{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T02:06:30Z","timestamp":1790647590343,"version":"4.1.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":223,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["440773101"],"award-info":[{"award-number":["440773101"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>Single-molecule localization microscopy (SMLM) can resolve intracellular structures down to the nanoscale, but often produces sparse and incomplete data. Particle averaging (PA) can aid with the reconstruction of complete structures, but traditional PA methods can suffer from template bias or the high computational costs of geometric alignment.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>To address these limitations, we developed a geometric deep learning (GDL) framework for enhanced, template-free 3D particle averaging. Our pipeline uses a GDL autoencoder, trained on high-fidelity simulated data, to map incomplete point clouds into a robust latent space. By averaging feature vectors directly within this space, our method bypasses the need for explicit 3D alignment. We validated our approach on simulated DNA origami and experimental nuclear pore complex (NPC) data. The latent space averaging successfully reconstructed NPC structures with key metrics (ring radius \u224846nm, ring distance \u224852nm) that are comparable to state-of-the-art methods. This work establishes a viable GDL pipeline for SMLM analysis, offering an efficient alternative to traditional PA. While the current model requires structure-specific training, our results highlight the significant potential of GDL for quantitative structural biology.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability<\/jats:title>\n                    <jats:p>https:\/\/github.com\/dianamindroc\/smlm<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioadv\/vbag228","type":"journal-article","created":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T11:35:26Z","timestamp":1786448126000},"source":"Crossref","is-referenced-by-count":0,"title":["Towards improved particle reconstruction for single-molecule localization microscopy using geometric deep learning"],"prefix":"10.1093","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3104-2129","authenticated-orcid":false,"given":"Diana","family":"Mindroc-Filimon","sequence":"first","affiliation":[{"name":"Department of Biotechnology and Biophysics, Biocenter, University of W\u00fcrzburg , W\u00fcrzburg,","place":["Germany"]},{"name":"Graduate School of Life Sciences , W\u00fcrzburg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1889-0406","authenticated-orcid":false,"given":"Dominic A","family":"Helmerich","sequence":"additional","affiliation":[{"name":"Department of Biotechnology and Biophysics, Biocenter, University of W\u00fcrzburg , W\u00fcrzburg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4978-9156","authenticated-orcid":false,"given":"Patrick","family":"Salome","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School , Boston, MA,","place":["United States"]},{"name":"Translational Radiation Oncology and Medical Physics in Radiation Oncology, German Cancer Research Center , Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1692-3219","authenticated-orcid":false,"given":"Markus","family":"Sauer","sequence":"additional","affiliation":[{"name":"Department of Biotechnology and Biophysics, Biocenter, University of W\u00fcrzburg , W\u00fcrzburg,","place":["Germany"]},{"name":"Rudolf Virchow Center for Integrative and Translational Bioimaging, University of W\u00fcrzburg , W\u00fcrzburg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8049-6186","authenticated-orcid":false,"given":"Philip","family":"Kollmannsberger","sequence":"additional","affiliation":[{"name":"Department of Biotechnology and Biophysics, Biocenter, University of W\u00fcrzburg , W\u00fcrzburg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,8,11]]},"reference":[{"key":"2026092821471300800_vbag228-B1","doi-asserted-by":"publisher","first-page":"752788","DOI":"10.3389\/fbinf.2021.752788","article-title":"Fourier ring correlation and anisotropic kernel density estimation improve deep learning based SMLM reconstruction of microtubules","volume":"1","author":"Berberich","year":"2021","journal-title":"Front Bioinform"},{"key":"2026092821471300800_vbag228-B2","doi-asserted-by":"publisher","first-page":"014003","DOI":"10.1088\/2050-6120\/3\/1\/014003","article-title":"Resolution improvement by 3D particle averaging in localization microscopy","volume":"3","author":"Broeken","year":"2015","journal-title":"Methods Appl Fluoresc"},{"key":"2026092821471300800_vbag228-B3","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2017.2693418","article-title":"Geometric deep learning: going beyond Euclidean data","volume":"34","author":"Bronstein","year":"2017","journal-title":"IEEE Signal Process Mag"},{"key":"2026092821471300800_vbag228-B4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s43586-020-00009-8","article-title":"DNA origami","volume":"1","author":"Dey","year":"2021","journal-title":"Nat Rev Methods Primers"},{"key":"2026092821471300800_vbag228-B5","doi-asserted-by":"publisher","first-page":"3228","DOI":"10.3390\/electronics12153228","article-title":"Fast context-awareness encoder for LiDAR point semantic segmentation","volume":"12","author":"Du","year":"2023","journal-title":"Electronics (Basel)"},{"key":"2026092821471300800_vbag228-B6","doi-asserted-by":"publisher","first-page":"858","DOI":"10.1109\/ISBI48211.2021.9434116","article-title":"Stacked. Pointnets for alignment of particles with cylindrical symmetry in single molecule localization microscopy","author":"Fan","year":"2021","journal-title":"2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI)"},{"key":"2026092821471300800_vbag228-B7","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780195182187.001.0001","volume-title":"Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State","author":"Frank","year":"2006"},{"key":"2026092821471300800_vbag228-B8","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00030"},{"key":"2026092821471300800_vbag228-B9","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1038\/s41592-018-0136-6","article-title":"Template-free 2D particle fusion in localization microscopy","volume":"15","author":"Heydarian","year":"2018","journal-title":"Nat Methods"},{"key":"2026092821471300800_vbag228-B10","doi-asserted-by":"publisher","first-page":"2847","DOI":"10.1038\/s41467-021-22006-5","article-title":"3D particle averaging and detection of macromolecular symmetry in localization microscopy","volume":"12","author":"Heydarian","year":"2021","journal-title":"Nat Commun"},{"key":"2026092821471300800_vbag228-B11","author":"Heydarian","year":"2021"},{"key":"2026092821471300800_vbag228-B12","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1038\/nrn.2017.129","article-title":"The nano-architecture of the axonal cytoskeleton","volume":"18","author":"Leterrier","year":"2017","journal-title":"Nat Rev Neurosci"},{"key":"2026092821471300800_vbag228-B13","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1242\/jcs.098822","article-title":"Super-resolution imaging visualizes the eightfold symmetry of gp210 proteins around the nuclear pore complex and resolves the central channel with nanometer resolution","volume":"125","author":"L\u00f6schberger","year":"2012","journal-title":"J Cell Sci"},{"key":"2026092821471300800_vbag228-B14","doi-asserted-by":"publisher","first-page":"220079","DOI":"10.1098\/rsob.220079","article-title":"Mapping molecular complexes with super-resolution microscopy and single-particle analysis","volume":"12","author":"Mendes","year":"2022","journal-title":"Open Biol"},{"key":"2026092821471300800_vbag228-B15","doi-asserted-by":"publisher","first-page":"e202311073","DOI":"10.1083\/jcb.202311073","article-title":"AI analysis of super-resolution microscopy: biological discovery in the absence of ground truth","volume":"223","author":"Nabi","year":"2024","journal-title":"J Cell Biol"},{"key":"2026092821471300800_vbag228-B16","doi-asserted-by":"publisher","first-page":"3137","DOI":"10.1038\/s41467-019-10948-w","article-title":"Super-resolution microscopy reveals ultra-low CD19 expression on myeloma cells that triggers elimination by CD19 CAR-T","volume":"10","author":"Nerreter","year":"2019","journal-title":"Nat Commun"},{"key":"2026092821471300800_vbag228-B17","doi-asserted-by":"publisher","author":"Qi","DOI":"10.1109\/CVPR.2017.16"},{"key":"2026092821471300800_vbag228-B18","doi-asserted-by":"publisher","first-page":"7478","DOI":"10.1021\/acs.chemrev.6b00667","article-title":"Single-molecule localization microscopy in eukaryotes","volume":"117","author":"Sauer","year":"2017","journal-title":"Chem Rev"},{"key":"2026092821471300800_vbag228-B19","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1038\/s41556-018-0251-8","article-title":"Super-resolution microscopy demystified","volume":"21","author":"Schermelleh","year":"2019","journal-title":"Nat Cell Biol"},{"key":"2026092821471300800_vbag228-B20","doi-asserted-by":"publisher","first-page":"1082","DOI":"10.1038\/s41592-021-01236-x","article-title":"Deep learning enables fast and dense single-molecule localization with high accuracy","volume":"18","author":"Speiser","year":"2021","journal-title":"Nat Methods"},{"key":"2026092821471300800_vbag228-B21","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1126\/science.1240672","article-title":"Nuclear pore scaffold structure analyzed by super-resolution microscopy and particle averaging","volume":"341","author":"Szymborska","year":"2013","journal-title":"Science"},{"key":"2026092821471300800_vbag228-B22","doi-asserted-by":"publisher","author":"Tchapmi","year":"2019","DOI":"10.1109\/CVPR.2019.00047"},{"key":"2026092821471300800_vbag228-B23","doi-asserted-by":"publisher","first-page":"btad587","DOI":"10.1093\/bioinformatics\/btad587","article-title":"Simulating structurally variable nuclear pore complexes for microscopy","volume":"39","author":"Theiss","year":"2023","journal-title":"Bioinformatics"},{"key":"2026092821471300800_vbag228-B24","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1038\/nprot.2011.336","article-title":"Direct stochastic optical reconstruction microscopy with standard fluorescent probes","volume":"6","author":"van de Linde","year":"2011","journal-title":"Nat Protoc"},{"key":"2026092821471300800_vbag228-B25","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"van der Maaten","year":"2008","journal-title":"J Mach Learn Res"},{"key":"2026092821471300800_vbag228-B26","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1038\/nature15381","article-title":"In situ structural analysis of the human nuclear pore complex","volume":"526","author":"von Appen","year":"2015","journal-title":"Nature"},{"key":"2026092821471300800_vbag228-B27","doi-asserted-by":"publisher","author":"Vries","DOI":"10.1101\/2022.06.17.496550"},{"key":"2026092821471300800_vbag228-B28","doi-asserted-by":"publisher","first-page":"3281","DOI":"10.1093\/bioinformatics\/btac320","article-title":"Joint registration of multiple point clouds for fast particle fusion in localization microscopy","volume":"38","author":"Wang","year":"2022","journal-title":"Bioinformatics"},{"key":"2026092821471300800_vbag228-B29","doi-asserted-by":"publisher","author":"Yang","DOI":"10.1109\/CVPR.2018.00029"},{"key":"2026092821471300800_vbag228-B30","doi-asserted-by":"publisher","author":"Yuan","DOI":"10.1109\/3DV.2018.00088"}],"container-title":["Bioinformatics Advances"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformaticsadvances\/advance-article-pdf\/doi\/10.1093\/bioadv\/vbag228\/70615182\/vbag228.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformaticsadvances\/article-pdf\/6\/1\/vbag228\/70615182\/vbag228.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformaticsadvances\/article-pdf\/6\/1\/vbag228\/70615182\/vbag228.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T01:47:18Z","timestamp":1790646438000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformaticsadvances\/article\/doi\/10.1093\/bioadv\/vbag228\/8759243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1,7]]}},"URL":"https:\/\/doi.org\/10.1093\/bioadv\/vbag228","relation":{},"ISSN":["2635-0041"],"issn-type":[{"value":"2635-0041","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026]]},"published":{"date-parts":[[2026]]},"article-number":"vbag228"}}