A Structural Principle for Macroscopic Neural Dynamics Correlations

A Structural Principle for Macroscopic Neural Dynamics Correlations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Structural Principle for Macroscopic Neural Dynamics Correlations CiRong Liu, Qihang Wu, Quan Wen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8297673/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A central question in neuroscience is how the brain’s structural connectivity gives rise to its emergent, correlated dynamics. These large-scale dynamical correlations underlie functional networks that support cognitive functions. Here, we identify coupling correlation—the similarity between the input connectivity profiles of brain regions—as a key structural determinant of macroscopic neural dynamical correlation. Using dynamical mean-field theory (DMFT) and numerical simulations of random neural network models, we demonstrate that coupling correlation quantitatively governs dynamical correlation. The functional form of this structure–function mapping is dictated by the eigenvalue spectrum of the coupling correlation matrix: networks with bulk eigenspectra exhibit an exact linear relationship, whereas biologically plausible long-tailed spectra yield an approximately linear mapping except when the magnitude of coupling correlation approaches unity. Particularly, a long-tailed spectrum is necessary to reproduce the appropriate magnitude and size-invariance of coupling correlations observed in empirical data, thereby sustaining non-vanishing dynamical correlations that may support brain function in large systems. The theoretical prediction of approximate linearity is consistently validated using empirical datasets that include both structural coupling and neural dynamics in humans, mice, and Drosophila. Together, these results provide a mechanistic and quantitative framework linking macroscopic brain network structure to emergent population dynamics—an essential step toward a unified theory of structure–function relationship in the brain. Biological sciences/Neuroscience/Computational neuroscience/Dynamical systems Biological sciences/Neuroscience/Computational neuroscience/Network models Biological sciences/Neuroscience/Computational neuroscience/Network models neural dynamics neural correlation dynamical mean-field theory random neural network structure-function relationship Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementaryinformation.pdf Supplementary information Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8297673","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":570287308,"identity":"232c7bc9-6eef-4f73-8ea2-82a2e69f490d","order_by":0,"name":"CiRong Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAoUlEQVRIiWNgGAWjYFAC5oYDDBUSJGlhBGo5Q6oWBsY2UjTwzz7YeJh3noWcOQPzww8MNXcIa5E4l9hwmHebhLFlA5uxBMOxZ4S1GPAwgrUkbjjAYAZ05GFitcwBaWH/RoqWBpAWHiJtkTjD2HBwzjEJY4PDPMUSCceI0MLfw3z4w5uaOjmD4+0bP3yoIUILAjADcQIpGkbBKBgFo2AU4AYAEZQ1I5J/LAsAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-7986-4615","institution":"Institute of Neuroscience Chinese Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"CiRong","middleName":"","lastName":"Liu","suffix":""},{"id":570287309,"identity":"f7d059c1-9a86-4f43-b0cc-96e681a8f114","order_by":1,"name":"Qihang Wu","email":"","orcid":"","institution":"Institute of Neuroscience Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Qihang","middleName":"","lastName":"Wu","suffix":""},{"id":570287310,"identity":"073d68f3-cb65-4167-87f3-3996647b0684","order_by":2,"name":"Quan Wen","email":"","orcid":"https://orcid.org/0000-0003-0268-8403","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Quan","middleName":"","lastName":"Wen","suffix":""}],"badges":[],"createdAt":"2025-12-07 04:30:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8297673/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8297673/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105565751,"identity":"f18be57f-5034-421b-ba5b-544f7a5e1ccc","added_by":"auto","created_at":"2026-03-27 12:54:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":19410580,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8297673/v1_covered_bd194344-335a-4fbe-8efb-9a47cdf78c7a.pdf"},{"id":99701546,"identity":"3153d97e-7c4a-421d-b3ab-aa7221be2aeb","added_by":"auto","created_at":"2026-01-07 11:50:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":8550301,"visible":true,"origin":"","legend":"Supplementary information","description":"","filename":"Supplementaryinformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8297673/v1/991a4ac0be96904625a60ddc.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A Structural Principle for Macroscopic Neural Dynamics Correlations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"neural dynamics, neural correlation, dynamical mean-field theory, random neural network, structure-function relationship","lastPublishedDoi":"10.21203/rs.3.rs-8297673/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8297673/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A central question in neuroscience is how the brain’s structural connectivity gives rise to its emergent, correlated dynamics. 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