Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Dissecting Rate-Limiting Processes in Biomolecular Condensate Exchange Dynamics

Ross Kliegman1,*, Eli Kengmana2, Rebecca Schulman2,3,4, and Yaojun Zhang1,5,†

  • *Contact author: rkliegm1@jhu.edu
  • †Contact author: yaojunz@jhu.edu

PRX Life 4, 033006 – Published 20 July, 2026

DOI: https://doi.org/10.1103/h9cl-j5x5

Abstract

An increasing number of biomolecules have been shown to phase-separate into biomolecular condensates—membraneless subcellular compartments capable of regulating distinct biochemical processes within living cells. The speed with which they exchange components with the cellular environment can influence how fast biochemical reactions occur inside condensates and how fast condensates respond to environmental changes, thereby directly impacting condensate function. While fluorescence recovery after photobleaching (FRAP) experiments are routinely performed to measure this exchange timescale, it remains a challenge to distinguish the various physical processes limiting fluorescence recovery and identify each associated timescale. Here, we present a reaction-diffusion model for condensate exchange dynamics and show that such exchange can differ significantly from that of conventional liquid droplets due to the presence of a percolated molecular network, which gives rise to different mobility species in the dense phase. In this model, exchange can be limited by diffusion of either the high- or low-mobility species in the dense phase, diffusion in the dilute phase, or the attachment (detachment) of molecules to (from) the network at the surface or throughout the bulk of the condensate. Combining analytic derivations and numerical simulations, we quantify the contributions of these distinct physical processes to the overall exchange timescale and predict an experimentally testable scaling relationship between the exchange timescale and condensate size. Our theory suggests that the exchange dynamics can be accelerated via a pore-mediated pathway in which molecules pass through the pores of the meshwork and attach directly in the condensate interior. Notably, this pathway permits a parameter regime in which the exchange timescale becomes independent of condensate size, a scaling behavior that is supported by our FRAP measurements on a biosynthetic DNA nanostar system. Our work offers insight into the rate-limiting physical processes that can control condensate material exchange, with implications for natural and engineered systems.

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

Collection on Physics of Biomolecular Condensates

From the fundamentals of phase separation, dynamics and structure of condensates in biological settings, to advanced imaging methods, this special collection presented by PRX Life showcases exciting and timely work on the physics of biomolecular condensates.

This Invited Collection is coordinated by PRX Life Associate Editor Christoph Weber, in consultation with Jerelle Joseph, Simon Alberti, and Tanja Mittag. Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers handled by the journal. The PRX Life editorial team managed the peer review and made all editorial decisions.

Article Text

Supplemental Material

References (92)

  1. S. F. Banani, 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. I. I. Cisse, I. Izeddin, S. Z. Causse, L. Boudarene, A. Senecal, L. Muresan, C. Dugast-Darzacq, B. Hajj, M. Dahan, and X. Darzacq, Real-time dynamics of RNA polymerase II clustering in live human cells, Science 341, 664 (2013).
  4. B. R. Sabari, A. Dall'Agnese, A. Boija, I. A. Klein, E. L. Coffey, K. Shrinivas, B. J. Abraham, N. M. Hannett, A. V. Zamudio, J. C. Manteiga, et al., Coactivator condensation at super-enhancers links phase separation and gene control, Science 361, eaar3958 (2018).
  5. T. Hirose, K. Ninomiya, S. Nakagawa, and T. Yamazaki, A guide to membraneless organelles and their various roles in gene regulation, Nat. Rev. Mol. Cell Biol. 24, 288 (2023).
  6. P. Li, S. Banjade, H.-C. Cheng, S. Kim, B. Chen, L. Guo, M. Llaguno, J. V. Hollingsworth, D. S. King, S. F. Banani, et al., Phase transitions in the assembly of multivalent signalling proteins, Nature (London) 483, 336 (2012).
  7. H. Wu, Higher-order assemblies in a new paradigm of signal transduction, Cell 153, 287 (2013).
  8. X. Su, J. A. Ditlev, E. Hui, W. Xing, S. Banjade, J. Okrut, D. S. King, J. Taunton, M. K. Rosen, and R. D. Vale, Phase separation of signaling molecules promotes T cell receptor signal transduction, Science 352, 595 (2016).
  9. A. Molliex, J. Temirov, J. Lee, M. Coughlin, A. P. Kanagaraj, H. J. Kim, T. Mittag, and J. P. Taylor, Phase separation by low complexity domains promotes stress granule assembly and drives pathological fibrillization, Cell 163, 123 (2015).
  10. A. Patel, H. O. Lee, L. Jawerth, S. Maharana, M. Jahnel, M. Y. Hein, S. Stoynov, J. Mahamid, S. Saha, T. M. Franzmann, et al., A liquid-to-solid phase transition of the ALS protein FUS accelerated by disease mutation, Cell 162, 1066 (2015).
  11. G. Gaglia, R. Rashid, C. Yapp, G. N. Joshi, C. G. Li, S. L. Lindquist, K. A. Sarosiek, L. Whitesell, P. K. Sorger, and S. Santagata, HSF1 phase transition mediates stress adaptation and cell fate decisions, Nat. Cell Biol. 22, 151 (2020).
  12. S. Wegmann, B. Eftekharzadeh, K. Tepper, K. M. Zoltowska, R. E. Bennett, S. Dujardin, P. R. Laskowski, D. MacKenzie, T. Kamath, C. Commins, et al., Tau protein liquid-liquid phase separation can initiate tau aggregation, EMBO J 37, EMBJ201798049 (2018).
  13. S. Alberti and A. A. Hyman, Biomolecular condensates at the nexus of cellular stress, protein aggregation disease and ageing, Nat. Rev. Mol. Cell Biol. 22, 196 (2021).
  14. J. Nam and Y. Gwon, Neuronal biomolecular condensates and their implications in neurodegenerative diseases, Front. Aging Neurosci. 15, 1145420 (2023).
  15. S. Spannl, M. Tereshchenko, G. J. Mastromarco, S. J. Ihn, and H. O. Lee, Biomolecular condensates in neurodegeneration and cancer, Traffic 20, 890 (2019).
  16. A. Boija, I. A. Klein, and R. A. Young, Biomolecular condensates and cancer, Cancer Cell 39, 174 (2021).
  17. K. Taniue and N. Akimitsu, Aberrant phase separation and cancer, FEBS J. 289, 17 (2022).
  18. X. Tong, R. Tang, J. Xu, W. Wang, Y. Zhao, X. Yu, and S. Shi, Liquid–liquid phase separation in tumor biology, Signal Transduction Targeted Ther. 7, 221 (2022).
  19. S. An, R. Kumar, E. D. Sheets, and S. J. Benkovic, Reversible compartmentalization of de novo purine biosynthetic complexes in living cells, Science 320, 103 (2008).
  20. A. M. Pedley, J. P. Boylan, C. Y. Chan, E. L. Kennedy, M. Kyoung, and S. J. Benkovic, Purine biosynthetic enzymes assemble into liquid-like condensates dependent on the activity of chaperone protein HSP90, J. Biol. Chem. 298, 101845 (2022).
  21. M. Prouteau and R. Loewith, Regulation of cellular metabolism through phase separation of enzymes, Biomolecules 8, 160 (2018).
  22. H. Wang, F. M. Kelley, D. Milovanovic, B. S. Schuster, and Z. Shi, Surface tension and viscosity of protein condensates quantified by micropipette aspiration, Biophys. Rep. 1, 100011 (2021).
  23. I. Lifshitz and V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19, 35 (1961).
  24. C. Wagner, Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung), Z. Elektrochem. 65, 581 (1961).
  25. M.-M. Poo and R. A. Cone, Lateral diffusion of rhodopsin in Necturus rods, Exp. Eye Res. 17, 503 (1973).
  26. P. Liebman and G. Entine, Lateral diffusion of visual pigment in photoreceptor disk membranes, Science 185, 457 (1974).
  27. J. Lippincott-Schwartz, E. Snapp, and A. Kenworthy, Studying protein dynamics in living cells, Nat. Rev. Mol. Cell Biol. 2, 444 (2001).
  28. F. Pincet, V. Adrien, R. Yang, J. Delacotte, J. E. Rothman, W. Urbach, and D. Tareste, FRAP to characterize molecular diffusion and interaction in various membrane environments, PLoS One 11, e0158457 (2016).
  29. K. A. Burke, A. M. Janke, C. L. Rhine, and N. L. Fawzi, Residue-by-residue view of in vitro FUS granules that bind the C-terminal domain of RNA polymerase II, Mol. Cell 60, 231 (2015).
  30. S. F. Banani, A. M. Rice, W. B. Peeples, Y. Lin, S. Jain, R. Parker, and M. K. Rosen, Compositional control of phase-separated cellular bodies, Cell 166, 651 (2016).
  31. S. Jain, J. R. Wheeler, R. W. Walters, A. Agrawal, A. Barsic, and R. Parker, ATPase-modulated stress granules contain a diverse proteome and substructure, Cell 164, 487 (2016).
  32. W. M. J. Aumiller, F. Pir Cakmak, B. W. Davis, and C. D. Keating, RNA-based coacervates as a model for membraneless organelles: Formation, properties, and interfacial liposome assembly, Langmuir 32, 10042 (2016).
  33. N. O. Taylor, M.-T. Wei, H. A. Stone, and C. P. Brangwynne, Quantifying dynamics in phase-separated condensates using fluorescence recovery after photobleaching, Biophys. J. 117, 1285 (2019).
  34. L. Hubatsch, L. M. Jawerth, C. Love, J. Bauermann, T. D. Tang, S. Bo, A. A. Hyman, and C. A. Weber, Quantitative theory for the diffusive dynamics of liquid condensates, eLife 10, e68620 (2021).
  35. S. Bo, L. Hubatsch, J. Bauermann, C. A. Weber, and F. Jülicher, Stochastic dynamics of single molecules across phase boundaries, Phys. Rev. Res. 3, 043150 (2021).
  36. F. Muzzopappa, J. Hummert, M. Anfossi, S. A. Tashev, D.-P. Herten, and F. Erdel, Detecting and quantifying liquid–liquid phase separation in living cells by model-free calibrated half-bleaching, Nat. Commun. 13, 7787 (2022).
  37. A. W. Folkmann, A. Putnam, C. F. Lee, and G. Seydoux, Regulation of biomolecular condensates by interfacial protein clusters, Science 373, 1218 (2021).
  38. C. F. Lee, Scaling law and universal drop size distribution of coarsening in conversion-limited phase separation, Phys. Rev. Res. 3, 043081 (2021).
  39. H. T. Nguyen, N. Hori, and D. Thirumalai, Condensates in RNA repeat sequences are heterogeneously organized and exhibit reptation dynamics, Nat. Chem. 14, 775 (2022).
  40. Y. Zhang, A. G. Pyo, R. Kliegman, Y. Jiang, C. P. Brangwynne, H. A. Stone, and N. S. Wingreen, The exchange dynamics of biomolecular condensates, eLife 12, RP91680 (2024).
  41. L. Hubatsch, S. Bo, T. S. Harmon, A. A. Hyman, C. A. Weber, and F. Jülicher, Transport kinetics across interfaces between coexisting liquid phases, eLife 14, RP106842 (2025).
  42. G. L. Dignon, R. B. Best, and J. Mittal, Biomolecular phase separation: From molecular driving forces to macroscopic properties, Annu. Rev. Phys. Chem. 71, 53 (2020).
  43. J. A. Joseph, A. Reinhardt, A. Aguirre, P. Y. Chew, K. O. Russell, J. R. Espinosa, A. Garaizar, and R. Collepardo-Guevara, Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy, Nat. Comput. Sci. 1, 732 (2021).
  44. A. N. Semenov and M. Rubinstein, Thermoreversible gelation in solutions of associative polymers. 1. Statics, Macromolecules 31, 1373 (1998).
  45. J. Wang, J.-M. Choi, A. S. Holehouse, H. O. Lee, X. Zhang, M. Jahnel, S. Maharana, R. Lemaitre, A. Pozniakovsky, D. Drechsel, et al., A molecular grammar governing the driving forces for phase separation of prion-like RNA binding proteins, Cell 174, 688 (2018).
  46. G. M. Ginell and A. S. Holehouse, An introduction to the stickers-and-spacers framework as applied to biomolecular condensates, in Phase-Separated Biomolecular Condensates: Methods and Protocols, edited by H.-X. Zhou, J.-H. Spille, and P. R. Banerjee (Springer US, New York, 2023), pp. 95–116.
  47. 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).
  48. T. Mittag and R. V. Pappu, A conceptual framework for understanding phase separation and addressing open questions and challenges, Mol. Cell 82, 2201 (2022).
  49. Z. Shen, B. Jia, Y. Xu, J. Wessén, T. Pal, H. S. Chan, S. Du, and M. Zhang, Biological condensates form percolated networks with molecular motion properties distinctly different from dilute solutions, eLife 12, e81907 (2023).
  50. T. Wu, M. R. King, Y. Qiu, M. Farag, R. V. Pappu, and M. D. Lew, Single-fluorogen imaging reveals distinct environmental and structural features of biomolecular condensates, Nat. Phys. 21, 778 (2025).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/h9cl-j5x5 for additional information about the theory, numerical simulations, and experiments, which includes Refs. [52, 53, 56, 60, 63, 92].
  52. J. Crank, The Mathematics of Diffusion, Oxford Science Publications (Clarendon Press, Oxford, UK, 1979).
  53. B. L. Sprague, R. L. Pego, D. A. Stavreva, and J. G. McNally, Analysis of binding reactions by fluorescence recovery after photobleaching, Biophys. J. 86, 3473 (2004).
  54. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258 (1958).
  55. R. Skeel and M. Berzins, A method for the spatial discretization of parabolic equations in one space variable, SIAM J. Sci. Stat. Comput. 11, 1 (1990).
  56. M. Branch, T. Coleman, and Y. Li, A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems, SIAM J. Sci. Comput. 21, 1 (1999).
  57. 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).
  58. L. Jawerth, E. Fischer-Friedrich, S. Saha, J. Wang, T. Franzmann, X. Zhang, J. Sachweh, M. Ruer, M. Ijavi, S. Saha, et al., Protein condensates as aging Maxwell fluids, Science 370, 1317 (2020).
  59. S. Biffi, R. Cerbino, F. Bomboi, E. M. Paraboschi, R. Asselta, F. Sciortino, and T. Bellini, Phase behavior and critical activated dynamics of limited-valence DNA nanostars, Proc. Natl. Acad. Sci. USA 110, 15633 (2013).
  60. Y. Sato, T. Sakamoto, and M. Takinoue, Sequence-based engineering of dynamic functions of micrometer-sized DNA droplets, Sci. Adv. 6, eaba3471 (2020).
  61. B.-j. Jeon, D. T. Nguyen, G. R. Abraham, N. Conrad, D. K. Fygenson, and O. A. Saleh, Salt-dependent properties of a coacervate-like, self-assembled DNA liquid, Soft Matter 14, 7009 (2018).
  62. S. Agarwal, D. Osmanovic, M. Dizani, M. A. Klocke, and E. Franco, Dynamic control of DNA condensation, Nat. Commun. 15, 1915 (2024).
  63. E. Kengmana, E. Ornelas-Gatdula, K.-L. Chen, and R. Schulman, Spatial control over reactions via localized transcription within membraneless DNA nanostar droplets, J. Am. Chem. Soc. 146, 32942 (2024).
  64. D. T. Nguyen, B.-j. Jeon, G. R. Abraham, and O. A. Saleh, Length-dependence and spatial structure of DNA partitioning into a DNA liquid, Langmuir 35, 14849 (2019).
  65. N. F. Dupuis, E. D. Holmstrom, and D. J. Nesbitt, Single-molecule kinetics reveal cation-promoted DNA duplex formation through ordering of single-stranded helices, Biophys. J. 105, 756 (2013).
  66. N. Conrad, T. Kennedy, D. K. Fygenson, and O. A. Saleh, Increasing valence pushes DNA nanostar networks to the isostatic point, Proc. Natl. Acad. Sci. USA 116, 7238 (2019).
  67. G. Palombo, S. Weir, D. Michieletto, and Y. A. Gutiérrez Fosado, Topological linking determines elasticity in limited valence networks, Nat. Mater. 24, 454 (2025).
  68. K. Bhandari, M. A. Cotten, J. Kim, M. K. Rosen, and J. D. Schmit, Structure–function properties in disordered condensates, J. Phys. Chem. B 125, 467 (2021).
  69. J. Zenk, C. Tuntivate, and R. Schulman, Kinetics and thermodynamics of Watson–Crick base pairing driven DNA origami dimerization, J. Am. Chem. Soc. 138, 3346 (2016).
  70. F. Bomboi, S. Biffi, R. Cerbino, T. Bellini, F. Bordi, and F. Sciortino, Equilibrium gels of trivalent DNA-nanostars: Effect of the ionic strength on the dynamics, Eur. Phys. J. E 38, 64 (2015).
  71. K. Skipper and S. F. J. Wickham, DNA nanostars that self-assemble into core-shell condensate microdroplets, Nanoscale Horiz. 11, 1320 (2026).
  72. S. Do, C. Lee, T. Lee, D.-N. Kim, and Y. Shin, Engineering DNA-based synthetic condensates with programmable material properties, compositions, and functionalities, Sci. Adv. 8, eabj1771 (2022).
  73. D. Y. Zhang and E. Winfree, Control of DNA strand displacement kinetics using toehold exchange, J. Am. Chem. Soc. 131, 17303 (2009).
  74. S. Jiang, H. Yan, and Y. Liu, Kinetics of DNA tile dimerization, ACS Nano 8, 5826 (2014).
  75. R. Takaki, L. Jawerth, M. Popović, and F. Jülicher, Theory of rheology and aging of protein condensates, PRX Life 1, 013006 (2023).
  76. W. M. Jacobs and D. Frenkel, Phase transitions in biological systems with many components, Biophys. J. 112, 683 (2017).
  77. D. Zwicker and L. Laan, Evolved interactions stabilize many coexisting phases in multicomponent liquids, Proc. Natl. Acad. Sci. USA 119, e2201250119 (2022).
  78. W. M. Jacobs, Theory and simulation of multiphase coexistence in biomolecular mixtures, J. Chem. Theory Comput. 19, 3429 (2023).
  79. Y. Qiang, C. Luo, and D. Zwicker, Scaling laws for phase coexistence in multicomponent mixtures, Phys. Rev. Res. 7, 043008 (2025).
  80. J. A. Ditlev, L. B. Case, and M. K. Rosen, Who's in and who's out—compositional control of biomolecular condensates, J. Mol. Biol. 430, 4666 (2018).
  81. J. D. Schmit and T. C. T. Michaels, Physical limits to acceleration of enzymatic reactions inside phase-separated compartments, Phys. Rev. E 109, 064401 (2024).
  82. S. Kent, K. Brown, C.-h. Yang, N. Alsaihati, C. Tian, H. Wang, and X. Ren, Phase-separated transcriptional condensates accelerate target-search process revealed by live-cell single-molecule imaging, Cell Rep. 33, 108248 (2020).
  83. J. Miné-Hattab, M. Heltberg, M. Villemeur, C. Guedj, T. Mora, A. M. Walczak, M. Dahan, and A. Taddei, Single molecule microscopy reveals key physical features of repair foci in living cells, eLife 10, e60577 (2021).
  84. M. L. Heltberg, J. Miné-Hattab, A. Taddei, A. M. Walczak, and T. Mora, Physical observables to determine the nature of membrane-less cellular sub-compartments, eLife 10, e69181 (2021).
  85. S. Hao, Y. J. Lee, N. B. Goldfajn, E. Flores, J. Liang, H. Fuehrer, J. Demmerle, J. Lippincott-Schwartz, Z. Liu, S. Sukenik, et al., YAP condensates are highly organized hubs, iScience 27, 109927 (2024).
  86. M.-T. Wei, S. Elbaum-Garfinkle, A. S. Holehouse, C. C.-H. Chen, M. Feric, C. B. Arnold, R. D. Priestley, R. V. Pappu, and C. P. Brangwynne, Phase behaviour of disordered proteins underlying low density and high permeability of liquid organelles, Nat. Chem. 9, 1118 (2017).
  87. N. Galvanetto, M. T. Ivanović, A. Chowdhury, A. Sottini, M. F. Nüesch, D. Nettels, R. B. Best, and B. Schuler, Extreme dynamics in a biomolecular condensate, Nature (London) 619, 876 (2023).
  88. V. Grigorev, N. S. Wingreen, and Y. Zhang, Conformational entropy of intrinsically disordered proteins bars intruders from biomolecular condensates, PRX Life 3, 013011 (2025).
  89. B. Wang, L. Zhang, T. Dai, Z. Qin, H. Lu, L. Zhang, and F. Zhou, Liquid–liquid phase separation in human health and diseases, Signal Transduction Targeted Ther. 6, 290 (2021).
  90. D. M. Mitrea, M. Mittasch, B. F. Gomes, I. A. Klein, and M. A. Murcko, Modulating biomolecular condensates: A novel approach to drug discovery, Nat. Rev. Drug Discov. 21, 841 (2022).
  91. R. Kliegman, E. Kengmana, R. Schulman, and Y. Zhang, Dissecting rate-limiting processes in biomolecular condensate exchange dynamics, [dataset and code] Johns Hopkins Research Data Repository, 2026, https://doi.org/10.7281/T1WY5RSP.
  92. N. Otsu, A threshold selection method from gray-level histograms, IEEE Trans. Syst. Man. Cybern. 9, 62 (1979).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation