Bifurcations and Ca2+ oscillations dynamics in a reduced Tsodyks-IP3-Li-Rinzel astrocyte network

Bifurcations and Ca2+ oscillations dynamics in a reduced Tsodyks-IP3-Li-Rinzel astrocyte network | 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 Research Article Bifurcations and Ca 2+ oscillations dynamics in a reduced Tsodyks-IP 3 -Li-Rinzel astrocyte network Xin Ge, Yaru Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7252839/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 tripartite synapse always links two neuronsand an astrocyte, while this astrocyte regulatessynaptic signal transmission between neurons by modulatingthe release of neurotransmitters through the oscillationof intracellular calcium ion (Ca2+). To investigateastrocytic network Ca2+ signaling regulation, thisstudy combines the Li-Rinzel Ca2+ oscillation model,Volman-Ben-Jacob’s inositol 1,4,5-trisphosphate (IP3)generation model, and the Li-Rinzel model to design asimplified Tsodyks-IP3-Li-Rinzel (TILR) astrocyte network.Using slow-fast dynamics method and comparison analysis of time series graphs of relevant variablesbefore and after dimensionality reduction, we parameterizeinactive neurotransmitter proportions via peakvalleyaveraging for boosting computational efficiency. Based on bifurcation theory, our TILR astrocyte networkundergoes two supercritical Hopf bifurcations withcodimension-one bifurcation parameter IP3 generationrate (rip3). Our simulations also reveal that the Ca2+ concentration ([Ca2+]) changes from a resting state toa decaying state oscillation and then to a sustainedlarge-amplitude oscillation when rip3 is near these twobifurcation thresholds. Furthermore, codimension-twobifurcation analysis in the (rip3, rL)-plane identifies aBogdanov-Takens (BT) point, which acts as an organizingcenter with three canonical bifurcation curve representationsmediating the global bistability-oscillationtransition. Moreover, simulations reveal that, under identicalconditions, low-frequency stimulation fails to generate Ca2+ oscillations, medium-frequency induces stable Ca2+ oscillations, while high-frequency increases theaverage [Ca2+] but disrupts the persistence of oscillations.Therefore, Ca2+ signal transduction is co-regulatedby rip3, rL and stimulation frequency. This proposedmulti-scale astrocyte network offers a theoretical frameworkfor translating computational data into neuropatho-logical interventions. TILR astrocyte network Ca2+ oscillations Dimensionality reduction Hopf bifurcation Bogdanov-Takens bifurcation Stimulation frequency Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7252839","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":498148791,"identity":"7fff32d1-6cae-43ff-9552-c8febb2f79de","order_by":0,"name":"Xin Ge","email":"","orcid":"","institution":"Jinan University","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Ge","suffix":""},{"id":498148792,"identity":"8e2a982e-17cf-404f-9ef5-96d7f5e118cb","order_by":1,"name":"Yaru Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYLCCBwYMcvbHmw8YgHkHiNGSYMBgzHDmWAIpWhgYEhtu5EB0ENRicPzsM4mEgsPGjDNyPhQXtjHI8d1IYPxcgE/LmXQziQSDw3LMPG83GM9sYzCWvJHALD0Dn5YDaWwgLcZs7LkbjHnbGBI33EhgY+bBp+X8M7CWxB6GnAcgLfWEtdyA2JI4gyOHAaQlwYCQFskbz5gtEgzSjQ14jhkY85yTMJx55mGzND4tfOfTGG98+GMtZ8De/MyYp8xGnu948sHP+LQoHECw2YARIwGkGRvwaGBgkEeSZn6AV+koGAWjYBSMWAAAudNLgd7Bu6IAAAAASUVORK5CYII=","orcid":"","institution":"Jinan University","correspondingAuthor":true,"prefix":"","firstName":"Yaru","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-07-30 12:23:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7252839/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7252839/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94473300,"identity":"2f83b012-a152-4bf6-af3f-6a25ac02c37f","added_by":"auto","created_at":"2025-10-27 15:43:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7430114,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7252839/v1_covered_c2625a1f-5a08-4c20-bfb4-e623d63a93b7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eBifurcations and Ca\u003csup\u003e2+\u003c/sup\u003e oscillations dynamics in a reduced Tsodyks-IP\u003csub\u003e3\u003c/sub\u003e-Li-Rinzel astrocyte network\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"TILR astrocyte network, Ca2+ oscillations, Dimensionality reduction, Hopf bifurcation, Bogdanov-Takens bifurcation, Stimulation frequency","lastPublishedDoi":"10.21203/rs.3.rs-7252839/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7252839/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA tripartite synapse always links two neuronsand an astrocyte, while this astrocyte regulatessynaptic signal transmission between neurons by modulatingthe release of neurotransmitters through the oscillationof intracellular calcium ion (Ca2+). To investigateastrocytic network Ca2+ signaling regulation, thisstudy combines the Li-Rinzel Ca2+ oscillation model,Volman-Ben-Jacob’s inositol 1,4,5-trisphosphate (IP3)generation model, and the Li-Rinzel model to design asimplified Tsodyks-IP3-Li-Rinzel (TILR) astrocyte network.Using slow-fast dynamics method and comparison analysis of time series graphs of relevant variablesbefore and after dimensionality reduction, we parameterizeinactive neurotransmitter proportions via peakvalleyaveraging for boosting computational efficiency. Based on bifurcation theory, our TILR astrocyte networkundergoes two supercritical Hopf bifurcations withcodimension-one bifurcation parameter IP3 generationrate (rip3). Our simulations also reveal that the Ca2+ concentration ([Ca2+]) changes from a resting state toa decaying state oscillation and then to a sustainedlarge-amplitude oscillation when rip3 is near these twobifurcation thresholds. Furthermore, codimension-twobifurcation analysis in the (rip3, rL)-plane identifies aBogdanov-Takens (BT) point, which acts as an organizingcenter with three canonical bifurcation curve representationsmediating the global bistability-oscillationtransition. Moreover, simulations reveal that, under identicalconditions, low-frequency stimulation fails to generate Ca2+ oscillations, medium-frequency induces stable Ca2+ oscillations, while high-frequency increases theaverage [Ca2+] but disrupts the persistence of oscillations.Therefore, Ca2+ signal transduction is co-regulatedby rip3, rL and stimulation frequency. 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