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<!DOCTYPE html> <html lang="en" class="no-js"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="applicable-device" content="pc,mobile"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="robots" content="max-image-preview:large"> <meta name="access" content="Yes"> <meta name="robots" content="noindex"> <meta name="360-site-verification" content="1268d79b5e96aecf3ff2a7dac04ad990" /> <title>Deconvolution and inference of spatial communication through optimization algorithm for spatial transcriptomics | Communications Biology </title> <meta name="journal_id" content="42003"/> <meta name="dc.title" content="Deconvolution and inference of spatial communication through optimization algorithm for spatial transcriptomics"/> <meta name="dc.source" content="Communications Biology 2025 8:1"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Nature Publishing Group"/> <meta name="dc.date" content="2025-02-14"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2025 The Author(s)"/> <meta name="dc.rights" content="2025 The Author(s)"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="Spatial transcriptomics technologies can capture gene expression at spatial loci. However, at certain resolutions, the obtained gene expression reflects the sum of either a heterogeneous or homogeneous set of cells, rather than individual cell. This limitation gives rise to the deconvolution algorithm to make cell-type inferences at each location. Yet, the vast majority of deconvolution methods that have been developed ignore the spatial information of the tissue and the communications between the cells or spots. To overcome these afflictions, we proposed a deconvolution method, non-negative least squares-based and optimization search-based deconvolution (NODE), that combines cell-type-specific information from single-cell RNA sequencing (scRNA-seq) and intercellular communications in tissue. NODE deconvolution algorithm, incorporating the spatial information of the tissue, allows us to quantify intercellular communications at the same instant. NODE can not only utilize optimization method to infer the deconvolution results of spatial transcriptomics data and reduce the probability of overfitting situations, but also make reasonable inferences for spatial communications. Subsequently, we applied NODE to four datasets to validate the correctness of the NODE deconvolution results and compare them with existing deconvolution algorithms. NODE also inferred spatial communications and validated them in tissue development of human heart. The non-negative least squares-based and optimization search-based deconvolution (NODE) algorithm employs optimization principles to elucidate cellular composition and spatial interactions within spatial transcriptomic data."/> <meta name="prism.issn" content="2399-3642"/> <meta name="prism.publicationName" content="Communications Biology"/> <meta name="prism.publicationDate" content="2025-02-14"/> <meta name="prism.volume" content="8"/> <meta name="prism.number" content="1"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="16"/> <meta name="prism.copyright" content="2025 The Author(s)"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://link.springer.com/articles/s42003-025-07625-8"/> <meta name="prism.doi" content="doi:10.1038/s42003-025-07625-8"/> <meta name="citation_pdf_url" content="https://www.nature.com/articles/s42003-025-07625-8.pdf"/> <meta name="citation_fulltext_html_url" content="https://link.springer.com/articles/s42003-025-07625-8"/> <meta name="citation_journal_title" content="Communications Biology"/> <meta name="citation_journal_abbrev" content="Commun Biol"/> <meta name="citation_publisher" content="Nature Publishing Group"/> <meta name="citation_issn" content="2399-3642"/> <meta name="citation_title" content="Deconvolution and inference of spatial communication through optimization algorithm for spatial transcriptomics"/> <meta name="citation_volume" content="8"/> <meta name="citation_issue" content="1"/> <meta name="citation_online_date" content="2025/02/14"/> <meta name="citation_firstpage" content="1"/> <meta name="citation_lastpage" content="16"/> <meta name="citation_article_type" content="Article"/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1038/s42003-025-07625-8"/> <meta name="DOI" content="10.1038/s42003-025-07625-8"/> <meta name="size" content="228666"/> <meta name="citation_doi" content="10.1038/s42003-025-07625-8"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1038/s42003-025-07625-8&api_key="/> <meta name="description" content="Spatial transcriptomics technologies can capture gene expression at spatial loci. However, at certain resolutions, the obtained gene expression reflects the sum of either a heterogeneous or homogeneous set of cells, rather than individual cell. This limitation gives rise to the deconvolution algorithm to make cell-type inferences at each location. Yet, the vast majority of deconvolution methods that have been developed ignore the spatial information of the tissue and the communications between the cells or spots. To overcome these afflictions, we proposed a deconvolution method, non-negative least squares-based and optimization search-based deconvolution (NODE), that combines cell-type-specific information from single-cell RNA sequencing (scRNA-seq) and intercellular communications in tissue. NODE deconvolution algorithm, incorporating the spatial information of the tissue, allows us to quantify intercellular communications at the same instant. NODE can not only utilize optimization method to infer the deconvolution results of spatial transcriptomics data and reduce the probability of overfitting situations, but also make reasonable inferences for spatial communications. Subsequently, we applied NODE to four datasets to validate the correctness of the NODE deconvolution results and compare them with existing deconvolution algorithms. NODE also inferred spatial communications and validated them in tissue development of human heart. The non-negative least squares-based and optimization search-based deconvolution (NODE) algorithm employs optimization principles to elucidate cellular composition and spatial interactions within spatial transcriptomic data."/> <meta name="dc.creator" content="Wang, Zedong"/> <meta name="dc.creator" content="Liu, Yi"/> <meta name="dc.creator" content="Chang, Xiao"/> <meta name="dc.creator" content="Liu, Xiaoping"/> <meta name="dc.subject" content="Computational models"/> <meta name="dc.subject" content="Software"/> <meta name="citation_reference" content="citation_journal_title=Nat. Rev. Genet.; citation_title=Spatial transcriptomics coming of age; citation_author=D. J Burgess; citation_volume=20; citation_publication_date=2019; citation_pages=317-317; citation_doi=10.1038/s41576-019-0129-z; citation_id=CR1"/> <meta name="citation_reference" content="Soldatov, R. et al. Spatiotemporal structure of cell fate decisions in murine neural crest. 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However, at certain resolutions, the obtained gene expression reflects the sum of either a heterogeneous or homogeneous set of cells, rather than individual cell. This limitation gives rise to the deconvolution algorithm to make cell-type inferences at each location. Yet, the vast majority of deconvolution methods that have been developed ignore the spatial information of the tissue and the communications between the cells or spots. To overcome these afflictions, we proposed a deconvolution method, non-negative least squares-based and optimization search-based deconvolution (NODE), that combines cell-type-specific information from single-cell RNA sequencing (scRNA-seq) and intercellular communications in tissue. NODE deconvolution algorithm, incorporating the spatial information of the tissue, allows us to quantify intercellular communications at the same instant. NODE can not only utilize optimization method to infer the deconvolution results of spatial transcriptomics data and reduce the probability of overfitting situations, but also make reasonable inferences for spatial communications. Subsequently, we applied NODE to four datasets to validate the correctness of the NODE deconvolution results and compare them with existing deconvolution algorithms. NODE also inferred spatial communications and validated them in tissue development of human heart."/> <meta property="og:image" content="https://static-content.springer.com/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig1_HTML.png"/> <meta name="format-detection" content="telephone=no"> <link rel="apple-touch-icon" sizes="180x180" href=/oscar-static/img/favicons/darwin/apple-touch-icon-92e819bf8a.png> <link rel="icon" type="image/png" sizes="192x192" href=/oscar-static/img/favicons/darwin/android-chrome-192x192-6f081ca7e5.png> <link rel="icon" type="image/png" sizes="32x32" href=/oscar-static/img/favicons/darwin/favicon-32x32-1435da3e82.png> <link rel="icon" type="image/png" sizes="16x16" href=/oscar-static/img/favicons/darwin/favicon-16x16-ed57f42bd2.png> <link rel="shortcut icon" data-test="shortcut-icon" href=/oscar-static/img/favicons/darwin/favicon-c6d59aafac.ico> <meta name="theme-color" content="#e6e6e6">   <link rel="stylesheet" media="print" 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NODE can not only utilize optimization method to infer the deconvolution results of spatial transcriptomics data and reduce the probability of overfitting situations, but also make reasonable inferences for spatial communications. Subsequently, we applied NODE to four datasets to validate the correctness of the NODE deconvolution results and compare them with existing deconvolution algorithms. NODE also inferred spatial communications and validated them in tissue development of human heart. The non-negative least squares-based and optimization search-based deconvolution (NODE) algorithm employs optimization principles to elucidate cellular composition and spatial interactions within spatial transcriptomic data.","datePublished":"2025-02-14T00:00:00Z","dateModified":"2025-02-14T00:00:00Z","pageStart":"1","pageEnd":"16","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","sameAs":"https://doi.org/10.1038/s42003-025-07625-8","keywords":["Computational models","Software","Life 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Biology","issn":["2399-3642"],"volumeNumber":"8","@type":["Periodical","PublicationVolume"]},"publisher":{"name":"Nature Publishing Group UK","logo":{"url":"https://www.springernature.com/app-sn/public/images/logo-springernature.png","@type":"ImageObject"},"@type":"Organization"},"author":[{"name":"Zedong Wang","affiliation":[{"name":"University of Chinese Academy of Sciences","address":{"name":"Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Yi Liu","affiliation":[{"name":"Shandong University","address":{"name":"School of Mathematics and Statistics, Shandong University, Weihai, China","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Xiao Chang","affiliation":[{"name":"Anhui University of Finance and Economics","address":{"name":"Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, China","@type":"PostalAddress"},"@type":"Organization"}],"email":"chxlaugh@aufe.edu.cn","@type":"Person"},{"name":"Xiaoping Liu","url":"http://orcid.org/0000-0002-3246-4227","affiliation":[{"name":"University of Chinese Academy of Sciences","address":{"name":"Key Laboratory of Systems Health Science of Zhejiang Province, School of Life Science, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China","@type":"PostalAddress"},"@type":"Organization"}],"email":"xpliu@ucas.ac.cn","@type":"Person"}],"isAccessibleForFree":true,"@type":"ScholarlyArticle"},"@context":"https://schema.org","@type":"WebPage"}</script> </head> <body class="" >  <noscript> <iframe src="https://www.googletagmanager.com/ns.html?id=GTM-MRVXSHQ" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript>   <noscript data-test="gtm-body"> <iframe 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</div> </div> </div> </div> </div> <div class="c-article-header"> <header> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Zedong-Wang-Aff1" data-author-popup="auth-Zedong-Wang-Aff1" data-author-search="Wang, Zedong">Zedong Wang</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup>, </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Yi-Liu-Aff2" data-author-popup="auth-Yi-Liu-Aff2" data-author-search="Liu, Yi">Yi Liu</a><sup class="u-js-hide"><a href="#Aff2">2</a></sup>, </li><li class="c-article-author-list__item c-article-author-list__item--hide-small-screen"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Xiao-Chang-Aff3" data-author-popup="auth-Xiao-Chang-Aff3" data-author-search="Chang, Xiao" data-corresp-id="c1">Xiao Chang<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><sup class="u-js-hide"><a href="#Aff3">3</a></sup> & </li><li class="c-article-author-list__show-more" aria-label="Show all 4 authors for this article" title="Show all 4 authors for this article">…</li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Xiaoping-Liu-Aff1" data-author-popup="auth-Xiaoping-Liu-Aff1" data-author-search="Liu, Xiaoping" data-corresp-id="c2">Xiaoping Liu<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><span class="u-js-hide"> <a class="js-orcid" href="http://orcid.org/0000-0002-3246-4227"><span class="u-visually-hidden">ORCID: </span>orcid.org/0000-0002-3246-4227</a></span><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul><button aria-expanded="false" class="c-article-author-list__button"><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-down-medium"></use></svg><span>Show authors</span></button> <div data-test="article-metrics"> <ul class="app-article-metrics-bar u-list-reset"> <li class="app-article-metrics-bar__item"> <p class="app-article-metrics-bar__count"><svg class="u-icon app-article-metrics-bar__icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-accesses-medium"></use> </svg>612 <span class="app-article-metrics-bar__label">Accesses</span></p> </li> <li class="app-article-metrics-bar__item app-article-metrics-bar__item--metrics"> <p class="app-article-metrics-bar__details"><a href="/article/10.1038/s42003-025-07625-8/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Explore all metrics <svg class="u-icon app-article-metrics-bar__arrow-icon" width="24" height="24" aria-hidden="true" focusable="false"> <use xlink:href="#icon-eds-i-arrow-right-medium"></use> </svg></a></p> </li> </ul> </div> <div class="u-mt-32"> </div> </header> </div> <div data-article-body="true" data-track-component="article body" class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>Spatial transcriptomics technologies can capture gene expression at spatial loci. However, at certain resolutions, the obtained gene expression reflects the sum of either a heterogeneous or homogeneous set of cells, rather than individual cell. This limitation gives rise to the deconvolution algorithm to make cell-type inferences at each location. Yet, the vast majority of deconvolution methods that have been developed ignore the spatial information of the tissue and the communications between the cells or spots. To overcome these afflictions, we proposed a deconvolution method, non-negative least squares-based and optimization search-based deconvolution (NODE), that combines cell-type-specific information from single-cell RNA sequencing (scRNA-seq) and intercellular communications in tissue. NODE deconvolution algorithm, incorporating the spatial information of the tissue, allows us to quantify intercellular communications at the same instant. NODE can not only utilize optimization method to infer the deconvolution results of spatial transcriptomics data and reduce the probability of overfitting situations, but also make reasonable inferences for spatial communications. Subsequently, we applied NODE to four datasets to validate the correctness of the NODE deconvolution results and compare them with existing deconvolution algorithms. NODE also inferred spatial communications and validated them in tissue development of human heart.</p></div></div></section> <div data-test="cobranding-download"> </div> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1186%2Fs13059-021-02362-7/MediaObjects/13059_2021_2362_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1186/s13059-021-02362-7?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1186/s13059-021-02362-7">SpatialDWLS: accurate deconvolution of spatial transcriptomic data </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">10 May 2021</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41467-023-37168-7/MediaObjects/41467_2023_37168_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1038/s41467-023-37168-7?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1038/s41467-023-37168-7">A comprehensive benchmarking with practical guidelines for cellular deconvolution of spatial transcriptomics </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">21 March 2023</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41467-020-15968-5/MediaObjects/41467_2020_15968_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://link.springer.com/10.1038/s41467-020-15968-5?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1038/s41467-020-15968-5">Inferring spatial and signaling relationships between cells from single cell transcriptomic data </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">29 April 2020</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1739921609, embedded_user: 'null' } }); </script> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1">Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>Spatially resolved transcriptomics technologies enable gene analysis to be conducted in situ on various tissues, resulting in gene expression data that inherently contains spatial information<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="Burgess, D. 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 (2021)." href="#ref-CR8" id="ref-link-section-d68010897e420_6">8</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Fischl, A. M., Heron, P. M., Stromberg, A. J. & McClintock, T. S. Activity-Dependent Genes in Mouse Olfactory Sensory Neurons. Chem. Senses 39, 439–449 (2014)." href="#ref-CR9" id="ref-link-section-d68010897e420_7">9</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 10" title="Moses, L. & Pachter, L. Museum of spatial transcriptomics. Nat. Methods 19, 534–546 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR10" id="ref-link-section-d68010897e423">10</a></sup>. However, most technologies are still limited by spatial resolution, and most of gene expression measurements of tissue in situ consist of a few heterogeneous cells rather than single cell<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Asp, M., Bergenstråhle, J. & Lundeberg, J. Spatially Resolved Transcriptomes-Next Generation Tools for Tissue Exploration. BioEssays: N. Rev. Mol., Cell. Dev. Biol. 42, e1900221 (2020)." href="#ref-CR11" id="ref-link-section-d68010897e427">11</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Rodriques, S. G. et al. Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Sci. (N. Y., N. Y.) 363, 1463–1467 (2019)." href="#ref-CR12" id="ref-link-section-d68010897e427_1">12</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Sci. (N. Y., N. Y.) 353, 78–82 (2016)." href="/article/10.1038/s42003-025-07625-8#ref-CR13" id="ref-link-section-d68010897e430">13</a></sup>. The limitation of spatial transcriptomics technology is due to the gene expression at each location of spatial transcriptomics data to be a mixture of a few cells. Therefore, deconvolution for each position of spatial transcriptomics data becomes an important task to reveal the spatial localization of cell types and characterize complex organizational structures<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 14" title="Liao, J., Lu, X., Shao, X., Zhu, L. & Fan, X. Uncovering an Organ’s Molecular Architecture at Single-Cell Resolution by Spatially Resolved Transcriptomics. Trends Biotechnol. 39, 43–58 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR14" id="ref-link-section-d68010897e434">14</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 15" title="Rao, A., Barkley, D., França, G. S. & Yanai, I. Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR15" id="ref-link-section-d68010897e437">15</a></sup>. The single-cell RNA sequencing (scRNA-seq) technology<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 16" title="Hwang, B., Lee, J. H. & Bang, D. Single-cell RNA sequencing technologies and bioinformaticspipelines. Exp. Mol. Med. 50, 1–14 (2018)." href="/article/10.1038/s42003-025-07625-8#ref-CR16" id="ref-link-section-d68010897e441">16</a></sup> can detect gene expression of each individual cell and plays a crucial role in aiding deconvolution algorithms to resolve cellular composition in spatial transcriptomics data.</p><p>The deconvolution algorithms designed for spatial transcriptomics data necessitate cell-type labeling data obtained from scRNA-seq<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 16" title="Hwang, B., Lee, J. H. & Bang, D. Single-cell RNA sequencing technologies and bioinformaticspipelines. Exp. Mol. Med. 50, 1–14 (2018)." href="/article/10.1038/s42003-025-07625-8#ref-CR16" id="ref-link-section-d68010897e448">16</a></sup>, such as SpaTalk<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Shao, X. et al. Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk. Nat. Commun. 13, 4429 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR17" id="ref-link-section-d68010897e452">17</a></sup>, RCTD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Cable, D. M. et al. Robust decomposition of cell type mixtures in spatial transcriptomics. Nat. Biotechnol. 40, 517–526 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR18" id="ref-link-section-d68010897e456">18</a></sup>, deconvSeq<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Andersson, A. et al. Single-cell and spatial transcriptomics enables probabilistic inference of cell type topography. Commun. Biol. 3, 565 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR19" id="ref-link-section-d68010897e460">19</a></sup>, Seurat<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="Stuart, T. et al. Comprehensive Integration of Single-Cell Data. Cell 177, 1888–1902.e1821 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR20" id="ref-link-section-d68010897e464">20</a></sup> and SPOTlight<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Elosua-Bayes, M., Nieto, P., Mereu, E., Gut, I. & Heyn, H. SPOTlight: seeded NMF regression to deconvolute spatial transcriptomics spots with single-cell transcriptomes. Nucleic Acids Res. 49, e50 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR21" id="ref-link-section-d68010897e469">21</a></sup>. Deconvolution of spatial transcriptomics data requires not only appropriate reference data (scRNA-seq) for cell-type labeling, but also appropriate mathematical models and algorithms. However, few of these existing deconvolution approaches adequately takes into account the rich information of intercellular interactions, spatial communications and spatial localization information of spatial transcriptomics in their algorithm modelling.</p><p>In the natural state, the organization of organisms usually carries continuity<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Stoltzfus, C. R. et al. CytoMAP: A Spatial Analysis Toolbox Reveals Features of Myeloid Cell Organization in Lymphoid Tissues. Cell Rep. 31, 107523 (2020)." href="#ref-CR22" id="ref-link-section-d68010897e476">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Dudas, M., Wysocki, A., Gelpi, B. & Tuan, T.-L. Memory Encoded Throughout Our Bodies: Molecular and Cellular Basis of Tissue Regeneration. Pediatr. Res. 63, 502–512 (2008)." href="#ref-CR23" id="ref-link-section-d68010897e476_1">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Bove, A. et al. Local cellular neighborhood controls proliferation in cell competition. Mol. Biol. cell 28, 3215–3228 (2017)." href="#ref-CR24" id="ref-link-section-d68010897e476_2">24</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="van Vliet, S. et al. Spatially Correlated Gene Expression in Bacterial Groups: The Role of Lineage History, Spatial Gradients, and Cell-Cell Interactions. Cell Syst. 6, 496–507.e496 (2018)." href="/article/10.1038/s42003-025-07625-8#ref-CR25" id="ref-link-section-d68010897e479">25</a></sup>. Therefore, the spatial transcriptomics data may contain intercellular communications between spots in the same tissue. Specifically, tissues are composed of multiple cells, so the cells not only express genes individually, but also are influenced from neighbors or other cells. Therefore, we can consider the mutual influence among spots to design a deconvolution algorithm by modeling the spatial communications for close spatial spots.</p><p>Here, we proposed a deconvolution method with spatial communication inference, named non-negative least squares-based and optimization search-based deconvolution (NODE), for deconvolution of cell types and inference of spot-to-spot communications for spatial transcriptomics. NODE is based on an optimization search model and non-negative least squares problem to use scRNA-seq data for deconvoluting spatial transcriptomics data and inferring spatial communications. As a result, NODE not only can accurately deconvolute spatial transcriptomics data, but also infer spatial communications among spots by integrating the spatial location information. At the same time, NODE can directly deconvolute the number of cells in each spatial spot, and this allows us to get the specifics of the cells in each location directly. NODE improves the accuracy compared with existing algorithms and another highlight of NODE is the ability to infer spatial communications. In other words, NODE can solve for spatial information flow and spatial communications from spatial transcriptomics data while deconvolution. Eventually, we illustrate the effect of NODE through extensive simulations and four published spatial transcriptomics datasets with different spatial patterns. In the simulated data and the three previous datasets, we focused on exploring the deconvolution performance of NODE. In the last dataset, we verified the deconvolution performance of NODE and its performance in inferring spatial communications. In the simulated data, NODE’s deconvolution results had the smallest error compared with the results of other algorithms. In the previous three real datasets, NODE also obtained more favorable deconvolution results. In the final real data, NODE not only successfully predicted the changes in cell distribution and number, but also accurately found out the spatial communications between the cells in the process of organ development.</p></div></div></section><section data-title="Results"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2">Results</h2><div class="c-article-section__content" id="Sec2-content"><h3 class="c-article__sub-heading" id="Sec3">Deconvolution for simulated data</h3><p>The details of NODE are depicted in the Method section, and its implementation is further described in the Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>, with a schematic of the method shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1</a>.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="The schematic overview of NODE."><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 1: The schematic overview of NODE.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig1_HTML.png?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig1_HTML.png" alt="figure 1" loading="lazy" width="685" height="766"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p>NODE is an optimization method to deconvolute the cell number of spots and cell distribution of tissue from spatial transcriptomics data. Except deconvolution, NODE can also explore spot-to-spot communications at spatial resolutions. NODE performs and returns functions both the results of the deconvolution and the inferred results of the spatial communications. <b>a</b> For cell-type deconvolution and spatial communications, it is necessary to provide single-cell RNA sequencing data and spatial transcriptomics data. Meanwhile, cell types information can be obtained from scRNA-seq data, and spatial coordinate’s information with coordinate annotation comes from spatial transcriptomics data. <b>b</b> NODE carries out the construction of initial models (<span class="mathjax-tex">$Y={X}_{1}\times {B}^{T}+{\acute{\varepsilon }}_{1}$</span>) and initial optimizations to find the main parts of the cellular composition and distribution matrix <span class="mathjax-tex">${X}_{1}$</span>. <b>c</b> On the basis of the initial optimization, <span class="mathjax-tex">${X}_{1}$</span> was used as the initial value of <span class="mathjax-tex">${X}_{2}$</span> on the model (<span class="mathjax-tex">$Y={W}_{1}\times Y+{X}_{2}\times {B}^{T}+{\acute{\varepsilon }}_{2}$</span>), NODE calculated the spatial communications (the communication matrix <span class="mathjax-tex">${W}_{1}$</span>) and quantifies the effects into gene expression, leading to a more accurate deconvolutional solution for the cellular composition and distribution matrix <span class="mathjax-tex">${X}_{2}$</span>. <b>d</b>, <b>e</b> In this process, NODE can obtain the composition of cells at different spatial locations, and the distribution of cells with single-cell resolution from the cell position and distribution matrix <span class="mathjax-tex">${X}_{2}$</span>. <b>f</b> In addition, NODE can also obtain the information flow of spatial communications between spots from the communication matrix <span class="mathjax-tex">${W}_{1}$</span>.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>We conducted an extensive simulation to evaluate the performance of NODE and compared it with five existing deconvolution methods: SpaTalk<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Shao, X. et al. Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk. Nat. Commun. 13, 4429 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR17" id="ref-link-section-d68010897e912">17</a></sup>, RCTD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Cable, D. M. et al. Robust decomposition of cell type mixtures in spatial transcriptomics. Nat. Biotechnol. 40, 517–526 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR18" id="ref-link-section-d68010897e916">18</a></sup>, deconvSeq<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Andersson, A. et al. Single-cell and spatial transcriptomics enables probabilistic inference of cell type topography. Commun. Biol. 3, 565 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR19" id="ref-link-section-d68010897e920">19</a></sup>, Seurat<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="Stuart, T. et al. Comprehensive Integration of Single-Cell Data. Cell 177, 1888–1902.e1821 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR20" id="ref-link-section-d68010897e924">20</a></sup>, and SPOTlight<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Elosua-Bayes, M., Nieto, P., Mereu, E., Gut, I. & Heyn, H. SPOTlight: seeded NMF regression to deconvolute spatial transcriptomics spots with single-cell transcriptomes. Nucleic Acids Res. 49, e50 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR21" id="ref-link-section-d68010897e928">21</a></sup> (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">2</a>). We used real scRNA-seq data to construct simulated spatial transcriptomics data for deconvolution (details in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). To simulate the tissue situation more extensively, we simulated spatial transcriptomics data with different spatial and cellular models for the same set of scRNA-seq data. By varying the number of spots, scRNA-seq data, and the cells’ spatial distribution structure, we constructed four simulated datasets (scenarios 1–4) with two replications (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>, <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">2</a>, and Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). We assessed the performance of NODE alongside five other deconvolution methods (SpaTalk, RCTD, Seurat, deconvSeq, and SPOTlight) in simulated data to evaluate NODE’s effectiveness. Firstly, the inference results of the deconvolution were obtained from the six deconvolution methods. Subsequently, we calculated the difference between the inferred results and simulated data at each position by the root mean square error (RMSE), counted the best-performing cases for each method and calculated the frequency of the optimal case for each method (details in Method).</p><p>Among the RMSE in the base case (scenario 1 replicate 1), NODE achieved the best results with the smallest RMSE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2a</a>). NODE also surpassed other methods with the smallest median RMSE (1.3213), outperforming SpaTalk (2.8793), RCTD (1.8106), Seurat (3.0844), deconvSeq (3.3473), and SPOTlight (2.3231) (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). After the base simulated case (scenario 1), we also simulated a wide range of scenarios (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>), and assessed the performance of NODE in different spatial and cellular situations. In scenario 2, we performed simulations with different spatial conditions (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). The median RMSE from NODE is 1.5931 (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a>), and the smallest RMSE from other 5 methods is 2.1131 from RCTD. Then we ranked the RMSE from the six methods in each spot for scenario 1 and scenario 2 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2b</a>). NODE also received a better ranking (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2b</a>). In addition, the spatial communications among spots were also correctly identified with high accuracy by NODE method (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c, d</a>). We first calculated the three kinds of correlation coefficients between the spot-to-spot communications inferred by NODE and the original spatial pattern of simulated data, and then we calculated the area under the curve (AUC) value (details in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>) of the results from the NODE inference by setting a threshold value (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c, d</a>. The details are described in Method). In the results, high correlation is obtained, Pearson correlation coefficient, Spearman’s rank correlation coefficient, Kendall’s tau rank correlation coefficient are 0.2761, 0.9416, and 0.9360 respectively (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c</a>), and the <i>p</i>-values of these correlation coefficients are significant and near to 0 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c</a>). And the spatial communications among spots are also correctly identified with high AUC value 0.843 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2d</a>). In scenario 3, we performed simulations for different cellular conditions (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). The median RMSE from NODE is 0.7184 (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">5</a>), which is smaller than other 5 methods, and the median RMSE from other 5 methods is at least 1.0667 (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a>). In scenario 4, our simulations were generated under different spatial conditions and different cellular conditions (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>). The NODE also performs better than other 5 methods with smallest RMSE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2a</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a>). And the spatial communications among spots were also correctly identified with high AUC value 0.847 by NODE method in scenario 4 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2d</a>). Subsequently, we repeated the simulated experiment for the four scenarios. In the repeated experiments, NODE performed very well except for the repetition of the base case (scenario 1 replicate 2), and it has a lower RMSE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2a</a>) and lower median of RMSE (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">10</a>) compared to other methods. Then we ranked the RMSE from the six methods in each spot and calculated percentages of the ranks for the six methods in all spots for all scenarios (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2b</a>). In the ranks of these deconvolution methods, NODE ranked high in the vast majority of spots (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2b</a>). In all results, NODE achieves a top ranking and performs best in both rank share (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2b</a>) and optimal ranking (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">11</a>), which reflects that NODE has a higher accuracy rate than other five methods. Furthermore, NODE demonstrated high accuracy in exploring cellular communications in the replicates of scenario 2 and scenario 4 (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c, d</a>). Specifically, NODE’s communication results exhibited a very high and significant correlation with the simulated data (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2c</a>). Additionally, we conducted AUC calculations by thresholding (details in Method), and NODE achieved impressive AUC values (0.849 in scenario 2 and 0.852 in scenario 4). Finally, we also compared the spatial scatter pie charts of each deconvolution results with the simulated results for different scenarios, the deconvolution results from NODE showed a high degree of agreement with the cell type distribution in the simulated data (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">12</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">19</a>), correspondingly, the other results showed significant differences in cell composition or cell number with the simulated data (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">12</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">19</a>). Overall, NODE performs better than the other five deconvolution methods on all simulated data.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="Analysis of deconvolution and spatial communications in simulations."><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 2: Analysis of deconvolution and spatial communications in simulations.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig2_HTML.png?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig2_HTML.png" alt="figure 2" loading="lazy" width="685" height="857"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>The simulated data consisted of four scenarios, each containing two replicates. In scenario 1, simulated data is the base state and all methods use scRNA-seq data matched to spatial transcriptomics data. In scenario 2, add different spatial patterns to the spatial transcriptomics data of scenario 1. In scenario 3, added a different cellular model to scenario 1 for cell culling. At the same time, we used the single-cell data after adding the cellular model for the construction of simulated data and all methods use scRNA-seq data matched to spatial transcriptomics data. In scenario 4, we incorporated both different cellular and spatial models to construct spatial transcriptomics data. All methods use scRNA-seq data matched to spatial transcriptomics data. <b>a</b> RMSE of cell distributions inferred by different deconvolution methods with simulated data for all simulated scenarios. The comparative deconvolution methods (x-axis) are NODE (red), SpaTalk (dark yellow), RCTD (green), Seurat (cyan), deconvSeq (blue), and SPOTlight (purple). We computed the RMSE of the deconvolution results versus the true values in each spot and tallied all the computed results as a box plot. In the figure, lower values of RMSE (y-axis) indicate more accurate deconvolution results. Each box plot ranges from the third and first quartiles with the median as the horizontal line, while whiskers represent 1.5 times the interquartile range from the lower and upper bounds of the box. <b>b</b> Comparison of deconvolution accuracy of different methods in simulations under all simulated scenarios. The comparative deconvolution methods (x-axis) are NODE, SpaTalk, RCTD, Seurat, deconvSeq, and SPOTlight. We further ranked the RMSE across methods for each simulated replicate and calculated the proportion of times that a method was ranked as a specific rank. Rank performances were displayed in the form of stacked bar plots with different colors representing ranks 1–6. <b>c</b> Performance of NODE in inferring spatial communications in simulated data with spatial models added. The four bar charts shows the degree of correlation and significance test results between NODE’s inferred results on spatial communications and the simulated data results in different scenarios and replicates. <b>d</b> The ROC space and AUC value of scenario 2 and scenario 4. “Scenario 2 ROC space” and “Scenario 4 ROC space” subfigures’ AUC values of NODE’s inferred results are calculated based on the original simulated results, and the AUC values show the degree of similarity between the two.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h3 class="c-article__sub-heading" id="Sec4">Analysis of mouse olfactory bulb (MOB)</h3><p>We applied NODE and other deconvolution methods to some published spatial transcriptomics datasets and all of these datasets were obtained from Spatial Transcriptomics (ST). We used scRNA-seq data from the same tissue with the spatial transcriptomics for deconvolution. Of these scRNA-seq data, three are from the 10x Chromium platform and the remaining one is obtained through inDrop. (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a> and Supplementary Tables <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">2</a>).</p><p>We first examined MOB data<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Sci. (N. Y., N. Y.) 353, 78–82 (2016)." href="/article/10.1038/s42003-025-07625-8#ref-CR13" id="ref-link-section-d68010897e1110">13</a></sup> from ST and its scRNA-seq data from 10x Chromium platform. For deconvolution, the MOB spatial transcriptomics data and its scRNA-seq data were obtained from the same tissue. The MOB data comprised 16,034 genes and 282 spatial locations. As a reference for deconvolution, we obtained scRNA-seq data from GSE121891 in the GEO database (<a href="https://www.ncbi.nlm.nih.gov/geo/">https://www.ncbi.nlm.nih.gov/geo/</a>). This scRNA-seq data was collected from the mouse olfactory bulb and contains 18,560 genes and 21746 cells. The mouse olfactory bulb (MOB) comprises three main anatomic layers organized in an inside-out fashion, annotated based on hematoxylin and eosin (H&E) staining images: the granule cell layer (GCL; main cell: granule cells denoted as GC), the mitral cell layer (MCL; main cell: mitral/tufted cells denoted as M-TC), and the glomerular layer (GL; main cell: periglomerular cells denoted as PGC) (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3a</a>). In result, the cell type compositions inferred by NODE accurately depicted such expected layered structure<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="Nagayama, S., Homma, R. & Imamura, F. Neuronal organization of olfactory bulb circuits. 8, 
 https://doi.org/10.3389/fncir.2014.00098
 
 (2014)." href="/article/10.1038/s42003-025-07625-8#ref-CR26" id="ref-link-section-d68010897e1124">26</a></sup>(Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3b</a>). We then compared the inferred results from various deconvolution methods for the three main anatomical layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3b</a>). In the six spatial scatter pie plots, the layering in the NODE inferred results aligned clearly with the distribution of the three main anatomical layers<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Sci. (N. Y., N. Y.) 353, 78–82 (2016)." href="/article/10.1038/s42003-025-07625-8#ref-CR13" id="ref-link-section-d68010897e1135">13</a></sup>(Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3b</a>). But it was not obvious that the SpaTalk, deconvSeq, and SPOTlight methods had similar layering. And the SpaTalk, deconvSeq, and SPOTlight methods exhibited less effective stratification (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3b</a>). To further assess NODE’s performance, the three layers of cells were individually delineated, and the inferred results from NODE and other deconvolution methods were overlaid on the tissue anatomy map to visually inspect whether the cell distribution of the inferred results matches that of the tissue (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3c</a>). The stratification observed in NODE’s extrapolated results aligned with the stratification in the H&E staining images. By contrast, SpaTalk, RCTD, Seurat, deconvSeq, and SPOTlight did not distinguish well between the three main anatomic layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3c</a>). Specifically, SpaTalk could not distinguish the MCL from GL, and the boundaries of GCL, GL in RCTD inferred results were not obvious. Meanwhile, there was a tendency of GCL spillover as inferred by RCTD. However, we could not find proof of this manifestation in histological sections. Seurat was unable to position the GL layer correctly, and deconvSeq cannot distinguish between all three major anatomical layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3c</a>). In deconvSeq’s results, GC occupied the whole spatial location of the MOB slices. M-TC were not found and PGC were mislocalized. SPOTlight cannot distinguish the three layers from each other, and the GC and PGC were present in almost all spatial locations from the SPOTlight deconvolution result. Correspondingly, NODE not only successfully distinguished the three cell layers, but also the arrangement of the three cell layers was highly consistent (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3c</a>) with the annotation of the sections<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 13" title="Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Sci. (N. Y., N. Y.) 353, 78–82 (2016)." href="/article/10.1038/s42003-025-07625-8#ref-CR13" id="ref-link-section-d68010897e1158">13</a></sup>. NODE correctly localized the major cells in the three-layer structure and clearly distinguished the boundaries of the three cell layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3c</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="The deconvolution results for MOB."><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 3: The deconvolution results for MOB.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig3_HTML.png?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig3_HTML.png" alt="figure 3" loading="lazy" width="685" height="856"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p><b>a</b> H&E staining of the olfactory bulb displays three anatomic layers that are organized in an inside-out fashion the GCL, MCL, and GL. Among them, the characteristic cell of the GCL layer is GC, the characteristic cell of the MCL layer is M-TC, and the characteristic cell of the GL layer is PGC. <b>b</b> The spatial scatter pie chart displays the proportion and composition of cells at each spatial location in the inferred results of different deconvolution methods. <b>c</b> The distribution of granule cells (GC), mitral/tufted cells (M-TC), and periglomerular cells (PGC) in the inferred results of different deconvolution methods. The results of GC, M-TC, and PGC inferred by different methods are arranged in order. Color is scaled by the proportion value. We compared the inferred results from different deconvolution methods (NODE, SpaTalk, RCTD, Seurat, donvSeq, and SPOTlight) for the three cells, and also compared these cells with MOB tissue sections. <b>d</b> “GC”, “M-TC”, and “PGC” subfigures represent the proportion of each of the three cell types (GC, M-TC, and PGC) inferred by NODE on each spatial location. The “<i>Penk</i>”, “<i>Cdhr1</i>”, and “<i>Apold1</i>” subfigures represent the expression levels of the three corresponding cell-type-specific marker genes (<i>Penk</i>, <i>Cdhr1</i>, and <i>Apold1</i>). Color is scaled by the proportion or gene expression value. <b>e</b> Comparison of AUC and ACC values for different deconvolution inference results. Higher values of AUC and ACC indicate that the cellular distribution of the inferred results is consistent with the distribution of the marker genes. Compared deconvolution methods include SpaTalk, RCTD, Seurat, deconvSeq, SPOTlight, and NODE. Briefly, we set cell thresholds and gene thresholds based on the color of each spatial location in Fig. 3d (details in Method). We then used these two thresholds and gene distributions with the cell distributions of inferred results of different deconvolution methods to construct confusion matrices and calculate the AUC (y-axis) and ACC (x-axis). <b>f</b> Comparison of the correlation coefficients of M-TC distribution vector with the expression vector of marker gene corresponding to M-TC by different deconvolution methods. The GCs and PGCs are in Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">20</a>, <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">21</a>. <b>g</b> Correlations in cell-type proportion across spatial locations between pairs of cell types inferred by NODE. Color is scaled by the correlation value.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>In deeper examination, we also extraordinarily marked the aggregation of major cells in the three anatomical layers and clearly identified the high expression areas of corresponding marker genes (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3d</a>). The consistency in the distribution of cells and their corresponding marker genes in the three major anatomical layers demonstrated the performance of NODE. Subsequently, we applied a threshold setting based on the classification of heat map colors and provided a quantitative description of the consistency between the distribution of marker genes and the distribution of cells (details in Method). From the results of further processing, the NODE obtained the optimal match from all methods in the distribution of major cell locations in the three anatomical layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3e</a>) by the AUC - accuracy (ACC) scatter. Meanwhile, we extracted the major cell distribution vectors of the anatomical layer and the corresponding marker gene expression vectors of the spatial transcriptomics data and calculated the Pearson correlation coefficients between them. A higher correlation coefficient means a closer distribution between the cell types and corresponding marker genes. NODE obtained a promising performance in the correlation coefficient test from all methods in the mitral cells layer (main cell: M-TC) (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3f</a>). For the remaining two layers of cells and their corresponding marker genes, the similar correlation coefficients were calculated and compared for all methods (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">20</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">21</a>). We also observed that multiple cell types from NODE show spatial colocalization patterns (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig3">3g</a> and Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">5</a>). Mitral/tufted cells (M-TC) and periglomerular cells (PGC) inferred by NODE are also spatially colocalized, providing spatial localization support for their reciprocal synapses with mitral/tufted cells dendritic tufts in the glomerulus<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="Kosaka, T. & Kosaka, K. in Encyclopedia of Neuroscience (ed Larry R. Squire) 59–69 (Academic Press, 2009)." href="/article/10.1038/s42003-025-07625-8#ref-CR27" id="ref-link-section-d68010897e1256">27</a></sup>.</p><p>To further validate NODE’s performance, we compared it with recent deconvolution methods in MOB data, including CARD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nat. Biotechnol. 40, 1349–1359 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR28" id="ref-link-section-d68010897e1263">28</a></sup>, GraphST<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with GraphST. Nat. Commun. 14, 1155 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR29" id="ref-link-section-d68010897e1267">29</a></sup>, SpaDecon<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Coleman, K., Hu, J., Schroeder, A., Lee, E. B. & Li, M. SpaDecon: cell-type deconvolution in spatial transcriptomics with semi-supervised learning. Commun. Biol. 6, 378 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR30" id="ref-link-section-d68010897e1271">30</a></sup>, SpatialDWLS<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="Dong, R. & Yuan, G.-C. SpatialDWLS: accurate deconvolution of spatial transcriptomic data. Genome Biol. 22, 145 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR31" id="ref-link-section-d68010897e1275">31</a></sup>, SpatialPrompt<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Swain, A. K., Pandit, V., Sharma, J. & Yadav, P. SpatialPrompt: spatially aware scalable and accurate tool for spot deconvolution and domain identification in spatial transcriptomics. Commun. Biol. 7, 639 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR32" id="ref-link-section-d68010897e1279">32</a></sup>, and SPADE<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 33" title="Lu, Y., Chen, Q. M. & An, L. SPADE: spatial deconvolution for domain specific cell-type estimation. Commun. Biol. 7, 469 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR33" id="ref-link-section-d68010897e1284">33</a></sup>. We also performed a hierarchical comparison with BASS<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="Li, Z. & Zhou, X. BASS: multi-scale and multi-sample analysis enables accurate cell type clustering and spatial domain detection in spatial transcriptomic studies. Genome Biol. 23, 168 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR34" id="ref-link-section-d68010897e1288">34</a></sup>. NODE demonstrated a more accurate hierarchical structure in the results, showing a clearer layering (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">22</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">23</a>). Additionally, we quantified the performance of these methods by calculating the correlation coefficients between two cellular layers (GCL and GL) and their respective marker genes (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">22</a>). Higher correlation coefficients indicate greater accuracy, with NODE achieving the highest correlation in GL and ranking second to CARD in GCL (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">22</a>). These results underscore NODE’s effectiveness and precision. More details of all methods results are described in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">22</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">23</a>).</p><h3 class="c-article__sub-heading" id="Sec5">Deconvolution of human pancreatic ductal adenocarcinoma (PDAC) data</h3><p>We then examined human pancreatic ductal adenocarcinoma (PDAC) data<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Moncada, R. et al. Integrating microarray-based spatial transcriptomics and single-cell RNA-seq reveals tissue architecture in pancreatic ductal adenocarcinomas. Nat. Biotechnol. 38, 333–342 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR35" id="ref-link-section-d68010897e1325">35</a></sup> for deconvolution. The spatial transcriptomics data and scRNA-seq data of PDAC were obtained from GEO database (<a href="https://www.ncbi.nlm.nih.gov/geo/">https://www.ncbi.nlm.nih.gov/geo/</a>) with accession number GSE111672. The PDAC’s spatial transcriptomics data were obtained from ST and scRNA-seq data were collected on the same tissue by inDrop. Following the original paper<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Moncada, R. et al. Integrating microarray-based spatial transcriptomics and single-cell RNA-seq reveals tissue architecture in pancreatic ductal adenocarcinomas. Nat. Biotechnol. 38, 333–342 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR35" id="ref-link-section-d68010897e1336">35</a></sup>, the tissue type of each region on the section has been labelled in PDAC (this tissue was denoted as PDAC-A). In the H&E staining of PDAC (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4a</a>), distinct colors in different regions of the tissue clearly indicate variations in cellular composition across these sections. The cell distribution of PDAC in different tissue regions (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b</a>) was marked according to the original publication<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Moncada, R. et al. Integrating microarray-based spatial transcriptomics and single-cell RNA-seq reveals tissue architecture in pancreatic ductal adenocarcinomas. Nat. Biotechnol. 38, 333–342 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR35" id="ref-link-section-d68010897e1347">35</a></sup>. Then, we calculated the deconvolution results for the PDAC spatial transcriptomics data using NODE and other deconvolution methods (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4c</a>). In the spatial scatter pie plot, NODE successfully identified spatial regionality similar to that observed in the case of sliced tissue. The cell’s color distribution in the NODE deconvolution result matched the color depth distribution of the sliced tissue (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). In contrast, none of the other deconvolution results showed such a cell distribution, especially in the boundary regions (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>), other deconvolution results can not accurately locate the demarcation line between the different regions (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). In contrast, NODE can accurately locate the distribution of tumors, tissues and ducts (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). In the inferred results of NODE, we can clearly see that NODE captured the stratification of different regions and revealed the fuzzy demarcation between cancer and non-cancer regions, between duct and stroma regions, and between cancer and pancreatic (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). However, none of the layering phenomena as annotated in the original publication were seen in the results of other deconvolution methods (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). The stratification results of SpaTalk with RCTD were not obvious, while Seurat, deconvSeq, and SPOTlight mis-localized many cells, resulting in a large number of cells appearing in inappropriate locations (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4b, c</a>). Subsequently, we labeled the aggregation states of both cancer clone B and duct centroacinar cells in the results obtained by NODE and other deconvolution methods (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4d</a>). The deconvolution results of NODE are consistent with the histological annotation distribution (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4d</a>). In contrast, SpaTalk and RCTD were unable to accurately detect the disaggregation of cancer and ductal areas, and deconvSeq, SPOTlight, and Seurat were unable to accurately locate ductal centriolar cells (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4d</a>). Then, we displayed a scale heat map of the proportion of each cell types inferred by NODE and the expression levels of corresponding cell-type-specific marker genes on each spatial location (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4e</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">24</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">29</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Zheng, B. et al. TM4SF1 as a prognostic marker of pancreatic ductal adenocarcinoma is involved in migration and invasion of cancer cells. Int J. Oncol. 47, 490–498 (2015)." href="#ref-CR36" id="ref-link-section-d68010897e1395">36</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Fu, F. et al. Role of Transmembrane 4 L Six Family 1 in the Development and Progression of Cancer. 7, 
 https://doi.org/10.3389/fmolb.2020.00202
 
 (2020)." href="#ref-CR37" id="ref-link-section-d68010897e1395_1">37</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 38" title="Xu, D. et al. Lost miR-141 and upregulated TM4SF1 expressions associate with poor prognosis of pancreatic cancer: regulation of EMT and angiogenesis by miR-141 and TM4SF1 via AKT. Cancer Biol. Ther. 21, 354–363 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR38" id="ref-link-section-d68010897e1398">38</a></sup>. The approximate consistency of the two distributions can also reveal the reasonableness of the deconvolution results of NODE (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">24</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">29</a>). Finally, we also examined the differences in the distribution of different cell types between cancer and non-cancer regions from the NODE results (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>). In the result, NODE accurately localized different cells to the corresponding regions, specifically, NODE localized tumor cells to the tumor region and non-tumor cells to the non-tumor region. In order to verify its robustness, we also annotated the distribution of cells in which neither tumor nor non-tumor features were present (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>), we found that the distribution of such cells was comparable between the two regions (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>). In performing this validation, we also mapped the tissue area distribution based on the annotated information in the original publication and further divided the cancerous (<i>n</i> = 150) and non-cancerous (<i>n</i> = 278) locations based on this distribution. Then, we tallied the proportion of cells corresponding to each capture location in the cancerous versus non-cancerous regions and drew a box-line diagram (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>). In the results of NODE, tumor-associated cells had a significant differential distribution in cancerous versus non-cancerous areas, and these cells were highly enriched in cancerous areas, such as cancer clone A and cancer clone B (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>). In the histological section annotation (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4c</a>), ductal cells were mainly distributed in the non-cancerous part, which was also verified in the difference test of duct centroacinar cells and duct terminal cells (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="The deconvolution in PDAC Data."><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 4: The deconvolution in PDAC Data.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig4_HTML.png?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig4_HTML.png" alt="figure 4" loading="lazy" width="685" height="845"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p><b>a</b> H&E staining of the PDAC. <b>b</b> Scatter plot displays four regions annotated from the original publication: cancer, pancreatic, ductal, and stroma regions. We manually segmented all the spots based on the original publication. <b>c</b> The spatial scatter pie chart displays the proportion and composition of cells at each spatial location in the inferred results of different deconvolution methods. <b>d</b> The cancer clone B cells and duct centroacinar cells in the inferred results of different deconvolution methods. The deconvolution methods in the figure are NODE, SpaTalk, RCTD, Seruat, deconvSeq, and SPOTlight. <b>e</b> “Cancer clone A”, “cancer clone B”, “duct centroacinar”, “duct terminal” and “fibroblasts” subfigures indicate the proportion of each cell types inferred by NODE on each spatial location. The “<i>TM4SF1</i>”, “<i>S100A4</i>”, “<i>CRISP3</i>”, “<i>TFF3</i>”, and “<i>CD248</i>” subfigures represent the expression levels of corresponding cell-type-specific marker genes. <b>f</b> Comparison of the proportion of cell types inferred from NODE in cancerous areas (<i>n</i> = 150) versus non-cancerous areas (<i>n</i> = 278) (x-axis), The y-axis represents the proportion of cells in different areas at each spatial location. Briefly, we counted the percentage of cells in all the spots that were in the cancerous vs. non-cancerous areas, and plotted them as a box-and-line graph. Each box plot ranges from the third and first quartiles with the median as the horizontal line, while whiskers represent 1.5 times the interquartile range from the lower and upper bounds of the box (cancerous areas is blue box and non-cancerous areas is pink box).</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Similarly, we also used CARD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nat. Biotechnol. 40, 1349–1359 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR28" id="ref-link-section-d68010897e1500">28</a></sup>, GraphST<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with GraphST. Nat. Commun. 14, 1155 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR29" id="ref-link-section-d68010897e1504">29</a></sup>, SpaDecon<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Coleman, K., Hu, J., Schroeder, A., Lee, E. B. & Li, M. SpaDecon: cell-type deconvolution in spatial transcriptomics with semi-supervised learning. Commun. Biol. 6, 378 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR30" id="ref-link-section-d68010897e1508">30</a></sup>, SpatialDWLS<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="Dong, R. & Yuan, G.-C. SpatialDWLS: accurate deconvolution of spatial transcriptomic data. Genome Biol. 22, 145 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR31" id="ref-link-section-d68010897e1512">31</a></sup>, SpatialPrompt<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Swain, A. K., Pandit, V., Sharma, J. & Yadav, P. SpatialPrompt: spatially aware scalable and accurate tool for spot deconvolution and domain identification in spatial transcriptomics. Commun. Biol. 7, 639 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR32" id="ref-link-section-d68010897e1516">32</a></sup>, and SPADE<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 33" title="Lu, Y., Chen, Q. M. & An, L. SPADE: spatial deconvolution for domain specific cell-type estimation. Commun. Biol. 7, 469 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR33" id="ref-link-section-d68010897e1521">33</a></sup> to analyze PDAC-A. We evaluated the performance of these methods, along with NODE, in distinguishing and localizing tissue types (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">23</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">30</a>). In the quantitative evaluation of PDAC, NODE ranked second in both correlation coefficient and AUC (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">40</a>). More details are described in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a>.</p><p>In addition, we also verified the performance of NODE in the face of mismatched scRNA-seq (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">31</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">32</a>). NODE showed good robustness and accuracy in the face of different scRNA-seq, and the performance of NODE does not change significantly due to the change of reference scRNA-seq data (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">31</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">32</a>). More details are described in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a>.</p><h3 class="c-article__sub-heading" id="Sec6">Human skin squamous cell carcinoma (SCC) ST dataset</h3><p>The NODE was then applied to the human skin squamous cell carcinoma (SCC) ST dataset<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Ji, A. L. et al. Multimodal Analysis of Composition and Spatial Architecture in Human Squamous Cell Carcinoma. Cell 182, 497–514.e422 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR39" id="ref-link-section-d68010897e1570">39</a></sup> for validation of spatial deconvolution. The SCC ST data and scRNA-seq were obtained from GEO database (<a href="https://www.ncbi.nlm.nih.gov/geo">https://www.ncbi.nlm.nih.gov/geo</a>) with accession number GSE144240. The NODE and other deconvolution methods were used on the SCC dataset with corresponding scRNA-seq data for the deconvolution exploration. In the SCC data, we focused on identifying tumor specific keratinocyte (TSK) in the tumor data and used TSK cells to analyze the deconvolution performance of NODE and other methods. We first labeled the expression of TSK corresponding marker genes <i>MMP10</i>, <i>PTHLH</i>, <i>LAMC2</i><sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Ji, A. L. et al. Multimodal Analysis of Composition and Spatial Architecture in Human Squamous Cell Carcinoma. Cell 182, 497–514.e422 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR39" id="ref-link-section-d68010897e1589">39</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5a</a>). After finding the major expression sites of the marker genes, we deduced that the distribution of TSK cells should roughly correspond to the distribution of marker gene expression. Applying NODE and other deconvolution methods to the data, the TSK distributions were extracted by each method (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5b</a>). From NODE’s results, the TSK distribution was generally consistent with the clustered distribution of marker genes (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5b</a>). Correspondingly, the SpaTalk, RCTD, and Seurat judged the inconspicuous gene aggregation spots as TSK cell aggregation locations, whereas the deconvSeq method was unable to find a specific distribution of TSK, and SPOTlight was unable to distinguish a gap where the TSK marker genes were not significantly expressed in the middle of several TSK cell aggregation sites (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5b</a>). Subsequently, we calculated the Pearson correlation coefficient between the deconvolution cell distribution and the distribution of the corresponding marker genes (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5c</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">33</a>, <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">34</a>). A higher correlation coefficient indicates that the cellular distribution from the inferred results is more similar to the distribution of the marker genes. The highest Pearson correlation coefficient was achieved by NODE with 0.4216 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5c</a>) and the correlation coefficients from other methods were lower than 0.4 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5c</a>). It means that the deconvolution results from the NODE is plausibility and accuracy. Then we used the spatial scatter pie plot (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5d</a>) to reveal the cellular composition from NODE in a tumor section, and to show the cell type of its tumor microenvironment. As a result, we clearly see the distribution of TSK with different tumor cells and we see the co-localized microenvironmental status of tumor cells and immune cells (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5d</a>). Afterward, we plotted a scatterplot (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5e</a>) and found the colocalization of cells in the tumor environment. In the scatterplot results explored by NODE, we found that there is a very clear colocalization of B-cells and T-cells with tumor cells, and the co-localization of these immune cells with tumors is significantly different from the aggregation of these immune cells with other non-tumor cells (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5e</a>). In order to better quantitatively describe such co-localization phenomena, we calculated Pearson correlation coefficients (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5f</a>) on our deconvolution results. Specifically, we considered the distribution of different cell types in the deconvolution result as a vector and the Pearson correlation coefficients can be calculated between cell types. From the correlation results, we can find that three tumor cells (Tumor_Kc_cyc, Tumor_Kc_Diff, and TSK) are co-localized with the immune cells (the B-cells) in the NODE deconvolution results (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5f</a>). It is consistent with existing knowledge about immune cell in the tumor environment<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Ji, A. L. et al. Multimodal Analysis of Composition and Spatial Architecture in Human Squamous Cell Carcinoma. Cell 182, 497–514.e422 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR39" id="ref-link-section-d68010897e1641">39</a></sup>. Finally, we also did a deconvolution probe of the remaining two sections<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Ji, A. L. et al. Multimodal Analysis of Composition and Spatial Architecture in Human Squamous Cell Carcinoma. Cell 182, 497–514.e422 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR39" id="ref-link-section-d68010897e1645">39</a></sup>, again identifying the distribution of TSK cells and their corresponding marker genes (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5g, h</a>, and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">35</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">37</a>). In these results, the distribution of TSK cells in the NODE deconvolution results showed a consistent distribution with the marker genes, in contrast to the other methods, which suffered from an inability to find the distribution correctly and an excess of false positives (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig5">5g, h</a>, and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">35</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">37</a>). In the remaining two sections, we also calculated the Pearson correlation coefficients of the distributions of TSK with the corresponding marker genes in the NODE deconvolution results, and NODE also achieved a more favorable ranking and correlation coefficient values (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">38</a>–<a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">43</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="The deconvolution analysis for SCC."><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 5: The deconvolution analysis for SCC.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig5_HTML.png?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig5_HTML.png" alt="figure 5" loading="lazy" width="685" height="889"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p><b>a</b> H&E staining of the SCC_P2.rep1 and heat map of marker genes (<i>PTHLH, MMP10, LAMC2</i>) corresponding to tumor specific keratinocyte (TSK). <b>b</b> The distribution of tumor specific keratinocyte (TSK) in the inferred results of different deconvolution methods. Color is scaled by the proportion value. <b>c</b> Correlation between TSK and corresponding marker gene <i>MMP10</i>. We calculated the correlation coefficients of TSK cells and their marker genes. Specifically, we consider the expression of marker genes in all spots as a vector, and the expression of TSK cells in all spots in the deconvolution results as a vector, and calculate the correlation coefficients of the two vectors. We calculated the correlation coefficients between TSK cells and the three marker genes (<i>PTHLH</i>s and <i>LAMC2</i>s in Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">33</a>, <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">34</a>), separately. The comparative deconvolution methods (x-axis) are NODE (dark yellow), SpaTalk (blue), RCTD (green), Seurat (cyan), deconvSeq (red), and SPOTlight (purple). A higher correlation (y-axis) indicates that the distribution of cells in the deconvolution result matches the distribution of marker genes more closely. <b>d</b> The spatial scatter pie chart displays the proportion and composition of cells at each spatial location in the inferred results of NODE deconvolution methods. <b>e</b> Cell-type decomposition by NODE at single-cell resolution for human skin SCC ST data. <b>f</b> Correlations in cell-type proportion across spatial locations between pairs of cell types inferred by NODE. Color is scaled by the correlation value. Co-localization of tumor and immune cells is boxed in red. <b>g</b> H&E staining of the SCC_P2.rep2, the heat map of marker genes (<i>PTHLH, LAMC2, MMP10</i>) corresponding to tumor specific keratinocyte (TSK) and distribution of TSK cells in NODE deconvolution results. Color is scaled by the proportion value. <b>h</b> H&E staining of the SCC_P2.rep3, the heat map of marker genes (<i>PTHLH, LAMC2, MMP10</i>) corresponding to tumor specific keratinocyte (TSK) and distribution of TSK cells in NODE deconvolution results. Color is scaled by the proportion value. We have labeled the aggregation of cells or marker genes with dark colors. The closer the color to red, the higher the percentage of TSK cells or marker genes.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>For NODE’s ability to recognize specific cells, we further explored this by comparing NODE to more methods in the SCC data. To assess NODE’s ability to recognize specific cell types, we further compared it to additional methods using SCC data (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a>). Specifically, we evaluated the localization and identification of TSK cells with NODE, CARD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 28" title="Ma, Y. & Zhou, X. Spatially informed cell-type deconvolution for spatial transcriptomics. Nat. Biotechnol. 40, 1349–1359 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR28" id="ref-link-section-d68010897e1750">28</a></sup>, GraphST<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 29" title="Long, Y. et al. Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with GraphST. Nat. Commun. 14, 1155 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR29" id="ref-link-section-d68010897e1754">29</a></sup>, SpaDecon<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Coleman, K., Hu, J., Schroeder, A., Lee, E. B. & Li, M. SpaDecon: cell-type deconvolution in spatial transcriptomics with semi-supervised learning. Commun. Biol. 6, 378 (2023)." href="/article/10.1038/s42003-025-07625-8#ref-CR30" id="ref-link-section-d68010897e1758">30</a></sup>, SpatialDWLS<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 31" title="Dong, R. & Yuan, G.-C. SpatialDWLS: accurate deconvolution of spatial transcriptomic data. Genome Biol. 22, 145 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR31" id="ref-link-section-d68010897e1762">31</a></sup>, SpatialPrompt<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Swain, A. K., Pandit, V., Sharma, J. & Yadav, P. SpatialPrompt: spatially aware scalable and accurate tool for spot deconvolution and domain identification in spatial transcriptomics. Commun. Biol. 7, 639 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR32" id="ref-link-section-d68010897e1767">32</a></sup>, and SPADE<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 33" title="Lu, Y., Chen, Q. M. & An, L. SPADE: spatial deconvolution for domain specific cell-type estimation. Commun. Biol. 7, 469 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR33" id="ref-link-section-d68010897e1771">33</a></sup>. NODE demonstrated accurate TSK identification by marker genes, and its results remained consistent across three duplicate data slices (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">23</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">44</a>). In contrast, results from CARD and SpaDecon varied significantly, likely due to spatial noise and batch effects, which often affect duplicated slices (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">8</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">45</a>). NODE’s stability under these conditions underscores its resistance to spatial noise and batch effects (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">44</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">45</a>). More details are described in <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">Supplementary Notes</a> <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a>.</p><p>Finally, we performed a quantitative evaluation (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">44</a>), calculating correlation coefficients and AUC values for TSK cells and their marker genes across all deconvolution methods (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">44</a>). NODE achieved the highest correlation coefficient and AUC values across all replicates and genes, indicating its superior performance (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">44</a>). More details are described in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">6</a>.</p><h3 class="c-article__sub-heading" id="Sec7">The analysis of developing human heart data</h3><p>In constructing the deconvolution model and algorithm, NODE thoroughly incorporates the consideration of spatial location and information transfer in spatial transcriptomics data. To further assess NODE’s performance in deconvolution and uncover spatial communication and information transmission, we applied NODE to a dataset of developing human heart<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1833">40</a></sup> to explore the spatial dynamics of cells during heart development.</p><h3 class="c-article__sub-heading" id="Sec8">Deconvolution performance of NODE in developing human heart</h3><p>The spatial transcriptomics dataset of the human developing heart<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1845">40</a></sup> contains three periods of development, which are 4-4.5, 6.5, and 9 post-conception weeks (PCW) respectively, and the corresponding scRNA-seq data is from the 6.5 PCW period of heart development<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1849">40</a></sup>. NODE utilized this scRNA-seq data to deconvolute the spatial transcriptomics dataset across three periods. In the results, NODE accurately identified the locations of different cells during development (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6a</a>). During the three periods of heart development, NODE pinpointed the emergence and aggregation locations of smooth muscle cells, mapping the smooth muscle cells to the top of the tissue (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6a</a>). In addition, NODE pinpointed the location of cardiomyocytes and located endothelium cells belonging to the endocardial cells. NODE also successfully distinguished the different localization of ventricular and atrial cardiomyocytes, mapping ventricular cardiomyocytes to the ventricular location in the four chambers of the heart and atrial cardiomyocytes to the atrial location (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6a</a>). We then focused on the localization of cell types during the 6.5 PCW period, and drew heat maps of two types of cardiac myocytes, smooth muscle cells, and cardiac neural crest cells & schwann progenitor cells based on NODE’s deconvolution results (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6b</a>). The localization of these cell types from the NODE’s deconvolution results is consistent with the studies in the original literature<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1866">40</a></sup>. In the NODE results, the atrial cardiomyocytes were mainly mapped to the upper position of the slice (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6b</a>), where the atria are primarily located<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1873">40</a></sup>, and the ventricular cardiomyocytes were mapped to the lower part of the slice (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6b</a>), where the ventricles are mostly located<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1880">40</a></sup>. Smooth muscle cells were localized to the upper right side of the section (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6b</a>), where the pulmonary veins are indeed the location of smooth muscle cell aggregates. Finally, NODE also found Cardiac neural crest cells & Schwann progenitor cells, a rare cell, and it was reassuring to know that NODE’s localization of the rare cell was also consistent with the original study<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1888">40</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 41" title="Sun, D., Liu, Z., Li, T., Wu, Q. & Wang, C. STRIDE: accurately decomposing and integrating spatial transcriptomics using single-cell RNA sequencing. Nucleic Acids Res. 50, e42 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR41" id="ref-link-section-d68010897e1891">41</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6b</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Cellular distribution and spatial communications in development of human heart."><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Fig. 6: Cellular distribution and spatial communications in development of human heart.</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig6_HTML.png?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs42003-025-07625-8/MediaObjects/42003_2025_7625_Fig6_HTML.png" alt="figure 6" loading="lazy" width="685" height="856"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p><b>a</b> The spatial scatter pie chart displays the proportion and composition of cells at each spatial location in the inferred results of NODE deconvolution methods. The three datasets are from the 4-4.5PCW, 6PCW, and 9PCW periods of the developing heart. The resulting pie charts of the deconvolution of each data reflect different cellular compositions and proportions, with each different color representing different cell types. <b>b</b> The distribution of atrial cardiomyocytes, ventricular cardiomyocytes, smooth muscle cells / fibroblast like, and cardiac neural crest cells & schwann progenitor cells in the inferred results of NODE deconvolution methods. Color is scaled by the proportion value <b>c</b>. Heatmap of spatial signal strength received or emitted at each spatial location during different periods of the developing heart. The sender represents the signal emitted state at different spatial locations of the slice, and the receiver represents the signal received state at different spatial locations of the slice. Color is scaled by the signal strength value (<b>d</b>) “4-4.5PCW informational roles”, “6.5PCW informational roles”, and “9PCW informational roles” subfigures demonstrate the informational roles of the spots in the spatial transcriptomics data during the three developmental periods, with yellow representing the spot that sends out signals, and purple representing the spot that receives signals. The “flow of information” subfigure demonstrates the flow of information between the spatial location in the tissue during the three developmental periods. <b>e</b> Correlation and significance calculations between the spatial communication matrix solved by NODE and the spatial signal transduction matrix calculated based on CellChat. Three correlation coefficients (Pearson correlation coefficient, Spearman’s Rank Correlation Coefficient, and Kendall’s rank correlation coefficient) and significance between the spatial signal matrices inferred by NODE and the spatial signal matrices computed based on CellChat in the three developmental periods. In the calculation of significance, we used the 1 - <i>p</i> value. <b>f</b> Spatially, the effect of signaling in tissues on specific cells in the developing human heart. The “ventricular cardiomyocytes” heatmap sufigure indicates the distribution of ventricular cardiomyocytes at different developmental periods with the degree of aggregation in different spatial locations. Color is scaled by the proportion value. The “sender” and “receiver” heatmap subfigures demonstrate the action signals received and sent at different spatial locations in slices from the first two developmental periods (4-4.5PCW and 6.5PCW). The heatmap with arrows indicates that the signals, after acting on a specific cell type, have an effect on a specific cell, causing the distribution of the specific cell to change accordingly to the period of development. In heatmap, color is scaled by the signal strength value. Finally, the “smooth muscle cells/fibroblast like” heatmap subfigure indicates the distribution of smooth muscle cells/fibroblast like at different developmental periods with the degree of aggregation in different spatial locations. Color is scaled by the proportion value. <b>g</b> The “endothelium” and “cardiomyocytes” subfigures demonstrate the distribution of endothelium in contact with cardiomyocytes and the distribution of cardiomyocytes in contact with endothelium, respectively. In these scatter plot, red or green dots represent cardiomyocytes or endothelium, and grey dots represent other cells. The “interaction” subfigure is the schematic diagram of the communications between cardiomyocytes and the spot where endothelium is located. The colors in each scatter pie chart represent the cellular composition at this spatial location, with different colors representing different cell types. <b>h</b> NODE-predicted signaling from endocardial cardiomyocytes to epicardial cardiomyocytes in three different periods of the heart. The “4-4.5 PCW endothelium”, “6.5 PCW endothelium”, and “9 PCW endothelium” subfigures demonstrate the distribution of endothelium in contact with cardiomyocytes during three developmental periods. The “4-4.5 PCW cardiomyocytes”, “6.5 PCW cardiomyocytes”, and “9 PCW cardiomyocytes” subfigures demonstrate the distribution of cardiomyocytes in contact with endothelium in three developmental periods. Finally, The “4-4.5 PCW signaling”, “6.5 PCW signaling”, and “9 PCW signaling” subfigures indicate NODE-predicted signaling between cardiomyocytes from the endocardial cells locations-epicardial cells locations. Arrows indicate the direction of signal transmission. The colors in each scatter pie chart represent the cellular composition at this spatial location, with different colors representing different cell types.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/article/10.1038/s42003-025-07625-8/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><h3 class="c-article__sub-heading" id="Sec9">Predicting the spatial communications from NODE in developing human heart</h3><p>NODE can also infer spatial communications and calculate the strength of spatial interactions. In the heart development data, we utilized this functionality of NODE to predict information flow and spatial communications during the period of heart development. First, we mapped the strength of messages sent and received in the spatial transcriptomics data in situ for three developmental periods and labeled the regions of the heatmap where information exchange was more active (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6c</a>). The heatmap shows the flow of information in tissues and intercellular interactions (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6c</a>). Subsequently, based on the location of the heatmap peaks we searched the main communication or information flow direction of spatial locations. Finally, the communication flow between spatial locations were identified from sender to receiver of the spatial position by NODE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6d</a>), and then the directed communication flow was mapped to the original tissue based on the spatial communication flow from NODE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6d</a>). To validate and quantify the performance of NODE in spatial communication, we computed spatial communication results based on CellChat<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Jin, S. et al. Inference and analysis of cell-cell communication using CellChat. Nat. Commun. 12, 1088 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR42" id="ref-link-section-d68010897e1965">42</a></sup> which is a famous cell-cell communications tool (Methods). Briefly, we first calculated the intercellular communications based on scRNA-seq data, and then mapped the cellular communications to the spatial locations based on NODE’s deconvolution to obtain the spatial communication matrix (details in Methods). Then, we then did three tests for correlation and significance (details in Methods) between the spatial communication matrix obtained by NODE and the spatial communication matrix mapped by CellChat at three periods of the heart development. The correlation coefficients between the spatial communication results from NODE and CellChat are high in the three period except Pearson correlation coefficient at 9PCW period (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6e</a>), and, in the significant test, all three <i>p</i>-values in the three correlations between the spatial communication results of NODE and CellChat were close to 0 (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6e</a>). It means that the spatial communications inferred by NODE is very similar with the communications from CellChat, and the spatial communications from NODE can be mutual corroboration with cellular communications from CellChat.</p><h3 class="c-article__sub-heading" id="Sec10">Predicting the spatial communications, development and information flow from NODE in developing human heart</h3><p>Finally, we predicted human heart development from the result of NODE spatial communications. In studies of the human heart<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e1987">40</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e1990">43</a></sup>, smooth muscle cells and ventricular cardiomyocytes have different characteristics at different periods of development. Briefly, the positional movement and development of smooth muscle cells is related to the development of the pulmonary veins, and the development of ventricular cardiomyocytes varies over time<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e1994">43</a></sup>. Advancing through the three developmental periods of the heart, NODE found the information flow targeting smooth muscle cells and ventricular cardiomyocytes and successfully predicted the development of these two types of cells over time<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e1998">43</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). During this developmental stage of cardiac tube growth and ring formation, there is an increasing number of newly differentiated cardiomyocytes and an increase in the length of the cardiac tube<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2005">43</a></sup>. Subsequently, as the four chambers of the heart form, there is an increased value of active cardiomyocyte division in the ventricular wall, particularly at the bottom rather than the top<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2010">43</a></sup>. A large portion of smooth-walled myocardium, called pulmonary myocardium, can be found on the dorsal wall of the left atrium in adults<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2014">43</a></sup>. During the formation of the four chambers of the heart, as a result, there will be four pulmonary orifices in the left atrium, and between these orifices there will be a large amount of smooth heart muscle<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2018">43</a></sup>. The aggregation of these cells evolved gradually during development, and these results are validated in the communication matrix from NODE (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). In the prediction process of heart development, firstly NODE found the distribution of ventricular cardiomyocytes and smooth muscle cells in the three developmental periods by deconvolution (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). By calculating the communication matrix and mapping information flows and communications in space (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>), NODE identified that these cells tended to receive more active messages, indicating increased communication activity (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). Specifically, NODE found that the degree of aggregation of these cells corresponded to the degree of aggregation of the information communications (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). And after these cells received the communications, their distribution produced a corresponding change in the next period (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). Therefore, NODE successfully found the regulated states of cardiomyocytes and smooth muscle cells in development and growth, and identified other spatial locations where cells proliferate and differentiate during cardiac development<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2041">43</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6f</a>). NODE not only predicted cellular changes in heart development, but also succeeded in finding the verified cell-to-cell communications<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2048">43</a></sup>. During the development of the four chambers of the heart, NODE identified an active communication on the side of the contacting endocardium touching the myocardium<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2053">43</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6g</a>). We separately labeled the cell distribution locations where cardiomyocytes and endothelium were in contact with each other (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6g</a>), and subsequently using NODE’s communication matrix to link the communications between cardiomyocytes and endothelium (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6g</a>). NODE findings are consistent with previous studies of cardiac development: there is active communication between the two types of cells at sites where the endothelium touches cardiomyocytes<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2066">43</a></sup>. Finally, NODE also found a possible pulse signal according to the original literature<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Asp, M. et al. A Spatiotemporal Organ-Wide Gene Expression and Cell Atlas of the Developing Human Heart. Cell 179, 1647–1660.e1619 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR40" id="ref-link-section-d68010897e2070">40</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2073">43</a></sup>. The epicardial cells were designated to the outer layer of the heart, and subsequently, based on the results of NODE’s deconvolution, we identified cardiomyocytes in the vicinity of the endocardial cells, and based on NODE’s communication matrix to find signaling from the cardiomyocytes at the endocardial cells to the cardiomyocytes at the epicardial cells. In other words, since the cardiomyocytes sending the signals were co-located with the endocardial cells and the cardiomyocytes receiving the signals were co-located with the epicardial cells, the direction of these communications were actually from the cardiomyocytes inside the heart to the cardiomyocytes outside the heart<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2078">43</a></sup> (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig6">6h</a>). This is very similar to the impulse signals found after E14.5 during the study of the mouse heart<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2085">43</a></sup>. After E14.5 in mice, there is the presence of electrical impulse signals traveling from endocardial cardiomyocytes to epicardial cardiomyocytes<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2089">43</a></sup>. Based on these findings, we predict that such impulses are likely to be present during the development of the human heart, which also highlights the performance of NODE in inferring spatial communications<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2093">43</a></sup>. In summary, NODE not only shows accurate deconvolution results but also demonstrates excellent performance in inferring spatial communications.</p></div></div></section><section data-title="Discussion"><div class="c-article-section" id="Sec11-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec11">Discussion</h2><div class="c-article-section__content" id="Sec11-content"><p>We proposed a method NODE based on an optimized model to deconvolute spatial transcriptome and NODE also has a preliminary capability to resolve spatial communications inferences. Overall, NODE can not only deconvolve spatial transcriptomics data, but also infer spatial communications or spatial interactions in the tissue. Finally, by applying NODE to the developing heart data, NODE successfully found tissue developmental conditions and spatial communications within tissues that have been validated in the literature<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2106">43</a></sup>, which demonstrates that NODE is very excellent in both deconvolution and inferring spatial communication. Compared to other deconvolution methods, one of the highlights of NODE is that the number of each cell type rather than the percentage of each cell type can be obtained directly from the deconvolution result. Since NODE introduces an optimization model, it allows NODE to arbitrarily select a portion of consecutive spots for deconvolution. Moreover, when NODE deconvolves, it also outputs the progress of the deconvolution, allowing the user to observe its intermediate progress. This process can help the user to continue the deconvolution process after being forced to stop using it (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">9</a>).</p><p>When NODE was created, its optimization idea was to optimize spot by spot, which can guarantee the accuracy of NODE to some extent. Since NODE takes into account local spot-to-spot communications, the number of selected surrounding spots affects the deconvolution results, and the number of spots can be set by the user. In this paper, the number of selected spots is globally standardized, and the number of surrounding spots is set to 4.</p><p>During the solution of the model, NODE can solve for spatial communication to improve the accuracy of the deconvolution by taking into account the information of the space. At the same time, we can also use other ideas to consider the continuity of organization in deconvolution with local information in spatial transcriptomics data. For example, we can try to utilize spatial models such as Gaussian kernel<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Sun, S., Zhu, J. & Zhou, X. Statistical analysis of spatial expression patterns for spatially resolved transcriptomic studies. Nat. Methods 17, 193–200 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR44" id="ref-link-section-d68010897e2119">44</a></sup> instead of communication matrices.</p><p>At the same time, the model has some room for improvement. As deconvolution method, the present method has some dependence on the reference single-cell data. Meanwhile, in the actual situation, the reference single-cell data may not perfectly satisfy the reference of spatial transcriptomics data, resulting in a certain error. Therefore, in the future, we can consider developing the deconvolution algorithm without reference<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 45" title="Miller, B. F., Huang, F., Atta, L., Sahoo, A. & Fan, J. Reference-free cell type deconvolution of multi-cellular pixel-resolution spatially resolved transcriptomics data. Nat. Commun. 13, 2339 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR45" id="ref-link-section-d68010897e2126">45</a></sup>, so as to further improve the accuracy and efficiency of the algorithm.</p><p>To further validate NODE’s performance in detecting cellular communication, we compared it with CellChat V2<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 46" title="Jin, S., Plikus, M. V. & Nie, Q. CellChat for systematic analysis of cell–cell communication from single-cell transcriptomics. Nat. Protoc. 
 https://doi.org/10.1038/s41596-024-01045-4
 
 (2024)." href="/article/10.1038/s42003-025-07625-8#ref-CR46" id="ref-link-section-d68010897e2134">46</a></sup> and CellCall<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 47" title="Zhang, Y. et al. CellCall: integrating paired ligand–receptor and transcription factor activities for cell–cell communication. Nucleic Acids Res. 49, 8520–8534 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR47" id="ref-link-section-d68010897e2138">47</a></sup>. NODE was the only method that fully identified spatial communications previously documented in the literature<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2142">43</a></sup>, while neither CellChat nor CellCall detected these communications<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2146">43</a></sup>. And both also did not find the electrical pulse signals that appear in the developmental cycle of the mouse heart (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">8</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">46</a>). In contrast, NODE was able to find potential communication situations (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">46</a>) and found communication messages similar to the electrical pulse signals during mouse heart development<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Buijtendijk, M. F. J., Barnett, P. & van den Hoff, M. J. B. Development of the human heart. Am. J. Med. Genet. Part C., Semin. Med. Genet. 184, 7–22 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR43" id="ref-link-section-d68010897e2160">43</a></sup> (Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">46</a>). In addition, we further validate the communication of NODE and verify the correlation of NODE with CellChat and CellCall at spot resolution. The performance of NODE in all these aspects highlights the inferential performance of NODE. It’s worth noting that although CellChat has been extended to spatial transcriptomic data, it still relies on prior spot annotation and provides lower-resolution communication results, limited to cell type-to-cell type or domain-to-domain interactions. On the other hand, CellCall is optimized for single-cell data, which may limit its effectiveness in spatial transcriptomic contexts (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">8</a>).</p><p>Additionally, we discuss NODE’s ability to resist spatial noise and batch effects (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">45</a>). Results show that NODE was the only method able to accurately identify cell distribution while withstanding spatial noise and batch effects (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a> and Supplementary Fig. <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">45</a>).</p><p>Finally, we also conducted a test of NODE in terms of computational performance, and the test found that NODE is superior in terms of memory footprint. NODE has good robustness when facing memory footprint challenges (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">7</a> and Supplementary Tables <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a>).</p><p>NODE integrates spatial communication and cellular composition into its modeling, enabling inference of spatial communication and deconvolution. However, this process requires NODE to optimize the communication information of every spot, leading to longer running times when processing spatial transcriptomic data with a large number of spots. So, it is a technique, which trades speed for accuracy, and this is a primary limitation of NODE. Although NODE does not have an advantage in terms of runtime, extensive testing demonstrates that it performs well in terms of memory usage (Supplementary Tables <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a> and <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a>). Finally, concerning the application of NODE and all analytical methods in each dataset, we summarized as Supplementary Table <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">5</a>.</p></div></div></section><section data-title="Methods"><div class="c-article-section" id="Sec12-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec12">Methods</h2><div class="c-article-section__content" id="Sec12-content"><h3 class="c-article__sub-heading" id="Sec13">Obtaining deconvolution and spatial communications from NODE</h3><p>NODE is a deconvolution and spatial communication inferring method for spatial transcriptomics studies, which study transcriptional profiling of multiple locations, each containing multiple single cells. The goal of NODE is to distinguish these single cells and probe their number in each location. Different from the previous methods, NODE takes into account intercellular communications to the calculation of deconvolution. NODE is based on non-negative least squares problem and optimization iterations. In the optimization, we considered not only the composition and number of cells in a spot but also the fact that the spots are not completely independent of each other. In our understanding, tissues in close proximity to each other tend to have similar compositions and more obvious cellular communications or interactions, while the tissues that stay away from each other are not similar in composition and have less obvious communications. However, there is no way to measure the degree of communication between spots, so we consider this degree of similarity and a decision variable, to be solved together in the deconvolution process. The flowchart of NODE algorithm is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1</a>, and NODE first perform initial modelling to isolate the main expression part of the genes (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1b</a>). Then, NODE will model the spatial communications, and the original optimization decomposition will be modelled in a more detailed way to get the final modelling situation (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1c</a>). During the optimization process, NODE can not only get more accurate deconvolution results (Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1d, e</a>), but also get the information flow of spatial communication (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1f</a>). In summary, NODE quantifies the spatial communications or interactions by modelling them with two optimizations for more accurate deconvolution modelling, which provides the possibility of exploring the spatial information.</p><p>NODE requires spatial transcriptomics data with corresponding spatial coordinate’s information, and scRNA-seq data with corresponding cell type information as input (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1a</a>). During deconvolution, NODE will transform the scRNA-seq into a reference basis matrix that consists of cell types with genes (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig1">1</a>). NODE actually uses the reference basis matrix to achieve the solution of the optimization.</p><p>Firstly, we build an optimization model to decompose the spatial transcriptomics data:</p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${{\rm{Y}}}={{{\rm{X}}}}_{1}{{{\rm{B}}}}^{{{\rm{T}}}}+{\acute{\varepsilon }}_{1}$$</span></div><div class="c-article-equation__number"> (1) </div></div><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${{\rm{Y}}}={{{\rm{W}}}}_{1}{{\rm{Y}}}+{{{\rm{X}}}}_{2}{{{\rm{B}}}}^{{{\rm{T}}}}+{\acute{\varepsilon }}_{2}$$</span></div><div class="c-article-equation__number"> (2) </div></div><p>The <span class="mathjax-tex">${{\rm{Y}}}$</span> denotes the matrix of the spatial transcriptomics data with a form <span class="mathjax-tex">${{\rm{n}}}\times {{\rm{g}}}$</span>. where (i, j) element represents the j gene’s expression value in spot i. Both <span class="mathjax-tex">${{{\rm{X}}}}_{1}$</span> and <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> denote <span class="mathjax-tex">${{\rm{n}}}\times {{\rm{k}}}$</span> cellular composition and distribution matrix, where each row represents the proportions of every cell type in each spatial location (spot) and each column represents different cell types. The (i, j) element in <span class="mathjax-tex">${{{\rm{X}}}}_{1}$</span> or <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> represents the number of cell type j in spot i. The <span class="mathjax-tex">${{\rm{B}}}$</span> matrix is the cell-type-specific reference basis matrix from scRNA-seq data. The row of the <span class="mathjax-tex">${{\rm{B}}}$</span> matrix represents gene, and <span class="mathjax-tex">${{\rm{B}}}$</span> matrix’s column represents cell type. The <span class="mathjax-tex">${{{\rm{W}}}}_{1}$</span> denotes the spatial communication matrix between spatial locations (spots). The value on its element represents the communication strength. The <span class="mathjax-tex">${\acute{\varepsilon }}_{1}$</span> and <span class="mathjax-tex">${\acute{\varepsilon }}_{2}$</span> is the residual between the estimated value and the true value. In the optimal solution of this model, <span class="mathjax-tex">${{{\rm{W}}}}_{1},$</span> <span class="mathjax-tex">${{{\rm{X}}}}_{1}$</span> and <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> are our decision variables that need be solved in iterations that minimize the residuals <span class="mathjax-tex">${\acute{\varepsilon }}_{1}$</span> and <span class="mathjax-tex">${\acute{\varepsilon }}_{2}$</span>. During the solution process, we performed multi-optimization.</p><p>In Eqs. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ1">1</a>) and (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ2">2</a>), <span class="mathjax-tex">${{{\rm{X}}}}_{1}$</span> is as the initial value of <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ2">2</a>). The multi-optimization of NODE is carried out in two parts, firstly NODE solves the main part of gene expression of spatial transcriptomics data according to Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ1">1</a>). Secondly, using the optimization result <span class="mathjax-tex">${{{\rm{X}}}}_{1}$</span> in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ1">1</a>) as the initial value of <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ2">2</a>), NODE will perform an optimization search of the spatial communication matrix <span class="mathjax-tex">${{{\rm{W}}}}_{1}$</span> and cellular composition and distribution matrix <span class="mathjax-tex">${{{\rm{X}}}}_{2}$</span> according to Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/article/10.1038/s42003-025-07625-8#Equ2">2</a>) with minimize the residual <span class="mathjax-tex">${\acute{\varepsilon }}_{2}$</span> (details in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>).</p><h3 class="c-article__sub-heading" id="Sec14">Reference basis matrix construction</h3><p>We used single-cell RNA-Seq data for reference basis matrix construction. There are two main steps in the construction of the reference basis matrix, (1) the genes that are expressed in both the scRNA-seq reference data and the spatial transcriptomics data were selected; (2) The gene expression was averaged for each cell type, and the matrix with average gene expression was used as the reference basis matrix (details in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>).</p><h3 class="c-article__sub-heading" id="Sec15">Simulations and deconvolution analysis evaluation</h3><p>All simulations are described in the Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">3</a>. In simulated data, we used <span class="mathjax-tex">$\widetilde{X}$</span> to denote the inferred result, and <span class="mathjax-tex">${{\rm{X}}}$</span> as the real results of the simulated data. After obtaining the inference results, we evaluated the performance of NODE by calculating the RMSE between <span class="mathjax-tex">$\widetilde{X}$</span> and <span class="mathjax-tex">${{\rm{X}}}$</span>, where n represents the number of spots and k represents the number of cell species. And RMSE is given by the following equation.</p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${{\rm{RMSE}}}=\sqrt{\frac{1}{{{\rm{nk}}}}\mathop{\sum }\limits_{{{\rm{i}}}=1}^{{{\rm{n}}}}\mathop{\sum }\limits_{{{\rm{j}}}=1}^{{{\rm{k}}}}{({\widetilde{X}}_{{{\rm{ij}}}}-{{{\rm{X}}}}_{{{\rm{ij}}}})}^{2}}$$</span></div></div><h3 class="c-article__sub-heading" id="Sec16">Methods comparison</h3><p>We compared NODE with five famous deconvolution methods: SpaTalk<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 17" title="Shao, X. et al. Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk. Nat. Commun. 13, 4429 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR17" id="ref-link-section-d68010897e3427">17</a></sup>(version1.0), RCTD<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 18" title="Cable, D. M. et al. Robust decomposition of cell type mixtures in spatial transcriptomics. Nat. Biotechnol. 40, 517–526 (2022)." href="/article/10.1038/s42003-025-07625-8#ref-CR18" id="ref-link-section-d68010897e3431">18</a></sup>(2.2.0), Seurat<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="Stuart, T. et al. Comprehensive Integration of Single-Cell Data. Cell 177, 1888–1902.e1821 (2019)." href="/article/10.1038/s42003-025-07625-8#ref-CR20" id="ref-link-section-d68010897e3435">20</a></sup>(4.3.0), deconvSeq<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 19" title="Andersson, A. et al. Single-cell and spatial transcriptomics enables probabilistic inference of cell type topography. Commun. Biol. 3, 565 (2020)." href="/article/10.1038/s42003-025-07625-8#ref-CR19" id="ref-link-section-d68010897e3439">19</a></sup>(0.3.0), and SPOTlight<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 21" title="Elosua-Bayes, M., Nieto, P., Mereu, E., Gut, I. & Heyn, H. SPOTlight: seeded NMF regression to deconvolute spatial transcriptomics spots with single-cell transcriptomes. Nucleic Acids Res. 49, e50 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR21" id="ref-link-section-d68010897e3443">21</a></sup>(0.1.7). For all methods, the recommended default parameter was used to set for the deconvolution analysis. The deconvolution results from RCTD, Seurat, deconvSeq and SPOTlight are cell type proportions. Therefore, when calculating the simulated data, it is necessary to multiply each cell proportion by the total number of cells in each spot to get the number of each cell type to complete the RMSE.</p><p>In exploring the performance of NODE in inferred communication, we refer to the CellChat (1.6.1)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Jin, S. et al. Inference and analysis of cell-cell communication using CellChat. Nat. Commun. 12, 1088 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR42" id="ref-link-section-d68010897e3450">42</a></sup>. In Cellchat, the recommended default parameter was used. And since the current version of CellChat does not infer spatial communications, we did a mapping. Specifically, we compute the communications between cell types based on CellChat and subsequently map these communications into spatial communications based on the result of the deconvolution of NODE to form a spot-spot communication matrix.</p><h3 class="c-article__sub-heading" id="Sec17">Real data analyses</h3><p>All real datasets used in this study are described in the Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a>. We applied the different methods to deconvolute the real datasets, and the same spatial transcriptomics data and the same scRNA-seq data are necessary for each analysis (details in Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">4</a>). After deconvolution, we calculated the percentage of each cell type in each spot based on the number of each cell type. For MOB and PDAC datasets, we compared the distribution of cells in the deconvolution results with the matched H&E image. Specifically, we stacked the results of the deconvolution of each method with the corresponding H&E image. In these data, we used cell type marker genes as surrogates to examine the spatial distribution of cell types on the tissue<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="Benner, P. & Vingron, M. Quantifying the tissue-specific regulatory information within enhancer DNA sequences. NAR Genom. Bioinforma. 3, lqab095 (2021)." href="/article/10.1038/s42003-025-07625-8#ref-CR48" id="ref-link-section-d68010897e3469">48</a></sup>. For the MOB dataset, we performed a Pearson’s correlation calculation. We find the marker gene corresponding to a specific cell type, treat the distribution of that cell type in all the spots as one vector, the expression of the marker gene in all the spots as another vector, and take the Pearson’s correlation for the two vectors. We quantify the performance of our deconvolution results in this way.</p><p>In addition to this, we also plotted figures by ggplot2 (R package), and set thresholds (Supplementary Note <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM1">1</a>) based on the color stratification of the R package plots, and performed the calculation of ACC (accuracy) and AUC (area under the curve) base on the thresholds. In this process, we dichotomized the expression of marker genes, setting spots above the threshold to 1 and below the threshold to 0. Similarly, we did the same for the distribution of cells in the deconvolution results, and then considered the expression of the processed marker genes as the real value, and the distribution of the cells as the predicted value, and carried out the ACC and AUC calculation. When performing thresholding, the thresholds used by all deconvolution methods are globally uniform. For the PDAC dataset, we manually divided the PDAC into regions based on the available literature. We performed a differential comparison of cell type distribution based on the delineated regions. Specifically, we did a statistical analysis of cell type distribution in cancerous and non-cancerous areas separately, and finally the results were superimposed in the same graph for comparison. For the SCC dataset, instead of stacking its deconvolution results against the corresponding H&E image, we did a comparison of the results against the corresponding H&E image as a whole. And we also performed the calculation of the correlation coefficient. For developing human heart data, we first plotted the results of the deconvolution and evaluated the results of the deconvolution of NODE based on the original literature, and then we showed the flow of information within the tissue during different development periods based on NODE’s inference of its spatial communications. Subsequently, we compared NODE’s communications inference with the spatial communication inference results obtained based on CellChat, calculated their correlation, and performed a significance test. Finally, we mapped in detail the spatial communications status of the spot-to-spot in the spatial transcriptomics data in different periods and found literature validation of these results.</p><h3 class="c-article__sub-heading" id="Sec18">Statistics and reproducibility</h3><p>All single-cell and spatial transcriptomics data used for simulation and real datasets are publicly available. The codes for other methods are also publicly accessible and default parameters are applied for all functions unless stated otherwise. For our method, we used Python language (version 3.9.9) and packages numpy (version 1.23.5), scipy (version 1.10.0), and pandas (version 2.2.2). Figs. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig2">2</a>a and <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/article/10.1038/s42003-025-07625-8#Fig4">4f</a> the upper and lower bounds of the boxplots represent the 75th and 25th percentiles, respectively. The center bars indicate the medians, and the whiskers denote values up to 1.5 interquartile ranges above the 75th or below the 25th percentiles.</p><h3 class="c-article__sub-heading" id="Sec19">Reporting summary</h3><p>Further information on research design is available in the <a data-track="click" data-track-label="link" data-track-action="supplementary material anchor" href="/article/10.1038/s42003-025-07625-8#MOESM2">Nature Portfolio Reporting Summary</a> linked to this article.</p></div></div></section> </div> <section data-title="Data availability"><div class="c-article-section" id="data-availability-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="data-availability">Data availability</h2><div class="c-article-section__content" id="data-availability-content"> <p>This study only used of publicly available datasets. These include the MOB dataset (<a href="http://www.spatialtranscriptomicsresearch.org">http://www.spatialtranscriptomicsresearch.org</a>) and scRNA-seq references is publicly available from GEO database (<a href="https://www.ncbi.nlm.nih.gov/geo/">https://www.ncbi.nlm.nih.gov/geo/</a>) with accession “GSE121891”; The spatial data and scRNA-seq data of human PDAC were from GEO database (GSE111672); The spatial data and scRNA-seq data of human SCC were from GEO database (GSE144240). The spatial transcriptomics data and scRNA-seq data of developing human heart are available at <a href="https://www.spatialresearch.org">https://www.spatialresearch.org</a>. All simulated datasets can be found at <a href="https://figshare.com/articles/dataset/NODE_simulated_data/28252061?file=51835676">https://figshare.com/articles/dataset/NODE_simulated_data/28252061?file=51835676</a> or <a href="https://github.com/wzdrgi/NODE">https://github.com/wzdrgi/NODE</a>.</p> </div></div></section><section data-title="Code availability"><div class="c-article-section" id="code-availability-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="code-availability">Code availability</h2><div class="c-article-section__content" id="code-availability-content"> <p>The NODE software package and source code have been deposited at <a href="https://github.com/wzdrgi/NODE">https://github.com/wzdrgi/NODE</a>. 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Yi Liu contributed to the data analyses. Zedong Wang developed NODE Python package and wrote the first manuscript draft. Xiao Chang and Xiaoping Liu designed and supervised the study. All authors contributed by comments and approved the final manuscript.</p><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding authors</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:chxlaugh@aufe.edu.cn">Xiao Chang</a> or <a id="corresp-c2" href="mailto:xpliu@ucas.ac.cn">Xiaoping Liu</a>.</p></div></div></section><section data-title="Ethics declarations"><div class="c-article-section" id="ethics-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="ethics">Ethics declarations</h2><div class="c-article-section__content" id="ethics-content"> <h3 class="c-article__sub-heading" id="FPar2">Competing interests</h3> <p>The authors declare no competing interests.</p> </div></div></section><section data-title="Peer review"><div class="c-article-section" id="peer-review-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="peer-review">Peer review</h2><div class="c-article-section__content" id="peer-review-content"> <h3 class="c-article__sub-heading" id="FPar1">Peer review information</h3> <p><i>Communications Biology</i> thanks the anonymous reviewers for their contribution to the peer review of this work. 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