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  • Open Access

Entropic clustering of stickers induces aging in biocondensates

Hugo Le Roy* and Paolo De Los Rios

  • *Contact author: HCV.Le-Roy@proton.me

Phys. Rev. E 113, 064405 – Published 9 June, 2026

DOI: https://doi.org/10.1103/4hfs-bsyw

Abstract

Biomolecular condensates are cellular phase-separated droplets that usually exhibit a viscoelastic mechanical response, a behavior rationalized by modeling the complex molecules that make up a condensate as stickers and spacers, which assemble into a network-like structure. Condensates usually exhibit a solidification over a long period of time (days), a phenomenon described as aging. The emergence of such a long timescale of evolution from microscopic processes, as well as the associated microscopic reorganization leading to aging, remains mostly an open question. In this article, we explore the connection between the mechanical properties of the condensates and their microscopic structure. We propose a minimal model for the dynamics of stickers and spacers and show that entropy maximization of spacers leads to an attractive force between stickers. Our system displays a surprisingly slow relaxation toward equilibrium, reminiscent of glassy systems and consistent with the liquid-to-solid transition observed. To explain this behavior, we study the clustering dynamics of stickers and successfully explain the origin of glassy relaxation.

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References (45)

  1. S. F. Banmnani, H. O. Lee, A. A. Hyman, and M. K. Rosen, Biomolecular condensates: Organizers of cellular biochemistry, Nat. Rev. Mol. Cell Biol. 18, 285 (2017).
  2. Y. Shin and C. P. Brangwynne, Liquid phase condensation in cell physiology and disease, Science 357, eaaf4382 (2017).
  3. J.-K. Ryu, C. Bouchoux, H. W. Liu, E. Kim, M. Minamino, R. de Groot, A. J. Katan, A. Bonato, D. Marenduzzo, D. Michieletto, F. Uhlmann, and C. Dekker, Bridging-induced phase separation induced by cohesin SMC protein complexes, Sci. Adv. 7, eabe5905 (2021).
  4. K. Rippe, Liquid–liquid phase separation in chromatin, Cold Spring Harb Perspect. Biol. 14, a040683 (2022).
  5. M. Hondele, R. Sachdev, S. Heinrich, J. Wang, P. Vallotton, B. M. A. Fontoura, and K. Weis, DEAD-box ATPases are global regulators of phase-separated organelles, Nature (London) 573, 144 (2019).
  6. A. Aulas, M. M. Fay, S. M. Lyons, C. A. Achorn, N. Kedersha, P. Anderson, and P. Ivanov, Stress-specific differences in assembly and composition of stress granules and related foci, J. Cell Sci. 130, 927 (2017).
  7. C.-Y. S. Lee, A. Putnam, T. Lu, S. He, J. P. T. Ouyang, and G. Seydoux, Recruitment of mRNAs to P granules by condensation with intrinsically-disordered proteins, eLife 9, e52896 (2020).
  8. S. Boeynaems, S. Alberti, N. L. Fawzi, T. Mittag, M. Polymenidou, F. Rousseau, J. Schymkowitz, J. Shorter, B. Wolozin, L. V. D. Bosch, P. Tompa, and M. Fuxreiter, Protein phase separation: A new phase in cell biology, Trends Cell Biol. 28, 420 (2018).
  9. C. A. Brackley, S. Taylor, A. Papantonis, P. R. Cook, and D. Marenduzzo, Nonspecific bridging-induced attraction drives clustering of DNA-binding proteins and genome organization, Proc. Natl. Acad. Sci. USA 110, E3605 (2013).
  10. L. M. Jawerth, M. Ijavi, M. Ruer, S. Saha, M. Jahnel, A. A. Hyman, F. Jülicher, and E. Fischer-Friedrich, Salt-dependent rheology and surface tension of protein condensates using optical traps, Phys. Rev. Lett. 121, 258101 (2018).
  11. I. Alshareedah, M. M. Moosa, M. Pham, D. A. Potoyan, and P. R. Banerjee, Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides, Nat. Commun. 12, 6620 (2021).
  12. J.-M. Choi, A. S. Holehouse, and R. V. Pappu, Physical principles underlying the complex biology of intracellular phase transitions, Annu. Rev. Biophys. 49, 107 (2020).
  13. L. Jawerth, E. Fischer-Friedrich, S. Saha, J. Wang, T. Franzmann, X. Zhang, J. Sachweh, M. Ruer, M. Ijavi, S. Saha, J. Mahamid, A. A. Hyman, and F. Jülicher, Protein condensates as aging Maxwell fluids, Science 370, 1317 (2020).
  14. M. Linsenmeier, M. Hondele, F. Grigolato, E. Secchi, K. Weis, and P. Arosio, Dynamic arrest and aging of biomolecular condensates are modulated by low-complexity domains, RNA and biochemical activity, Nat. Commun. 13, 3030 (2022).
  15. M. Farag, S. R. Cohen, W. M. Borcherds, A. Bremer, T. Mittag, and R. V. Pappu, Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations, Nat. Commun. 13, 7722 (2022).
  16. S. Ray et al., α-synuclein aggregation nucleates through liquid–liquid phase separation, Nat. Chem. 12, 705 (2020).
  17. Y. Shen, A. Chen, W. Wang, Y. Shen, F. S. Ruggeri, S. Aime, Z. Wang, S. Qamar, J. R. Espinosa, A. Garaizar, P. St George-Hyslop, R. Collepardo-Guevara, D. A. Weitz, D. Vigolo, and T. P. J. Knowles, The liquid-to-solid transition of FUS is promoted by the condensate surface, Proc. Natl. Acad. Sci. USA 120, e2301366120 (2023).
  18. S. Ranganathan and E. Shakhnovich, The physics of liquid-to-solid transitions in multi-domain protein condensates, Biophys. J. 121, 2751 (2022).
  19. R. Takaki, L. Jawerth, M. Popović, and F. Jülicher, Theory of rheology and aging of protein condensates, PRX Life 1, 013006 (2023).
  20. A. Garaizar, J. R. Espinosa, J. A. Joseph, G. Krainer, Y. Shen, T. P. Knowles, and R. Collepardo-Guevara, Aging can transform single-component protein condensates into multiphase architectures, Proc. Natl. Acad. Sci. USA 119, e2119800119 (2022).
  21. I. Alshareedah, W. M. Borcherds, S. R. Cohen, A. Singh, A. E. Posey, M. Farag, A. Bremer, G. W. Strout, D. T. Tomares, R. V. Pappu, T. Mittag, and P. R. Banerjee, Sequence-specific interactions determine viscoelasticity and ageing dynamics of protein condensates, Nat. Phys. 20, 1482 (2024).
  22. T. Wu, M. R. King, M. Farag, R. V. Pappu, and M. D. Lew, Single fluorogen imaging reveals spatial inhomogeneities within biomolecular condensates, Nat. Phys. 21, 778 (2025).
  23. G. A. Parada and X. Zhao, Ideal reversible polymer networks, Soft Matter 14, 5186 (2018).
  24. J. Song, N. Holten-Andersen, and G. H. McKinley, Non-Maxwellian viscoelastic stress relaxations in soft matter, Soft Matter 19, 7885 (2023).
  25. O. Lieleg, J. Kayser, G. Brambilla, L. Cipelletti, and A. R. Bausch, Slow dynamics and internal stress relaxation in bundled cytoskeletal networks, Nat. Mater. 10, 236 (2011).
  26. L. Berthier, Dynamic heterogeneity in amorphous materials, Physics 4, 42 (2011).
  27. F. Dar, S. R. Cohen, D. M. Mitrea, A. H. Phillips, G. Nagy, W. C. Leite, C. B. Stanley, J.-M. Choi, R. W. Kriwacki, and R. V. Pappu, Biomolecular condensates form spatially inhomogeneous network fluids, Nat. Commun. 15, 3413 (2024).
  28. W. Götze and M. Sperl, Logarithmic relaxation in glass-forming systems, Phys. Rev. E 66, 011405 (2002).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4hfs-bsyw for derivations of the binding rate, the details of the Gillespie algorithm, the mean-field pair probability distribution, the volume contraction estimate, and the computation of the viscoelastic modulus.
  30. D. Poland and H. A. Scheraga, Phase transitions in one dimension and the helix—coil transition in polyamino acids, J. Chem. Phys. 45, 1456 (1966).
  31. P. M. McCall, K. Kim, A. Shevchenko, M. Ruer-Gruss, J. Peychl, J. Guck, A. Shevchenko, A. A. Hyman, and J. Brugués, A label-free method for measuring the composition of multicomponent biomolecular condensates, Nat. Chem. 17, 1891 (2025).
  32. L. M. C. Janssen, Mode-coupling theory of the glass transition: A primer, Front. Phys. 6, 97 (2018).
  33. Z. W. Wu, W. Kob, W.-H. Wang, and L. Xu, Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt, Nat. Commun. 9, 5334 (2018).
  34. W. Kob and H. C. Andersen, Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture. II. Intermediate scattering function and dynamic susceptibility, Phys. Rev. E 52, 4134 (1995).
  35. J.-P. Bouchaud, Anomalous relaxation in complex systems: From stretched to compressed exponentials, in Anomalous Transport (Wiley, Weinheim, 2008), Chap. 11, pp. 327–345.
  36. F. Guillemin and A. Simonian, Transient characteristics of an M/M/∞ system, Adv. Appl. Probab. 27, 862 (1995).
  37. S. Biswas and D. A. Potoyan, Molecular drivers of aging in biomolecular condensates: Desolvation, rigidification, and sticker lifetimes, PRX Life 2, 023011 (2024).
  38. A. Compte and J.-P. Bouchaud, Localization in one-dimensional random random walks, J. Phys. A: Math. Gen. 31, 6113 (1998).
  39. P. Sollich, F. Lequeux, P. Hébraud, and M. E. Cates, Rheology of soft glassy materials, Phys. Rev. Lett. 78, 2020 (1997).
  40. J. P. Bouchaud, Weak ergodicity breaking and aging in disordered systems, J. Phys. I 2, 1705 (1992).
  41. E. M. Bertin and J.-P. Bouchaud, Subdiffusion and localization in the one-dimensional trap model, Phys. Rev. E 67, 026128 (2003).
  42. I. L. Morgan, R. Avinery, G. Rahamim, R. Beck, and O. A. Saleh, Glassy dynamics and memory effects in an intrinsically disordered protein construct, Phys. Rev. Lett. 125, 058001 (2020).
  43. H. Le Roy, J. Song, D. Lundberg, A. V. Zhukhovitskiy, J. A. Johnson, G. H. McKinley, N. Holten-Andersen, and M. Lenz, Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels, Sci. Adv. 10, eadl5056 (2024).
  44. H. Le Roy and P. De Los Rios, cpp_file_aging_condensate: c++ simulation code for aging condensates, 2025, https://github.com/HugoLeRoy94/cpp_file_aging_condensate.
  45. H. Le Roy and P. De Los Rios, Parallel_gillespie: Parallel Gillespie algorithm implementation, 2025, https://github.com/HugoLeRoy94/Parallel_gillespie.

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