Whole brain alignment of spatial transcriptomics between humans and mice with BrainAlign

Abstract

The increasing utilization of mouse models in human neuroscience research places higher demands on computational methods to translate findings from the mouse brain to the human one. In this study, we develop BrainAlign, a self-supervised learning approach, for the whole brain alignment of spatial transcriptomics (ST) between humans and mice. BrainAlign encodes spots and genes simultaneously in two separated shared embedding spaces by a heterogeneous graph neural network. We demonstrate that BrainAlign could integrate cross-species spots into the embedding space and reveal the conserved brain regions supported by ST information, which facilitates the detection of homologous regions between humans and mice. Genomic analysis further presents gene expression connections between humans and mice and reveals similar expression patterns for marker genes. Moreover, BrainAlign can accurately map spatially similar homologous regions or clusters onto a unified spatial structural domain while preserving their relative positions.

Comparative transcriptomics of whole brains across species is vital in neuroscience. Here, authors develop a deep learning method, BrainAlign, to align spatial transcriptomics across human and mouse brains. BrainAlign identifies conserved brain regions and uncovers similar patterns for marker genes.

Introduction

Animal models are essential in neuroscience research and serve a crucial role in comprehending diseases, devising treatments, and acquiring data unattainable in humans. Among various species employed to model the human brain, the mouse has garnered prominence due to its swift life cycle, facile husbandry practices, and susceptibility to genetic engineering^1–3. However, mapping findings from the mouse to the human at the whole-brain level is not straightforward due to the significant evolutionary divergence that started 80 million years ago⁴. For example, the human cortex area is expanded more-than-1000-fold larger, and the human brain contains a more-than-1000-fold number of neurons than the mouse. That implies that only a few parts of the human cortex potentially have corresponding homologs in the mouse cortex^5,6. In addition, due to historical reasons, the researchers use inconsistent terminology to refer to similar neuroanatomical areas in mouse and human brains. Therefore, it is critical to project the brain features across species into the same space and discover shared buildings and functions of organizations while accounting for diversity between species.

Molecular-level alignment studies such as single-cell integration methods are mostly focused on addressing cross-species homologies via investigations on cell-type commonality and diversity across species^7–10. However, the datasets of those studies are extracted from specific local tissues instead of the whole brain without spatial coordinates^8,11 because of the technical limitations and high cost of single-cell or single-nucleus RNA-sequencing^12,13. Another kind of method conducting the connectivity mapping using brain imaging data, considering that brain regions are specialized in their unique connections compared to the other regions in the brain^14,15. However, when comparing mice and humans, the lack of established neuroanatomical homologs in mice limits the use of this framework.

The availability of whole-brain spatial transcriptomic (ST) dataset of multiple species^16–19 facilitates the cross-species whole-brain comparison. A preceding study showed that the differential expression patterns of thousands of genes across the brain regions were conserved across mammalian species²⁰. Another study manipulated the expression of homologous genes to directly register cross-species brains into a shared reference frame to enable point-by-point comparisons between species²¹. Nonetheless, it is only designed for mapping in-situ hybridization (ISH) data of species (e.g., voles and mice) with more morphological brain similarity. Another study selected an initial set of about 3000 one-to-one homologous genes and achieved the mouse-human neuroanatomical correspondences using a supervised fully-connected neural network³. However, this study has the following limitations. First, the visual qualitative RNA ISH scoring in the ISH data¹⁶ used for mice may be impacted by observer bias and too raw to quantify more subtle staining differences²². Second, this study didn’t account for the data scale discrepancy or batch effect between the two datasets. Third, it was restricted to one-to-one homologies shared by two species but not many-to-many homologous relations. Fourth, the study utilized the known brain region names as output labels in a supervised learning manner, ignoring meaningful structural domains that may violate the brain region boundary and forcing the distribution of STs toward man-defined regions. As a result, the embeddings in the latent space are highly correlated with the brain regions.

To this end, we developed BrainAlign to map the mouse and human brain spatial transcriptomics into a shared space without labels for whole-brain alignment based on two microarray sequencing datasets^17,19. To overcome the issue of data scale discrepancy and learn general embeddings for human and mouse brain STs, we constructed a heterogeneous graph neural network trained with a kind of contrastive loss in a self-supervised manner²³. We showed that BrainAlign mapped mouse and human spots into the same space and facilitated the alignment of most homologous regions between mouse and human. Besides, BrainAlign reveals the similarity of gene expression patterns between the two species in the learned gene embedding space. Furthermore, we examined the spatial domain-specific spot embeddings on the hippocampus to show BrainAlign mapped similar expression patterns in the corresponding spatial domain across mice and humans. We expected BrainAlign could reveal conserved and discrepant properties among the brains of many other species.

Results

Overview of BrainAlign

BrainAlign takes the gene expression matrices and spatial 3D coordinates of spots of humans and mice as input. Given the cross-species data heterogeneity, BrainAlign employs a heterogeneous graph neural network (HGNN) to model spot-spot, gene-gene, and spot-gene relations. It is trained through contrastive learning to inject information about STs into the embeddings (Fig. 1).

Fig. 1. Overview of cross-species whole-brain spatial transcriptomics integration.

a Generation procedure of mouse and human whole-brain bulk spatial transcriptomics. The sliced brain sections are segmented into spots sequenced on 10x genomics platforms. The spots are then mapped to 3D space and assigned a spatial coordinate. The left brain images, created with BioRender.com, released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license. b Overview of BrainAlign. Cross-species spots and genes are viewed as two types of nodes in a graph. The edges between genes represent many-to-many orthologs, and the edges between spots are determined by spatial neighborhood relations. A heterogeneous neural network with graph attention is developed to encode the graph and trained with self-supervised loss constructed via contrastive learning, and k is the number of graph neural network layers. There are two kinds of contrast: intrinsic contrast and multi-hop contrast for each node type. The final loss $\mathcal{L}$ is the sum of loss for spot and gene node, i.e., ${\mathcal{L}}_{spot}$ and ${\mathcal{L}}_{gene}$.

BrainAlign represents both spots and genes as nodes, non-zero expression of a gene in a spot as a spot-gene edge, gene homology as an edge between two genes that are not constrained to one-to-one orthologs, and spatial proximity between spots as a spot-spot edge (Fig. 1b) (“Methods” section). BrainAlign initially learns relation-based embeddings for all nodes based on their properties under each relation type and utilizes an attention layer to combine the embeddings of different relations (Fig. 1b). BrainAlign uses multiple relationships through multi-hop message passing and concatenates the learned embeddings with their original attributes to obtain the final embeddings for each node using node-type-based linear propagation. The contrast loss comprises the sum of multi-hop contrast and intrinsic contrast loss. The multi-hop loss for each node is a weighted sum of one-hop and two-hop contrast. The final contrasting loss $\mathcal{L}$ is the sum of loss for spot nodes and gene nodes, i.e., ${\mathcal{L}}_{spot}$ and ${\mathcal{L}}_{gene}$.

We applied BrainAlign to the processed mouse and human gene expression data and 3D coordinates of spots^17,19. BrainAlign successfully maps cross-species spots and genes into a shared embedding space, enabling various cross-species brain analyses.

BrainAlign facilitates comprehensive alignment of mouse and human whole-brain STs

The two-dimensional visualization of embeddings for mouse and human spots extracted by BrainAlign using UMAP²⁴ demonstrates a well-aligned representation (Fig. 2a). The heatmap of embeddings for two species reveals mixed patterns with evident clustering blocks (Supplementary Fig. 1a). The Seurat alignment score (SAS)²⁵ between the mouse and human embeddings by BrainAlign is significantly higher than that produced by Principal Component Analysis (PCA) (0.810 vs 0.0825) (Fig. 2b). On this task, we also compared BrainAlign with Beauchamp-FCN³, and the batch effect removing method Harmony²⁶, and Scanorama²⁷ to demonstrate its superiority (Fig. 2b, Supplementary Fig. 2). The integration performance of Harmony is significantly lower than BrainAlign. The competing methods for removing batch effects such as Harmony have not been designed to handle such complicated heterogeneity and HGNN used by BrainAlign is designed to overcome such severe heterogeneity on a heterogeneous graph.

Fig. 2. Alignment of whole-brain spots across humans and mice.

a UMAP of brain STs spots alignment across species before and after integration with PCA, Beauchamp-FCN³, Scanorama, Harmony, and BrainAlign. b Alignment score before and after integration with BrainAlign and the other methods. c Spots' correlations for those in homologous regions pairs (n = 20) and randomly selected pairs (n = 5547) before (P-value = 0.111 > 0.05) and after (P-value = 6.86 × 10⁻⁸ < 10⁻⁷) integration with BrainAlign. With BrainAlign, the spots' correlations show significantly different patterns. The center line, box limits, and whiskers denote the median, upper and lower quartiles, and 1.5× interquartile range in the boxplot, respectively. Data are presented as mean values ± SD. The P-value for a two-sided hypothesis test whose null hypothesis is that the means of the two groups are equal, using Welch’s t-test with Bonferroni correction. d The correlations within the homologous regions between mouse and human before (P-value = 0.319 > 0.05) and after (P-value = 2.28 × 10⁻² < 0.05) data alignment. The x-axis and y-axis are the average correlation of the spots within the region for humans and mice, respectively. The error bands are 95% confidence intervals by a bootstrap of 1000 times. The P-value for a two-sided hypothesis test whose null hypothesis is that the slope is zero, using the Wald test with t-distribution of the test statistic. e Venn diagram of identified homologous region pairs. 17 homologous pairs (with replications) have been identified in 20 homologous pairs from 76 clusters obtained using the Leiden algorithm. f 3D visualization of the alignment of the mouse and human spots. Gray: 76 cluster pairs; black: 3 unidentified homologous region pairs; red: 17 identified homologous pairs. The 3D coordinates of spots are designed based on the 2D UMAP coordinates and species order (mouse: 1, human: 0). g The correlations of homologous region pairs across species before and after alignment. Each square represents the mean value of correlations of corresponding homologous region pairs. The homologous region pairs display more highly correlated patterns after data integration. Source data are provided as a Source Data file.

The UMAP representation of spot embeddings from 20 pairs of homologous regions also depicts the clear alignment patterns (Supplementary Fig. 1d), suggesting the canonical mouse-human homologous brain regions are expected to exhibit functional and genomic similarities³. The overall correlation between spots from two species in the homologous regions is significantly higher than that of randomly selected spots of all regions in the aligned embedding space (P-values = 6.86 × 10⁻⁸) (Fig. 2c). After data alignment, the mean correlation of all samples within each homologous region pair is positively correlated across species (Fig. 2d), indicating that the spatial transcriptomics information in the embeddings supports the conserved properties of brain regions. The high significance of linear regression measured by P-value excludes the influence of the spot number correlation (Supplementary Fig. 1b), indicating BrainAlign could align the corresponding spots of local brain regions between humans and mice correctly. We further revealed 76 spatial cluster pairs from the mouse and human spots using the Leiden algorithm (resolution = 9)²⁸ based on the embeddings. The distributions of the spot number in each cluster between the two species are quite different, displaying the brain structural divergence between mice and humans (Supplementary Fig. 1c). 17 homologous pairs out of 20 homologous region pairs from spot clusters shared by humans and mice were identified in the embedding space (Fig. 2e, f), validating that the learned spot embeddings preserve the information in homologous regions. For the three unidentified homologous region pairs (visual areas and cuneus, flocculus and cerebellar cortex X (Cb-X), claustrum) in mouse and human brain, their STs consistency may be relatively low compared to the other homologous pairs. Besides, in the heatmap, where each value represents the mean correlation for all pairwise spots from the corresponding pair of regions (Fig. 2g), homologous region pairs display more highly correlated diagonal patterns after data alignment. We found almost all the mean correlation values of cluster pairs exceed the mean correlation line of homologous region pairs (Supplementary Fig. 1e), indicating the biological significance of clustering.

To estimate how much information is lost by projecting the mouse and human datasets into the same space using BrainAlign, we use the reconstruction loss of a neural network trained on the embeddings and features to estimate the information loss. The neural network architecture is similar to that in Supplementary Fig. 3a with different input (the embedding dimension) and output dimensions (the number of genes used). The training loss is a mean square error (MSE). The training settings including hyper-parameters and architectures are identical among methods. On the mouse and human whole-brain datasets (Supplementary Fig. 4a), BrainAlign achieved significantly lower reconstruction loss than all the other methods on the mouse dataset while having significantly higher reconstruction loss than other methods. The reconstruction loss and integration performance are negatively related. We speculate that the reasons for this phenomenon are the relatively low resolution of the human, the significant difference in resolution between the mouse and human spots, and the amount of information contained as explained before. BrainAlign achieved significantly lower reconstruction loss than all the other methods for all three experiments (Supplementary Fig. 4). The discrepancy is high to two orders of magnitude, and we attribute it to two reasons. First, BrainAlign not only utilized one-to-one gene orthologs but also used multi-to-multi gene orthologs. Besides, some highly variable species-specific genes are also appended to the heterogeneous graph. However, the other methods only integrated datasets using one-to-one homologous genes, resulting in low reconstruction information. Second, for the remaining methods, an additional step of batch correction is required or integrated into the method package, and it possibly removes some species-specific information. While BrainAlign integrates those datasets on a graph, avoiding the deletion of essential information. In summary, the reconstruction loss of BrainAlign is below 1, which is a relatively low value, showing its low loss of species-specific information.

BrainAlign captures conservative and divergent properties between the anatomically defined regions in mice and humans

We first considered the correspondence between the homologous regions and the spot clusters. The heatmap for the proportion of spots from the homologous regions in the named clusters displays consistent patterns in mice and humans (Fig. 3a), which indicates that BrainAlign can map the same anatomically defined regions of mouse and human brains into the same clusters. The 20 regions in mice and humans are one-to-one corresponding homologous regions, i.e., the rows in the two heatmaps are aligned. Regions such as claustrum, Simple lobule, and Flocculus contain too few spots (For mouse, Claustrum: 78, Simple lobule: 31, Flocculus: 32; For human, claustrum: 47, VI: 32, X: 7), while the number of spots in the cluster is generally higher (The average number is 496.51, the minimum number is 89), resulting in low proportions of those regions in clusters.

Fig. 3. Analysis of the anatomical regions shows similar patterns in humans and mice.

The 20 regions in mice and humans are one-to-one corresponding homologous regions, i.e., the rows in the two heatmaps are aligned. a The alignment between homologous regions and the obtained clusters. Given the order of regions, the clusters are ordered according to their corresponding enriched homologous regions. The clusters were named according to the spot proportion of regions in the clusters (“Methods” section). b Heatmap of the mean Pearson correlation coefficient for spots from pairwise cross-species regions. Each square represents the mean value of correlations of corresponding region pairs, and rows and columns are hierarchically clustered. Layer-wise structural patterns of similarity are evident between anatomically defined brain regions. Source data are provided as a Source Data file.

Based on the 88 and 64 regions in human and mouse brains obtained from the AHBA and AMBA atlases^16,19 and correlation patterns between different anatomically defined regions, we observed clear conservative or disparate patterns among them. We can see clear layer-wise similar structural patterns between anatomically defined brain regions (Fig. 3b). The functional homogeneity across species explains most of these patterns. Regions in the human cerebellar cortex such as V correlate highly with the simple lobule, cerebellum, flocculus, culmen, pons, lateral septal complex, medulla, Barrington nucleus, and central lobule, which mainly belong to the cerebellum and hindbrain (red frame on the top). However, the lateral septal complex belongs to the striatum¹⁶ and exists as an exception that is explainable because of its wide function field²⁹. As shown in the green frame of Fig. 3b, mouse lateral septal complex in the cerebral nuclei, Barrington nucleus, and central lobule of cerebellar cortex correlates highly with human cerebellar nuclei in the telencephalon, globus pallidus of cerebral nuclei, and subthalamus from diencephalon, displaying almost the same level of homogeneity degree between pons. These facts probably facilitate the identification of many-to-many homologous regions.

Mouse midbrain, hypothalamus, and fiber tracts correlate highly with anatomically near subregions such as septal nuclei, substantia innominata, and globus pallidus in the cerebral nuclei, hypothalamus, epithalamus, subthalamus, and thalamus in the diencephalon, and inferior colliculus, superior colliculus, midbrain tegmentum, a pretectal region in the mesencephalon, and pons in the myelencephalon (yellow frame). The human gyruses in the isocortex correlate significantly with mouse regions such as the primary motor area in the mouse isocortex¹⁹. Except for significantly higher correlation among hippocampal regions such as CA1 field and subiculum in mouse and human brains (cyan and black frames), the amygdala and piriform cortex in the human brain also exhibit similar high alignment patterns with hippocampal regions, amygdala and piriform cortex subregions such as cortical amygdalar area, reflecting that the reciprocal dependence between amygdala and hippocampus during the encoding of emotional memories^30,31 holds across mouse and human. The high correlation between piriform cortex regions and hippocampal regions is probably due to spatial proximity since the regions are all in the limbic lobe and belong to the cerebral cortex^16,19. The conservative patterns hold without clustering (Supplementary Fig. 5). The Seurat alignment score heatmap also displays similar while weaker signal patterns (Supplementary Fig. 6a).

We also computed the Seurat alignment score (SAS)²⁵ between mouse and human regions and subsequently excluded region pairs falling below the 99th percentile threshold to extract the most conservative regions (Supplementary Fig. 7). Apart from well-established highly homogeneous regions, such as the CA1 region in both mouse and human brains, the majority of regions exhibit strong alignment not only with their corresponding homology but also with other regions, e.g., mouse hypothalamus aligns highly with septal nuclei and substantia innominata that belong to the basal forebrain, which is close to hypothalamus and thought to be important in regulating arousal and attention³². The analysis for 15 mouse parent regions and 16 human parent regions depicts consistent patterns (Supplementary Fig. 6b, c, Supplementary Fig. 8a–c). The isocortex in mice is well aligned with the frontal lobe, insula, parietal lobe, temporal lobe, occipital lobe, and limbic lobe, which compose the neocortex in the human brain, depicting the enlargement of human isocortex in the evolution³³.

Besides exploring the conservative or disparate patterns among anatomically defined regions, we also computed the embedding similarities measured by Pearson correlation for the large clusters and sub-clusters within the isocortex, pons, thalamus, and hypothalamus. For cluster pairs in the whole brain or sub-clusters in homologous regions, most of them exhibit more distinct group patterns than homologous region pairs (Supplementary Figs. 9, 10a–c and 11a, b) as shown before (Supplementary Fig. 1e). Since spots in clusters are not constrained to anatomical tissue regions, this reflects that the definition of anatomical regions deserves further investigation. Considering that some spots might be far from the cluster center, the definition of brain regions is supposed to use both spatial and gene expression information. Sub-clusters within the isocortex, pons, thalamus, and hypothalamus across mice and humans are correlated hierarchically (Supplementary Figs. 10a–c and 11a, b). This shows that the homology between cluster or region pairs tends to be hierarchical. Not only do some larger regions or clusters of mouse and human exhibit significantly higher correlations but also subregions within homologous regions or sub-cluster pairs also have similarity specificity. For homologous region pairs of pons, the correlation heatmap highlights one special heterogeneous sub-cluster, i.e., Pons-13, and it is consistent between mice and humans (Supplementary Fig. 10c, d). This sub-cluster pair possibly indicates a homologous region pair within the pons. Besides, we also have presented the similarity heatmap across non-homologous region pairs, e.g., human cingulate gyrus and mouse thalamus. We found that there may exist homologous sub-region pairs within non-homologous region pairs. The mean correlation of most highly correlated sub-clusters (top 20) within non-homologous region pairs (i.e., human cingulate gyrus and mouse thalamus) is close to the mean correlation within all the 20 homologous regions (P-value = 1.00) (Supplementary Fig. 11c, d) and the mean correlation of all sub-clusters in the human cingulate gyrus and mouse thalamus is significantly lower (P-value = 3.16 × 10⁻⁵) than the mean correlation between all the 20 homologous regions.

BrainAlign reveals the similarity of gene expression patterns

The visualization of gene embeddings using UMAP shows that BrainAlign could well align the cross-species gene expression patterns (Fig. 4a). The three-dimensional visualization of alignment between genes across species also illustrates that gene ortholog relations are well-maintained (Fig. 4b, Supplementary Fig. 12a). The genes are aggregated into two major categories (Fig. 4a–c). The GSEA analysis shows the functional enrichment of the two major gene modules, which is conservative between mice and humans (Supplementary Fig. 13a, b). The first gene module is related to the cerebellum, caudate nucleus, occipital lobe, neuropeptide hormone activity, exocytic vesicle, regulation of ion transport, oligodendrocyte progenitor cell in the embryonic prefrontal cortex, glutamatergic neuron, subpallium, striatum and rhombomere 3. The second module enriches the hypothalamus, spinal cord, relaxation of cardiac muscle, astrocyte in the embryonic prefrontal cortex, somatomotor areas, dorsal pallium or isocortex, cerebral cortex, frontal cortex, and primary motor area. Besides, the correlation between homologous genes is significantly higher than that between randomly picked cross-species genes (P-value≈0) (Fig. 4d), demonstrating that information of orthologs is integrated into the gene embeddings using BrainAlign.

Fig. 4. Genomic analysis of the embeddings obtained from BrainAlign.

a UMAP of genes embedding across human and mouse. b 3D visualization of alignment of genes across species. The line plot represents orthologs. c Heatmap of gene embeddings. Genes are mixed and present gene module block patterns. d Comparison of gene correlations for homologous genes (n = 2674) and (n = 118020) randomly selected genes (random down-sampling ratio = %1) from the two species. The center line, box limits, and whiskers denote the median, upper and lower quartiles, and 1.5× interquartile range in the boxplot, respectively. Data are presented as mean values ± SD. Homologous genes' correlation is significantly higher than that of randomly selected genes (P-value = 0). The P-value for a two-sided hypothesis test whose null hypothesis is that the means of the two groups are equal, using Welch’s t-test with Bonferroni correction for multiple comparisons. e UMAP of gene modules clustered by the Leiden algorithm. f Homologous gene proportion in the spots clusters of both species. The top 60 significant DEGs were called from spot clusters. Homologous gene proportion shows species specificity across clusters. g Dot plots of DEGs' expression in homologous region pairs. As shown in the black frames, the DEG genome expression patterns are very similar, though the DEGs are not orthologs. The DEGs were first picked and their expression on brain regions was calculated. The dot color denotes the mean expression level of DEGs in groups, and the dot size represents the fraction of spots that expressed the DEGs. The right bar plots indicate the group spot numbers. h Gene ontology (GO) enrichment similarity for each pair of homologous regions. Each square represents the overlap ratio of GO terms enriched by DEGs from one gene module for one homologous region pair. i The GO enrichment (measured by P-value) of DEGs in mouse and human claustrum. The enriched GO terms are identical for different gene sets, and the rank of GO terms according to the P-value are generally similar for the same gene set. We ranked the GO terms by enrichment for each species separately and selected GO terms with identical functions. The P-value for a two-sided hypothesis test whose null hypothesis is that the frequency of genes in the input list belonging to a particular gene set is equal to the expected frequency by chance, using Fisher’s exact test with Benjamini-Hochberg correction for multiple comparisons. Source data are provided as a Source Data file.

After clustering the gene embeddings, genes from two species were mixed and presented gene module block patterns (Fig. 4c). All the genes are clustered into 10 clusters with differential percentages of gene orthologs (Supplementary Fig. 13b) and functional variety (Supplementary Fig. 14) by the Leiden algorithm²⁸ (Fig. 4e). We picked the top 60 significant differentially expressed genes (DEGs) of all spot clusters, and homologous gene proportion shows the specificity of DEGs homology across clusters (Fig. 4f). We can see that the DEGs’ expression patterns are very similar (Fig. 4g), though the DEGs are not orthologs. The DEG expression patterns (Supplementary Fig. 12c) are not as similar as that in Fig. 4g, though the DEGs of the two species are orthologs. Therefore, marker genes may not be transferable across species while the marker genes’ expression patterns are transferable. The GSEA of the DEGs presents some similar patterns in the corresponding regions of the two species. For each pair of homologous regions from mice and humans, we first called DEGs for two species, respectively, and we conducted the gene set enrichment analysis (GSEA) separately, which means that gene sets such as “Allen_Brain_Atlas_down” are different for mice and humans. The GSEA of the DEGs presents some similar patterns in the corresponding regions of the two species. For example, the DEG enrichment in the claustrum of mouse and human from gene module 3 shows identical GO terms (Fig. 4h). We listed the most significant identical GO terms for differentially expressed genes in the mouse and human claustrum, respectively (Fig. 4i). The P-values were computed via GESApy, denoting the overlap between the given gene list and known reference gene sets. For the most enriched GO terms, the rank of GO terms according to the P-value is generally similar for the same reference gene set. For example, for the mouse and human claustrum neuron projection (GO:0043005), P-values are the highest in three identical GO terms (GO:0043005, GO:0099501, GO:0030672). This showed that the common enriched DEGs of homologous regions share similar gene expression patterns mirroring similar gene functional networks. An exception is regular neuron projection or brain region GO terms (Fig. 4i), the same enriched GO terms include exocytic vesicle membrane and synaptic vesicle membrane, where synaptic vesicles are a specialized subset of exocytic vesicles³⁴. GSEA for spot clusters also presents similar results (Supplementary Figs. 15 and 16). In summary, gene alignment helps to find common biological mechanisms across species.

BrainAlign enables alignment of spatial domain-specific spots of homologous regions across two species

The spatial locations of different transcriptional expression patterns in the brain are critical for understanding the biological functions and describing interactive brain connectome³⁵. The “spatial domain” is considered as regions with similar spatial expression patterns^36,37. We compared BrainAlign with other competing data integration methods, i.e., PCA, Beauchamp-FCN, Harmony²⁶, and Scanorama²⁷, on the mouse and human hippocampus. Only BrainAlign mapped the corresponding region pairs to a larger cluster while keeping the regions separate for one species, and it achieve a higher AMI and ARI between regions and clusters derived with the mclust algorithm³⁸ compared to other methods (Supplementary Fig. 17a–c). Therefore, BrainAlign offers better performance with clustering tissues than competing methods. We examined the spatial domain-specific spot embeddings on the hippocampus to show that BrainAlign could reveal similar expression patterns in the same domain across mice and humans. The UMAP of spot embeddings belonging to CA1, CA2, CA3, dentate gyrus, and subiculum in both mouse and human datasets shows clear region borders (Fig. 5a). In Fig. 5b, the top and middle panels display the original spatial distribution of samples from mouse and human hippocampal regions in the given three-dimensional space, respectively. The bottom panel presents the UMAP visualization of corresponding region pairs in the embedding space. The spots belonging to the same region are still closely located. The fold change values in alignment score between homologous and non-homologous regions in the embedding space are approximately 3, demonstrating a strong alignment of the spatial structures of homologous regions in the mouse and human hippocampus (Fig. 5c).

Fig. 5. Spatial domain-specific spot alignment for hippocampal regions across species.

a UMAP visualization for spot embeddings belonging to CA1, CA2, CA3, Dentate gyrus, and Subiculum in both the mice and humans. b Spatially similar homologous regions for the hippocampus are mapped into a shared domain while preserving their relative positions with BrainAlign. The top and middle panels are the original spatial distributions of mouse and human hippocampal regions, respectively; the bottom panel is a 3D UMAP visualization of corresponding pairs of mouse and human hippocampal regions in the embedding space. The figures are made via scattering the 3D coordinates and the color denotes different domains. c The fold change of alignment score between the homologous and non-homologous regions in the embedding space. The fold change values are approximately 3, indicating a strong alignment between the homologous regions. d Abstract graph generated using PAGA based on the spot embeddings of the hippocampus from both mouse and human. The alignment of region structures provides a clear spatial relationship between them. e Visualization of the marker genes for CA1, CA2, CA3, DG, and Subiculum regions in both mouse and human. The figures are made via scattering the UMAP 3D coordinates and the color denotes spot-gene expression level. It reveals significant consistency in the marker gene expression distribution between homologous regions (rows 1 and 4). However, the marker gene function does not maintain well between homologous genes mapping (rows 1, and 3 for mouse marker genes and corresponding human genes, and rows 4, and 2 for human marker genes and corresponding mouse genes). Source data are provided as a Source Data file.

Based on the abstract graph generated by PAGA³⁹ for the spot embeddings of the hippocampus from the two species (Fig. 5d), we can observe the correspondence of the same regions with a clear visualization of the spatial relationships between them. The marker genes in each hippocampus region also showed similar patterns in the two species. We visualized CA1, CA2, CA3, DG, and Subiculum regions in both mouse and human, along with the corresponding mouse marker genes Itpka⁴⁰, Amigo2⁴¹, Hs3st4⁴², Lrrtm4⁴³, Nts⁴⁴ and human marker genes NEUROD6, SCGN⁴⁵, TSPAN18, PDYN, and GFRA1 in the shared embedding space, and observed significant consistency in the expression distribution of marker genes^16,19,37 between homologous regions, demonstrating the accurate alignment of spatial domains across species. However, the marker gene function does not maintain well between homologous genes mapping, as shown in rows 1, and 3 for mouse, and rows 2, and 4 for human marker genes in Fig. 5e. This phenomenon is consistent with the result that homologous genes are probably not transferable across species in the last section as shown in Fig. 4g and Supplementary Fig. 7c.

As a verification of this conclusion, we checked this point on the mouse, marmoset, and macaque hippocampus⁴⁶ and explored the mouse marker genes on CA1, CA2, CA3, and dentate gyrus and their homologous genes for macaques (Supplementary Fig. 18). Those homologous genes of the mouse brain region markers also did not show significant differential expression in macaques, even though they showed marker function for marmosets, especially for Amigo2 and Lrrtm4 (red circle). As for gene Lrrtm4, it is essential for normal excitatory synapse development and function in dentate gyrus granule cells in mice⁴³, and we speculate that as the evolution went, the development of the hippocampus indicated wider excitatory synapse activities, requiring spatially wider expression of gene Lrrtm4. The datasets of mice and macaques are all generated through Stereo-seq⁴⁷ and thus have not so much data heterogeneity as datasets used in this paper, excluding the effects of noise. Therefore, our point about homologous genes as marker genes of brain regions not being transferable across species should hold.

In addition, we did a similar analysis for isocortex subregions across mice and humans (Supplementary Fig. 19) and selected five isocortex sub-region pairs with SAS. We also examined the spatial mapping of spot embeddings belonging to five clusters of thalamus in mouse and human datasets (Supplementary Fig. 20). The two experiments demonstrated that the integrated ST space could enable the identification of spatially close domains from mouse and human brains.

Discussion

In this work, we designed a heterogeneous graph neural network with self-supervised learning to overcome the heterogeneity between mouse and human whole-brain STs datasets. Notably, initialization of the embeddings using CAME¹⁰ ensures the preservation of brain region structure or spot information while maintaining the generality of self-supervised learned embeddings in BrainAlign. That makes BrainAlign learn better gene embedding relations than measured with CAME by the alignment score of homologous regions and correspondence of gene orthologs.

In the similarity analysis of anatomical regions in the embedding space, we noticed several distinct regions violating the continual consistency between structural order and mean correlations. In the mouse brain, the thalamus, lateral septal complex, retrosplenial area, and postpiriform transition area have a significantly stronger or weaker correlation with human regions. In the human brain, the piriform cortex, paraterminal gyrus, and amygdala display different correlation patterns with mouse brain regions. Those special regions are not necessarily homologous but lowly correlated in the embedding space except for the mouse postpiriform transition area and human piriform cortex. Moreover, those regions are connected to many other regions and perform as important biological hubs, which shows that the conservative cross-species patterns are biologically informative. In the mouse brain, nerve fibers project out of the mouse thalamus to the cerebral cortex in all directions, allowing hub-like exchanges of information⁴⁸, and the lateral septum is implicated as a hub that regulates a variety of effects, such as reward, feeding, anxiety, fear, sociability, and memory⁴⁹, and the mouse retrosplenial cortex functions as an integrative hub for sensory and motor signals of navigation and memory⁵⁰ and the postpiriform transition area refers to a transition zone at the boundary between the amygdala and the cerebral cortex⁵¹. In the human brain, the function of the piriform cortex relates to olfaction, which is the perception of smell and is increasingly studied as a model circuit for cortical sensory processing⁵². The amygdala is a major emotional processing center and links emotions to many other brain abilities, especially memories, learning, and senses⁵³. The paraterminal gyrus is a small gyrus that sits inferior to the rostrum of the corpus callosum and is thought to be involved in depression.

Generally, we believe that the whole-brain comparative analysis is a valuable topic worth investigating in such an AI-enabled way due to its complexity in data. We believe the HGNN used in this study could be a promising tool for general comparative transcriptomics analysis. We have also applied BrainAlign to the mouse and macaque hippocampus datasets sequenced by Stereo-seq^46,47, and the corresponding homologous regions are aligned together accurately (Supplementary Fig. 21a). To test the performance of BrainAlign for cross-technology datasets integration, we have applied BrainAlign to the mouse hippocampus dataset sequenced by Slide-seqV2⁵⁴ and macaque hippocampus dataset sequenced by Stereo-seq, and the corresponding homologous regions are aligned together accurately (Supplementary Fig. 22). These experiments demonstrated that BrainAlign is available for cross-technology and cross-species datasets integration.

In addition, we have done two experiments to evaluate whether BrainAlign captures key information of the individual datasets. We split the whole-brain dataset into training and test ones for each species. We then trained a two-layer neural network on the training dataset (Supplementary Fig. 3a), and computed the anatomical region prediction accuracy on the test dataset. We also did a similar experiment on the combined dataset composed of two species ones. The result shows that BrainAlign improves the prediction of agreed-upon anatomy for the mouse dataset, and the prediction accuracy of BrainAlign on the mouse dataset is significantly higher than that of PCA, Beauchamp-FCN, Harmony, and Scanorama. However, the prediction accuracy of BrainAlign on the human dataset is lower than PCA, Beauchamp-FCN, Harmony, and Scanorama. BrainAlign achieved a higher or more competitive classification accuracy than Harmony and Scanorama. We did similar experiments on mouse and macaque hippocampus ST datasets sequenced by Stereo-seq. The prediction accuracy of BrainAlign is significantly higher than that of Harmony and Scanorama on both the mouse and human hippocampus datasets (Supplementary Fig. 21e). We speculate that the reason is the relatively low resolution of the human data, the significant difference in resolutions of the mouse and human spots, and the amount of information contained. To align the mouse and human data together, BrainAlign extracted common information from these two species, and it tends to abandon part of human-specific information in the human ST data since the resolution of the mouse data is much higher and the spot number is much larger. The performance of BrainAlign on the AMI between regional labels (Supplementary Figs. 3d, 21d, 22e) and reconstruction loss also verified this phenomenon (Supplementary Fig. 4).

Here, we only considered the whole-brain ST integration for two species, and the whole-brain ST integration for multiple species is expected. Such datasets are rare due to the high cost of data generation, indicating that integrating local region STs into the whole-brain dataset should be a promising direction. The resolution of the human dataset is too raw to uncover more detailed findings. One of the possible solutions is to integrate single-cell resolved brain ST datasets of various regions into a whole-brain dataset. ScRNA-seq data lacking 3D spatial information annotated with brain region labels are also possibly helpful. Besides, mice and humans are all mammals and share relatively close evolution paths with more one-to-one homologous genes in the heterogeneous graph. Brain integration for evolutionary distant species using BrainAlign should be a good attempt.

We observed that most marker gene expression patterns were not transferable for cross-species gene orthologs, but the marker gene expression patterns were similar in homologous regions or clusters. Previous studies showed that the same gene families had cell-type specificity in both species with different patterns across cell types⁸. Marker genes of cell types were generally not transferable across species¹⁰. Muscle and neuron cells shared conserved marker genes across seven species, while the other cell types did not⁵⁵. Examining the orthologous transcription factors (TFs) reveals their cell category specificity and functional importance in cell identity regulation. Given the brain regions consist of diverse cell types and TFs, the marker gene pattern similarity between region pairs is still vague. As for the lack of Amigo2 expression specificity in macaque (Supplementary Fig. 18), given the important function of the Amigo gene family in displaying CA2 function about activation of CA2 pyramidal neurons relevant to social memory^56,57, we speculate this phenomenon is due to the expansion of pyramidal neurons with evolution in the hippocampus in highly socialized species such as macaque. Since the hippocampus size of the macaque is much larger than the other two animals. However, it requires further detailed analysis for verification of the speculation.

In this research, we only used gene and spot as input to construct the graph neural network. Other datasets (e.g., the protein interaction networks⁵⁸) may boost larger graphs for integration and alignment. Besides, for many species, it is promising to quantitatively compare brain spot transcriptomes across species without all the knowledge of orthologous gene mapping, gene annotations, or reference genomes⁵⁹.

Methods

This research did not involve any biological experiments, human participants, or animal subjects, and thus did not require ethical approval. We focused on integrating mouse¹⁷ and human¹⁹ whole-brain STs datasets. Both datasets include gene expression matrices and spatial 3D coordinates of spots (Fig. 1a), with the mouse data exhibiting a higher resolution relative to the human data, where the mouse spot amount is almost tenfold that for humans.

Data description

Mouse data

The processed mouse gene expression data and spot three-dimensional coordinates were obtained first¹⁷. The left hemispheres of three male mouse brains were cut into 10-μm sections. 75 coronal sections that covered the entire AP axis onto ST arrays were hybridized for one hemisphere. Each imaged brain hemisphere section was aligned and the positions of the ST spots in the tissue were measured using a computational framework designed to generate reference maps⁶⁰ with the Allen mouse brain reference atlas (AMBA; www.brain-map.org). We acquired 64 anatomical brain regions for this mouse dataset. We also generated a set of 15 broad regions for visualization.

Human data

Human gene expression data and spot three-dimensional coordinates were obtained from the AHBA¹⁹ following the preprocessing procedures³, spot locations were mapped from histology data into MR space using Inkscape and BioImage Suite¹⁹. To obtain the anatomical region reference for each spot, we used the hierarchical ontology from the AHBA, using the Allen Institute’s API. We aggregated and pruned the neuroanatomical hierarchy as in ref. ³, resulting in 88 human brain regions. We also generated a set of 16 broad regions as in ref. ³ for visualization and annotation.

Hippocampus data

We downloaded the hippocampus data profiled by Stereo-seq from the Brain Science Data Center at the Chinese Academy of Sciences and selected the slices T315 (4540 spots), T447 (28566 spots), and T36 (28499 spots) in the mouse, marmoset, and macaque datasets, respectively⁴⁶. We cropped the slice ’Puck_200115_08’ in the mouse hippocampus dataset⁵⁴ sequenced by Slide-seqV2 to 21919 spots.

Data preprocessing

We downloaded the processed mouse gene expression data directly. The complete dataset contains 15,326 unique genes across 34,053 spots after quality control. We pre-processed the human gene expression data using the abagen package in Python (https://abagen.readthedocs.io/en/stable/)^19,20,61 as in ref. ³. We acquired a gene-by-spot expression matrix with 15,627 genes and 3682 spots across all donors. Both mouse and human expression arrays were log-transformed. For PCA, Beauchamp-FCN, Harmony, and Scanorama, we selected 6000 highly variable one-to-one homologous genes. We applied PCA to the datasets of two species separately after selecting 6000 HVGs. Before the integration, we used sc.pp.normalize_total() and sc.pp.log1p() from SCANPY to normalize the data. Moreover, we used sc.pp.combat() to achieve batch effect correction. These methods performed poorly without this step.

Gene selection

We selected highly variable genes (HVGs) and differentially expressed genes (DEGs) for downstream procedures. We used SCANPY⁶² built-in function highly_variable_genes() to identify the top 2000 genes with the highest dispersions as HVGs. We computed the DEGs using brain regions and clusters generated by the Leiden algorithm²⁸ with resolution = 1 separately for mouse and human datasets by a Student’s t-test performed through the function rank_genes_groups() from SCANPY⁶². We merged the DEGs for brain regions and clusters. The genes used as the spot features were shared between species. We first took the top 70 DEGs for each region and retained genes with one-to-one homology in another species. We then took the union of the resulting two sets of genes for input, denoted as ${\mathcal{G}}_m$, ${\mathcal{G}}_h$ for mouse and human, respectively. We combined both HVGs and DEGs from mouse and human data to decide the node genes used for constructing the GNN. We denote the homologous genes for ${\mathcal{G}}_m$, ${\mathcal{G}}_h$ as ${\mathcal{G}}_m^{\left(hom\right)}$, ${\mathcal{G}}_h^{\left(hom\right)}$, respectively. Finally, we utilize ${\mathcal{G}}_m\cup {\mathcal{G}}_h^{\left(hom\right)}$, ${\mathcal{G}}_h\cup {\mathcal{G}}_m^{\left(hom\right)}$ as the node genes for two species separately, where ∪ represents “union” of sets. The dimensions of the initial node features of the human and mouse spots are 3554 and 3311, respectively, which correspond to the number of considered genes. In the hippocampus experiments, we selected 6244 and 7605 genes for mice and macaques in the same-platform experiment, and 6256 and 6180 genes for mice and macaques in the cross-platform experiment.

Gene orthology

Following the step in ref. ¹⁰, we downloaded the gene multi-to-multi homology (orthologs) information from the BioMart web server derived from the Ensembl Compara pipeline⁶³. We used the mouse as the anchor species and downloaded the homology mapping file.

BrainAlign

Construction of the cross-species heterogeneous graph

Following¹⁰, after selecting HVGs and DEGs, we extended them using homologous mappings across species to form the gene sets for building the heterogeneous graph. We built the “spot-spot” edges in the HGNN via KNNs measured by the spatial distance of spot 3D coordinates. We searched top k = 5 KNNs for each spot as its neighbors and assigned edges and directly produced the gene-gene edges according to the multi-to-multi gene homology mappings. We determined the spot-gene edges through whether the gene expression was zero or nonzero.

Node feature initialization

For stable convergence and maintenance of the brain region or spot clusters, we used the first layer output of the trained CAME model¹⁰ as spot and gene initial features of BrainAlign. In CAME, the gene initial embedding is obtained via aggregation of neighboring spot embeddings. It is noteworthy that the first layer output of CAME only induced information of “region” or “cluster” labels for only one species, the self-supervised training setting was not affected. In the whole-brain mouse and human datasets, only mouse region labels are used. No regional labels are used in the mouse and macaque hippocampus datasets, and only cluster labels of pre-clustering on one-to-one genes are used for initializing embeddings. Furthermore, we averaged the initial features of homologous genes to inject the homology information into the gene embeddings.

Self-supervised mechanisms in the graph neural network

Instead of using predefined meta-paths, just as in ref. ²³, BrainAlign first globally learns the relation-based embeddings for all nodes from the neighbor properties under each relation type and then uses an attentive fusion module to combine them. Self-supervised learning is achieved by automatically generating positive and negative spots and optimizing the model through contrastive learning. Then a multi-hop contrast is used to optimize the regional structure information by utilizing the strong correlation between nodes and their neighbor-graphs. And multiple relationships are taken into consideration by multi-hop message passing.

Notations

Initially, an attributed heterogeneous network is defined as $G=\left(V,E,X,\mathcal{T},\mathcal{R}\right)$, which consists of a set of nodes V, a set of edges E, the node feature matrix X, the set of node types $\mathcal{T}$ and the set of edge types $\mathcal{R}$. For heterogeneous networks, $\mid \mathcal{T}\mid >1$ and/or $\mid \mathcal{R}\mid >1$ is required. Besides, for a node v ∈ V, the p-hop neighborhood of v is defined as ${\mathcal{N}}_v^p$, the set of vertices that are reachable from v after p hops. For a specific relation r, the p-hop relation-based neighborhood of v is defined as ${\mathcal{N}}_v^p\left(r\right)$. Here, one-hop means two nodes are directly connected, while p-hop means two nodes are connected by p one-hop relations. For example, “spot 1-gene 1” and “gene 1-spot 2” are one-hop relations, and the two-hop relation “spot 1-spot 2” is induced from the two one-hop relations as “spot 1-gene 1-spot 2”. Formally, in a graph G, a p-hop relation-based neighbor-graph of the node v is defined as ${\mathcal{G}}_v^{{\pi }_p}$, where π_p = r₁r₂…r_p is used to denote a path $t_1{\to }^{r_1}{t}_2{\to }^{r_2}$$\dots {\to }^{r_p}{t}_{p+1}$ with a sequence of p edge types $\left\{r_1,r_2,\dots ,r_p\right\}$ and node types $\left\{t_1,t_2,\dots ,t_{p+1}\right\}$. The types of nodes and edges in the path can be repeated. The p-hop relation set of node with type t is defined as $R_t^p$, e.g., $R_t^1$ denotes all the possible one-hop relation set of node with type t.

Encoding layer

BrainAlign learns the embedding of a node from its relevant one-hop relation-based neighbor-graphs by employing a relation-based encoder to encode the multi-typed nodes and edges of the spot-gene graph. For node i_t of type t, we generate the relation r_t-based embedding of the k-th layer by averaging (MEAN) the representations of its relevant one-hop neighbors as follows:

$${\mathbf{u}}_{r_t}^k\left(i_t\right)=\delta \left({\mathit{\Theta }}_{r_t}^k\cdot \mathrm{MEAN}\left(\left\{{\mathbf{h}}_j^{k-1}\mid j\in {\mathcal{G}}_{i_t}^{{\pi }_{1,r_t}}\right\}\right)\right),$$ 1

where ${\mathbf{u}}_{r_t}^k\left(i_t\right)$ denotes the 1-hop neighbor embedding of the i_t-th spot, δ denotes the ReLU activation function, ${\mathit{\Theta }}_{r_t}^k$ is a matrix to be learned for the relation r_t in the k-th layer, ${\mathbf{h}}_j^{k-1}$ is the representation of the neighbor j in the (k − 1)-th layer, and ${\mathcal{G}}_{i_t}^{{\pi }_{1,r_t}}$ denotes the one-hop neighbor-graph of node i_t based on relation r_t.

For all nodes of type t, important learning parameters are shared by default. For all nodes in V_t, the coefficients of each relation r_t in ${\mathcal{R}}_t^1$ can be formulated as:

$$e_{r_t}^k=\frac{1}{∣V_t∣}{\sum }_{i_t\in V_t}\tanh \left({\left({\mathbf{q}}_t^k\right)}^{\top }\cdot \left({\mathbf{W}}_t^k\cdot {\mathbf{u}}_{r_t}^k\left(i_t\right)+{\mathbf{b}}_t^k\right)\right),$$ 2

where ${\mathbf{W}}_t^k$ is a linear transformation parameter matrix, ${\mathbf{q}}_t^k$ is the learnable attention vector, and ${\mathbf{b}}_t^k$ is the learnable bias vector in the k-th layer. Then, to fairly integrate these relation-based embeddings for nodes of type t, the standard coefficient ${\beta }_{r_t}^k$ is obtained by normalizing $\left\{e_{r_t}^k\mid r_t\in R_t^1\right\}$ with a softmax function:

$${\beta }_{r_t}^k=\mathrm{softmax}\left(e_{r_t}^k\right)=\frac{\exp \left(e_{r_t}^k\right)}{{\sum }_{r_t\in R_t^1}\exp \left(e_{r_t}^k\right)}.$$ 3

Eventually, focusing on node i_t in V_t, its unique representation in the k-th layer can be produced by the following linear combination:

$${\mathbf{h}}_{i_t}^k={\sum }_{r_t\in {\mathcal{R}}_t^1}{\beta }_{r_t}^k\cdot {\mathbf{u}}_{r_t}^k\left(i_t\right).$$ 4

Multi-hop message passing

BrainAlign employs a multi-hop contrast optimization to enhance the regional structure information by leveraging the strong correlations between nodes and their neighbors. Since directly learning the node embedding by aggregating features of its one-hop neighbors is insufficient to capture diverse graph structures, we stack multiple encoding layers to derive multi-hop message passing. For this purpose, we concatenate the learned embedding with their original attributes to get the final embedding for each type of node by a node-type-based linear propagation:

$${\mathbf{z}}_{i_t}={\widehat{\mathbf{W}}}_t\cdot \left[{\mathbf{h}}_{i_t}^k\parallel {\mathbf{x}}_{i_t}\right],$$ 5

where ${\widehat{\mathbf{W}}}_t$ is a matrix to be learned for all nodes of type $t,{\mathbf{h}}_{i_t}^k$ and ${\mathbf{x}}_{i_t}$ are the representations and attributes of the node i_t with type t, respectively, and [ ⋅ ∥ ⋅ ] is a concatenation operation.

Contrastive loss

In BrainAlign, self-supervised learning is approached via contrastive learning, automatically generates positive and negative spots, and optimizes the model through contrastive learning. Negative spots for one-hop and two-hop contrasts are generated by shuffling the learned node representations. Positive spots for p-hop (p = 1, 2) contrast are p-hop neighbor-graph vectors. The contrast loss in BrainAlign comprises the sum of intrinsic contrast loss and multi-hop contrast. For intrinsic contrast, a discriminator computes the probability score for each intrinsic pair, i.e., the learned node embeddings and the original attribute, using a standard binary cross-entropy objective function. The multi-hop loss for each node is a weighted sum of one-hop and two-hop contrast. The total loss $\mathcal{L}$ is the sum of loss for both spot and gene node, i.e., ${\mathcal{L}}_{spot}$ and ${\mathcal{L}}_{gene}$.

Intrinsic contrast

We introduced the intrinsic contrast to capture the mutual dependence between learned node embeddings and the original attributes. We used a discriminator $\mathcal{D}$ to compute the probability score for each of the intrinsic pairs and present the objective function with a standard binary cross-entropy:

$${\mathcal{L}}_t^S=-\frac{1}{∣V_t∣}\sum _{i_t\in V_t}\left(\log \mathcal{D}\left({\mathbf{z}}_{i_t},{\mathbf{x}}_{i_t}\right)+\log \left(1-\mathcal{D}\left({\tilde{\mathbf{z}}}_{i_t},{\mathbf{x}}_{i_t}\right)\right)\right).$$ 6

The discriminator $\mathcal{D}$ is a bilinear function as follows:

$$\mathcal{D}\left({\mathbf{z}}_{i_t},{\mathbf{x}}_{i_t}\right)=\sigma \left({\tilde{\mathbf{z}}}_{i_t}^{\top }\cdot {\mathit{\Omega }}_t^d\cdot {\mathbf{x}}_{i_t}\right),$$ 7

where σ is the logistic sigmoid nonlinearity and ${\mathit{\Omega }}_t^d$ is a trainable matrix.

Multi-hop contrast

For the learned type t node representations ${\mathbf{Z}}_t=\left\{{\mathbf{z}}_{i_t}\mid i_t\in V_t\right\}$, we first corrupted them to get negative spots by shuffling them in a row-wise manner, denoted as ${\tilde{\mathbf{Z}}}_t=\left\{{\tilde{\mathbf{z}}}_{i_t}\mid i_t\in V_t\left[idx,\right]\right\}$, where idx is the shuffled indices and ${\tilde{\mathbf{z}}}_{i_t}$ is the negative spot embedding of node i_t. Then, we extracted one-hop and two-hop relation-based neighbor-graphs for each node and obtained the neighbor-graph level summary vectors by a readout function $\mathcal{A}:{\mathbb{R}}^{N^{\prime }\times d}\to {\mathbb{R}}^d$, where $N^{\prime }$ indicates the neighbor-graph size and d is the dimension of latent representations. For each node, a set of one-hop and two-hop neighbor-graph vectors are used as positive spots. Specifically, we use ${\mathrm{S}}_{i_t}^1=\left\{{\mathrm{s}}_{i_t}^{r_t}\mid r_t\in R_t^1\right\}$ and ${\mathrm{S}}_{i_t}^2=\left\{{\mathrm{s}}_{i_t}^{r_t^2}\mid r_t^2\in R_t^2\right\}$ to denote the gathers of one-hop and two-hop neighbor-graph vectors of the node i_t, respectively. And $r_t^2$ represents a 2-hop relation for a node with type t. After that, we used the margin triplet loss for one-hop contrastive learning of node i_t :

$${\ell }_1^{i_t}={\sum }_{r_t\in R_t^1}\left(\max \left(\sigma \left({\mathbf{z}}_{i_t}^{\top }\cdot {\mathbf{s}}_{i_t}^{r_t}\right)-\sigma \left(\widetilde{{\mathbf{z}}_{i_t}^{\top }}\cdot {\mathbf{s}}_{i_t}^{r_t}\right)+ϵ,0\right)\right),$$ 8

and two-hop contrastive learning of node i_t :

$${\ell }_2^{i_t}={\sum }_{r_t^2\in R_t^2}\left(\max \left(\sigma \left({\mathbf{z}}_{i_t}^{\top }\cdot {\mathbf{s}}_{i_t}^{r_t^2}\right)-\sigma \left({\tilde{\mathbf{z}}}_{i_t}^{\top }\cdot {\mathbf{s}}_{i_t}^{r_t^2}\right)+ϵ,0\right)\right),$$ 9

where σ is the logistic sigmoid nonlinearity and ϵ is the margin value. For all nodes with type t, we summarize the multi-hop contrast loss as following:

$${\mathcal{L}}_t^C=\frac{1}{∣V_t∣}{\sum }_{i_t\in V_t}\left(\lambda {\ell }_1^{i_t}+\left(1-\lambda \right){\ell }_2^{i_t}\right),$$ 10

where λ is the tunable coefficient.

Finally, we joined all modules’ losses and obtained the final objective $\mathcal{L}$ for all types of nodes (spot and gene in this work):

$$\mathcal{L}={\sum }_{t\in \mathcal{T}}\left({\mathcal{L}}_t^C+{\mathcal{L}}_t^S\right),$$ 11

where $\mathcal{T}$ comprises two types of node, i.e., gene and spot.

The training settings of BrainAlign

In the experiment, the embedding dimension is set to 128. We used the AdamW optimizer⁶⁴ with an initial learning rate of 0.02, and the learning rate of each parameter group decayed by 0.5 every ten epochs. We also adopted early stopping with a patience of 30 epochs. The maximum number of iterations is set to 150. We used 2-hop message passing to learn the node embedding, ϵ is set to 0.8, and λ is set to 0.5. The dropout rate in the fully-connected layers is set to 0.7, and the leaky rectified linear unit was used as the activation function⁶⁵.

Analysis methods

Clustering spot and gene embeddings

We used the Leiden algorithm implemented in the SCANPY package⁶². For spot embedding clustering, we set the resolution as 9 for proper cluster fineness. Similarly, for gene embedding clustering, we set the resolution as 1.5.

Naming clusters with brain region names

We referred to ref. ¹⁷ to name the spot clusters in the embedding space. Each cluster name was given by combining mouse and human region names or acronyms. For example, ‘0-TH-TH’ represents the first cluster of spots mainly from the mouse and human thalamus. Specifically, for each species, if the rate of region spot number in one cluster/species spot number in one cluster exceeds P = 0.3, the region name or acronym is appended to the cluster name. If the proportions of all region spots in one cluster are below P, the ‘mixed(region name or acronym with the maximum count number)’ is appended to the cluster name, e.g., ‘1-PIR-mixed(CI)’.

Identification of homologous brain regions

The procedure for identifying the homologous brain regions is as follows: (1) Clustering spot embeddings using the Leiden algorithm²⁸ with resolution equaling 9; (2) Identifying highly correlated spot pairs, i.e., spots from different species that are grouped as highly correlated cluster pairs (clustered to the same cluster across species); (3) Aligning clusters and brain regions. When the spot proportion of some region ranks the top three in the cluster, this cluster represents this region. Those homologous brain region pairs are identified by mapping the highly correlated cluster pairs to region pairs. For example, if the proportion of spots with the region labeled “thalamus” ranks top three in spots of cluster ‘0-TH-TH’ for both species, this cluster is seen as a representation of the thalamus region in mice and humans, and the homologous pairs “Thalamus-thalamus” is identified.

Identifying differentially expressed genes

We used the Wilcoxon test implemented in the package SCANPY⁶² to identify differentially expressed genes for each spatial domain with the FDR threshold of 1% (Benjamin-Hochberg adjustment).

Generating abstracted graph

We employed the PAGA algorithm³⁹ implemented in package SCANPY⁶² to depict spatial trajectory. The PAGA graphs were visualized by the function scanpy.pl.paga(), while the coordinates of points were reset to discriminate species.

Gene set enrichment analysis

We used the function gseapy.enrichr implemented in the package GSEApy⁶⁶ to identify enriched GO terms for a specific gene list. For mice and humans, we selected eight biologically important gene sets related to the brain atlas, cell types, cell markers, biological process, cellular component, molecular function, and gene atlas for GSEA.

Cross-species overlap ratio of GO terms

For each pair of regions or clusters from mouse and human, we selected the DEGs and then conducted gene set enrichment on the DEGs list. The enriching GO terms were filtered by the adjusted P-value < 0.05 (Wilcox test, Bonferroni correction). For the i-th GO term set of mouse ${\mathrm{S}}_i^m$ and the j-th GO term set of mouse ${\mathrm{S}}_j^h$, the overlap ratio of GO terms was computed by the following formula:

$${\mathrm{OR}}_{ij}=\frac{1}{2}\left(\frac{\mid {\mathrm{S}}_i^m\cap {\mathrm{S}}_j^h\mid }{\mid {\mathrm{S}}_i^m\mid }+\frac{\mid {\mathrm{S}}_i^m\cap {\mathrm{S}}_j^h\mid }{\mid {\mathrm{S}}_i^h\mid }\right).$$

After this, we applied the row and column z-scores to the overlap index matrix to normalize it. For each pair of regions or clusters from mice and humans, we selected the DEGs and then conducted gene set enrichment on the DEG list. The enriching GO terms were filtered by the adjusted P-value < 0.05 using the Wilcox test (Bonferroni correction adjusted).

Seurat alignment score

We adopted the Seurat alignment score (SAS) to evaluate the alignment of spots or genes in the embedded space, that is, the mixing of embeddings between species. SAS ranges from 0 to 1, and higher values indicate better mixing. Here, we calculated SAS as described in ref. ²⁵ with the Python implementation in ref. ⁶⁷. SAS is defined as:

$$\mathrm{SAS}=1-\frac{\overline{x}-\frac{K}{N}}{K-\frac{K}{N}},$$

where $\overline{x}$ is the average number of spots from the same species among the K-nearest neighbors (different datasets were first subsampled to the same number of spots as the smallest dataset), and N is the number of species. We set K to 1% of the subsampled spot number.

Statistics and reproducibility

No statistical method was used to predetermine the sample size. No data were excluded from the analyses. The experiments were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment. More information was provided in the Reporting summary file.

Reporting summary

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

Author contributions

S.Z. conceived and supervised the project. B.Z. developed and implemented the BrainAlign algorithm. B.Z., S.Q.Z., and S.Z. validated the methods and wrote the manuscript. S.Q.Z. and S.Z. supervised the project. All authors read and approved the final manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

Source data for Figs. 2–5 is available with this paper. The datasets analyzed in this study are all from publicly available datasets. We obtained the processed mouse gene expression data and 3D coordinates of spots from https://www.molecularatlas.org/. We downloaded the human expression data and 3D MRI coordinates of spots from the Allen Institute’s API. We downloaded the gene ortholog mappings from the BioMart web server: (http://www.ensembl.org/biomart/martview). We obtained the mouse, marmoset, and macaque Hippocampus datasets from the Brain Science Data Center at the Chinese Academy of Sciences (https://cstr.cn/33145.11.BSDC.1684593483.1659922723465732098). We downloaded the mouse hippocampus dataset (ID: CP815) profiled by Slide-seqV2 from https://singlecell.broadinstitute.org/. Source data are provided with this paper.

Code availability

The code of data processing and BrainAlign is accessible via this link on GitHub⁶⁸: https://github.com/zhanglabtools/BrainAlign/.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-50608-2.