResponse: Thank you for this comment. As suggested, in the revised manuscript, we have substantially\nexpandedtheDiscussionsectiontobettersituateourfindingswithintheexistingliteratureandclarifytheir\nconceptualimplications.\n8. Thelinkprovidedtoreproducetheoriginalanalysesinthispaperisnotfunctional(https://github.\ncom/Naomi-Ding/SF-Gradient-Coupling - 404 not found). It is thus not possible to evaluate\norreviewthecodeusedtoproducethesefindings.\nResponse: WethanktheReviewerforflaggingthis. Wehavemadeourfullcodebasepubliclyavailableon\nGitHub (https://github.com/Zhao-team/SF-Gradient-Coupling) to facilitate indepen-\ndepen-\ndentverificationofouranalyses.\n9. As aminorpoint, the figures aregenerally quitedense, makingthe textand smallerfigure panelsdifficult\ntoparse. Also,themagnitudeandtopographyofgroupdifferencesaredifficulttoevaluatewhenadultand\nchild effects are not presented on the same scale (e.g., Fig 1d-j; f-l, but the point holds throughout the\nmanuscript).\nResponse: Thankyouforyourcomments. Intherevisedmanuscript,wehaverevisedallfigurestobemore\nvisuallyaccessiblebyincreasingfontsizesandreorganizingsubfigures. Whenfeasible,wepresentcohort-\nrelated effects using a common scale to facilitate evaluation of both the magnitude and spatial pattern of\ngroupdifferences. ForselectedsubfiguresincludingFig. 2a,b,dandFig. 2g,h,j,weretainedtheoriginal\nscaling to allow clearer visualization of the intrinsic brain organizational hierarchies within each cohort,\n17\nwhichwouldbelessdiscernibleunderasharedscale. Importantly,allacross-cohortcomparisonsarenow\nbasedonformalstatisticaltestsratherthanvisualinspectionalone.\nThis study introduces and characterizes a novel neuroimaging metric, structural-functional (SF) gradient cou-\npling, which quantifies the alignment between structural and functional gradients both globally and within dis-\ntinct brain networks. The authors examine how this coupling varies across developmental stages, differs by\nsex, relates to behavior and mental health, and reflects genetic and transcriptomic influences. Given that the\ngradients are derived separately for functional and structural modalities, and thereby their rank order does not\nnecessarilycorrespondacrossmodalities, theauthorsoptedtoexploreallpossiblegradientpairingstocapture\nthe full coupling pattern. This is an innovative contribution, as structural-functional coupling has rarely been\ninvestigatedacrossmultipledimensions. Below,Ioutlineseveralconcernsthatshouldbeaddressed.\nResponse: We really appreciate the Referee for taking the time reviewing our paper and the positive and con-\nstructive feedback. In this revision, we have thoroughly addressed all the comments, and our point-to-point\nresponseisprovidedbelow.\n1. Themanuscriptclaimsthat“structuralgradientsprimarilyreflectedthetopologyoflong-rangewhitemat-\nter pathways.” However, this claim is not directly supported by any figure. The authors should clarify\nhow this interpretation is derived from their results or cite relevant references to support the statement.\nIt would also be helpful to provide validation using existing structural (non-functional) atlases (such as\nthe Desikan-Killiany atlas, which is already used in this paper) by comparing FCG1 and SCG1 scores\nacross anatomical parcellations. For instance, Figure 2b shows that SCG1 exhibits much greater vari-\nability across subjects within each functional network compared to FCG1, suggesting that FCG1 is more\nconsistent across individuals within these networks. If SCG1 scores show lower variance within anatom-\nical parcellations, this would lend support to the interpretation that structural gradients reflect stable\ntopologicalfeaturesofbrainanatomy.\nResponse: WethanktheReviewerforpointingoutthisambiguousphrasingintheoriginalmanuscript. In\nthe revised paper, we have removed this claim and replaced it with a more neutral, empirically grounded\ndescriptionthatreads: “TheaveragedSCandFCmatricesexhibitedpronouncednetwork-levelmodularity,\nproviding the organizational scaffold that underlies subsequent gradient and coupling analyses (Supple-\nmentaryFig. 1a). Consistentwiththisorganization,thegradientscapturelow-dimensionalrepresentations\noftheseconnectivitypatterns,withSCGsandFCGsemphasizingdistinctspatialtransitionsacrosscortical\nsystems(Marguliesetal.,2016;Parketal.,2021).”.\nRegarding the suggestion on comparing FCG1 and SCG1 scores under the Desikan-Killiany atlas, we\nfirst clarify that the boxplots in Figure 2b, h do not depict subjects’ gradient scores. Instead, they show\nparcel-averagedgradientvalueswithineachfunctionalsubnetwork,andthereforequantifyparcelwisespa-\ntialvariabilityratherthanindividualvariability. FollowingtheReviewer’srecommendation,weexamined\nSCG and FCG patterns with respect to Desikan-Killiany parcels. These analyses did not provide strong\nstatistical support for the stronger claim that structural gradients “primarily” reflect long-range anatomi-\ncal topology relative to functional gradients. We therefore refrain from making that claim in the revised\nmanuscriptandlimitourinterpretationtotheobserved,data-drivendifferencesbetweenSCGsandFCGs.\nThecorrespondingdescriptionsinSupplementaryFig. 1aandtheResultsandDiscussionsectionshave\nbeenupdatedaccordingly.\n2. In Figure 2, the authors describe the adult structural gradients as exhibiting greater bilateral symmetry\nandspatialprecisioncomparedtothechildgroup,whichissupportedbythevisualizations. However,the\n19\nboxplotsforadultSCG1andSCG2inFigure2bsuggestgreaterinter-subjectvariabilityingradientscores\ncompared to those in the child group (Figure 2h). This apparent dissociation between spatial refinement\nand increased variability is intriguing from a developmental perspective. I recommend that the authors\nincludeabriefdiscussionofthispoint,asitwouldstrengthentheinterpretationofage-relatedchangesin\nstructuralgradientorganization. Additionally,pleaseprovidedetailsabouttheboxplots. Forexample,do\ntheboxesrepresentsubjects,andwhatdothecenterlineandboxboundariesindicate?\nResponse: We thank the Reviewer for this insightful suggestion. We have now explicitly included rel-\nevant discussions on this aspect in the Discussion section as follows: “A related developmental feature\nof SCGs was the dissociation between large-scale spatial organization and local dispersion of gradient\nvalues. Inadults,principalstructuralgradientsexhibitedclearerlarge-scalespatialorganization,includ-\ning more pronounced bilateral symmetry, while at the same time showing greater dispersion of gradient\nvalues within specific subnetworks. Importantly, these observations reflected distinct aspects of gradient\nstructure: large-scale spatial organization captures the gradients layout across the cortex, whereas lo-\ncal dispersion reflects heterogeneity in gradient expression across vertices within subnetworks. From a\ndevelopmental perspective, this apparent dissociation suggested that maturation may support more sta-\nble global organization of structural gradients while allowing increased heterogeneity in how individual\nverticesexpressthesegradients.”\nInaddition, wehave clarifiedtheconstructionoftheboxplotsintherevised manuscript. Theboxplotsdo\nnotrepresentsubject-levelvariability. Instead,theysummarizecohort-levelgradientscoresacrosscortical\nvertices. Thesevertex-levelscoreswerethengroupedaccordingtotheYeo-7functionalnetworks,andthe\nboxplots show the distribution of vertex scores within each network. The center line corresponds to the\nmedianvertexscore,theboxdenotestheinterquartilerange(IQR),andwhiskersrepresent1.5×IQR,with\npointsoutsidethewhiskersplottedasoutliers. ThisclarificationhasbeenaddedtotheFigure2captionin\ntherevisedpaper.\n3. In several instances, the manuscript blends discussions with descriptions of results. Here are two exam-\nples: “This pattern was consistent with prior findings of reduced structure-function correspondence in\ntransmodal regions [21]” and “This aligned with previous findings of sex-related differences in SF cou-\nplingpatterns[26].”Forclarity,Irecommendseparatingthepresentationofresultsfromtheirdiscussion.\nResponse: WethanktheReviewerforthishelpfulsuggestion. Intherevisedmanuscript,wehavecompre-\nhensively reorganized the text to maintain a clearer separation between Results and Discussion sections.\nTheResultssectionnowfocusesondescribingempiricalfindings,whileliterature-basedcommentaryhas\nbeenmovedtotheDiscussionsection.\n4. In the behavioral prediction model, it remains unclear what the input features were, specifically, whether\nthe subnetwork-level coupling features were used jointly in a multivariate prediction model or entered\nindependentlyforeachsubnetwork. Thekernelridgeregression(KRR)methodisdescribedusingasingle\nfeature vector x , but the manuscript does not clarify whether this x represents a concatenated 400×7\ni i\nfeature vector (aggregating coupling features across all seven subnetworks) or whether each subnetwork\nwasmodeledseparately. WhileFigures3d-gdisplaynetwork-specificfeatureimportancebars,suggesting\nthat predictions may have been conducted separately for each subnetwork, Figure 3a includes only one\norangeboxtorepresentpredictionperformanceforsevennetworks,whichisconfusing. Irecommendthat\n20\ntheauthorsclarifyhowtheinputfeatureswereconstructedandhowthepredictionmodelwasimplemented\nforbothmacro-andsubnetwork-levelcoupling.\nResponse: We appreciate the Reviewer’s attention to this important technical detail. Throughout behav-\nioralpredictionanalyses,eachscaleofSFGCfeaturesweremodeledjointlyinasinglemultivariatemodel.\nFormacroscaleSFGC,wefittedonepredictionmodelpercohort,whereeachsubject’sinputfeaturevector\nconsists of the full set of 400 (20×20) gradient couplings, and both KRR and MLP were trained on this\njoint feature space. For subnetwork-level SFGC, we concatenated the coupling features from all subnet-\nworks into a single feature vector, which had a dimension of 5,600 (400 gradient couplings ×14 Yeo-7\nsubnetworks). Similarly, each KRR and MLP model were trained on this joint 5,600-dimensional feature\nspace. Thenetwork-specificfeature-importanceprofilesshowninFigure3d-gwerederivedfromthissin-\ngle subnetwork-level model and are therefore directly comparable across subnetworks. We have clarified\nthis modeling strategy in the Structural-functional gradient coupling, Associations between gradient\ncouplingandbehavioraloutcomesandModelperformanceandfeatureimportancesubsectionsofthe\nMethodssection,andhavemodifiedrelatedtextforFigure3intheResultssection.\n5. The sentence in the results stating that ”heritability estimates decreased monotonically with increasing\ngradient coupling” appears inconsistent with the directionality shown in Figures 4a and 4b (and related\npanels). Specifically, the “average absolute values” in both 4a and 4b exhibit a decreasing trend as\ncoupling weakens, suggesting that stronger coupling is associated with higher heritability estimates, not\nlower. I’mnotsureifImayhavemissedsomething,soIkindlyasktheauthorstoclarifythispoint.\nResponse: Thank you for catching this ambiguity and for the careful reading. The original phrasing\nintended to describe the ordering of coupling indices across functional and structural gradients, not the\nmagnitudeofcouplingstrength. Ourresultsshowedthatgradientcouplingpairsinvolvinglower-orderSC\nand FC gradients exhibit both stronger coupling and higher heritability, whereas coupling that involves\nhigher-order gradients shows weaker coupling and lower heritability. Thus, the hierarchical decline in\nheritabilitymirrorsthehierarchicaldeclineincouplingstrengthacrossgradientorders,nottherelationship\nbetweenheritabilityandthemagnitudeofcouplingperse.\nWe agree that the statement could bring confusion and have revised the text accordingly to remove this\nambiguity and now explicitly state that heritability decreases systematically across couplings involving\nhigher-ordergradients,consistentwiththepatternsshowninFigure4a-d,j-m.\n6. Themanuscriptstatesthat“individualgradientswerealignedbyconstructingacohort-leveltemplateand\napplying Procrustes rotation.” I assume the correction has been done within each cohort. However, it\nis unclear whether gradients were aligned across the child and adult groups prior to comparison. Since\ngradient directions can arbitrarily flip across groups in diffusion embedding, direct group comparisons\nmaybeconfoundedwithoutproperalignment.\nResponse: We thank the Reviewer for this thoughtful comment. In our study, Procrustes alignment was\nperformedseparatelywithinABCDandHCP-YAtoensureconsistentgradientorientationattheindividual\nlevelwithinthatcohort. Wedidnotperformcross-cohortProcrustesalignmentinordertoavoidforcingthe\ntwocohortsintoanartificiallysimilarembedding. Weagreethatgradientaxesfromdiffusionembedding\ncan, in principle, flip across cohorts; however, this potential cross-cohort sign flip does not affect any of\nourdownstreamanalyses. Specifically,(i)thecross-cohortspatialcorrespondenceinSCGsandFCGswas\n21\nderived from the absolute value of their spatial correlation, and the cross-cohort difference in SFGC for\neach gradient pair was calculated based on the magnitude of the cohort-level coupling values; (ii) brain-\nbehavior prediction was performed within each cohort, so out-of-sample correlations between predicted\nandobservedscoresareinvarianttoaglobalsignflipofSFGC;and(iii)ACEheritabilityanalysesquantify\nvariancecomponents,whicharealsomathematicallyunchangedbymultiplyinggradientvaluesby−1. In\naddition, we have applied a comprehensive across-cohort harmonization of both gradients and SFGC to\nremove scanner, site, and study/pipeline effects before conducting any comparisons between ABCD and\nHCP-YA. The full procedure is now described in the Data harmonization subsection in the Methods\nsection. This ensures that group differences reflect biological rather than preprocessing-related variation.\nTakentogether,thesedesignchoicesensurethatanypotentialarbitrarydifferencesingradientsignacross\ncohortsdonotconfoundourgroupcomparisonsortheresultinginferences.\n7. While the study compares findings across the ABCD and HCP datasets, which differ in both age range\nanddatasource,thescanningprotocolsandpreprocessingpipelineswerenotconsistentbetweenthetwo.\nAlthough the ABCD data underwent harmonization, there is no indication that the data were harmonized\nacross cohorts. If not, this should be acknowledged and discussed as a potential limitation. Additionally,\nthe preprocessing procedures (particularly for the ABCD dataset) are not described in sufficient detail.\nI recommendthattheauthorsprovidegreatermethodologicaltransparencyregardingtheimagingprotocols\nandpreprocessingsteps.\nResponse: WethanktheReviewerfortheseimportantcommentsonpreprocessingandharmonization. In\ntherevisedmanuscript,wehaveimplementedacomprehensivequality-controlandharmonizationpipeline\nforbothgradientsandSFGCbeforeperforminganyanalyses,andwenowprovidemoredetaileddescrip-\ntionsofthepreprocessingstepsforeachdataset.\nSpecifically, because direct comparisons between ABCD and HCP-YA can be confounded by differences\nin acquisition protocols, preprocessing pipelines, and multi-site versus single-site sampling, we first in-\ntroduced the Human Connectome Project-Development (HCP-D) dataset (Somerville et al., 2018) as a\nbridgingcohort. HCP-DisacompanionstudytoHCP-YAthatextendstheHCPframeworktoparticipants\naged 5-21 years, uses imaging protocols and processing pipelines closely aligned with those of HCP-YA,\nandsamplesanagerangethatoverlapswithABCD.Forthesereasons,HCP-Dprovidesaprincipledbridge\nthatallowsustoseparatestudy-andpipeline-relatedeffectsfromgenuinedevelopmentaldifferenceswhen\ncomparingABCDandHCP-YA.\nOnthisbasis,ourharmonizationprocedureproceedsintwostages. First,weappliedstrictmotionquality\ncontrolbyexcludingparticipantswithlargemeanframewisedisplacement(mean FD> 0.3mm),yielding\nfinalsamplesof5343ABCD,93HCP-D,and875HCP-YAparticipants. Second,weperformedComBat-\nbasedharmonization(Johnson,C.Li,andRabinovic,2007)usingthesvaRpackage(Leeketal.,2012).\nWithin cohorts, ABCD data were harmonized for scanner and site effects, and HCP-D data were har-\nmonized for site effects only; no scanner or site harmonization was required for the single-site HCP-YA\ncohort. Inallcases,scanner/siteweremodeledasbatchvariablesandageandsexwereincludedascovari-\nates,therebypreservingage-andsex-relatedvariationwhileremovingscannerandsitedifferences.\nToaddressremainingstudy-andpipeline-relateddifferencesbetweenABCDandHCP-YA,wethenaligned\nABCD to HCP-YA through HCP-D. Specifically, we performed ComBat harmonization with study indi-\ncator (ABCD vs. HCP-D) as the batch effect and age and sex as covariates, which allowed us to estimate\nthe mean study-effect difference between ABCD and HCP-D, denoted as ∆ . We then applied\nABCD−HCP\nthismeanstudyeffect∆ toeachindividualsubjectfromHCP-YA,therebyplacingABCDand\nABCD−HCP\npipelineartifacts. AsshowninSupplementaryFig.5,thisstrategysubstantiallyimprovesharmonization\nquality,particularlybymitigatingpronouncedmotion-andscanner-relatedeffectsintheABCDcohort.\nFor consistency, we applied this harmonization procedure before using gradients, macroscale SFGC, or\nsubnetworkSFGCinanydownstreamanalyses,andwereranallanalyseswiththeseharmonizedmeasures,\nwithupdatedresultsreportedintherevisedmanuscript. Themainfindingsremainrobust: SFGCcontinues\ntoemergeasapredictiveandheritableendophenotypethatreflectsdevelopmental,behavioral,andgenetic\ninfluences, and the key cross-cohort differences are not explained by scanner, site, or motion effects. All\nofthesequality-controlandharmonizationsteps,togetherwithmoreexplicitdescriptionsofpreprocessing\nandmotionexclusioncriteria,arenowincludedintheImagingprocessingandconnectivityconstruction\nandDataharmonizationsubsectionsoftheMethodssection.\n8. Inthemaintext,theauthorsreferto”psychiatricsymptoms”whendescribingassociationswithsubnetwork-\nlevel coupling, whereas Figure 3a labels this category as ”Mental Health.” For consistency and clarity, I\nrecommendusingthesameterminologythroughoutthemanuscript.\nResponse: WethanktheReviewerforthishelpfulsuggestion. Wehaverevisedtheterminologythroughout\nthe manuscript to ensure consistency and now uniformly use the term “Mental Health” to describe this\nbehavioraldomaininboththemaintextandfigures.\n9. Throughoutthemanuscript,theauthorsprimarilyfocusonthecouplingbetweenthefirstgradients(FCG1\nvs. SCG1). However, no explicit rationale is provided for prioritizing these gradients over higher-order\nones. The authors do mention (p.7): “To illustrate this coupling heterogeneity, we focused on two repre-\nsentativegradientpairs,FCG1:SCG1andFCG1:SCG2,eachshowingstrongalignmentinoneagegroup\nbut weak alignment in the other.” It would be informative to also report heritability and transcriptomics\nanalysesbasedonFCG1:SCG2coupling.\nResponse: We thank the Reviewer for this helpful suggestion. To clarify, all our primary analyses,\nincludingcross-cohortcomparisons,behaviouralassociations,andheritabilityanalyses,arebasedonSFGC\nindices derived from the full set of 20 × 20 functional-structural gradient combinations rather than on\nany single gradient pair. The place we introduce an individual pair is when illustrating how SFGC mani-\nfests within Yeo-7 and Desikan-Killiany subnetworks. In that context, we focus on a representative pair,\nFCG1:SCG1,becausetheprincipalgradientsexplainthelargestproportionofvarianceandshowdifferent\npatterns in the cortical hierarchy across cohorts, making them the most interpretable for demonstrating\nheterogeneityacrossnetworks. Thisexampleisusedtoshowthatsomesubnetworks(e.g.,sensory/motor)\nremainstronglycoupledwhileothers(e.g.,DMN,controlnetworks)aremoredecoupled,inlinewithprior\nwork. ItdoesnotdefineorconstraintheSFGCmeasuresusedindownstreamanalyses.\nFor the heritability analyses, as shown in Figure 4, we systematically quantified heritability for all 20 ×\n20FC-SCgradientcombinations,FCGi:SCGj withi,j = 1,...,20,summarizingboththeglobalaverage\npatternsandthespatial/subnetwork-leveldistributionofgeneticinfluenceacrossallcouplingpairs. These\nresults demonstrate a hierarchical structure in genetic contributions that decreases with higher-order gra-\ndient indices. Building on this global characterization, we now chose to only highlight the FCG1:SCG1\npair in the main text because it consistently exhibited the strongest and most spatially coherent heritable\nsignal in both cohorts, making it the most biologically interpretable and statistically robust phenotype for\ndownstreamtranscriptomicenrichmentanalyses.\n23\n10. Whenevaluating“gradientcouplingstrengthacrossdifferentdevelopmentalstages,”theauthorscompare\nchildren (ABCD) and adults (HCP) as two broad groups. It may be beneficial to further divide the child\ncohort into narrower age bands to better capture the developmental evolution of SF gradient coupling\nacrosschildhoodandadolescence. Althoughthismaybeconstrainedbythelimitedagerangeofthecurrent\nABCD dataset (a point that could be acknowledged as a limitation), future work could address this using\ntheHCPDevelopmentdataset. Suchanapproachwouldofferamorefine-grainedviewofdevelopmental\ntrajectoriesandcouldalsohelpmitigatecross-cohortharmonizationconcernsraisedearlier.\nResponse: We thank the Reviewer for this valuable suggestion. We agree that finer age segmentation\ncould,inprinciple,provideamoredetailedviewofdevelopmentalchangesinSFGC.However,theABCD\nbaseline cohort used here spans a relatively narrow age range (9-10 years), so further subdividing this\nsamplewouldsubstantiallyreducepowerandlimittheinterpretabilityofanyinferred“trajectories”. Inthe\nrevisedmanuscript,wenowexplicitlyacknowledgethisasalimitationandclarifythatourcurrentanalyses\nareintendedtoprovideabroadcross-sectionalcontrastbetweenlatechildhoodandearlyadulthood,rather\nthantomodelcontinuousdevelopmentalchange.\nAstheReviewernotes,futureworkusinglongitudinalfollow-updataandbroaderdevelopmentalcohorts,\nsuchasHCP-Development,willbebettersuitedtocharacterizingfiner-grainedtrajectoriesofSFGCacross\nchildhoodandadolescence. Intherevision,weactuallyincorporatetheHCP-Developmentdatasetintoour\nComBat-basedharmonizationprocedureasabridgingcohort,whichhelpsreducecross-cohortconfounds\nandbetterlinksABCDandHCP-YA.Consistentwiththis,wehavealsorevisedthewordingintheIntro-\nductionandDiscussionsectionstoremoveorrephraseanylanguagethatcouldbeinterpretedasimplying\ntrajectories,temporalprogression,orcausalrelationships,andnowpresentourcross-cohortresultsstrictly\nasdescriptiveandassociationalfindings.\nReferences\nJohnson,WEvan,ChengLi,andArielRabinovic(2007).“Adjustingbatcheffectsinmicroarrayexpressiondata\nusingempiricalBayesmethods”.In:Biostatistics8.1,pp.118–127.\nLeek,JeffreyTetal.(2012).“Thesvapackageforremovingbatcheffectsandotherunwantedvariationinhigh-\nthroughputexperiments”.In:Bioinformatics28.6,pp.882–883.\nMargulies,DanielSetal.(2016).“Situatingthedefault-modenetworkalongaprincipalgradientofmacroscale\ncorticalorganization”.In:ProceedingsoftheNationalAcademyofSciences113.44,pp.12574–12579.\nPark, Bo-yong et al. (2021). “Signal diffusion along connectome gradients and inter-hub routing differentially\ncontributetodynamichumanbrainfunction”.In:Neuroimage224,p.117429.\nSomerville, Leah H et al. (2018). “The Lifespan Human Connectome Project in Development: A large-scale\nstudyofbrainconnectivitydevelopmentin5–21yearolds”.In:Neuroimage183,pp.456–468.\nReviewer 4\nIco-reviewedthismanuscriptwithoneofthereviewerswhoprovidedthelistedreports. ThisispartoftheNature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early\nCareerResearcherswhoco-reviewmanuscripts.\nResponse: We sincerely thank you for your thoughtful review and valuable feedback. We have carefully ad-\ndressedallthecommentsintherevisedmanuscript.\n“Brain Functional-Structural Gradient Coupling Reflects\nDevelopment, Behavior and Genetic Influences”\nWe sincerely thank all the reviewers for their remaining comments and suggestions. We have thoroughly ad-\ndressedallthethemandprovideddetailedpoint-by-pointresponsesinthisletter.\nReviewer 1\nTheauthorsaretobecommendedfortheirthoroughrevisionofthemanuscript,andIappreciatetheinclusionof\nthestatisticaldetailsunderlyingtheanalyses. However,Ibelievethetextwouldstillbenefitfromsomeadditional\nrephrasingtoimproveclarity.\nResponse: We sincerely appreciate Reviewer 1 for the thoughtful review of our work and for offering encour-\naging and constructive feedback. In this revision, we have thoroughly considered all comments and provided a\ndetailed,point-by-pointresponsebelow.\n1. lines107-109: “TheaveragedSCandFCmatricesexhibitedpronouncednetwork-levelmodularity,provid-\ningtheorganizationalscaffoldthatunderliessubsequentgradientandcouplinganalyses(Supplementary\nFig. 1a).” It is not clear to me how Supp. Fig 1a is a good representation of “pronounced network-level\nmodularity”.\nResponse: We thank the reviewer for this helpful comment. We agree that Supplementary Fig. 1a pro-\nvides a visual illustration of network-level structure rather than a formal quantification of modularity. To\navoid overstatement and improve clarity, we have revised the sentence as follows: “The averaged SC and\nFC matrices displayed clear network-level structure (Supplementary Fig. 1a), forming the connectivity\nframeworkforsubsequentgradientandcouplinganalyses.”\n2. Lines109-110. “Consistentwiththisorganization,thegradientscapturedlow-dimensionalrepresentations\noftheseconnectivitypatterns,withSCGsandFCGsemphasizingdistinctspatialtransitionsacrosscortical\nsystems.” Thisisveryuncleartome. Whatdefines“low-dimensionalrepresentationsoftheseconnectivity\npatterns”,andhowdoSCGandFCGemphasize“distinctspatialtransitionsacrosscorticalsystems”?\nResponse: We thank the reviewer for pointing out the lack of clarity. We agree that the original wording\nwas too abstract. Our intention was to describe gradients as low-dimensional summaries of the structural\nandfunctionalconnectivitymatricesobtainedthroughdiffusionembedding. Toimproveclarityandavoid\n1\nambiguousphrasing,wehaverevisedthesentenceasfollows: “Applyingdiffusionembeddingtothecon-\nnectivity affinity matrices yielded a small number of principal gradient axes that summarize large-scale\npatternsinSCandFC.”\n3. Lines100-101. “leveragingmultimodalrawneuroimagingdataspanningchildhood(n=7,938)toadult-\nhood (n= 944), we constructed SC and FC for each subject from T1-weighted, diffusion, and functional\nmagneticresonanceimaging(MRI)data”Pleaserephrasetoindicatethatthesearetwodifferentcohorts.\nResponse: Wethankthereviewerforthissuggestion. Wehaverevisedthesentencetoexplicitlyclarifythat\nthe childhood and adulthood samples were derived from two independent cohorts (ABCD and HCP-YA),\nrather than a single continuous developmental sample. Now the sentense reads: “Leveraging multimodal\nneuroimaging data from two independent cohorts, including children from the ABCD study and young\nadultsfromtheHCPcohort,...”.\n4. line 124. “while the second SCG exhibited greater bilateral symmetry (p= 0.52) and spatial precision,\nindicating refined network segregation.” the word “greater” suggests that there is a difference, which is\nnotsupportedbythep-value. Isthisatypo?\nResponse: Wethankthereviewerforthiscarefulobservation. Sincehemisphericasymmetrywasassessed\nwithineachcohortseparately,wehaverevisedthesentencetoprovideastatisticallygroundeddescription:\n“In adults, the first SCGsimilarly separated VINand SMN, whilethe second SCGdid not exhibit signif-\nicanthemisphericasymmetry(pairedt-testp = 0.52), displayingabilaterallysymmetricspatialpattern.”\n5. Figure2. Isuggestreorderingthefigure,soitalignswiththedevelopmentalstages. i.e.,childrenontheleft\nsideandadultsontherightside. lines237-251. Iappreciatetheinformationaboutthefeatureimportance,\nbutthewordingappearstooverstatethefindings. Thesearenumericaldifferencesinfeatureimportance,\nand I do not think phrasing it as indication of “higher involvement”/”decreased involvement” is suitable\nwithoutanystatisticalteststhatexaminesdifferencesbetweenthegroups.\nResponse: We thank the reviewer for these helpful suggestions. Figure 2 has been reordered so that\nchildren are shown on the left and adults on the right, consistent with the developmental progression. In\naddition,weagreethatthepreviouswordingforfeatureimportancewastoostrong,asthesevaluesreflect\ndescriptive numerical differences rather than formally tested between-group effects. We have therefore\nrevised the text to use more neutral language and avoid implying statistical significance where no direct\ngroupcomparisonwasperformed.\nMinorissues:\nfixtypoline168\nI don’t think it necessary to state “FDR-corrected paired t-test” in the main text, standard reporting of\nstatistics(e.g.,t=x,p-adjusted=x)wouldbesufficientandwouldimprovereadability\nDue to the various types of t tests and the existance of both FDR-correction and Bonferroni-correction in\nthemanuscript,wefinditnecessarytokeeptheterm“FDR-correctedpairedt-tests”fortechnicalclarity.\nReviewer 2\nI thank the authors for their thorough response to my comments. I have two additional minor points for clarifi-\ncation:\nResponse: We appreciate Reviewer 2’s positive feedback and insightful suggestions. We have carefully ad-\ndressed all the comments in the revised manuscript. Our detailed, point-by-point responses are provided below.\n- The 2nd FC gradient produced from the HCP young adult cohort (Figure 2A) is quite different from pre-\nviously published corresponding gradient in previous work using the same dataset (e.g., Margulies et al.,\n2016). Couldtheauthorscommentwhythismaybe? Inadults,weusuallyexpectclearerdifferentiationof\nvisual-somatomotornetworksasthe2ndgradient,whilethisratherlookslikeatask-positive/tasknegative\npattern.\nResponse: We thank the reviewer for this insightful observation. We agree that the second functional\nconnectivitygradient(FCG2)derivedfromtheHCPyoungadultcohortdifferssomewhatfromthepattern\nreported in Margulies et al., 2016. Importantly, in our results the visual and somatomotor systems still\noccupy opposite ends of the gradient, consistent with the expected large-scale sensory differentiation, al-\nthoughadditionalnetworksappearmorepronounced,givingthegradientapatternthatvisuallyresembles\natask-positive/task-negativeaxis.\nOnelikelyreasonliesindifferencesintherepresentationofthefunctionalconnectome. WhileMargulies\netal.,2016derivedgradientsfromadensewhole-brainconnectomeincludingbothcorticalgrayordinates\nand subcortical voxels, our SBCI framework focuses on the cortical manifold and constructs gradients\nusing an atlas-free cortical representation (Cole et al., 2021). Prior work has shown that gradient values\ncan vary depending on the spatial representation of the connectome and analysis choices (Vos de Wael\netal.,2020;Nenningetal.,2024).\nInaddition,higher-ordergradients(e.g.,FCG2andFCG3)canbesensitivetosmallvariationsinconnectiv-\nityrepresentationwhentheirassociatedeigenvaluesarerelativelyclose(around0.12and0.10,respectively,\ninMarguliesetal.,2016),whichisconsistentwithperturbationtheoryforeigenspacestability(Davisand\nKahan, 1970). As a result, large-scale patterns such as sensory differentiation and task-related contrasts\nmaybedistributeddifferentlyacrossthesecondandthirdgradients.\nWe have included this methodological clarification in the Methods section (under the subsection “Func-\ntionalandstructuralgradientconstruction”)toensuretechnicalclarity. Takentogether,thesefactorslikely\nexplain the modest differences observed in FCG2 while preserving the fundamental large-scale organiza-\ntionofcorticalconnectivity.\n- Pages3-4: twodifferentsamplesizesarereportedforthepediatriccohort(5,343vs7,938)–pleaseclarify.\nsamplesizefromthissentenceandnowreportthefinalanalyticsamplesizesclearlyintheMethodssection.\nReferences\nCole,Martinetal.(2021).“Surface-BasedConnectivityIntegration:anatlas-freeapproachtojointlystudyfunc-\ntionalandstructuralconnectivity”.In:HumanBrainMapping42.11,pp.3481–3499.\nDavis, Chandler and William Morton Kahan (1970). “The rotation of eigenvectors by a perturbation. III”. In:\nSIAMJournalonNumericalAnalysis7.1,pp.1–46.\nMargulies,DanielSetal.(2016).“Situatingthedefault-modenetworkalongaprincipalgradientofmacroscale\ncorticalorganization”.In:ProceedingsoftheNationalAcademyofSciences113.44,pp.12574–12579.\nNenning,Karl-Heinzetal.(2024).“Fastconnectivitygradientapproximation:maintainingspatiallyfine-grained\nconnectivitygradientswhilereducingcomputationalcosts”.In:CommunicationsBiology7.1,p.697.\nVos de Wael, Reinder et al. (Mar. 2020). “BrainSpace: a Toolbox for the Analysis of Macroscale Gradients in\nNeuroimaging and Connectomics Datasets”. In: Communications Biology 3.1, pp. 1–10. ISSN: 2399-3642.\nDOI:10.1038/s42003-020-0794-7.(Visitedon05/02/2023).\nReviewer 3\nThe authors have thoroughly addressed all my concerns. I specifically commend the inclusion of the HCP-\nDevelopment dataset to perform harmonization. This resolves my concern regarding the comparability of data\nacrosscohortsandsignificantlystrengthensthevalidityoftheresults. Ihavenofurthercomments.\nResponse: We really appreciate the Referee for taking the time reviewing our paper and the positive and con-\nstructive feedback. In this revision, we have thoroughly addressed all the comments, and our point-to-point\nresponseisprovidedbelow.\nReviewer 4\nIco-reviewedthismanuscriptwithoneofthereviewerswhoprovidedthelistedreports. ThisispartoftheNature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early\nCareerResearcherswhoco-reviewmanuscripts.\nResponse: We sincerely thank you for your thoughtful review and valuable feedback. We have carefully ad-\ndressedallthecommentsintherevisedmanuscript.\n4"}]

Decision letter