An information-theoretic metric learning approach for cross-species transcriptome integration: Identifying sex differentiation transcriptomic structure between protogynous fishes and mouse

An information-theoretic metric learning approach for cross-species transcriptome integration: Identifying sex differentiation transcriptomic structure between protogynous fishes and mouse | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article An information-theoretic metric learning approach for cross-species transcriptome integration: Identifying sex differentiation transcriptomic structure between protogynous fishes and mouse Takahisa Hamano This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8564120/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Sexual differentiation is a fundamental process conserved across animals; nonetheless, cross-species comparisons remain limited. Here, I applied information-theoretic metric learning (ITML) to project mouse testis RNA-seq data into a three-dimensional space trained on protogynous fish transcriptomes, using stage-to-stage expression change geometry rather than gene identity or annotation. ITML was anchored with dmrt1 and amh , revealing conserved clustering of known sex differentiation genes (e.g., bmp8b and stra8 ). Rather than serving as a direct differentiation model, this framework provides a structural reference for evaluating whether transcriptomic changes align with conserved developmental trajectories, offering a framework for identifying novel candidates in mammalian sex differentiation. Computational Biology cross-speceis ITML machine learning RNA-seq sex differentiation Figures Figure 1 Figure 2 1. Introduction In multicellular organisms, cell differentiation constitutes a central mechanism for sustaining life. While induced pluripotent stem (iPS) cell studies have advanced our understanding of differentiation mechanisms, 1 several aspects of sex differentiation remain unresolved. Although numerous studies have focused on individual genes involved in vertebrate sex differentiation, the higher-order regulatory architecture remains unresolved. The temporal sequence in which the network is activated, as well as the identity of any upstream master regulator, is still unclear. Moreover, while many vertebrate lineages employ a broadly similar set of conserved factors, how these components interact and how their regulatory wiring is organized differ across taxa and remain poorly understood. This lack of clarity highlights the need for biological systems in which large-scale reorganization of the sex differentiation program can be directly observed. Protogynous fishes, which undergo postnatal sex change, offer a unique comparative model. Protogynous sex change is a minority strategy among vertebrates, in which individuals mature first as females and subsequently transition to males. This transition typically occurs in social species, often those for hierarchical groups, where the reproductive opportunity of a dominant male creates strong selective pressure for rapid and coordinated remodeling of the gonad. As a result, protogynous sex change unfolds over a remarkably short timescale—on the order of a week—yet proceeds through histological stages that show notable parallels to the maturation processes observed in other vertebrate gonads. These features create a biological context in which large-scale transcriptomic reorganization occurs in a temporally well-defined manner, providing a tractable framework for examining how developmental modules are sequentially reorganized and whether such modules retain comparable geometric signatures across distant species. Here, consecutive transcriptomic transitions during sex change were summarized as stage-to-stage differences, denoted as Δ1–Δ3 in this study, based on previously published gonadal staging of bluehead wrasse and orange-spotted grouper. 2, 3 Previous research suggests that transcriptomic shifts during sex change are not unique to fish but reflect conserved patterns across taxa. 2–5 The aim here was simply to observe what emerges when mouse data are mapped into a transcriptomic space learned from sex-changing fish. Information-theoretic metric learning (ITML) is a method that adjusts distances in a data space so that certain pairs of data remain close together (must-link constraints) while others remain apart (cannot-link constraints). 6 In biological terms, a must-link means that two factors that act together in the same functional module are positioned close to each other in the learned space. Unlike principal component analysis (PCA), which reduces dimensions but produces axes without direct biological interpretation, or standard clustering methods, which require the researcher to predefine the number of clusters, ITML allows such biological relationships to directly shape the geometry of the space. Gene sets involved in developmental processes often display coordinated expression patterns, which can be interpreted as geometric relationships in transcriptomic space. This view, widely adopted in systems biology, provides a conceptual basis for examining whether such organizational principles persist across species. 7 This makes it particularly suitable for testing whether conserved organization of sex differentiation genes emerges across species. By anchoring the learned space with biologically meaningful constraints, ITML provides a principled framework for investigating whether similar developmental trajectories give rise to comparable geometric organization across species. Studies on gene expression during sexual differentiation have revealed classical regulatory pathways. For instance, dmrt1 functions as a key regulator of male development, whereas amh acts as a major inhibitor of female development. 8 In this study, dmrt1 and amh were used as must-link constraints because both are widely recognized opposing regulators of vertebrate sex differentiation. Their well-established antagonistic roles make them convenient and interpretable anchors for structuring the learned space. Most previous studies of sex differentiation have focused on individual genes, their names, or their annotated molecular functions, 8, 9 rather than on the structural relationships among their expression trajectories. The central question of this study is whether biologically meaningful organization emerges when sex-related genes are compared not by their names or annotated functions, but by the geometry of their stage-to-stage expression changes. 2. Materials & Methods 2.1. Datasets RNA-seq datasets of bluehead wrasse ( Thalassoma bifasciatum , control female stage, stage 3, stage 4, and terminal male stage from PRJNA293777), orange-spotted grouper ( Epinephelus coioides , ovarian phase 4, early stage, late stage, and testis phase from PRJDB9134), and mouse ( Mus musculus , embryonic days 9.5, 11.5, and 13.5 from PRJNA178509 and postnatal day 6 from PRJNA189510) 2, 3, 10, 11 were obtained from the Sequence Read Archive. Individual SRR accession numbers are listed in Supplementary Table 1. In this study, stage-to-stage differences (Δ1–Δ3) were defined as three representative transcriptomic transitions extracted from each species’ staging system. Although the source studies include additional early or late phases, these show minimal deviation relative to adjacent stages and thus contribute little to capturing the principal developmental trajectory. Δ1 represents the initial shift from a preceding stable state. Δ2 corresponds to the intermediate transition along the trajectory, situated between the early and late phases. Δ3 represents the late-stage transition, characterized by movement toward the masculinized or differentiated state as the trajectory approaches its final configuration. 2.2. Processing Reads were processed on the Galaxy platform (Trimmomatic, FastQC, Salmon, Trinity). 12 The Galaxy environment was chosen because it provides a fully documented, reproducible workflow with widely adopted community tools, thereby ensuring transparency and accessibility, especially for complex multi-species RNA-seq datasets, and avoiding tool-specific biases by standardizing the preprocessing steps. 2.3. Summarizing and annotation Transcript-level counts were summarized using R (tximport). Protein annotation was performed using DIAMOND blastx against the UniProtKB protein FASTA file for Actinopterygii (NCBI Taxonomy ID: 7898). 13 Murine RNA-seq data were processed as in fish, except that GENCODE release M37 (GRCm39) was used in tximport. 2.4. Normalization Python was used for the downstream steps. Expression values were transformed as log2(TPM+1) and standardized to gene-wise z-scores. TPM normalization allows comparability across samples. The log2(TPM+1) transformation stabilizes variance and reduces the skewness of highly expressed genes while preserving dynamic range, making the data more suitable for downstream clustering and metric learning. The “+1” avoids undefined values for low-abundance genes. 2.5. Gene filtering Fish datasets were filtered. Two complementary filters were used to capture highly expressed and dynamically changing genes. (i) A quantity-based filter retained the top 1,500 genes by total log2(TPM+1) across stages. (ii) A difference-based filter emphasized mid-transition by requiring Δ2 to fall within the top 30% of Δ2 values and exceed both Δ1 and Δ3. From this subset, genes were further filtered by requiring both Δ1 and Δ3 to fall within the top 15% and retaining the intersection of these sets. This final set was ranked by Δ1, and the top 1,500 genes were selected, reflecting the focus on mid- and early transition. The union of these sets (5,857 genes) was regarded as a candidate sex change-related gene for each species (Table S1; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). This dual filter captured both quantitatively abundant genes and those with dynamic stage-specific changes. Focusing on Δ2 reflects histological studies, demonstrating that mid-transition stages share some similarities with murine E11.5–E13.5 differentiation. 14 2.6. Metric learning ITML based on filtered fish datasets was performed using Python (metric-learn), with dmrt1 and amh as must-link constraints. Cannot-link constraints were generated geometrically. Distance bounds were defined by percentile statistics (65th for cannot-link and 60th for must-link). Percentile thresholds (65th and 60th) were used because they balanced inclusiveness with discrimination: looser thresholds failed to separate anchors from background noise, while stricter cutoffs excluded known sex genes. These empirical values provided stable and reproducible spaces across multiple datasets. The python scripts for ITML are available in Supplementary Table S2 (Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). 2.7. Projection Following z-score standardization and stage-to-stage differences, the mouse data (77,232 genes; Table S3; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464) were projected into the ITML space trained on fish transcriptomes. The top 100 mouse genes closest to dmrt1 / amh anchors were extracted. The python scripts for projection are presented in Supplementary Table S4a and S4b (Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). 3. Results Here, I demonstrate a straightforward pipeline method and its result for cross-species projections. The workflow is illustrated in Figure 1. In the learned ITML space, classical sex genes (e.g., dmrt1a ) in bluehead wrasse were plotted around the must-link anchors (Figure 2, Table S5; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). Previous studies have suggested histological parallels between the Δ2 stage of sex change in bluehead wrasse and murine gonadal development between E11.5 and E13.5. 2, 14, 15 This correspondence was not used as an alignment constraint, but rather motivated the choice of this murine developmental window as a reference context for cross-species projection into the ITML space. As a result of this projection, some classical sex differentiation-related genes, including bmp8b , stra8 , dnmt3b , bmi1 , and tdrd1 , have been plotted around must-link anchors derived from protogynous fishes (Table S6a–d; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). 16–20 In addition, eleven murine genes ( bmp8b , dbndd1 , arl4d , stambp , best1 , aipl1 , Gm5475, Gm38351, Gm7932, Gm56886, and ENSMUSG00000138379) appeared in the proximity of two anchors. No murine genes appeared in the proximity of three or more anchors. Predicted or poorly annotated gene models, including Gm-designated loci and unnamed Ensembl gene IDs (ENSMUSG), were also retrieved. Notably, bmp8b , a gene well-known for its involvement in sex differentiation, was positioned close to both dmrt1 and amh of bluehead wrasse. Moreover, unannotated genes and potential lncRNAs were positioned close to the must-link anchors. 4. Discussion Through construction of ITML, 6 the observed organization of murine genes around anchors learned from protogynous fish suggests that cross-class metric learning captures conserved transcriptomic structure across species. In this study, the organization of murine genes was assessed not based on individual gene names or annotated functions, but on the geometry of stage-to-stage expression differences, represented as Δ vectors. Specifically, this geometry reflects similarity in the direction, gradient, magnitude, and temporal distribution of expression changes between successive developmental stages. 6 Under this framework, structural similarity can be captured even when the underlying gene sets differ, provided that the histological and developmental contexts are comparable. 21 Consistent with this view, the present analysis successfully recovered murine genes in close proximity to anchors defined by protogynous fish genes that are classically implicated in sex differentiation, without applying any functional or annotation-based gene selection. Importantly, the recovery of multiple well-established sex differentiation genes should not be interpreted as a trivial confirmation of known biology. Rather, it serves as an internal consistency check of the learned metric space, demonstrating that biologically meaningful signals can emerge without explicitly encoding gene identity or functional annotation. In the present analysis, only amh and dmrt1 were used as anchors. Genes positioned in close proximity to these anchors exhibited similarity in their expression change vectors across developmental stages. 6 As a consequence, a gene set containing classical sex differentiation genes emerged near the anchors in the learned space. Furthermore, several genes with established functions outside classical sex differentiation pathways were also positioned near the anchors. For example, dbndd1 is a testis-enriched gene predominantly expressed in post-meiotic male germ cells, 22 yet it appeared in close proximity to the anchors at earlier developmental stages in the present analysis. Similarly, aipl1 , which is classically characterized as a retina-associated chaperone factor, 23 was also positioned near the anchors despite its well-established role in the visual system. These genes may represent transcripts that are broadly stable and therefore tend to appear near multiple anchors. Alternatively, their positioning may reflect the reuse of conserved regulatory components in developmental contexts distinct from those in which they were originally characterized. 24 Based on ITML alone, these possibilities cannot be distinguished, and such genes are therefore best regarded as candidates with unresolved biological relevance rather than definitive regulators of sex differentiation. Notably, this also implies that uncharacterized genes located near the anchors share comparable expression dynamics with the anchors and with well-established sex differentiation genes, suggesting that they may participate in the same developmental trajectories despite lacking prior functional annotation. Because proximity in the ITML space is defined by similarity in expression dynamics rather than direct biological interaction, false-positive proximity cannot be excluded, and may in part reflect technical factors associated with transcriptome preprocessing and annotation. The positioning of bmp8b near both dmrt1 and amh is particularly notable, given its known role in coordinating early germ cell development and testis differentiation. 20 This spatial relationship supports the view that the learned space reflects higher-order regulatory organization rather than isolated gene effects. The anchors define reference directions within the developmental space, and genes located in their vicinity represent components belonging to the same organizational layer of gene expression underlying testis development. Indeed, bmp8b has been classically associated with cellular proliferation within the gonad and with interactions between germ cells and somatic cells, 20 and can therefore be regarded as belonging to the same developmental layer as amh and dmrt1 . In addition to annotated genes, the proximity of uncharacterized genes and potential lncRNAs to the must-link anchors highlights a key advantage of this approach: genes are prioritized based on their geometric relationship within the learned space rather than on prior annotation. This suggests that the framework may identify conserved regulatory components that are overlooked by annotation-driven analyses. The validity of the present approach has already been supported by its ability to recover classical sex differentiation genes in close proximity to the anchors. The appearance of lncRNAs and unannotated genes near the anchors further suggests that these genes may share comparable developmental relevance with the anchors during early mouse testis development. However, it should also be noted that the ITML thresholds employed in this study were intentionally set to relatively mild values. As a result, the possibility that some unrelated lncRNAs or unannotated genes were drawn toward the anchor vicinity due to this permissive parameter setting cannot be excluded. More broadly, this framework provides a structural reference for comparing developmental trajectories across species. Rather than claiming to resolve differentiation mechanisms directly, the method offers a way to evaluate whether transcriptomic changes follow comparable organizational paths. Rather than classifying genes based on their names or existing annotations, the present framework focuses on the geometric similarity of expression changes derived from the abstracted Δ1–Δ3 representation. This design confers robustness by avoiding dependence on specific annotation systems or functional definitions and, in principle, allows the same structural organization to be recovered even if annotation schemes are revised. At the same time, Δ1–Δ3 should be regarded as a coarse-grained approximation of developmental dynamics, prioritizing structural stability over local temporal precision. Consequently, the approach is inherently dependent on the definition of stage boundaries. Future incorporation of more finely resolved developmental stages or higher temporal resolution datasets is expected to enable a more detailed characterization of developmental trajectory geometry. Future applications may include retraining ITML with Δ3-weighted datasets to explore conserved regulators associated with later stages of gametogenesis, such as sperm maturation. In this context, the learned geometric space could serve as a reference for evaluating whether experimental differentiation systems, including iPS-derived models. In this sense, the approach functions as a conceptual compass rather than a recipe for differentiation. By projecting iPS-derived or in vitro differentiation data into a space defined by conserved developmental geometry, it becomes possible to assess whether observed transcriptional changes align with trajectories associated with stable germ cell maturation, as opposed to merely exhibiting marker gene expression. Such an evaluation framework may help distinguish transient or aberrant differentiation states from those that recapitulate conserved organizational patterns of gametogenesis. References Takahashi K, Yamanaka S, Induction of pluripotent stem cells from mouse embryonic and adult fibroblast cultures by defined factors. Cell 126 :663–76, 2006. 10.1016/j.cell.2006.07.024. Todd EV, Ortega-Recalde O, Liu H, Lamm MS, Rutherford KM, Cross H, et al., Stress, novel sex genes, and epigenetic reprogramming orchestrate socially controlled sex change. Sci Adv 5 :eaaw7006, 2019. 10.1126/sciadv.aaw7006. 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Zhao GQ, Deng K, Labosky PA, Liaw L, Hogan BL, The gene encoding bone morphogenetic protein 8B is required for the initiation and maintenance of spermatogenesis in the mouse. Genes Dev 10 :1657–1669, 1996. 10.1101/gad.10.13.1657. Stuart T, Satija R, Integrative single-cell analysis. Nat Rev Genet 20 : 257–272, 2019. 10.1038/s41576-019-0093-7 Hermo L, Pelletier RM, Cyr DG, Smith CE, Surfing the wave, cycle, life history, and genes/proteins expressed by testicular germ cells. Part 2: changes in spermatid organelles associated with development of spermatozoa. Microsc Res Tech . 73 :279–319, 2010. 10.1002/jemt.20787. Galieva A, Karabelsky A, Egorov AD, Restoring sight: The journey of AIPL1 from discovery to therapy. Int J Mol Sci . 26 :12066, 2005. 10.3390/ijms262412066. Macneil LT, Walhout AJ, Gene regulatory networks and the role of robustness and stochasticity in the control of gene expression. Genome Res . 21 :645–657, 2011. 10.1101/gr.097378.109. Table Table 1 is available in the Supplementary Files section. Additional Declarations The authors declare no competing interests. Supplementary Files Table1.xlsx Individual SRR accession numbers using in this study Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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Gene expression values were summarized, normalized (log2TPM, gene-wise z-score, and stage-wise Δ), and filtered by quantity- and difference-based criteria. The candidate sets were then used for information-theoretic metric learning (ITML) with \u003cem\u003edmrt1\u003c/em\u003e/\u003cem\u003eamh\u003c/em\u003e anchors, and the mouse genes were projected into the learned space.\u003c/p\u003e","description":"","filename":"Fig1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8564120/v1/5362ba0b8515a4f01450bbb9.jpg"},{"id":100106623,"identity":"2eb243fd-9ea2-40df-9cce-d4b7f2c98a76","added_by":"auto","created_at":"2026-01-13 05:21:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":680912,"visible":true,"origin":"","legend":"\u003cp\u003e3D ITML mapping learned from two protogynous fishes (\u003cem\u003edmrt1\u003c/em\u003e and \u003cem\u003eamh\u003c/em\u003e).\u003c/p\u003e\n\u003cp\u003eThe selected 5,857 genes were plotted in 3D (stage-wise differences) using ITML. \u003cem\u003edmrt1\u003c/em\u003eand \u003cem\u003eamh\u003c/em\u003e from bluehead wrasse and orange-spotted groupers were used as must-link constraints. Cannot-link constraints were automatically generated based on geometry-based criteria. Distance bounds for ITML were defined using percentile statistics (65th for cannot-link and 60th for must-link). Murine genes were projected onto the 3D ITML space.\u003c/p\u003e","description":"","filename":"Fig2itml3d.png","url":"https://assets-eu.researchsquare.com/files/rs-8564120/v1/7acee9f5c7c83f3e2cafc837.png"},{"id":100382045,"identity":"d22d916c-9b46-451b-8661-e7503097f6b6","added_by":"auto","created_at":"2026-01-16 10:40:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1850457,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8564120/v1/eeb13040-82c8-4485-80df-67f412b520e0.pdf"},{"id":100106619,"identity":"0e17a110-af11-4d12-9456-1f4cc6755bcc","added_by":"auto","created_at":"2026-01-13 05:21:31","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":10591,"visible":true,"origin":"","legend":"\u003cp\u003eIndividual SRR accession numbers using in this study\u003c/p\u003e","description":"","filename":"Table1.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8564120/v1/f0c093e169699a2bc4cc1d52.xlsx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eAn information-theoretic metric learning approach for cross-species transcriptome integration: Identifying sex differentiation transcriptomic structure between protogynous fishes and mouse\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn multicellular organisms, cell differentiation constitutes a central mechanism for sustaining life. While induced pluripotent stem (iPS) cell studies have advanced our understanding of differentiation mechanisms,\u003csup\u003e1\u003c/sup\u003e several aspects of sex differentiation remain unresolved. Although numerous studies have focused on individual genes involved in vertebrate sex differentiation, the higher-order regulatory architecture remains unresolved. The temporal sequence in which the network is activated, as well as the identity of any upstream master regulator, is still unclear. Moreover, while many vertebrate lineages employ a broadly similar set of conserved factors, how these components interact and how their regulatory wiring is organized differ across taxa and remain poorly understood. This lack of clarity highlights the need for biological systems in which large-scale reorganization of the sex differentiation program can be directly observed. Protogynous fishes, which undergo postnatal sex change, offer a unique comparative model. Protogynous sex change is a minority strategy among vertebrates, in which individuals mature first as females and subsequently transition to males. This transition typically occurs in social species, often those for hierarchical groups, where the reproductive opportunity of a dominant male creates strong selective pressure for rapid and coordinated remodeling of the gonad. As a result, protogynous sex change unfolds over a remarkably short timescale\u0026mdash;on the order of a week\u0026mdash;yet proceeds through histological stages that show notable parallels to the maturation processes observed in other vertebrate gonads. These features create a biological context in which large-scale transcriptomic reorganization occurs in a temporally well-defined manner, providing a tractable framework for examining how developmental modules are sequentially reorganized and whether such modules retain comparable geometric signatures across distant species. Here, consecutive transcriptomic transitions during sex change were summarized as stage-to-stage differences, denoted as \u0026Delta;1\u0026ndash;\u0026Delta;3 in this study, based on previously published gonadal staging of bluehead wrasse and orange-spotted grouper.\u003csup\u003e2, 3\u003c/sup\u003e Previous research suggests that transcriptomic shifts during sex change are not unique to fish but reflect conserved patterns across taxa.\u003csup\u003e2\u0026ndash;5\u003c/sup\u003e The aim here was simply to observe what emerges when mouse data are mapped into a transcriptomic space learned from sex-changing fish.\u003c/p\u003e\n\u003cp\u003eInformation-theoretic metric learning (ITML) is a method that adjusts distances in a data space so that certain pairs of data remain close together (must-link constraints) while others remain apart (cannot-link constraints).\u003csup\u003e6\u0026nbsp;\u003c/sup\u003eIn biological terms, a must-link means that two factors that act together in the same functional module are positioned close to each other in the learned space. Unlike principal component analysis (PCA), which reduces dimensions but produces axes without direct biological interpretation, or standard clustering methods, which require the researcher to predefine the number of clusters, ITML allows such biological relationships to directly shape the geometry of the space. Gene sets involved in developmental processes often display coordinated expression patterns, which can be interpreted as geometric relationships in transcriptomic space. This view, widely adopted in systems biology, provides a conceptual basis for examining whether such organizational principles persist across species.\u003csup\u003e7\u003c/sup\u003e This makes it particularly suitable for testing whether conserved organization of sex differentiation genes emerges across species. By anchoring the learned space with biologically meaningful constraints, ITML provides a principled framework for investigating whether similar developmental trajectories give rise to comparable geometric organization across species. Studies on gene expression during sexual differentiation have revealed classical regulatory pathways. For instance, \u003cem\u003edmrt1\u003c/em\u003e functions as a key regulator of male development, whereas \u003cem\u003eamh\u003c/em\u003e acts as a major inhibitor of female development.\u003csup\u003e8\u003c/sup\u003e In this study, \u003cem\u003edmrt1\u003c/em\u003e and \u003cem\u003eamh\u003c/em\u003e were used as must-link constraints because both are widely recognized opposing regulators of vertebrate sex differentiation. Their well-established antagonistic roles make them convenient and interpretable anchors for structuring the learned space.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMost previous studies of sex differentiation have focused on individual genes, their names, or their annotated molecular functions,\u003csup\u003e8, 9\u003c/sup\u003e rather than on the structural relationships among their expression trajectories. The central question of this study is whether biologically meaningful organization emerges when sex-related genes are compared not by their names or annotated functions, but by the geometry of their stage-to-stage expression changes.\u003c/p\u003e"},{"header":"2.\tMaterials \u0026 Methods","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.1. Datasets\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;RNA-seq datasets of bluehead wrasse (\u003cem\u003eThalassoma bifasciatum\u003c/em\u003e, control female stage, stage 3, stage 4, and terminal male stage from PRJNA293777), orange-spotted grouper (\u003cem\u003eEpinephelus coioides\u003c/em\u003e, ovarian phase 4, early stage, late stage, and testis phase from PRJDB9134), and mouse (\u003cem\u003eMus musculus\u003c/em\u003e, embryonic days 9.5, 11.5, and 13.5 from PRJNA178509 and postnatal day 6 from PRJNA189510)\u003csup\u003e2, 3, 10, 11\u003c/sup\u003e were obtained from the Sequence Read Archive. Individual SRR accession numbers are listed in Supplementary Table 1. In this study, stage-to-stage differences (\u0026Delta;1\u0026ndash;\u0026Delta;3) were defined as three representative transcriptomic transitions extracted from each species\u0026rsquo; staging system. Although the source studies include additional early or late phases, these show minimal deviation relative to adjacent stages and thus contribute little to capturing the principal developmental trajectory. \u0026Delta;1 represents the initial shift from a preceding stable state. \u0026Delta;2 corresponds to the intermediate transition along the trajectory, situated between the early and late phases. \u0026Delta;3 represents the late-stage transition, characterized by movement toward the masculinized or differentiated state as the trajectory approaches its final configuration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.2. Processing\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eReads were processed on the Galaxy platform (Trimmomatic, FastQC, Salmon, Trinity).\u003csup\u003e12\u0026nbsp;\u003c/sup\u003eThe Galaxy environment was chosen because it provides a fully documented, reproducible workflow with widely adopted community tools, thereby ensuring transparency and accessibility, especially for complex multi-species RNA-seq datasets, and avoiding tool-specific biases by standardizing the preprocessing steps.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.3. Summarizing and annotation\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTranscript-level counts were summarized using R (tximport). Protein annotation was performed using DIAMOND blastx against the UniProtKB protein FASTA file for Actinopterygii (NCBI Taxonomy ID: 7898).\u003csup\u003e13\u0026nbsp;\u003c/sup\u003eMurine RNA-seq data were processed as in fish, except that GENCODE release M37 (GRCm39) was used in tximport.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.4. Normalization\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePython was used for the downstream steps. Expression values were transformed as log2(TPM+1) and standardized to gene-wise z-scores. TPM normalization allows comparability across samples. The log2(TPM+1) transformation stabilizes variance and reduces the skewness of highly expressed genes while preserving dynamic range, making the data more suitable for downstream clustering and metric learning. The \u0026ldquo;+1\u0026rdquo; avoids undefined values for low-abundance genes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.5. Gene filtering\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFish datasets were filtered. Two complementary filters were used to capture highly expressed and dynamically changing genes. (i) A quantity-based filter retained the top 1,500 genes by total log2(TPM+1) across stages. (ii) A difference-based filter emphasized mid-transition by requiring \u0026Delta;2 to fall within the top 30%\u0026nbsp;of\u0026nbsp;\u0026Delta;2\u0026nbsp;values\u0026nbsp;and exceed both \u0026Delta;1 and \u0026Delta;3. From this subset, genes were further filtered by requiring both \u0026Delta;1 and \u0026Delta;3 to fall within the top 15% and retaining the intersection of these sets. This final set was ranked by \u0026Delta;1, and the top 1,500 genes were selected, reflecting the focus on mid- and early transition. The union of these sets (5,857 genes) was regarded as a candidate sex change-related gene for each species (Table S1; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). This dual filter captured both quantitatively abundant genes and those with dynamic stage-specific changes. Focusing on \u0026Delta;2 reflects histological studies, demonstrating that mid-transition stages share some similarities with murine E11.5\u0026ndash;E13.5 differentiation.\u003csup\u003e14\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.6. Metric learning\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eITML based on filtered fish datasets was performed using Python (metric-learn), with \u003cem\u003edmrt1\u003c/em\u003e and \u003cem\u003eamh\u0026nbsp;\u003c/em\u003eas must-link constraints. Cannot-link constraints were generated geometrically. Distance bounds were defined by percentile statistics (65th for cannot-link and 60th for must-link). Percentile thresholds (65th and 60th) were used because they balanced inclusiveness with discrimination: looser thresholds failed to separate anchors from background noise, while stricter cutoffs excluded known sex genes. These empirical values provided stable and reproducible spaces across multiple datasets. The python scripts for ITML are available in Supplementary Table S2 (Zenodo DOI: https://doi.org/10.5281/zenodo.18189464).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.7. Projection\u003c/em\u003e\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFollowing z-score standardization and stage-to-stage differences, the mouse data (77,232 genes; Table S3; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464) were projected into the ITML space trained on fish transcriptomes. The top 100 mouse genes closest to \u003cem\u003edmrt1\u003c/em\u003e/\u003cem\u003eamh\u003c/em\u003e anchors were extracted. The python scripts for projection are presented in Supplementary Table S4a and S4b (Zenodo DOI: https://doi.org/10.5281/zenodo.18189464).\u003c/p\u003e"},{"header":"3. Results","content":"\u003cp\u003eHere, I demonstrate a straightforward pipeline method and its result for cross-species projections. The workflow is illustrated in Figure 1. In the learned ITML space, classical sex genes (e.g., \u003cem\u003edmrt1a\u003c/em\u003e) in bluehead wrasse were plotted around the must-link anchors (Figure 2, Table S5; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464). Previous studies have suggested histological parallels between the \u0026Delta;2 stage of sex change in bluehead wrasse and murine gonadal development between E11.5 and E13.5.\u003csup\u003e2, 14, 15\u003c/sup\u003e This correspondence was not used as an alignment constraint, but rather motivated the choice of this murine developmental window as a reference context for cross-species projection into the ITML space. As a result of this projection, some classical sex differentiation-related genes, including \u003cem\u003ebmp8b\u003c/em\u003e, \u003cem\u003estra8\u003c/em\u003e, \u003cem\u003ednmt3b\u003c/em\u003e, \u003cem\u003ebmi1\u003c/em\u003e, and \u003cem\u003etdrd1\u003c/em\u003e, have been plotted around must-link anchors derived from protogynous fishes (Table S6a\u0026ndash;d; Zenodo DOI: https://doi.org/10.5281/zenodo.18189464).\u003csup\u003e16\u0026ndash;20\u003c/sup\u003e In addition, eleven murine genes (\u003cem\u003ebmp8b\u003c/em\u003e, \u003cem\u003edbndd1\u003c/em\u003e, \u003cem\u003earl4d\u003c/em\u003e, \u003cem\u003estambp\u003c/em\u003e, \u003cem\u003ebest1\u003c/em\u003e, \u003cem\u003eaipl1\u003c/em\u003e, Gm5475, Gm38351, Gm7932, Gm56886, and ENSMUSG00000138379) appeared in the proximity of two anchors. No murine genes appeared in the proximity of three or more anchors. Predicted or poorly annotated gene models, including Gm-designated loci and unnamed Ensembl gene IDs (ENSMUSG), were also retrieved. Notably, \u003cem\u003ebmp8b\u003c/em\u003e, a gene well-known for its involvement in sex differentiation, was positioned close to both \u003cem\u003edmrt1\u003c/em\u003e and \u003cem\u003eamh\u003c/em\u003e of bluehead wrasse. Moreover, unannotated genes and potential lncRNAs were positioned close to the must-link anchors.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"4.\tDiscussion","content":"\u003cp\u003eThrough construction of ITML,\u003csup\u003e6\u003c/sup\u003e the observed organization of murine genes around anchors learned from protogynous fish suggests that cross-class metric learning captures conserved transcriptomic structure across species. In this study, the organization of murine genes was assessed not based on individual gene names or annotated functions, but on the geometry of stage-to-stage expression differences, represented as \u0026Delta; vectors. Specifically, this geometry reflects similarity in the direction, gradient, magnitude, and temporal distribution of expression changes between successive developmental stages.\u003csup\u003e6\u003c/sup\u003e Under this framework, structural similarity can be captured even when the underlying gene sets differ, provided that the histological and developmental contexts are comparable.\u003csup\u003e21\u003c/sup\u003e Consistent with this view, the present analysis successfully recovered murine genes in close proximity to anchors defined by protogynous fish genes that are classically implicated in sex differentiation, without applying any functional or annotation-based gene selection.\u003c/p\u003e\n\u003cp\u003eImportantly, the recovery of multiple well-established sex differentiation genes should not be interpreted as a trivial confirmation of known biology. Rather, it serves as an internal consistency check of the learned metric space, demonstrating that biologically meaningful signals can emerge without explicitly encoding gene identity or functional annotation. In the present analysis, only \u003cem\u003eamh\u003c/em\u003e and \u003cem\u003edmrt1\u003c/em\u003e were used as anchors. Genes positioned in close proximity to these anchors exhibited similarity in their expression change vectors across developmental stages.\u003csup\u003e6\u003c/sup\u003e As a consequence, a gene set containing classical sex differentiation genes emerged near the anchors in the learned space. Furthermore, several genes with established functions outside classical sex differentiation pathways were also positioned near the anchors. For example, \u003cem\u003edbndd1\u003c/em\u003e is a testis-enriched gene predominantly expressed in post-meiotic male germ cells,\u003csup\u003e22\u003c/sup\u003e yet it appeared in close proximity to the anchors at earlier developmental stages in the present analysis. Similarly, \u003cem\u003eaipl1\u003c/em\u003e, which is classically characterized as a retina-associated chaperone factor,\u003csup\u003e23\u003c/sup\u003e was also positioned near the anchors despite its well-established role in the visual system. These genes may represent transcripts that are broadly stable and therefore tend to appear near multiple anchors. Alternatively, their positioning may reflect the reuse of conserved regulatory components in developmental contexts distinct from those in which they were originally characterized.\u003csup\u003e24\u003c/sup\u003e Based on ITML alone, these possibilities cannot be distinguished, and such genes are therefore best regarded as candidates with unresolved biological relevance rather than definitive regulators of sex differentiation. Notably, this also implies that uncharacterized genes located near the anchors share comparable expression dynamics with the anchors and with well-established sex differentiation genes, suggesting that they may participate in the same developmental trajectories despite lacking prior functional annotation. Because proximity in the ITML space is defined by similarity in expression dynamics rather than direct biological interaction, false-positive proximity cannot be excluded, and may in part reflect technical factors associated with transcriptome preprocessing and annotation.\u003c/p\u003e\n\u003cp\u003eThe positioning of \u003cem\u003ebmp8b\u003c/em\u003e near both \u003cem\u003edmrt1\u003c/em\u003e and \u003cem\u003eamh\u003c/em\u003e is particularly notable, given its known role in coordinating early germ cell development and testis differentiation.\u003csup\u003e20\u003c/sup\u003e This spatial relationship supports the view that the learned space reflects higher-order regulatory organization rather than isolated gene effects. The anchors define reference directions within the developmental space, and genes located in their vicinity represent components belonging to the same organizational layer of gene expression underlying testis development. Indeed, \u003cem\u003ebmp8b\u003c/em\u003e has been classically associated with cellular proliferation within the gonad and with interactions between germ cells and somatic cells,\u003csup\u003e20\u003c/sup\u003e and can therefore be regarded as belonging to the same developmental layer as \u003cem\u003eamh\u003c/em\u003e and \u003cem\u003edmrt1\u003c/em\u003e.\u003c/p\u003e\n\u003cp\u003eIn addition to annotated genes, the proximity of uncharacterized genes and potential lncRNAs to the must-link anchors highlights a key advantage of this approach: genes are prioritized based on their geometric relationship within the learned space rather than on prior annotation. This suggests that the framework may identify conserved regulatory components that are overlooked by annotation-driven analyses. The validity of the present approach has already been supported by its ability to recover classical sex differentiation genes in close proximity to the anchors. The appearance of lncRNAs and unannotated genes near the anchors further suggests that these genes may share comparable developmental relevance with the anchors during early mouse testis development. However, it should also be noted that the ITML thresholds employed in this study were intentionally set to relatively mild values. As a result, the possibility that some unrelated lncRNAs or unannotated genes were drawn toward the anchor vicinity due to this permissive parameter setting cannot be excluded.\u003c/p\u003e\n\u003cp\u003eMore broadly, this framework provides a structural reference for comparing developmental trajectories across species. Rather than claiming to resolve differentiation mechanisms directly, the method offers a way to evaluate whether transcriptomic changes follow comparable organizational paths. Rather than classifying genes based on their names or existing annotations, the present framework focuses on the geometric similarity of expression changes derived from the abstracted \u0026Delta;1\u0026ndash;\u0026Delta;3 representation. This design confers robustness by avoiding dependence on specific annotation systems or functional definitions and, in principle, allows the same structural organization to be recovered even if annotation schemes are revised. At the same time, \u0026Delta;1\u0026ndash;\u0026Delta;3 should be regarded as a coarse-grained approximation of developmental dynamics, prioritizing structural stability over local temporal precision. Consequently, the approach is inherently dependent on the definition of stage boundaries. Future incorporation of more finely resolved developmental stages or higher temporal resolution datasets is expected to enable a more detailed characterization of developmental trajectory geometry.\u003c/p\u003e\n\u003cp\u003eFuture applications may include retraining ITML with \u0026Delta;3-weighted datasets to explore conserved regulators associated with later stages of gametogenesis, such as sperm maturation. In this context, the learned geometric space could serve as a reference for evaluating whether experimental differentiation systems, including iPS-derived models. In this sense, the approach functions as a conceptual compass rather than a recipe for differentiation. By projecting iPS-derived or \u003cem\u003ein vitro\u0026nbsp;\u003c/em\u003edifferentiation data into a space defined by conserved developmental geometry, it becomes possible to assess whether observed transcriptional changes align with trajectories associated with stable germ cell maturation, as opposed to merely exhibiting marker gene expression. Such an evaluation framework may help distinguish transient or aberrant differentiation states from those that recapitulate conserved organizational patterns of gametogenesis.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTakahashi K, Yamanaka S, Induction of pluripotent stem cells from mouse embryonic and adult fibroblast cultures by defined factors. \u003cem\u003eCell\u003c/em\u003e \u003cstrong\u003e126\u003c/strong\u003e:663\u0026ndash;76, 2006. 10.1016/j.cell.2006.07.024.\u003c/li\u003e\n\u003cli\u003eTodd EV, Ortega-Recalde O, Liu H, Lamm MS, Rutherford KM, Cross H, et al., Stress, novel sex genes, and epigenetic reprogramming orchestrate socially controlled sex change. \u003cem\u003eSci Adv\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e:eaaw7006, 2019. 10.1126/sciadv.aaw7006.\u003c/li\u003e\n\u003cli\u003eWu X, Yang Y, Zhong C, Guo Y, Wei T, Li S, Lin H, Liu X, Integration of ATAC-seq and RNA-seq unravels chromatin accessibility during 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Here, I applied information-theoretic metric learning (ITML) to project mouse testis RNA-seq data into a three-dimensional space trained on protogynous fish transcriptomes, using stage-to-stage expression change geometry rather than gene identity or annotation. ITML was anchored with \u003cem\u003edmrt1\u003c/em\u003eand \u003cem\u003eamh\u003c/em\u003e, revealing conserved clustering of known sex differentiation genes (e.g., \u003cem\u003ebmp8b\u003c/em\u003e and \u003cem\u003estra8\u003c/em\u003e). Rather than serving as a direct differentiation model, this framework provides a structural reference for evaluating whether transcriptomic changes align with conserved developmental trajectories, offering a framework for identifying novel candidates in mammalian sex differentiation.\u003c/p\u003e","manuscriptTitle":"An information-theoretic metric learning approach for cross-species transcriptome integration: Identifying sex differentiation transcriptomic structure between protogynous fishes and mouse","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-13 05:21:26","doi":"10.21203/rs.3.rs-8564120/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"64312d81-3a7a-4555-88a3-d451dc59a969","owner":[],"postedDate":"January 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61036889,"name":"Computational Biology"}],"tags":[],"updatedAt":"2026-01-13T05:21:26+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-13 05:21:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8564120","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8564120","identity":"rs-8564120","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}