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arxiv: 2605.26027 · v1 · pith:FBM7GKDDnew · submitted 2026-05-25 · ❄️ cond-mat.soft

Liquid-Liquid Phase Separation in a Minimal Explicit-Solvent Lattice Model Mimicking Protein Solutions

Siddhartha Roy , Rakesh S. Singh This is my paper

Pith reviewed 2026-06-29 19:12 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords liquid-liquid phase separationbiomolecular condensateslattice modelquenched disorderphase diagramsmorphologyprotein-solvent interactions
0
0 comments X

The pith

Protein-solvent and protein-crowder interactions regulate condensate morphology and stability.

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

The paper employs a minimal lattice-gas model with explicit solvent and quenched disorder to mimic crowders in protein solutions. Computations produce phase diagrams with UCST, closed-loop, and reentrant transitions as protein-solvent interactions change, both at equilibrium and out of equilibrium. Binary protein mixtures exhibit partially wetted, fully wetted, segregative, and associative morphologies without disorder, while quenched disorder expands the range of complex forms. The work concludes that protein-solvent and protein-crowder interactions join protein-protein interactions as tunable controls over condensate behavior.

Core claim

Using an explicit-solvent minimal statistical mechanical model based on the lattice-gas Hamiltonian with quenched disorder, the study shows that protein-solvent and protein-crowder interactions, together with protein-protein interactions, act as key regulatory parameters for modulating condensate morphology and stability. The computed phase diagrams reveal rich behavior including upper critical solution temperature, closed-loop, and reentrant transitions, while binary mixtures display a spectrum of phase-separated morphologies that broaden under quenched disorder.

What carries the argument

Lattice-gas Hamiltonian with quenched disorder, which encodes crowders and explicit solvent-protein interactions to compute phase behavior and morphology.

If this is right

  • Varying protein-solvent interactions produces UCST, closed-loop, and reentrant phase transitions at both equilibrium and out-of-equilibrium conditions.
  • Binary protein mixtures without disorder form partially wetted, fully wetted, segregative, and associative morphologies whose boundaries depend sensitively on protein-solvent parameters.
  • Introduction of quenched disorder generates a wider set of complex morphologies controlled by the combined protein-protein, protein-solvent, and protein-crowder parameters.
  • The identified interaction parameters can serve as design handles for stimuli-responsive condensates in future studies.

Where Pith is reading between the lines

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

  • Small shifts in solvent quality or crowder concentration could switch a system between different phase-transition types in cellular environments.
  • The model's sensitivity to quenched disorder suggests that spatial heterogeneity in crowder distribution may stabilize or destabilize condensates in ways not captured by uniform mean-field treatments.
  • Extending the lattice model to include explicit chain connectivity or sequence-specific interactions could test whether the reported morphology changes persist in more detailed representations.

Load-bearing premise

The lattice-gas Hamiltonian with quenched disorder sufficiently represents the interactions in real biomolecular systems to predict phase behavior and morphology.

What would settle it

Direct measurement of phase diagrams and droplet shapes in a real protein-crowder-solvent mixture, with interaction strengths matched to the model parameters, that fails to reproduce the predicted UCST, reentrant, or morphological transitions.

Figures

Figures reproduced from arXiv: 2605.26027 by Rakesh S. Singh, Siddhartha Roy.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Proteins are represented with particles having two internal states, native (n, denoted by a blue filled circle) and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a)). The representative snapshots and the correspond￾ing protein composition profiles are shown in Figs. 2(d) and 2(e). Thus, the phase diagram contains two distinct UCST lines — designated as UCST-I and UCST-II — situated be￾tween the phases P1-P2 and P3-P4, respectively, along with an LCST line between P2 and P3. This exhibits notable simi- [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Temperature dependence of average fraction of unfolded state proteins ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Reentrant phase behavior under different protein-cluster interactions is shown. Here, the total fraction of pinned particles [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Phase diagram showing the phase behavior of the binary protein mixture in the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Phase diagrams of the binary protein system in the presence of an impurity cluster (or crowder) for different protein [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Biomolecular condensates play essential roles in cellular processes, and recent efforts have focused on understanding their assembly and rational design principles. In this study, we have employed an explicit-solvent minimal statistical mechanical model based on the lattice-gas Hamiltonian with quenched disorder -- which mimics crowders -- to investigate how protein-solvent and protein-crowder interactions influence condensate phase behavior and morphology. The computed phase diagrams reveal rich behavior, including upper critical solution temperature (UCST), closed-loop, and reentrant type transitions under varying protein-solvent interactions at both equilibrium and out-of-equilibrium conditions. We elucidated the origin of these phase behavior changes and examined the role of protein-crowder interactions in modulating condensed phase morphology and stability. We further extended this model to binary protein mixtures where we studied the phase behavior in the presence and absence of quenched disorder. Without disorder, the system exhibits diverse phase-separated morphologies -- partially wetted, fully wetted, segregative, and associative -- with phase boundaries delicately sensitive protein-solvent interactions. The introduction of quenched disorder (or crowder) leads to a broader spectrum of complex morphologies, dictated by the interplay among protein-protein, protein-solvent, and protein-crowder interaction parameters. In general, this work underscores that protein-solvent and protein-crowder interactions, together with protein-protein interactions, can act as key regulatory parameters for modulating condensate morphology. These insights may guide future computational and experimental studies of liquid-liquid phase separation in biomolecular systems aimed at designing stimuli-responsive 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

0 major / 3 minor

Summary. The manuscript introduces a minimal explicit-solvent lattice-gas model with quenched disorder (representing crowders) to examine how protein-solvent and protein-crowder interactions, in addition to protein-protein interactions, control liquid-liquid phase separation. Phase diagrams are reported for UCST, closed-loop, and reentrant transitions under variation of protein-solvent strength at both equilibrium and out-of-equilibrium conditions; binary protein mixtures are analyzed for morphologies (partially/fully wetted, segregative, associative) with and without disorder, showing that crowders broaden the range of complex morphologies.

Significance. If the reported phase behavior is robust, the work supplies a transparent, minimal statistical-mechanical framework that isolates the regulatory roles of solvent and crowder interactions. This is useful for generating qualitative design principles for stimuli-responsive condensates and for motivating targeted experiments, though the model remains a coarse-grained representation rather than a quantitative predictor for real biomolecular systems.

minor comments (3)
  1. [Methods and Results sections on out-of-equilibrium simulations] The abstract states that out-of-equilibrium results rest on the model's dynamics, but the main text should explicitly specify the Monte Carlo or kinetic rules employed, the criteria for equilibration, and any convergence tests performed on the reported phase boundaries.
  2. [Figure captions and parameter tables] Figure captions and text should clarify whether the interaction strengths are scanned on a uniform grid or chosen post-hoc to produce particular morphologies; a table listing the exact parameter values used for each reported diagram would improve reproducibility.
  3. [Model definition] The quenched-disorder implementation (site occupation probabilities, disorder averaging procedure) should be stated with a concrete equation or pseudocode so that readers can assess how crowder effects are statistically sampled.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our manuscript, the assessment of its significance, and the recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper deploys a lattice-gas Hamiltonian with quenched disorder as an explicit model and reports phase diagrams and morphologies obtained by direct variation of the stated interaction parameters (protein-protein, protein-solvent, protein-crowder). No step equates a reported transition or morphology to a quantity defined by a fitted parameter, nor does any central claim rest on a self-citation chain that itself reduces to the target result. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that the lattice-gas model with quenched disorder captures essential protein-solvent-crowder physics, plus several interaction strengths that are varied rather than derived.

free parameters (2)
  • protein-solvent interaction strength
    Varied across values to produce UCST, closed-loop, and reentrant transitions.
  • protein-crowder interaction strength
    Varied to modulate condensed-phase morphology and stability.
axioms (1)
  • domain assumption Lattice-gas Hamiltonian with quenched disorder accurately mimics crowders in protein solutions.
    Invoked to justify the model setup for studying condensate phase behavior.
invented entities (1)
  • quenched disorder representing crowders no independent evidence
    purpose: To introduce fixed obstacles that affect protein phase separation.
    Introduced in the model to study crowder effects on morphology.

pith-pipeline@v0.9.1-grok · 5808 in / 1364 out tokens · 57171 ms · 2026-06-29T19:12:56.715003+00:00 · methodology

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Reference graph

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