Quantifying neuronal differentiation using temporal topological persistence

Temporal topology provides an interpretable framework for neuronal morphogenesis | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Temporal topology provides an interpretable framework for neuronal morphogenesis Killian Rigaux , Andre Ferreira Castro , View ORCID Profile Lida Kanari doi: https://doi.org/10.1101/2025.06.02.657366 Killian Rigaux 1 The Quantum Plumbing Lab, Ecole Polytechnique Federale de Lausanne (EPFL), 1015 Lausanne, Switzerland; Find this author on Google Scholar Find this author on PubMed Search for this author on this site Andre Ferreira Castro 2 School of Life Sciences, Technical University of Munich, Freising, Germany; Find this author on Google Scholar Find this author on PubMed Search for this author on this site Lida Kanari 3 Mathematical Institute, University of Oxford Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Lida Kanari For correspondence: lida.kanari{at}gmail.com Abstract Info/History Metrics Supplementary material Preview PDF Abstract Neuronal morphogenesis arises through coordinated neurite dynamics that generate cell-type specific dendritic branching during development. Recent advances in high-throughput time-lapse imaging techniques have transformed our ability to track such growth dynamics, yielding comprehensive anatomical datasets of neuronal morphologies. However, quantifying these structural trajectories during neuronal development remains a major challenge. We introduce the Temporal Topological Morphology Descriptor (TTMD), a framework that combines persistent topology with time-resolved neuronal imaging to quantify developmental trajectories of neuronal architecture. Applying TTMD to datasets of Drosophila sensory neurons, we show that developmental stages, branching processes, and mutant-specific growth dynamics can be decoded directly from topology without manual feature selection. Topological morphology descriptor (TMD) accurately resolve major developmental transitions in Class I Drosophila neurons, whereas temporal topology (TTMD) is required to uncover subtle alterations in branch dynamics caused by mutations in actin regulatory pathways in Class III \textit{Drosophila} neurons. TTMD further enables automated topological tracking of branch emergence and retraction across development, overcoming the limitations of labor-intensive manual annotation. These results demonstrate that temporal topology provides a unified and interpretable language for neuronal morphogenesis, enabling the automated analysis of developmental neuroanatomy, and identifying pathological alterations in neuronal structure. Competing Interest Statement The authors have declared no competing interest. Footnotes Updated to add results and for corrections of previous content. Funder Information Declared Medical Research Council, https://ror.org/03x94j517 , MR/Z504804/1 Copyright The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license . View the discussion thread. Back to top Previous Next Posted May 20, 2026. Download PDF Supplementary Material Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Temporal topology provides an interpretable framework for neuronal morphogenesis Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. 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Share Temporal topology provides an interpretable framework for neuronal morphogenesis Killian Rigaux , Andre Ferreira Castro , Lida Kanari bioRxiv 2025.06.02.657366; doi: https://doi.org/10.1101/2025.06.02.657366 Share This Article: Copy Citation Tools Temporal topology provides an interpretable framework for neuronal morphogenesis Killian Rigaux , Andre Ferreira Castro , Lida Kanari bioRxiv 2025.06.02.657366; doi: https://doi.org/10.1101/2025.06.02.657366 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Neuroscience Subject Areas All Articles Animal Behavior and Cognition (7629) Biochemistry (17660) Bioengineering (13881) Bioinformatics (41910) Biophysics (21436) Cancer Biology (18576) Cell Biology (25480) Clinical Trials (138) Developmental Biology (13368) Ecology (19887) Epidemiology (2067) Evolutionary Biology (24302) Genetics (15598) Genomics (22482) Immunology (17726) Microbiology (40360) Molecular Biology (17163) Neuroscience (88534) Paleontology (666) Pathology (2830) Pharmacology and Toxicology (4821) Physiology (7637) Plant Biology (15129) Scientific Communication and Education (2045) Synthetic Biology (4290) Systems Biology (9817) Zoology (2269)