The cellular and molecular basis of gyrus-sulcus specialization in the primate brain

Abstract

Gyri and sulci are key anatomical features of the primate cerebral cortex, distinguished by their structural and functional specialization, yet their cellular and molecular foundations remain poorly understood. Here we utilized single-cell spatial transcriptomics data from adult male macaque monkey brains and developed gsModel, a customized deep learning framework that distinguishes sulci from gyri. Relying solely on local cell-type composition, gsModel achieved over 90% accuracy in the classification task, outperforming alternative machine learning models and predictors based on anatomical features. By integrative analysis with diffusion MRI tractography, we found that these compositional distinctions align with systematic variations in structural connectivity, linking local molecular architecture to macroscale wiring. Embedding-guided analyses further revealed key cell types and marker genes contributing to sulcus-gyrus differences, highlighting prominent contributions from upper-layer glutamatergic neurons and oligodendrocytes, as well as distinct gene regulatory networks underlying their expression profiles. Together, this work establishes a molecular framework linking microscale molecular architecture to macroscale cortical organization, providing a basis for mechanistic studies of region-specific structural and functional specialization in the primate cortex.

This study uncovers how differences in brain cell composition help define cortical folds and reveals a link between microscopic cellular organization and large-scale brain networks in primates.

Introduction

The cerebral cortex is a hallmark of mammalian brains, characterized by its folded structure, composed of gyri and sulci. While these anatomical features were once viewed primarily as structural landmarks, they are now increasingly recognized for their distinct and complex roles in brain functions. The morphology of gyri and sulci contributes to the organization and connectivity of cortical regions, with emerging evidence suggesting that these structures are functionally specialized^1–3.

Gyri and sulci exhibit structural and functional divergence, including differences in axonal fiber density⁴, connectivity^5,6, and cognitive roles^2,7. The local morphology of these structures has been shown to predict functional activity within different cortical regions. For instance, gyri are often associated with regions of higher axonal fiber density⁴, whereas sulci tend to have more compact neural arrangements⁸. In addition, gyral regions exhibit greater temporal variance in resting-state fMRI signals⁹, suggesting a more dynamic functional state. Conversely, sulcal regions tend to show more stable but higher-frequency signals, potentially indicating more specific, localized functions³. This distinction is further reflected in their functional connectivity patterns. Gyral regions typically exhibit stronger intrinsic and extrinsic connectivity, facilitating long-range communication across the cortex. In contrast, sulcal regions tend to demonstrate more isolated functional activity. These structural and functional differences suggest that gyri are more involved in global information processing, while sulci may be specialized for more localized or regional interactions^1,4.

The structural and functional distinctions between gyri and sulci are unlikely to arise from mechanical folding alone. As molecular programs governing axon guidance and synaptic specification are known to regulate the formation of neural circuit connectivity¹⁰, it is therefore plausible that the functional divergence documented between gyri and sulci may reflect underlying differences in molecular architecture, leading to the hypothesis that gyri and sulci are characterized by distinct molecular landscapes that contribute to their differential functional properties. The finding that a high percentage of genes mutated in human cortical malformations are differentially expressed between prospective gyri and sulci in ferrets¹¹ underscores the importance of these expression differences in normal cortical development and the etiology of these disorders. However, investigations into the molecular differences between gyri and sulci have primarily focused on development^11–14, leaving their distinct profiles in the adult brain largely uncharacterized. Although some studies have offered functional interpretation from a molecular perspective¹⁵, these analyzes were usually confined to species lacking complex gyrification (e.g., marmosets), and reliance on simple models may also lead to potential biases in the candidate gene list. Thus, a systematic molecular analysis is required to fully characterize the differences between gyri and sulci.

Furthermore, understanding the local molecular architecture of gyri and sulci may illuminate mechanisms underlying macroscale cortical wiring. During development, graded expression of transcription factors and signaling molecules across the cortical sheet governs the specification of areal identities, establishing region-specific molecular programs that shape downstream connectivity¹⁶. In the adult brain, gene expression has been shown to underlie synchronous functional network activity and to associate with axonal connectivity patterns¹⁷, suggesting that molecular identity continues to encode information about network organization beyond the developmental period. Moreover, the dominant axis of transcriptional variation across the human cortex has been shown to align with anatomical hierarchy and to predict macroscale patterns of cortical specialization¹⁸, directly linking local molecular identity to large-scale network organization. Collectively, these findings motivate the hypothesis that gyri and sulci possess distinct molecular and cellular identities that reflect their functional specialization and shape their roles in large-scale cortical network organization.

In this study, we leveraged high-resolution Stereo-seq data from the macaque cortex along with computational approaches to develop a customized transformer architecture model called gsModel to predict gyri or sulci based on cell-type composition. Through this approach, we identified key cell types and marker genes that provide insights into the molecular differences between gyri and sulci, spanning from cellular organization to genetic regulation. A refined gsModel also showed the ability to distinguish the cellular heterogeneity of seven distinct sulci. We further integrated diffusion MRI tractography data to link these molecular differences with structural connectivity patterns. Subsequently, transcriptome-based network analysis uncovered distinct regulatory characteristics distinguishing gyri and sulci. Overall, our study provides a molecular and cellular characterization of gyrus-sulcus differences across the macaque cortex, establishing a framework for understanding the biological basis of cortical folding patterns in the adult primate cortex.

Results

Classification model for distinguishing gyri and sulci based on cellular organization

Using previously published spatial transcriptome data of the macaque cortex¹⁹, we first divided each cortical section into columnar segments with a median width of 3.72-mm along the direction perpendicular to the cortical sheet, and manually annotated the loci of each gyrus and sulcus based on the Paxinos atlas²⁰ (Fig. 1a). We defined 737 gyral and 613 sulcal areas, encompassing 25 anatomically defined sulci, across 140 coronal sections from three macaque monkeys (Supplementary Fig. 1a). The cellular composition within each sulcus and gyrus was then systematically quantified according to the annotation in the previous study¹⁹. Notably, cell-type compositions showed clear differences between gyri and sulci, which was shown by more diverse cellular neighborhoods located in gyri than those in sulci (Supplementary Fig. 1b).

Fig. 1. Performance and visualization of gsModel for distinguishing gyri and sulci based on cellular organization.

a Schematic representation of gsModel architecture. The framework consists of a customized backbone comprising three transformer layers, designed to process cellular organization data, followed by a fully connected classifier for label prediction. b, c Comparative performance evaluation of gsModel. gsModel was benchmarked against conventional machine learning classifiers, including Support Vector Machines, Random Forests, and Logistic Regression, as well as a convolutional neural network (CNN) architecture. Model performance was quantified using (b) F1 score and (c) accuracy metrics. Bar graphs show the mean ± standard deviation (SD) of n = 21, 18 and 13 sections (for macaque 1, 2 and 3) per group. d Principal Component Analysis (PCA) visualization of raw cellular organization data. Samples are colored according to (left) gyrus or sulcus classification and (right) cortical lobe assignment. e Principal Component Analysis (PCA) visualization of gsModel embeddings. Samples are colored according to (left) gyrus or sulcus classification and (right) cortical lobe assignment. f Spatial distribution of the gsModel score, indicating potential gyrus or sulcus regions across whole-brain slices along the anterior-posterior (AP) axis.

To distinguish sulci from gyri based on their cellular compositions, we developed gsModel, a customized transformer architecture configured with two attention heads and three hidden layers (Fig. 1a). To better represent the spatial information, cell-type compositions across 20 consecutive segments were used as a sequence input for the model. The final hidden state of the encoder output was passed to a four-layer classifier for downstream prediction. The model was trained using binary cross-entropy with logits loss and optimized via the Adam algorithm. To generate prediction labels, a sigmoid activation function was applied to the classifier output, producing a vector representing class probabilities. The class label with the highest probability score in the output vector was assigned as the final prediction.

Using sliding windows for each segment within gyri or sulci, we generated a total of 67,635 samples from 84 coronal sections of Macaque #1 as the training set (Supplementary Fig. 1a). For the test sets, we allocated 16,929 samples from 21 sections of Macaque #1, 10,935 samples from 13 sections of Macaque #2, and 13,122 samples from 18 sections of Macaque #3 (Supplementary Fig. 1a), ensuring representation across all three individuals. Although an overlapping sliding window approach was employed for data augmentation and sample generation, all samples used in the testing of the gsModel were drawn from non-overlapping, independent sections or individuals with no shared segments between training and test sets. The gsModel accurately classified gyri and sulci based on cellular composition, achieving high accuracy even for independent test sets from sections of the same individual or different subjects (92.23% for Macaque #1, 86.61% for Macaque #2, 80.61% for Macaque #3). To benchmark prediction performance, we compared gsModel against a range of classification algorithms, including traditional machine learning algorithms (Logistic Regression, Random Forest, SVM) and deep learning architectures (CNN). The results demonstrated that gsModel consistently outperformed other classification models across all three macaques (Fig. 1b, c) and exhibited superior robustness, underscoring its reliability in distinguishing sulci from gyri.

To visualize the embeddings from the classification model, we performed principal component analysis (PCA) on the output of the last hidden layer of gsModel. Notably, samples from gyri and sulci were clearly segregated along the first principal component (PC1) of the model-derived embeddings based on cellular composition (Fig. 1e). This segregation was further demonstrated by spatial visualization of PC1 values in representative Stereo-seq maps (Fig. 1f). By contrast, the two structures were indistinguishable by PCA using raw cell-type compositions in each segment (Fig. 1d). Additionally, PCA visualization colored by cortical lobe revealed that the original cell-type composition exhibited pronounced regional bias, as samples derived from the same region showed strong clustering tendency. However, after model processing, the sample distribution primarily reflected differences between gyri and sulci, with regional distinctions no longer discernible (Fig. 1e), indicating that our model captured gyrus-sulcus differences rather than region- or sample-specific biases. To examine whether the model overemphasizes fold identity at the expense of areal variation, we performed additional lobe-stratified experiments (insular was not included due to no annotated samples from gyri in this lobe). We computed F1 scores and accuracy separately for each lobe to examine whether the model performance is consistent across regions (Supplementary Fig. 1c, d). Our results indicated that gsModel maintained robust performance across all major lobes, suggesting that the embeddings capture biologically meaningful areal variation rather than merely fold identity. Furthermore, we trained (i) leave-one-lobe-out models (8 lobes) and (ii) single-lobe models, and compared them to the full model (9 lobes). The results showed that the leave-one-lobe-out models achieved performance comparable to the full model (Supplementary Fig. 1e), whereas single-lobe models showed substantially reduced generalization (Supplementary Fig. 1f). These results suggested that the model was not simply relying on lobe-specific folding patterns, but instead learned representations that were generalizable across cortical areas.

To further explore whether cellular composition could distinguish among various anatomically defined sulci, we quantified the cellular organizational entropy of each cell type across sulci. This was calculated based on the mean proportional representation of each cell type within segments of each sulcus. We observed that different cell types exhibited distinct distribution patterns across sulci, with some showing relatively low entropy values (Supplementary Fig. 2a), suggesting their potential utility in sulcus-specific classification.

Building upon these observations, we constructed a classification model using cellular composition data derived from seven sulci (including cingulate sulcus for cgs, lateral fissure for lf, superior temporal sulcus for sts, principal sulcus for ps, superior arcuate sulcus for sar, intraparietal sulcus for ips, circular sulcus for cir), each spanning at least three brain regions. This selection ensured broad regional coverage while focusing on well-defined sulcal structures. For model development and evaluation, we allocated 19,197 window samples derived from 75 sections of Macaque 1 to the training set and reserved the remaining 4698 samples from 18 non-overlapping brain sections of the same animal as the held-out test set. This stratified partitioning approach ensured representative samples in both sets while maintaining complete separation between training and testing data sources. The model architecture largely mirrored gsModel, with the key modification being an output layer expanded to seven classification units to accommodate multi-class prediction. This adaptation enabled the model to produce probability distributions across all seven sulcal classes while maintaining computational efficiency.

Using the top three principal components of the embedding derived from the cellular composition, we found that sliding window samples were clustered together according to sulcal identity (Fig. 2a). The classification model achieved an average F1 score of 77% on the test dataset, with individual sulcus-specific F1 scores ranging from 60% to 96% (Fig. 2b). As shown in the confusion matrix, a higher proportion of correct predictions was along the main diagonal, reflecting the model’s robust classification capability (Fig. 2c). Further analysis revealed that the top principal components were particularly effective for distinguishing samples from the cgs, lf, and ips (Fig. 2d), enabling clear separation of these sulci in a low-dimensional space (Fig. 2e). To visualize the spatial distribution of these components, we mapped the top principal component values onto a whole-brain section (Fig. 2f, and Supplementary Fig. 2b). We then identified cell types most strongly correlated with the top principal components, including GLU L2.2 ITGA4/CHST9, GLU L4/5/6.2 SMYD1/ST8SIA2 and GLU L3/4/5.1 SYT2/SV2C. Samples from the three sulci clustered more tightly within their respective groups when visualized using these cell types (Fig. 2g). The spatial distribution of these cell types showed that in some sulci, the distinctive distributions of these cell types aligned well with the model predictions. In others, the correspondence was less pronounced and needed more top-correlated cell types (top 3 cell types used for PC1), likely reflecting the fact that the predictive model integrates contributions from multiple cell types. The selected cell types capture a substantial portion of the predictive signal, but do not fully reproduce the overall pattern achieved by the complete model (Fig. 2h, and Supplementary Fig. 2c). These results indicate that different sulci exhibit distinct cell-type compositions, which are promising characteristics for accurate sulcus identification. These compositional differences may underlie functional specialization across sulcal regions, consistent with previous observations of sulcus-specific connectivity patterns and functional roles²¹.

Fig. 2. Cellular organization effectively differentiates various sulcus identity.

a Principal Component Analysis (PCA) visualization of embeddings obtained from the sulci model. Sliding window samples are colored according to sulcus identity. b Bar plot of F1 score denoting the prediction performance on each sulcus and the average. c Heatmap illustrating the confusion matrix for each sulcus in the multi-sulci model. d Violin plot showing the distribution of three principal components of window samples in each sulcus (n = 19,197). Overlaid box plots indicate the median (center line), interquartile range (box), and 1.5× interquartile range (whiskers). e Ternary plot illustrating the distribution of three principal components in samples from cgs, lf and ips. f Spatial distribution of the three principal components of embeddings obtained with the sulci model in a brain section. g Ternary plot illustrating relative ratio of the key cell types correlated with the three principal components in samples from cgs, lf and ips. h Spatial distribution of the cell types highly correlated with the principal components in the multi-sulci model in the macaque cortex. (PC1 used top 3 cell types, including GLU L2.2 ITGA4/CHST9, GLU L4/5.5 WFDC11/CALD1 and GLU L4.1 TYR/SOST).

Superior discriminative power of cellular composition for distinguishing gyri and sulci

Morphological and cell distribution differences between gyri and sulci have been well established. Previous studies have used maximum and minimum curvature values to identify gyral crests (local maximum) and sulcal fundi (local minimum), with mean curvature also employed to delineate gyri and sulci³. Moreover, gyri typically exhibit greater average convexity than sulci², whereas neuronal density varies between these regions in a cortex-specific manner, which may relate to mechanical factors underlying cortical folding^22,23. Therefore, we evaluated classification performance based on morphological metrics measurable in our 2D sections, including curvature (quantified here as the radius of curvature), thickness, cortical symmetry and cell density (Fig. 3a, and Supplementary Fig. 2a), and compared these with performance using the PC1 of cellular compositions (Fig. 3b). Linear regression models revealed that the F1 score using PC1 from gsModel was substantially higher than those using morphological features (Fig. 3c). These results indicate that cellular composition provides a more effective feature for distinguishing gyri from sulci.

Fig. 3. Cellular organization effectively differentiates sulci from gyri and correlates with connectome patterns.

a Illustration of curvature and symmetry indices. b Violin plot depicting the distributions of curvature, thickness, symmetry index, cell density and principal component 1 (PC1) in gyri and sulci. c Bar plot of F1 scores benchmarking PC1, curvature, thickness, symmetry, and cell density. d Representative dMRI tractography seeded from the fundus of the lateral fissure (left) and the crown of the supramarginal gyrus (right) in an ex vivo macaque brain. Streamlines are overlaid on a coronal structural image and are colored by local orientation (red, left - right; green, anterior-posterior; blue, superior-inferior). The 3D orientation axes indicate left (L), right (R), anterior (A), posterior (P), superior (S), and inferior (I). Scale bar, 10 mm. e Cumulative distribution plot illustrating the distribution of fiber lengths in gyri and sulci (n = 6,370,285). f Cumulative distribution plot of the number of fiber terminations within the cortex across gyral and sulcal regions (n = 72,397). g ROC curves of the mean fiber length of fiber tracts originated from the segments between the ground truth (stratified by the mean) and the predicted results based on the embeddings from gsModel (n = 46,522 training samples, n = 11,630 samples from a test set and n = 14,727 samples from another independent test set). h ROC curves of the mean fiber length of fiber tracts originated from the segments between the ground truth (stratified by the mean) and the predicted results of samples from the short and long groups (stratified by the mean).

Structural connectivity differences between gyri and sulci have been consistently reported^3,4. To investigate whether these connectivity differences correspond to cellular-level variations, we examined the relationship between fiber tract organization and cell-type composition. We utilized diffusion MRI (dMRI) tractography to obtain whole-brain connectome data and quantified fiber origins, terminations, and lengths across 6.3 million fibers from 107 sections covering 150 termination regions, following matching against the gsModel data. We observed that dMRI tractography patterns differed substantially between cortical landmarks. For example, tractography seeded from the fundus of the lateral fissure showed distinct connectivity profiles compared to seeding from the supramarginal gyrus (Fig. 3d, and Supplementary Fig. 3g, h). Our analysis revealed that fibers originating from gyri exhibited greater average length than those from sulci (Wilcoxon rank-sum test p < 0.001, W = 5.82 × 10¹², estimated difference in location = 1.61, 95% CI = 1.608–1.613) (Fig. 3e). Furthermore, fibers from gyral segments terminated in a broader range of brain regions than those from sulcal segments (Wilcoxon rank-sum test p < 0.001, W = 6.94 ×10⁸, estimated difference in location = 7.20 × 10⁻⁵, 95% CI = 3.70 × 10⁻⁵−3.21 × 10⁻⁷) (Fig. 3f). These findings support the notion that gyri predominantly mediate long-range connectivity, whereas sulcal regions exhibit more localized connections, consistent with previous observations^3,4.

We next investigated whether local cell-type composition can predict axonal projection patterns. Using cell-type embeddings derived from gsModel for each spatially defined sliding window segment, we constructed a model to predict the composition of fiber terminations for each segment (see “Methods”). Samples were split into the training set and two test sets: Test set 1 (including overlapped segments at the sliding-window level with the training set) and Test set 2 (completely independent, without overlapped segments with the training set). The model achieved high predictive accuracy, with mean cosine similarities of 0.94 in the training set, 0.93 in Test set 1 and 0.55 in the independent Test set 2 between predicted and observed fiber termination profiles (Supplementary Fig. 3b). In contrast, cosine similarities derived from within-lobe permutation samples were consistently low (<0.2). To further validate the prediction specificity, we evaluated whether the predicted fiber termination profiles correctly matched their corresponding ground truth regions. When we compared each prediction against all ground truth regions, the correctly matched region consistently showed the highest cosine similarity (Supplementary Fig. 3c), demonstrating that cell-type composition accurately predicts the specific pattern of fiber terminations. Within-lobe prediction demonstrated consistent performance across lobes in Test set 1, while slight variability was observed in Test set 2 (Supplementary Fig. 3d), likely due to distributional shifts inherent to independent validation.

Interestingly, we observed that the prediction performance was improved with increasing projection distance (Supplementary Fig. 3e). To assess whether the specific representational structure learned by the gsModel encodes information related to the geometric scale of axonal projections, we next examined whether gsModel-derived embeddings can predict the mean length of all fibers originating from a given column, which is a quantitative measure of long-range structural connectivity (see “Methods”). The results demonstrated that gsModel embeddings have predictive ability for mean fiber length (AUC = 0.87 for Test set 1 and AUC = 0.70 for Test set 2) (Fig. 3g). Although performance was attenuated in the fully independent Test set 2, this phenomenon could be explained by the inherent difficulty of the task that the model is asked to predict macroscale structural connectivity from local cellular embeddings that capture microscale transcriptomic organization within spatially restricted windows. To eliminate the influence of cortical regions, we also stratified performance by lobe and found that lobe-level AUC scores were consistently higher than chance across brain regions (Supplementary Fig. 3f), demonstrating that the predictive value of gsModel embeddings is not attributable to lobe-level confounding factors but truly carries genuine predictive signal for structural connectivity. By contrast, using raw cell-type composition in place of gsModel embeddings yielded a lower AUC of 0.66 on Test set 2, suggesting that the gsModel representations capture predictive structure beyond what is available in unprocessed composition vectors.

When samples were divided into short and long fiber groups using mean fiber length as a cutoff, the long-fiber group showed higher prediction accuracy than the short-fiber group in both Test set 1 (AUC = 0.75 for short vs. 0.80 for long) and Test set 2 (AUC = 0.57 vs. 0.61) (Fig. 3h), suggesting that gsModel embeddings are more informative for predicting long-range connectivity patterns. This pattern is consistent with the notion that long-range projections integrate information across large cortical distances and are therefore more likely to reflect broad regional molecular identity that gsModel embeddings can reliably capture. In contrast, short-range connectivity may depend more heavily on fine-grained local circuit properties that are not fully resolved at the level of regional embeddings, rendering it comparatively harder to predict from the current gyrus-sulcus representations. This may also be attributed to the relatively lower cellular complexity in sulci (Supplementary Fig. 1b), where short-range fibers predominate, and consequently higher-resolution inputs may be required to accurately predict short-range connectivity in these samples. Together, these results indicate that local cell-type composition is a promising predictor for projection patterns.

Characterization of major cell types in distinguishing gyri from sulci

To identify cell types that critically contribute to gyrus-sulcus differences, we employed two complementary feature selection strategies. First, feature importance was assessed using permutation importance with 10 permutations per feature, quantified by the decrease in F1 score. Second, we calculated the Spearman correlation coefficient between the PC1 and the proportion of each cell type across segments. To identify key cell types that contributed to the gsModel, we selected the intersection of the top 30 cell types from each ranking method. Because vascular and leptomeningeal cells largely reflect vascular and meningeal anatomical features rather than cortical cellular organization, they were excluded from downstream analyzes despite their high predictive importance. This yielded 14 key cell types, including 8 glutamatergic, 1 GABAergic and 5 non-neuronal cell types (Fig. 4a). Clusters were annotated based on iterative unsupervised clustering followed by identification of marker genes in each cluster (see “Methods”). The identification of these key cell types was largely consistent across cortical lobes, with slight variability in the occipital lobe, possibly due to its inherent differences in cellular composition resulting from the absence of Layer 4 (Fig. 4b, and Supplementary Fig. 4a). We further examined the proportional differences of each identified cell type between gyrus and sulcus regions. It was notable that the proportional changes in some top-ranked cell types were relatively subtle (Supplementary Fig. 4b), which could have been overlooked without our integrative modeling approach. To validate the biological significance of these 14 cell types, we used the expression level of top 50 marker genes of the identified top-featured cell types to classify gyrus versus sulcus regions, and found that the AUC score of the marker-based classification task substantially outperformed that using background genes, as well as those using other control gene sets, including random genes and randomly selected cell-type markers (Fig. 4c), indicating that these cell types represent key cellular features underlying gyrus-sulcus differences.

Fig. 4. Characterization of major cell types in distinguishing gyri from sulci.

a Smoothed dot plot depicting feature importance and absolute Spearman correlation coefficients with PC1. Solid lines represent LOESS fits, and shaded areas indicate the 95% confidence intervals of the fitted curves. b Radar plot of GLU L2/3.13 ROS1/MGP depicting the rank of feature importance and the rank of absolute Spearman correlation coefficients with PC1 of each filtered key cell type across cortical lobes. c Heatmap illustrating the mean prediction performance for distinguishing gyri from sulci based on the top marker gene expression levels of the characterized key cell types and other background genes or random gene sets. d Spatial distribution of the cell type GLU L2/3.13 ROS1/MGP in the macaque cortex. e Smoothed plot depicting the relative celltype percentage across segments in the macaque and marmoset brain section of GLU L2/3.13 ROS1/MGP. Scatter plots show a random sample of 1000 observations. Solid lines represent LOESS fits, and shaded areas indicate the 95% confidence intervals of the fitted curves. Statistical comparisons were performed using all observations (macaque, n = 138,854; marmoset, n = 24,228) with a two-sided Kolmogorov–Smirnov test (D = 0.507, p < 2.2 × 10⁻¹⁶). f Spatial distribution of the cell type OLG.3 ANLN/CNDP1 in the macaque cortex. g Smoothed plot depicting the relative celltype percentage across segments in the macaque and marmoset brain section of OLG.3 ANLN/CNDP1. Scatter plots show a random sample of 1000 observations. Solid lines represent LOESS fits, and shaded areas indicate the 95% confidence intervals of the fitted curves. Statistical comparisons were performed using all observations (macaque, n = 68,210; marmoset, n = 28,174) with a two-sided Kolmogorov–Smirnov test (D = 0.127, p < 2.2 × 10⁻¹⁶). h Spatial distribution of the cell type GLU L2/3.13 ROS1/MGP in the marmoset cortex. i Spatial distribution of the cell type OLG.3 ANLN/CNDP1 in the marmoset cortex. j Bar plot of F1 score illustrating the prediction performance for distinguishing gyri from sulci based on the cellular organization of five groups from the top key cell types. Bar graphs show the mean ± standard deviation (SD). Each group includes n = 21, 18 and 13 brain sections from macaques 1 (orange), 2 (red) and 3 (yellow), respectively. k Spatial distribution of the prediction score of each cell type group, indicating potential gyrus or sulcus regions across whole-brain slices.

Spatial visualization of the top 14 cell types revealed distinct gyral or sulcal preferences in the spatial transcriptome map. For example, the glutamatergic cell type GLU L2/3.13 ROS1/MGP was found enriched in gyri of the macaque cortex, with cell type abundance exhibiting distinct oscillations that notably decreased in the sulcus region (Fig. 4d, e, and Supplementary Fig. 5a, b). Similarly, the non-neuronal cell type OLG.3 ANLN/CNDP1 showed a comparable oscillatory pattern in its segment ratio, but with a significant increase in the gyrus regions (Fig. 4f, g, and Supplementary Fig. 5c, d). We then normalized and compared the distribution of cell type abundance across segments between macaques and marmosets (Fig. 4e, g). As expected, no oscillation was observed in the ratio of the best-hit mapped cell types in the marmoset cortex along corresponding regions where gyri and sulci are absent, contrasting with the macaque cortex (Fig. 4e, g–i). By contrast, a similar oscillation pattern of these cell types was observed in the known calcarine sulcus of the marmoset cortex (Supplementary Fig. 5e, f). We further analyzed an independent spatial transcriptomic dataset of human cortex from Han et al.²⁴ (see “Methods”), where we examined the AUC score distribution of the top 50 markers of the corresponding cell types. Interestingly, a similar pattern to that in the macaque cortex was present in the sulcus region of the human cortex (Supplementary Fig. 5g, h). These results provide additional support for region-specific differences in cell-type composition between gyri and sulci, underscoring their utility as discriminative features for classification.

To compare the contributions of different cell subclasses in distinguishing sulci from gyri, we trained logistic regression models using top features from each subclass group, thereby minimizing the impact of fine-tuned hyperparameters. According to the F1 score, the group of glutamatergic cell types enriched in layers II/III exhibited the best and most robust performance across all three macaques (72.28% for Macaque #1, 71.61% for Macaque #2, 65.23% for Macaque #3) (Fig. 4j), highlighting their superior discriminative power compared to other cell subclasses. Furthermore, a comparison of the spatial distribution of predicted scores generated by models from different subclass groups indicated that the model utilizing layer II/III-enriched glutamatergic cell types maximized the score separation between gyri and sulci relative to other cell types (Fig. 4k, and Supplementary Fig. 5i). Together, these results demonstrate that glutamatergic cell types in layers II/III exhibit the comparatively stronger association with cortical morphology. The distinctive distribution patterns of these neurons represent a characteristic cellular feature of gyral-sulcal organization, highlighting their role in the cellular basis of cortical folding in the primate cortex.

Feature genes and their regulatory networks in distinguishing sulci from gyri

Furthermore, we systematically assessed the feasibility of classifying gyri and sulci using marker genes of the top-featured cell types. Given the inherent sparsity of Stereo-seq data, we aggregated the spatial transcriptomic profiles by binning cells across every 20 consecutive segments to enhance data density and statistical reliability. To determine the influence of marker gene numbers on classification performance, we incrementally increased the number of selected genes from top 5 to top 100 per cell type, and evaluated corresponding changes in model performance. Classification performance, as measured by the F1 score, improved with additional marker genes but reached a plateau when the top 50 marker genes per top-feature cell type were utilized (85.14%, 427 unique genes across all subclass groups due to partial overlap). Notably, the F1 score showed no further improvement when the number of marker genes was doubled to 100 (85.21%, 789 unique genes), indicating that 50 marker genes per cell type were sufficient to achieve optimal classification performance under the current analytical framework (Fig. 5a).

Fig. 5. Feature genes and their regulatory networks in distinguishing sulci from gyri.

a Dot plot illustrating the F1 scores of gene models based on various number of top markers. b Spatial distribution of the prediction score based on top 50 markers of each key cell type, indicating potential gyrus or sulcus regions across whole-brain slices (left). Smoothed line plot illustrating the relative score distribution across segments in the brain section (right), sulci regions highlighted in red. c Spatial distribution of the prediction score based on top 50 markers of each GLU L2/3 cell type, indicating potential gyrus or sulcus regions across whole-brain slices (left). Smoothed line plot illustrating the relative score distribution across segments in the brain section (right), sulci regions highlighted in red. d Function annotation of top 50 markers of each cell type correlated with sulci. Tree plots show semantic similarity clustering of the top 10 enriched Gene Ontology (GO) biological process terms. GO enrichment analysis was performed using a one-sided hypergeometric test with Benjamini–Hochberg false discovery rate (FDR) correction (adjusted p < 0.05). e Function annotation of top 50 markers of each cell type correlated with gyri. Tree plots show semantic similarity clustering of the top 10 enriched Gene Ontology (GO) biological process terms. GO enrichment analysis was performed using a one-sided hypergeometric test with Benjamini–Hochberg false discovery rate (FDR) correction (adjusted p < 0.05). f Heatmap illustrating mean AUC scores of 12 regulons in gyri and sulci. g Regulatory networks based on the top 50 markers of each key cell types, genes colored according to the differential expression tendency, all TFs labeled. h Part of the regulatory network based on the top 50 markers of each key cell types that involved CUX2 and ZEB1, genes colored according to the differential expression tendency. i Spatial distribution of the CUX2 regulon AUC score across segments in a brain section (left). Smoothed line plot illustrating the score across segments in the brain section (right), sulci regions highlighted in red. Solid lines represent generalized additive model (GAM) fits, and shaded areas indicate the 95% confidence intervals of the fitted curves. j Spatial distribution of the ZEB1 regulon AUC score across segments in a brain section (left). Smoothed line plot illustrating the score across segments in the brain section (right), sulci regions highlighted in red. Solid lines represent GAM fits, and shaded areas indicate the 95% confidence intervals of the fitted curves.

Building on these findings, we examined the spatial distribution of the model-predicted scores across the cortical landscape. We present the predicted scores generated by the logistic regression model based on the expression levels of the top 50 marker genes from each top-featured cell type. These scores exhibited a spatially oscillatory pattern across gyral and sulcal regions (Fig. 5b, and Supplementary Fig. 6a). Consistent with our previous findings, the model utilizing only the marker genes from layer II/III-enriched glutamatergic cell types produced prediction scores comparable to those generated using marker genes from all cell type groups (Fig. 5c, and Supplementary Fig. 6b). This result further demonstrates the association between layer II/III glutamatergic cells and the anatomical differentiation of gyri and sulci.

Based on the distribution patterns of cell-type-specific enrichment across gyri and sulci, we categorized the 427 marker genes into gyrus-correlated and sulcus-correlated gene lists and performed functional enrichment analysis for each set. The results showed divergence in gene ontology categories (Fig. 5d, e). Sulcus-enriched genes were significantly linked to plasma membrane-bounded cell projection morphogenesis, in addition to general developmental terms such as multicellular organism development and anatomical structure development. This enrichment points to sulcus-specific roles in cellular structural remodeling and process extension, consistent with the strong representation of genes like PLP1 and MAG involved in oligodendrocyte process outgrowth and membrane dynamics. In contrast, gyrus-enriched genes showed highly significant enrichment for synaptic signaling pathways, including chemical synaptic transmission, trans-synaptic signaling, and anterograde trans-synaptic signaling, driven by core synaptic genes such as SNAP25 and SYT1. These results indicate enhanced neuronal communication and synaptic specialization in gyral regions. Collectively, these differential enrichments reveal sulcus- versus gyrus-dependent transcriptional programs and provide molecular correlates of functional specialization between the two cortical domains.

To uncover the regulatory networks critical for gyrus-sulcus classification, we identified 12 significantly enriched regulons within the spatial transcriptomic profile using pySCENIC²⁵, revealing key transcriptional modules orchestrating sulcus-/gyrus-specific gene expression patterns (Fig. 5f). Regulon activity analysis revealed that CUX2(+) was more active in gyri, whereas ZEB1(+) showed higher activity in sulci (Fig. 5i, j, and Supplementary Fig. 6c, d), suggesting distinct regulatory mechanisms between the two regions. Given that CUX2 is a well-established marker of upper-layer neurons, and that differences in cell-type composition between gyri and sulci may substantially contribute to the observed differences in connectivity and gene regulatory networks, we further evaluated the CUX2 regulon activity specifically within upper-layer neurons. Notably, this stratified analysis yielded consistent results (two-sided Wilcoxon rank-sum test: W = 119,005, p = 0.0314; Benjamini–Hochberg FDR = 0.0365), and the distribution of the corresponding AUC score also supported the robustness of our original conclusions (Supplementary Fig. 6e, f). We thus constructed the gene regulatory networks for the two regulons (Fig. 5g, h). CUX2, a transcription factor predominantly expressed in upper cortical layer neurons, regulates dendrite development and synapse formation. Among its target genes, NRN1 encodes an activity-dependent protein that promotes dendritic outgrowth and synaptic maturation. ZEB1, conversely, is known to maintain neural progenitor cells in an undifferentiated state by repressing differentiation programs. Its downstream targets include GRM7 and GRID2, both encoding glutamate receptors involved in excitatory neurotransmission. Given that CUX2 activity is enriched in gyral regions whereas ZEB1 shows preferential activity in sulcal regions, these transcription factors may contribute to the establishment or maintenance of region-specific cellular compositions that distinguish gyri from sulci in the mature cortex.

Discussion

Our study reveals that gyri and sulci exhibit distinct cell-type compositions. These cellular signatures are sufficiently robust to serve as discriminative features for accurately classifying cortical regions into gyri or sulci using our predictive model. Given that our dataset encompasses multiple cortical areas and includes over twenty sulci, potential biases due to regional variation were minimized, supporting the generalizability of our findings. By interrogating the model-learned top features, we identified key cell types and their marker genes that distinguish sulci and gyri, identifying the importance of upper-layer glutamatergic neurons and oligodendrocytes. These findings suggest that both laminar-specific neuronal populations and myelination-related glial cells contribute to the anatomical and functional divergence of cortical folds. Furthermore, we demonstrate that these cytoarchitectural differences correlate with distinct tractography-derived fiber patterns.

The finding that gsModel embeddings trained on local cell-type composition can predict macroscale structural connectivity in a fully independent test set, which is significantly above both chance level and the performance of raw composition vectors, suggests that local molecular architecture is not independent of large-scale wiring organization. The stronger predictive performance observed for long-fiber connections further supports this interpretation that regions with extensive long-range projections tend to have more distinctive and spatially consistent molecular signatures, making their connectivity profiles more decodable from local cellular composition alone. These results indicate that local cell-type composition carries a meaningful imprint of macroscale structural connectivity, linking local cell-type composition to cortical connectivity, highlighting the association between cellular architecture and structural and functional specialization of the primate cortex. Furtherly, our work extends previous studies on linking molecular and cellular features to connectivity across modalities and species. In mouse, spatial gene expression gradients and cell-type enrichment have been shown to accurately reconstruct mesoscale structural connectivity derived from classical anterograde tracing and in line with chemoaffinity principles^26–29. Similarly, retrograde tracing in macaque has established neuron density as the strongest architectural correlate of cortical connectivity³⁰. In humans, genome-wide associations have been identified for macroscale dMRI-derived structural connectivity³¹. Distinct from these region- or voxel-level approaches, our study introduces a gyrus/sulcus-centric perspective. The embeddings extracted from the gsModel also robustly predicted the mean fiber length associated with each segment. This provides a framework linking cellular molecular profiles directly to both cortical folding patterns and connectivity features. While our finding aligns with previous multimodal studies showing that molecularly defined cell types exhibit distinct projection patterns³², and that transcriptome-defined subtypes correspond to projection-specific neuronal classes³³, our study provides large-scale and systematic evidence of this relationship using comprehensive cellular-resolution data.

Our results revealed the enrichment of some layer II/III glutamatergic neurons in gyri and some oligodendrocyte subtypes in sulci, and identified glutamatergic cell types from layers II/III as top features distinguishing gyri from sulci. These cellular composition differences have significant functional implications. Previous studies have demonstrated that gyri exhibit stronger functional connectivity with other regions, are more functionally integrated, and serve as global functional connection centers, while sulci show weaker long-range connectivity, are more functionally segregated, and are primarily involved in local information processing^1,3,34. Our finding that local cell-type composition predicts structural connectivity patterns suggests a cellular mechanism underlying these functional differences. Specifically, layer II/III pyramidal neurons are major sources of cortical projections and play critical roles in amplifying cortical output and integrating information across cortical areas³⁵. The preferential enrichment of these neurons in gyral regions may contribute to the observed stronger long-range connectivity and functional integration in gyri. Additionally, oligodendrocytes, which produce myelin sheaths that regulate signal transmission efficiency, emerged as key discriminative features for sulci. Notably, myelin sheath orientation differs between gyri and sulci, with radially oriented sheaths at gyral crests and tangentially oriented sheaths at sulcal fundi², potentially contributing to differences in connectivity strength and signal propagation dynamics. Together, these findings suggest that the distinct cellular compositions of gyri and sulci provide the structural substrate for their specialized functional roles in cortical information processing.

In addition, we identified differential transcription factors that may be involved in the molecular diversity between sulci and gyri. CUX2 (CUT-like homeobox TF) regulates neuronal proliferation and differentiation in the developing neocortex, particularly in upper cortical layers II-IV, and modulates dendrite branching, spine morphogenesis, and synaptogenesis, thereby contributing to the maturation of projection neurons³⁶. In the adult cortex, CUX2 expression is largely confined to pyramidal neurons of the upper layers, where it continues to regulate molecular identity and connectivity. Developmental studies in the ferret have shown that CUX2 is among the key transcription factors shaping cortical fold formation¹²; its expression is most highly enriched in specific progenitor subtypes (particularly bRGα) within the germinal zones of prospective sulcal regions, where it modulates progenitor proliferation, direct neurogenesis, and neuronal output to establish the folding protomap. Moreover, overexpression of CUX2 further induces additional folds and upregulates synaptic maturation programs. In the adult macaque cortex, however, we observed elevated CUX2 regulon activity specifically in gyral regions. This may reflect a context-dependent shift in cellular, microenvironmental, and functional roles of CUX2. During embryogenesis, CUX2 operates primarily in neural progenitors within a dynamic niche of active proliferation and mechanical forces that drive sulcal indentation, whereas in the mature brain it functions in post-mitotic upper-layer projection neurons within a stabilized cortical architecture. Importantly, the gyral enrichment persists even when analysis is restricted to L2/3 excitatory neurons alone, suggesting a cell-intrinsic transcriptional difference rather than a mere compositional effect of differential upper-layer density between gyri and sulci. Consequently, the CUX2 regulon remains selectively active in adult gyral tissue, indicating that the networks established during development are repurposed from shaping the germinal protomap to sustaining the greater laminar thickness, synaptic complexity, and enhanced connectivity that characterize mature gyri. Our finding extends these developmental observations and demonstrates that CUX2-regulated gene networks remain differentially active between gyri and sulci in the mature brain. The enrichment of CUX2 target genes related to synaptic function and dendritic development in gyral regions suggests ongoing roles in maintaining the distinct cytoarchitecture and connectivity of gyri. ZEB1 (zinc finger E-box binding homeobox TF) is a transcriptional repressor that drives epithelial-mesenchymal transition by targeting genes like IL2 (interleukin-2) and CDH1 (E-cadherin) and suppresses neuronal differentiation. Its precise downregulation in neural progenitors during development is required for proper neuronal maturation and migration, preventing precocious neurogenesis³⁷. The influence of ZEB1 on progenitor proliferation and differentiation may support progenitor maintenance by balancing stem cell pools and neuronal output^15,38. The enrichment of ZEB1 regulon activity in adult sulci is therefore intriguing and suggests the persistence of a ZEB1-driven transcriptional program in mature sulcal tissue may reflect a relatively more plastic or progenitor-like molecular state compared to gyri, which is consistent with ZEB1’s established role in maintaining cells in an undifferentiated state during development. By modulating these fundamental processes of neurogenesis and neuronal migration, ZEB1 may serve as a potential molecular link between genetic regulation and the physical process of cortical folding. Together, networks regulated by CUX2 and ZEB1 exhibited gyri- and sulci- specific regulatory mechanisms, highlighting the gyri-/sulci- dependent transcriptional programs and molecular basis of functional divergence.

While this study provides valuable insights into the molecular characteristics associated with cortical gyrification, several limitations should be acknowledged. It should be noted that our analyzes were conducted on adult samples, capturing the outcomes of gyrification rather than the dynamic processes underlying its formation. Future studies incorporating developmental data, particularly from early stages, are necessary to elucidate the temporal mechanisms driving cortical gyrification development. Besides, our investigation focused exclusively on molecular and cellular features, potentially not accounting for other factors such as biomechanical forces that may contribute to gyrification. The interplay between molecular mechanisms and physical properties, such as cortical tension or tissue stiffness, warrants further exploration to achieve a more comprehensive understanding of gyral formation. Furthermore, the generalizability of our findings remains uncertain. While we validated key cell types using cross-species datasets, it should be noted that cross-species cell-type mapping reflects transcriptomic similarity and may not represent perfect one-to-one biological equivalence. Although macaques share neuroanatomical similarities with humans, interspecies differences in developmental trajectories and cortical organization require additional studies to validate the generalizability of our results to human brain development.

Methods

Animal care

Animal protocol was approved (ION-2019011) by the Biomedical Research Ethics Committee of CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences. Animal care complied with the guidelines of this committee.

Macaque data and cluster annotation

The spatial transcriptomic data of macaques were annotated as described in the original study¹⁹. The dataset comprised three male macaques (#1 6-year-old, #2 7-year-old, #3 4-year-old) spanning 161 coronal brain sections and over 42 million annotated cortical cells in the spatial transcriptomic map, providing broad coverage across cortical gyri and sulci. Independent biological replicates from multiple animals and brain sections enabled robust model training and evaluation. Cell types were defined from snRNA-seq data through iterative Leiden clustering with batch correction via BBKNN. Glutamatergic neurons, GABAergic neurons, and non-neuronal subclasses were identified based on canonical marker genes and previously reported cell-type markers. Stereo-seq cells were annotated using Spatial-ID, which transferred labels from the snRNA-seq reference via a deep neural network and refined them with a graph convolution network incorporating spatial information. To facilitate clear distinction between clusters, each cluster was named by selecting the two top-ranking marker genes identified from the analysis (for example, GLU L2.2 ITGA4/CHST9 indicates the second cluster of L2 subclass of glutamatergic neurons with ITGA4 and CHST9 as the two most specific markers).

Cortical segmentation on spatial transcriptomic sections

On each spatial transcriptomic section of the macaque brain, the cortex was partitioned into small columnar segments. First, the cortex contours were manually delineated, and corresponding boundary points along the outer (pial) and inner (white-matter) edges of the cortex were specified. We then used Python scripts from the CCSegThickness toolkit (github.com/chrisadamsonmcri/CCSegThickness) to generate columnar segments.

Briefly, a 2D harmonic scalar field was obtained by solving the Laplace equation with boundary conditions fixed to 0 at the inner cortical boundary and 1 at the outer boundary. The vector field orthogonal to the gradient of this scalar field was then used to generate lines that originated from equally spaced seed points along the inner boundary and terminated at the outer boundary. These non-intersecting lines defined a set of column-like partitions of the cortical ribbon, hereafter referred to as spatial transcriptomic (ST) segments.

Identification of gyri and sulci on spatial transcriptomic sections

Gyri and sulci on each spatial transcriptomic section were identified by reference to the Paxinos macaque brain atlas. To reduce manual annotation effort, we first selected candidate segments likely to lie within gyral crowns or sulcal fundi.

For each section, we extracted the midline skeleton of the cortical ribbon and computed its curvature along the skeleton. Local maxima and minima of curvature were detected, and the ST segments containing these extrema were collected as candidate gyral and sulcal segments, respectively. These candidates were then visually compared with their corresponding sections in the Paxinos atlas, and segments whose location and shape matched the atlas anatomy were manually labeled as specific gyri or sulci according to their Paxinos nomenclature.

gsModel for gyri and sulci classification

In this study, we developed a deep learning framework based on a customized architecture, termed gsModel, to classify gyri and sulci using high-dimensional spatial transcriptomics data. Brain sections were first ordered according to their anterior-posterior (AP) positions. Approximately 20% of sections were then selected as the held-out test set by assigning every fifth section to the test set, with the remaining sections used for training. The input data were preprocessed by segmenting spatial segment cell-type composition into sliding windows of fixed length (sequence length = 20) and encoding them into numerical tensors. gsModel was trained for 50 epochs with a binary cross-entropy loss function and optimized using the Adam optimizer (lr = 1e-4) with a ReduceLROnPlateau learning rate scheduler (mode = “min”, factor = 0.1, patience = 3). The model architecture consists of a transformer encoder and a multi-layer perceptron classifier. The encoder is implemented using a modified BERT configuration tailored for numerical input, comprising three transformer layers, each containing a multi-head self-attention module with two attention heads. The representations from the final encoder layer are flattened into a single feature vector and passed to a four-layer fully connected classifier to generate the final class logits.

Benchmark for model performance

To evaluate performance, we conducted tests using separate datasets across multiple macaque brain samples. Additionally, we benchmarked gsModel against traditional machine learning classifiers, including support vector machines, random forests, and logistic regression, as well as alternative deep learning architectures such as CNN. A 1D convolutional neural network composed of two convolution-pooling blocks followed by three fully connected layers was adopted and trained for 100 epochs with cross-entropy loss and the Adam optimizer (lr = 0.001, weight_decay = 5e-4) with a ReduceLROnPlateau learning rate scheduler (mode =  “min”). Model performance was assessed using accuracy and F1 score metrics.

Model performance visualization

The raw input features, which were tensors representing the sliding window sample of spatial segment cell-type composition, were flattened and reshaped into a 2D array as the raw embeddings to prepare them for PCA. While the model embeddings were extracted from the last hidden state of the gsModel model. Specifically, the raw input features were passed through the customized architecture, and the output embeddings were obtained by reshaping the last_hidden_state tensor.

Principal Component Analysis was applied to reduce the dimensionality of the embeddings to two principal components. This was done using the PCA class from sklearn.decomposition. The PCA transformation retained the maximum variance in the data while reducing it to two dimensions. Each point in the reduced embeddings scatter plot represented a sample, and the color of the points corresponded to the labels (gyrus or sulcus, cortical lobes). Spatial distribution was visualized with the plot_density function from the R package Nebulosa (https://github.com/powellgenomicslab/Nebulosa). This approach smooths discrete per-spot scores into a continuous spatial distribution to facilitate visualization of regional enrichment patterns.

Quantification of gyral and sulcal shape

To quantify the local shape of annotated gyri and sulci on the spatial transcriptomic sections, we computed several metrics for each labeled segment: curvature, thickness, and a symmetry index.

For a given gyral or sulcal segment, we defined its local region as the union of the target segment and its 50 neighboring ST segments on each side along the cortical ribbon. The midline skeleton of this local region was extracted and used for subsequent analysis. The thickness was defined as the mean thickness (mm) of each column in the segment. The curvature was defined as the ratio between the total arc length of the skeleton and the straight-line Euclidean distance between its endpoints (quantified here as the radius of curvature).

To assess symmetry, we quantified the minimal distance between each skeleton and a rigidly transformed version of its mirror image. Specifically, the skeleton curve was mirrored, and all possible in-plane rigid transformations (translations and rotations) of the mirrored curve were considered. The symmetry index was defined as the minimal average point-to-point distance between the original skeleton and any rigidly transformed version of its mirrored counterpart.

Model to classify various sulci

Samples from seven sulci, each spanning at least three anatomically distinct brain regions, were selected for the sulci model training. Input features were consistent with those used in the gsModel framework, while output labels were one-hot encoded to represent sulcus identity. The sulci model architecture followed a similar design to gsModel, incorporating a customized backbone with three transformer layers and a fully connected output layer for multi-class classification. The model was trained for 50 epochs using cross-entropy loss and the Adam optimizer (lr = 1e-4), with a ReduceLROnPlateau learning rate scheduler (mode = “min”, factor = 0.1, patience = 3) applied to enhance convergence.

Classification performance comparison based on curvature, thickness, symmetry, cell density and principal component 1

Cell density was determined by dividing the number of cells contained in the columnar segment originating from gyri or sulci by the area of the corresponding segment (an area value of 1 represents an actual area of 2500 μm²).

The comparison of model classification performance based on curvature, thickness, symmetry, cell density and principal component 1 was conducted using a linear model (function lm with R) to predict the gyrus or sulcus label and evaluate the accuracy and F1 score for each factor. Samples from gyri were labeled as 1, and samples from sulci as 0. A linear regression model was fitted to predict the binary label using the factor as the independent variable. The predicted probabilities were then thresholded at 0.5 to generate binary prediction labels. F1 score was calculated based on the value given by confusionMatrix.

Macaque dMRI acquisition and preprocessing

The diffusion MRI (dMRI) data were obtained from a previously published ex vivo macaque dataset³⁹. In brief, dMRI was acquired from a male macaque (4.5 years old) with an isotropic spatial resolution of 250 μm, a matrix size of 278 × 256  × 238, 126 directions with a b-value of 4800 s/mm², and seven non-diffusion-weighted images (b = 0). Raw dMRI data were preprocessed using the MRtrix3 pipeline⁴⁰, including denoising, distortion correction, diffusion tensor fitting, and estimation of tissue-specific response functions. Fiber orientation distributions were then computed using multi-tissue, multi-shell constrained spherical deconvolution. Spatial transcriptomic sections were rigidly reconstructed in 3D on a slice-by-slice basis and subsequently nonlinearly registered to the fractional anisotropy (FA) volume of the dMRI dataset using Advanced Normalization Tools.

Tractography for anatomically defined gyri and sulci

The transformation obtained from the registration between spatial transcriptomic sections and the dMRI volume was used to warp ST segment boundaries defined in the section space into dMRI space. The ST segment boundaries thus transformed into dMRI space were used to determine gray-white matter interface positions for tractography seeding. For each ST segment boundary, we identified its nearest point on the gray-white matter boundary and used these points as seeds for whole-brain dMRI tractography with the tckgen command in MRtrix3⁴⁰. A total of 100 million dMRI streamlines were generated. Streamlines were truncated at the point where they re-entered the cortex. For each dMRI streamline, the start ST segment was defined as the ST segment nearest to its first point, and the end ST segments were defined as all ST segments within one voxel (0.25 mm) of the point at which the streamline re-entered the cortex.

Fiber termination composition prediction based on gsModel embeddings of cellular composition

To predict the fiber termination composition of segments with the corresponding gsModel embeddings, a one-dimensional convolutional neural network was employed as the source encoder, consisting of two convolutional layers (kernel size = 3, padding = 1), each followed by a ReLU activation. The model took the embeddings from the last layer of gsModel as input. The extracted features were aggregated using an adaptive average pooling layer and subsequently projected into a latent space through a fully connected layer with dropout (rate = 0.2). The encoded source representation was then matched with learnable destination embeddings via a dot-product operation, scaled by a learnable temperature parameter, and normalized using a softmax function to produce a probability distribution over destinations. The model was trained for 30 epochs using the AdamW optimizer (learning rate = 0.0003, weight decay = 0.001). The loss function was defined as the negative log-likelihood between the predicted logits and the target count distribution. Gradient clipping (max norm = 1.0) was applied during training to improve stability.

Fiber length prediction based on gsModel embeddings of cellular composition

To predict the mean length of fibers originating from the middle column of a segment with the corresponding gsModel embeddings, a one-dimensional convolutional neural network regressor was employed for the regression task, consisting of two Conv1D layers (kernel size = 3, padding = 1) with GELU activations, followed by global average pooling and a fully connected head with dropout (rate = 0.2). The Huber loss was used as the objective to improve robustness on long-tailed data. The model was trained for 30 epochs using the AdamW optimizer (learning rate = 0.001, weight decay = 0.0001) with a ReduceLROnPlateau scheduler (factor = 0.5, patience = 3).

Feature importance evaluation

Feature importance was assessed using a permutation-based approach to quantify the contribution of each feature to the model performance. Specifically, the impact of permuting individual features was evaluated based on the predictive F1 score of the model. For each feature, the values were randomly shuffled across all samples while keeping other features unchanged. The predictions of the model were then recalculated with the permuted dataset, and the performance metric, here F1 score adopted, was computed. The difference between the baseline performance using the original dataset and the performance after permutation was recorded as the importance score for that feature. This process was repeated 10 times to account for variability, and the average importance score was calculated for each feature.

Transcriptomics validation for top features

For each section, stereo-seq data were aggregated by segment within gyri or sulci. With samples labeled as gyri or sulci, FindAllMarkers from R package Seurat was utilized to get the ROC value for each gene with parameters test.use = “roc”, return.thresh = 0. The absolute deviation of the AUC from 0.5 was calculated for each gene to measure its discriminatory power, and compared between marker genes of the top features and genes not included in the top feature marker gene list. The random gene/random marker performance was evaluated by randomly selecting 50 genes from the corresponding candidate set, computing the absolute deviation of the AUC from 0.5 for each selection, repeating the process independently 10 times, and taking the mean as the final result.

Cross-species data and cell types mapping

The marmoset data referenced in this study were from Huang et al.⁴¹. The best-hit cell-type mapping between macaque and marmoset was performed based on MetaNeighbor⁴². For each macaque cell type, the marmoset cell type with the highest MetaNeighbor AUROC score was designated as its best hit.

The human data reference in this study were available in CNGB (Han et al.²⁴, 2026, bioRxiv; Accession code CNGB: CNP0007621, https://db.cngb.org). The top 50 marker genes for each key cell type were used to calculate AUC scores using the R package AUCell to assess the presence of these cell types in each sample.

Meta-feature model by cell-type subclass to classify gyri and sulci

With flattened top features filtered based on specific cell-type subclasses using predefined annotations, meta-feature models for various cell-type subclasses to classify gyri and sulci were established using logistic regression (LogisticRegression from sklearn.linear_model) to ensure the prediction F1 score could be used for comparison of cell-type subclass contribution, since deep learning architecture would be influenced by the fine-tuning of hyperparameters.

Gene model to classify gyri and sulci

To study the potential transcriptomic difference between gyri and sulci, spatially resolved gene expression data were aggregated using a sliding window approach along segments. For each top-ranked feature cell type in the model gsModel, the top marker genes were selected based on predefined annotations and used to construct input features for downstream analysis.

To determine the optimal number of genes for model saturation, logistic regression (LogisticRegression from sklearn.linear_model) was applied to evaluate the relationship between model performance and the number of input genes.

Gene regulatory network

Considering the sparsity of the Stereo-seq data, cells from each gyrus or sulcus area were aggregated to obtain bulk profiles for downstream analysis. The regulons underlying the top 50 markers of characterized key cell-type features (427 genes) that contributed to the classification were identified with pySCENIC²⁵ using the processed spatial transcriptomic data (min_genes 10; mode dask_multiprocessing). The motif annotation file motifs-v9-nr.hgnc-m0.001-o0.0.tbl and the corresponding ranking database hg38__refseq-r80__10kb_up_and_down_tss.mc9nr.genes_vs_

motifs.rankings.feather were obtained from the official pySCENIC resources. The function get_regulons_AUC was employed to obtain the AUC score for each gyrus or sulcus area given by pySCENIC, based on which the heatmap was plotted. To visualize the spatial distribution of these regulons, the gene list for each regulon was extracted with the function get_regulons and regulonsToGeneLists, then the corresponding AUC score for each segment was recalculated with AUCell_calcAUC from R package AUCell. The smoothed plot was plotted based on the mean segment AUCell score ranging from quantile 0.01 to 0.99. The gene regulatory network was visualized with R package igraph and ggraph based on the adjacency files generated by pySCENIC.

Function enrichment annotation

The function enrichment annotation was done with enrichGO of R package clusterProfiler⁴³ (OrgDb = org.Hs.eg.db, pAdjustMethod = “fdr”, pvalueCutoff = 0.05, qvalueCutoff = 0.05, ont = “BP”, minGSSize = 3, maxGSSize = Inf). R package enrichplot was employed to organize the result pathways into a tree plot.

Reporting summary

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

Author contributions

Methodology, Y.B., T.S. and Y.Z.; Investigation, Y.B., and T.S.; Formal Analysis, Y.B., and T.S.; Data Curation, Y.B., T.S., H.W., J.M., and Q.Y.; Visualization, Y.B., and T.S.; Writing - Original Draft, Y.B.; Writing - Review & Editing, Y.B., T.S., C.L., and Y.S.; Conceptualization and supervision, C.L., and Y.S.

Peer review

Peer review information

Nature Communications thanks Michael Hawrylycz, Fenna Krienen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

The project was supported by National Science and Technology Innovation 2030 Major Program (STI2030-2021ZD0200100 and STI2030-2022ZD0205000), National Key Research and Development Program of China (No. 2024YFC3408000), National Natural Science Foundation of China (NSFC) Outstanding Youth Foundation (No. T2422026), National Natural Science Foundation of China (No. U23A6010, 32427802), Shanghai Science and Technology Development Funds (23QA1410400), the National Sponsored Postdoctoral Researcher Program of Year 2025 (GZB20250590) and China Postdoctoral Science Foundation.

Data availability

The spatial transcriptomic datasets analyzed in this study are publicly available from CNGB Nucleotide Sequence Archive (accession code: CNP0002035, CNP0005746 and CNP0007621. Source data underlying the figures are provided with this paper. Source data are provided with this paper.

Code availability

The code used in this study is available at GitHub (https://github.com/yqbai/gsmodel).

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77086-y.