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arxiv: 2605.28651 · v1 · pith:LJOT7EYNnew · submitted 2026-05-27 · ❄️ cond-mat.soft · physics.bio-ph· q-bio.MN

Determinants of Phase-Separation Propensities, Material States, and Material Properties of Biomolecular Condensates

Huan-Xiang Zhou This is my paper

Pith reviewed 2026-06-29 09:37 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-phq-bio.MN
keywords biomolecular condensatesphase separationspinodal decompositionviscoelasticityintermolecular interactionsliquid dropletsgelsaggregates
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The pith

Phase-separation thresholds for biomolecules track excess chemical potential set by interaction strength and valency, with material states hinging on whether spinodal decomposition runs to completion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper supplies theoretical relations that tie the onset concentration for biomolecular phase separation to the excess chemical potential inside the dense phase, which itself rises with stronger or higher-valency intermolecular contacts. Liquid droplets appear when phase separation proceeds fully, but amorphous dense liquids, reversible aggregates, and gels appear when spinodal decomposition arrests early because interactions are too weak, too strong, or directional. Gels grow by tip extension under directional bonds while aggregates grow by interior monomer addition to increase contact number. The average lifetime of those bonds fixes the stress relaxation time, which then sets whether a condensate shows elastic response under shear, shear thickening or thinning, and the wide range of zero-shear viscosities observed across different condensates.

Core claim

The saturation concentration for phase separation equals the point at which the excess chemical potential in the dense phase balances the dilute-phase value, with the excess term governed by interaction strength and valency. Liquid droplets form by complete phase separation while amorphous liquids, aggregates, and gels arise when spinodal decomposition terminates prematurely owing to overly weak, overly strong, or directional interactions; gels in particular advance by directional tip growth whereas aggregates advance by interior addition that maximizes valency. The mean lifetime of intermolecular bonds determines the stress relaxation time that governs viscoelasticity, shear-dependent flow,

What carries the argument

Excess chemical potential in the dense phase (tied to interaction strength and valency) for separation thresholds; premature termination of spinodal decomposition (modulated by interaction weakness, strength, or directionality) for material states; stress relaxation time set by mean intermolecular bond lifetime for viscoelastic and viscous properties.

If this is right

  • Stronger or higher-valency interactions lower the concentration needed for phase separation.
  • Directional interactions favor gels through tip growth rather than uniform droplet formation.
  • Reversible aggregates form when molecules add at interior sites to maximize contacts instead of directional extension.
  • Longer bond lifetimes raise the relaxation time and thereby increase viscosity while enabling shear thickening or thinning.
  • Different condensates display orders-of-magnitude viscosity differences because their bond lifetimes differ.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The frameworks suggest that cells could tune condensate material state by modulating interaction directionality or lifetime without changing overall concentration.
  • Synthetic design of condensates with prescribed flow properties would follow from choosing bond lifetimes and valencies to set the relaxation time.
  • The distinction between tip-driven gels and valency-driven aggregates points to separate regulatory mechanisms that could be tested by altering interaction geometry in model systems.
  • If premature arrest is the dominant route to solid-like states, then mutations that alter interaction range or strength should shift the boundary between liquid and arrested states in a predictable way.

Load-bearing premise

Non-liquid states arise specifically because spinodal decomposition stops early due to interaction details rather than from equilibrium thermodynamics or other kinetic routes.

What would settle it

Direct imaging or scattering data showing a gel or aggregate forming under interaction conditions where spinodal decomposition should reach full completion, or a liquid droplet forming when interactions are predicted to cause arrest.

Figures

Figures reproduced from arXiv: 2605.28651 by Huan-Xiang Zhou.

Figure 1
Figure 1. Figure 1: Phase separation and the resulting binodal. (a) Stages of phase separation via spinodal decomposition. (1) Concentration fluctuations in a supersaturation solution (box 0) produce dense regions; (2) condensation results in connected domains with multiple tips; (3¢) tip growth yields system-spanning networks, whereas (3) further condensation toward domain centers breaks up inter￾domain necks; (4) intra-doma… view at source ↗
Figure 4
Figure 4. Figure 4: Phase-separation properties of XXssXX peptides. (a-d) Phase diagrams of FFssFF, LLssLL, 1:1 mixture of IIssII and AAssAA, and VVssVV. Similar to the mixture, IIssII only formed gels. (e) Correlation between threshold concentration at pH 7 and amino-acid molecular mass. (f, g) Molecular [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

Phase separation of various materials has been studied for one and a half centuries. In the last two decades, phase separation of proteins and nucleic acids has received enormous attention, due its relevance to cellular functions. However, many of the observations on the resulting biomolecular condensates lack a theoretical underpinning. The first goal of this Account is to put forward theoretical frameworks for the phase-separation propensities, material states, and material properties of biomolecular condensates. Using these frameworks, I rationalize mechanistic interpretations from our recent experimental and computational studies, and synthesize these studies with prior literature to draw new conclusions. For phase-separation propensities, I relate the threshold (or saturation) concentration to the excess chemical potential in the dense phase, which in turn depends on intermolecular interaction strength and valency. For material states, I posit that liquid droplets form via complete phase separation, whereas amorphous dense liquids, reversible aggregates, and gels arise from premature termination of spinodal decomposition, due to overly weak or overly strong interactions or directional interactions. In particular, gels and aggregates are different forms of dynamically arrested states, with gels driven by tip growth via directional interactions whereas aggregates driven by monomer addition at interior sites to maximize valency. For material properties, I highlight the crucial roles of the stress relaxation time, which is determined by the mean lifetime of intermolecular bonds in a condensate. This relaxation time dictates how the condensate manifests viscoelasticity, including shear thickening and shear thinning, and accounts for the wide variation in zero-shear viscosity among different condensates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. This Account proposes theoretical frameworks for phase-separation propensities, material states, and material properties of biomolecular condensates. It relates the threshold (saturation) concentration to the excess chemical potential in the dense phase, which depends on intermolecular interaction strength and valency. Liquid droplets are said to form via complete phase separation, whereas amorphous dense liquids, reversible aggregates, and gels arise from premature termination of spinodal decomposition due to overly weak, overly strong, or directional interactions (with gels via tip growth and aggregates via interior monomer addition to maximize valency). Material properties are linked to the stress relaxation time set by the mean lifetime of intermolecular bonds, which governs viscoelasticity (including shear thickening/thinning) and viscosity variation. The frameworks are used to rationalize the author's recent experimental and computational studies and to synthesize them with prior literature.

Significance. If the frameworks hold, they could offer a unifying conceptual synthesis connecting molecular-scale interaction parameters to condensate behaviors and properties, aiding interpretation of cellular functions and material design. The paper explicitly integrates multiple studies into new conclusions, providing a broad perspective that may guide future work if the posited relations receive quantitative support.

major comments (1)
  1. [Framework for material states] In the framework for material states: the claim that amorphous dense liquids, reversible aggregates, and gels arise specifically from premature termination of spinodal decomposition (due to weak/strong/directional interactions) rather than equilibrium thermodynamic outcomes (e.g., equilibrium gels via percolation or directional bonding) is presented without a derivation, quantitative conditions, or explicit comparison that rules out the alternatives. This distinction is load-bearing for the central classification of material states.
minor comments (1)
  1. The text would benefit from explicit definitions or standard references for key quantities such as 'excess chemical potential in the dense phase' and 'mean lifetime of intermolecular bonds' to improve accessibility for readers outside the immediate subfield.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: In the framework for material states: the claim that amorphous dense liquids, reversible aggregates, and gels arise specifically from premature termination of spinodal decomposition (due to weak/strong/directional interactions) rather than equilibrium thermodynamic outcomes (e.g., equilibrium gels via percolation or directional bonding) is presented without a derivation, quantitative conditions, or explicit comparison that rules out the alternatives. This distinction is load-bearing for the central classification of material states.

    Authors: The manuscript is an Account proposing conceptual frameworks to synthesize our recent studies with the literature rather than deriving them from first principles. The posited distinction between complete phase separation and premature termination of spinodal decomposition is based on kinetic arguments and observations from our experimental and computational work. We agree that the Account does not include a quantitative derivation, explicit conditions, or direct comparison ruling out equilibrium alternatives such as percolation-driven gels. In the revised version we will add a paragraph in the material-states section that acknowledges these alternatives, references relevant percolation and directional-bonding literature, and clarifies the rationale for emphasizing the kinetic mechanism in the systems we discuss. revision: yes

Circularity Check

0 steps flagged

No significant circularity: frameworks presented as independent posits applied to own data

full rationale

The paper explicitly puts forward theoretical frameworks via statements such as 'I relate the threshold concentration to the excess chemical potential' and 'I posit that liquid droplets form via complete phase separation, whereas ... arise from premature termination of spinodal decomposition'. These are introduced as the author's frameworks rather than derived from or reduced to the mentioned 'our recent experimental and computational studies'. The studies are described as the objects being rationalized by the frameworks, not as the source or justification of the frameworks themselves. No equations, fitted parameters, or self-citation chains are exhibited that would make any claimed prediction equivalent to its inputs by construction. Self-mention of own work occurs only in the application step and does not load-bear the central premises.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is inferred from concepts explicitly invoked: interaction strength and valency as determinants of chemical potential, spinodal decomposition as the underlying kinetic process, and bond lifetime as the sole determinant of relaxation time. No numerical free parameters are stated.

free parameters (3)
  • intermolecular interaction strength
    Invoked as the primary variable controlling both threshold concentration and whether phase separation completes or arrests.
  • valency
    Invoked as a second variable that modulates excess chemical potential and the driving force for aggregation versus gelation.
  • mean lifetime of intermolecular bonds
    Directly equated to the stress relaxation time that governs all viscoelastic properties.
axioms (1)
  • domain assumption Phase separation proceeds via spinodal decomposition whose termination is controlled by interaction strength and directionality.
    Used to classify liquid droplets versus gels and aggregates without additional kinetic modeling.

pith-pipeline@v0.9.1-grok · 5812 in / 1461 out tokens · 29304 ms · 2026-06-29T09:37:58.260055+00:00 · methodology

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Reference graph

Works this paper leans on

16 extracted references · 3 canonical work pages

  1. [1]

    dense liquid

    DETERMINANTS OF MATERIAL STATES In addition to the threshold concentrations of XXssXX peptides, Figure 4a-d also displays the material states formed under various combinations of peptide concentration (𝐶) and pH.13 FFssFF (Figure 4a) formed liquid droplets in all 𝐶–pH combinations tested; the same was true for LLssLL (Figures 4b and 2a) and MMssMM, except...

    2024

  2. [2]

    "4𝐼2𝜋𝑘*𝑇𝑑4 [7b] 26 where 𝑑 is the hard-core diameter of the particles, 𝑔(𝑟) is the radial distribution function, 𝜙

    and their dynamics at a wide-range of spatial and temporal scales, molecular-level interpretations of these properties should be seen as tentative. 4.1. Why Do Biomolecular Condensates Have Similar Surface Tensions? Surface tension is a fundamental property of all liquids, including biomolecular condensates in the liquid-droplet state. Indeed, the spheric...

    2024

  3. [3]

    CONCLUDING REMARKS Based on our studies over the past decade, I have presented here theoretical frameworks for the phase-separation propensities, material states, and material properties, which have largely been missing in the biomolecular condensate literature. Using these frameworks, I have rationalized mechanistic interpretations from our recent experi...

    1988

  4. [4]

    A.; Ren, J.; Svergun, D.; Chen, A.; Yang, P.; Zeng, A

    (25) Nie, J.; Zhang, X.; Hu, Z.; Wang, W.; Schroer, M. A.; Ren, J.; Svergun, D.; Chen, A.; Yang, P.; Zeng, A. P. A globular protein exhibits rare phase behavior and forms chemically regulated orthogonal condensates in cells. Nat Commun 2025, 16,

    2025

  5. [5]

    W.; Holehouse, A

    43 (26) Martin, E. W.; Holehouse, A. S.; Peran, I.; Farag, M.; Incicco, J. J.; Bremer, A.; Grace, C. R.; Soranno, A.; Pappu, R. V .; Mittag, T. Valence and Patterning of Aromatic Residues Determine the Phase Behavior of Prion-Like Domains. Science 2020, 367, 694-699. (27) Tombs, M. P.; Newsom, B. G.; Wilding, P. Protein solubility: Phase separation in ara...

    2020

  6. [6]

    (53) Huggins, M. L. Solutions of Long Chain Compounds. J Chem Phys 1941, 9, 440-440. (54) Flory, P. J. Thermodynamics of High Polymer Solutions. J Chem Phys 1942, 10, 51-61. 46 (55) Gibbs, J. W. On the Equilibrium of Heterogeneous Substances. Trans Conn Acad Arts Sci 1876; 1878, 3, 108–248; 343–524. (56) Mazarakos, K.; Zhou, H. X. Multiphase organization ...

    1941

  7. [7]

    N.; Mathur, P.; Stavrakis, S.; deMello, A

    (68) Makasewicz, K.; Schneider, T. N.; Mathur, P.; Stavrakis, S.; deMello, A. J.; Arosio, P. Formation of multicompartment structures through aging of protein-RNA condensates. Biophys J 2025, 124, 115-124. (69) Qin, S.; Zhou, H. X. A Fixed-V olume Variant of Gibbs-Ensemble Monte Carlo Yields Significant Speedup in Binodal Calculation. arXiv 2025, 2512.188...

    work page arXiv 2025

  8. [8]

    S.; Weinhardt, V .; Kovacs, D.; Van Lindt, J.; Larabell, C.; Van Den Bosch, L.; Das, R.; Tompa, P

    (74) Boeynaems, S.; Holehouse, A. S.; Weinhardt, V .; Kovacs, D.; Van Lindt, J.; Larabell, C.; Van Den Bosch, L.; Das, R.; Tompa, P. S.; Pappu, R. V .; et al. Spontaneous Driving Forces Give Rise to Protein-RNA Condensates with Coexisting Phases and Complex Material Properties. Proc. Natl. Acad. Sci. USA 2019, 116, 7889-7898. (75) Espinosa, J. R.; Joseph,...

    2019

  9. [9]

    Improved Predictions of Phase Behaviour of Intrinsically Disordered Proteins by Tuning the Interaction Range

    (82) Tesei, G.; Lindorff-Larsen, K. Improved Predictions of Phase Behaviour of Intrinsically Disordered Proteins by Tuning the Interaction Range. Open Res. Eur. 2023, 2,

    2023

  10. [10]

    A.; Jacobs, W

    (83) An, Y .; Webb, M. A.; Jacobs, W. M. Active Learning of the Thermodynamics-Dynamics Trade-off in Protein Condensates. Sci. Adv. 2024, 10, eadj2448. (84) MacAinsh, M.; Dey, S.; Zhou, H. X. Direct and indirect salt effects on homotypic phase separation. eLife 2024, 13, RP100282. (85) Zhang, Y .; Li, S.; Gong, X.; Chen, J. Toward Accurate Simulation of C...

    work page arXiv 2024

  11. [11]

    (91) Kota, D.; Zhou, H. X. Macromolecular Regulation of the Material Properties of Biomolecular Condensates. J Phys Chem Lett 2022, 5285-5290. (92) Qin, S.; Zhou, H. X. Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform. J Phys Chem B 2019, 123, 8203-8215. (93) Ahn, S. H.; Qin, S.; Zhang, J. Z.; McCammon, J. A.; Z...

    2022

  12. [12]

    ATP Biphasically Modulates LLPS of TDP-43 PLD by Specifically Binding Arginine Residues

    (98) Dang, M.; Lim, L.; Kang, J.; Song, J. ATP Biphasically Modulates LLPS of TDP-43 PLD by Specifically Binding Arginine Residues. Commun. Biol. 2021, 4,

    2021

  13. [13]

    K.; Forman-Kay, J

    51 (99) Toyama, Y .; Rangadurai, A. K.; Forman-Kay, J. D.; Kay, L. E. Mapping the Per-Residue Surface Electrostatic Potential of CAPRIN1 along Its Phase-Separation Trajectory. Proc. Natl. Acad. Sci. USA 2022, 119, e2210492119. (100) Kota, D.; Prasad, R.; Zhou, H. X. Adenosine Triphosphate Mediates Phase Separation of Disordered Basic Proteins by Bridging ...

    work page arXiv 2022

  14. [14]

    W.; Thomasen, F

    (137) Martin, E. W.; Thomasen, F. E.; Milkovic, N. M.; Cuneo, M. J.; Grace, C. R.; Nourse, A.; Lindorff-Larsen, K.; Mittag, T. Interplay of folded domains and the disordered low-complexity domain in mediating hnRNPA1 phase separation. Nucleic Acids Res 2021, 49, 2931-2945. (138) Otis, J. B.; Sharpe, S. Sequence Context and Complex Hofmeister Salt Interact...

    2021

  15. [15]

    (151) Zhou, H. X. Viscoelasticity of Biomolecular Condensates Conforms to the Jeffreys Model. J. Chem. Phys. 2021, 154, 041103. (152) Cox, W. P.; Merz, E. H. Correlation of dynamic and steady flow viscosities. J Polym Sci 1958, 28, 619-622. (153) Cross, M. M. Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems. J Colloid Sci 19...

    2021

  16. [16]

    Macromolecules 1998, 31, 1386-1397

    Linear Dynamics. Macromolecules 1998, 31, 1386-1397. 58 (160) Shen, Z.; Jia, B.; Xu, Y .; Wessén, J.; Pal, T.; Chan, H. S.; Du, S.; Zhang, M. Biological Condensates Form Percolated Networks with Molecular Motion Properties Distinctly Different from Dilute Solutions. eLife 2023, 12, e81907. (161) Grimm, M.; Jeney, S.; Franosch, T. Brownian motion in a Maxw...

    1998