Random crosslinks generate anomalous scaling of dynamic modulus of biomolecular condensates

Random crosslinks generate anomalous scaling of dynamic modulus of biomolecular condensates | 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 Random crosslinks generate anomalous scaling of dynamic modulus of biomolecular condensates Jie Lin, Bohan Lyu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8073628/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 Biomolecular condensates are viscoelastic, and their mechanical properties are intimately related to their biological functions. However, the connection between microscopic networks formed by intermolecular crosslinks and viscoelasticity is still elusive. Here, we model biomolecular condensates as random crosslinked polymer solutions to elucidate how random connectivity fundamentally alters their viscoelasticity. We decompose the entire solution into multiple tree networks and demonstrate that for networks with size n , their spectra of relaxation rates λ exhibit a power-law scaling p n (λ) ∼ λ -1/3 with a lower cutoff λ min ∼ n -3/2 . By integrating all networks, we show that for the entire solution, random crosslinks generate an abundance of soft modes involving multiple linear polymers with a flat spectrum of relaxation rates. The soft modes cause anomalous linear frequency scaling of the dynamic modulus, in particular, they significantly boost the low-frequency storage modulus relative to uncrosslinked systems. Our predictions agree quantitatively with the experimental data from distinct biomolecular condensates. Biological sciences/Biophysics/Biopolymers in vivo Biological sciences/Biophysics/Intrinsically disordered proteins Physical sciences/Materials science/Biomaterials/Biomaterials – proteins Physical sciences/Materials science/Soft materials/Rheology Physical sciences/Materials science/Soft materials/Polymers Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementalMaterial.pdf Supplemental Material 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. 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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-8073628","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":554226189,"identity":"5384bd28-f371-4224-82c5-ef2cdf166f72","order_by":0,"name":"Jie 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However, the connection between microscopic networks formed by intermolecular crosslinks and viscoelasticity is still elusive. Here, we model biomolecular condensates as random crosslinked polymer solutions to elucidate how random connectivity fundamentally alters their viscoelasticity. We decompose the entire solution into multiple tree networks and demonstrate that for networks with size \u003ci\u003en\u003c/i\u003e, their spectra of relaxation rates \u003ci\u003eλ\u003c/i\u003e exhibit a power-law scaling \u003ci\u003ep\u003csub\u003en\u003c/sub\u003e(λ) ∼ λ\u003csup\u003e-1/3\u003c/sup\u003e\u003c/i\u003e with a lower cutoff \u003ci\u003eλ\u003c/i\u003e\u003csub\u003emin\u003c/sub\u003e ∼ \u003ci\u003en\u003csup\u003e-3/2\u003c/sup\u003e\u003c/i\u003e. By integrating all networks, we show that for the entire solution, random crosslinks generate an abundance of soft modes involving multiple linear polymers with a flat spectrum of relaxation rates. The soft modes cause anomalous linear frequency scaling of the dynamic modulus, in particular, they significantly boost the low-frequency storage modulus relative to uncrosslinked systems. 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