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REVIEW 3 major objections 5 minor 73 references

Droplet growth, Ostwald's rule, and emergence of order in Fused in Sarcoma

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Simulations predict FUS-LC fibril-like cores form least-stable-first, following Ostwald's rule, with the same C-terminal core initiating droplet formation.

desk verdict The headline core-ordering claim is invalidated by an internal arithmetic contradiction in the corrected MFPTs, though the multichain simulations and testable core-3 contacts are worth engaging. read the letter →

arxiv 2506.21792 v1 pith:NKE2M6EC submitted 2025-06-26 cond-mat.soft q-bio.BM

Farkhad Maksudov (1) , Mauro L. Mugnai (2) , Laura Dominguez (1 , 3) , Dmitrii Makarov (1 , 4) , D. Thirumalai (1) ((1) Department of Chemistry , The University of Texas at Austin
show 14 more authors
(2) Institute of Soft Matter Synthesis Metrology Georgetown University Washington (3) Departamento de Fisicoquimica Facultad de Quimica Universidad Nacional Autonoma de Mexico Coyoacan CDMX Mexico (4) Oden Institute for Computational Engineering Sciences University of Texas at Austin Austin)
This is my paper
classification cond-mat.softq-bio.BM PACS 87.15.hm64.75.Gh
keywords FUS-LCphaseseparationOstwald'sruleofstagesfibrilformationkineticsintrinsicallydisorderedproteinscoarse-grainedsimulationsN*statesAlphaFoldstructureprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper predicts the order in which fibril-like structures appear in FUS-LC, the 214-residue low-complexity domain of the RNA-binding protein Fused in Sarcoma, which phase-separates into droplets and slowly matures into fibers. Using coarse-grained simulations and rare fibril-shaped N* conformations of the isolated monomer as reference states, the authors find that the least stable core, core-3 (residues 155-190), forms first, followed by core-2 (residues 112-150), and finally the most stable core-1 (residues 39-95). Because formation speed runs opposite to stability, the result is an instance of Ostwald's rule of stages, and the same simulations show that core-3 residues 164-176 make the earliest inter-chain contacts, initiating droplet formation, which then coarsens by Ostwald ripening. If the prediction holds, it explains why the core-2 fibril seen in truncated FUS-LC never appears in the full-length domain, and it tells experimenters which region to probe in the earliest stages of assembly.

What carries the argument

The argument is carried by three pieces of machinery. The first is the N* state framework: long equilibrium simulations of the isolated monomer enumerate rare, fibril-like excited conformations, identified by a structural overlap parameter $\chi$ that compares each sampled conformation against a reference fibril structure, namely the experimental solid-state NMR structure for core-1 (PDB 5W3N), the cryo-EM structure for core-2 (PDB 6XFM), and AlphaFold2/3-predicted models for core-3. The second is first-passage analysis: Brownian dynamics trajectories record the first time each monomer reaches an N* state from the random-coil ground state, and because most trajectories never observe that transition within the simulation window, a maximum-likelihood correction that assumes exponential waiting times converts the truncated observed distributions into true mean first-passage times. The third is multichain simulation of 200 chains, which yields nucleation-like droplet formation, Ostwald-ripening coarsening, and phase equilibrium verified by near-equal chemical potentials in the two phases; quenching the droplet to its inherent structure shows $\beta$-strand content concentrated in the cores, with the highest propensity in core-3 before core-1 forms. The identity that carries the Ostwald claim is a simple inversion: the mean first-passage times satisfy $\langle\tau_{c.1}\rangle > \langle\tau_{c.2}\rangle > \langle\tau_{c.3}\rangle$ while the stabilities run in the opposite direction, so the fastest-forming core (core-3) is the least stable and the slowest-forming core (core-1) is the most stable.

What would settle it

Residue-resolved kinetics of FUS-LC maturation would settle it: time-resolved solid-state NMR or single-molecule FRET pairs reporting on residues 39-95 (core-1) versus 155-190 (core-3) should detect ordered $\beta$-structure at core-3 within hours and at core-1 only after days, and if the first ordered region to appear is core-1 instead, the hierarchy is wrong. Independently, an experimental structure of the core-3 fibril (e.g., from FUS 141-214, which forms core-3 fibrils in vitro) that places $\beta$-strands differently than the AlphaFold models would invalidate the core-3 reference and the mean first-passage times measured against it.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a kinetic hierarchy among the three fibril-forming cores of FUS-LC. Fibril-like N* conformations of core-3 (residues 155-190) are reached first, with corrected mean first-passage times of $\langle\tau\rangle \approx 405$ ms (S-bend) and 426 ms (U-bend), followed by core-2 (residues 112-150) at about 685 ms and core-1 (residues 39-95) last at about 1554 ms. The stabilities run in the opposite direction, with core-1 the most stable and core-3 the least ($\Delta F_{1,3S} = -2.70 \pm 0.10$ kcal/mol), so formation time and stability are inversely correlated, as Ostwald's rule of stages requires. Multichain SOP-IDP simulations of 200 chains support the thermodynamic side of the picture: chemical potentials in the dense and dilute phases are equal within noise ($\Delta\mu/\langle\mu_c\rangle = 0.003 \pm 0.03$), coexisting concentrations of about 16 mM and 0.28 mM match experiments, and the earliest, most persistent inter-chain contacts involve residues 164-176, the segment with the highest monomer $\beta$-strand propensity. The paper concludes that core-3 initiates FUS-LC assembly and that the order of fibril-like structure formation is core-3, then core-2, then core-1.

Load-bearing premise

The load-bearing premise is that the AlphaFold-predicted structures used as the reference for core-3 are accurate enough proxies for the real core-3 fibril; the paper explicitly says it does not claim those structures are correct, and if they are wrong, the computed formation time for core-3, and the predicted core-3 then core-2 then core-1 ordering built on it, would not describe real FUS-LC.

Editorial extensions

If this is right

  • The kinetic ordering is a falsifiable prediction: in full-length FUS-LC, ordered $\beta$-structure should first appear at residues 155-190 and only later at residues 39-95, en route to the mature cross-$\beta$ fibril.
  • Because core-1 and core-2 are nearly tied in stability yet core-1 forms much more slowly, the core-2 fibril found in the truncated FUS-LC-C construct is kinetically preempted in the full-length protein.
  • Removing core-3 speeds up core-1 and core-2 formation by roughly 3-fold and 11-fold, making the C-terminal core a kinetic gate; perturbations in residues 155-190 should shift the onset of full FUS-LC fiber formation.
  • The simulated coexisting concentrations (about 16 mM dense, 0.28 mM dilute) and the near-equality of chemical potentials put the model's phase equilibrium on the same footing as the measured values.
  • The same N*-state plus corrected-first-passage protocol should transfer to other low-complexity domains such as TDP-43, where the paper expects the same Ostwald-type staging to appear.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A decisive test the paper does not run: residue-resolved kinetics (time-resolved solid-state NMR, or FRET pairs reporting on residues 39-95 versus 155-190) should see $\beta$-rich contacts at core-3 within hours and at core-1 only after days; if the first ordered region is core-1 instead, the hierarchy is wrong.
  • Because the core-3 reference structures are predictions, an experimental structure of the core-3 fibril (e.g., from FUS 141-214, which forms core-3 fibrils in vitro) would either confirm or overturn the computed core-3 formation time, making it the single most decisive check.
  • The deletion results suggest a graded control the paper does not map: variants that stabilize core-3 (for example ALS-linked mutations near residues 164-176) should further delay core-1 formation, while destabilizing core-3 should accelerate it.
  • Applied more broadly, the N*-state plus corrected-first-passage protocol could rank nucleation-prone segments in other low-complexity domains (TDP-43, hnRNPA1) and predict which segment seeds their fibers; that generalization is the paper's stated ambition but not yet demonstrated.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper uses SOP-IDP coarse-grained simulations of FUS-LC and variants to address three related questions: the relative kinetics of formation of three fibril-like cores (core-1, core-2, and a predicted core-3), the thermodynamics and growth mechanism of FUS-LC droplets, and the role of core-3 in initiating assembly. The central claim is that the mean first-passage times to the fibril-like N* states satisfy core-3 < core-2 < core-1, and that these times are inversely correlated with the relative stabilities of the cores, in accord with Ostwald's rule of stages. Multichain simulations are used to argue that droplets form by nucleation and coarsen by an Ostwald-ripening-like mechanism, that chemical potentials in the coexisting phases are nearly equal, and that simulated phase densities agree with experiments. The paper also reports AlphaFold2/3 structural models for core-3 and uses them to identify residues 164–176 as an early interchain contact hub. The manuscript is clearly written in broad strokes and is rich in comparisons to experimental data, but several load-bearing numerical and textual issues need to be resolved before the main ordering claim can be accepted.

Significance. If the predicted kinetic ordering and the inverse stability-kinetics relation hold, the work would be a valuable example of Ostwald's rule of stages in a physiologically relevant IDP and would provide a concrete structural interpretation of the early events in FUS-LC assembly. The paper deserves credit for anchoring the model to experimental fibril structures for core-1 and core-2, for testing predictions against experimental dense-phase concentrations and conformation-sensitive measurements (SAXS, FRET, DEER), and for explicitly attempting to correct censored first-passage data with a maximum-likelihood formula that has been validated on solvable models. The inferred central role of residues 164–176 is supported by existing hydrogel truncation experiments. However, the headline numerical result is currently not reproducible as reported, and the core-3 reference structures that determine the kinetics are explicitly disclaimed by the authors as potentially incorrect.

major comments (3)
  1. [Results, 'Ostwald's rule of stages'; Eq. (2); Methods 'True Mean FPT'] The corrected mean first-passage times reported in the Results are not attainable from the stated data and Eq. (2). For core-1 the text states NS=200, NO=42, NE=158, and T=280 ms (the Methods states T=240 ms). Since every observed FPT is nonnegative, Eq. (2) is bounded above by (NS·T)/NO, which evaluates to 1333 ms for T=280 ms (or 1143 ms for T=240 ms), yet the paper reports a corrected value of 1554±16 ms. For core-2, the bound is 644 ms for T=280 ms (or 552 ms for T=240 ms), while the reported value is 685±10 ms. The raw first-passage times do not significantly separate core-2 from core-3 (Welch p>0.6), so the core-3-before-core-2 step of the central ordering rests entirely on this censoring correction. The authors must recompute the corrected MFPTs from the raw trajectory data, report the actual estimates with their bounds, and state which T value was used; as written, the headline ordering is supported by numbers that are mathematically impossible under the paper's own formula.
  2. [Discussion, 'Core-3 structure prediction'; Results, 'Structural model for core-3'] The paper explicitly states, 'We do not claim that any of the predicted structures of core-3 are correct in reality.' This disclaimer is in direct tension with the load-bearing use of those structures: the first-passage times to the core-3 U-bend and S-bend N* states are defined through structural overlap with AlphaFold-generated reference fibrils, and the statement that core-3 forms before core-2 and core-1 depends on those times. The paper notes that AlphaFold predictions for IDRs and fold-switching proteins have been criticized, and the internal check against experimental structures is only available for core-1 and core-2. The authors should either provide a concrete external validation of the core-3 model (for example, a comparison to future ssNMR or cryo-EM data, or a mutation-based kinetic test of the predicted 155–190 contact pattern) or substantially weaken the kinetic-ordering conclusion, since the predicted MFPTs would not correspond to real FUS-LC assembly if the core-3 reference structures are wrong.
  3. [Results, 'Chemical potentials in the two phases are similar'] This section contains a self-contradictory sentence that undermines the phase-equilibrium claim. After reporting a relative chemical potential difference of 0.003±0.03 and a Jensen-Shannon divergence of 0.01, the text states: 'Given that the system size that can be reliably simulated is small (maximum of 200 chains), the conclusion that the chemical potentials between the coexisting phases are similar is unreasonable.' If the word 'unreasonable' is intended, then the subsequent calculation of coexisting densities from the equality of chemical potentials is not justified; if it is a typo for 'reasonable', the sentence should be corrected. Either way, the manuscript must be revised so that the stated conclusion is consistent with its own text.
minor comments (5)
  1. [Methods, 'Transition to fibril-like monomer N* states' vs Results] The trajectory duration is given as 280 ms in the Results section but as 240 ms in the Methods; the discrepancy must be reconciled because the censoring correction in Eq. (2) depends directly on T.
  2. [Results, 'Ostwald's rule of stages' and Methods, 'True Mean FPT'] The symbols NS, NE, and NO used in Eq. (2) are not defined when the equation is first invoked; the definitions appear only later in the Methods, and the hat notation d⟨τc.i⟩ is never explicitly defined as an estimate.
  3. [Results, 'Core 3 residues drive FUS-LC condensation'] The text contains a typographical error, 'FUC-LC', which should read 'FUS-LC'.
  4. [Results, 'Chemical potentials in the two phases are similar'] The phrase 'polymer chains chains exhibit' contains a duplicated word and should read 'polymer chains exhibit'.
  5. [Discussion, 'Core-3 structure prediction'] The possessive 'Ostwalds's rule' contains an extra apostrophe and should be 'Ostwald's rule'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the core-3/core-2/core-1 ordering is a genuine simulation result conditioned on stated reference structures, not an input restatement; the reported MFPT arithmetic inconsistency is a correctness flaw, not a circular step.

full rationale

The paper's central claim, the kinetic ordering core-3 followed by core-2 and finally core-1, is obtained by running SOP-IDP Brownian dynamics simulations and measuring first passage times to N* states defined by structural overlap with reference fibril structures: experimental NMR structure 5W3N for core-1, cryo-EM structure 6XFM for core-2, and AlphaFold2/3-predicted structures for core-3. The reference structures are inputs, but the MFPTs and stabilities are computed from the model, so the ordering is not equivalent to the inputs by construction. The AlphaFold dependence of core-3 is explicitly disclaimed in the paper ('We do not claim that any of the predicted structures of core-3 are correct in reality'), which is a genuine external-validity limitation rather than circularity. The Ostwald-rule correlation is model-internal because both stabilities and MFPTs come from the same simulations, but the model was not fitted to reproduce that correlation, and the paper anchors against independent experiments on droplet densities, monomer conformations, and experimentally observed fibril timescales (50 hours for core-3, 5-7 days for core-1). The one serious issue is an internal arithmetic inconsistency: using Eq. (2), NS=200, NO=42 for core-1, NO=87 for core-2, and T=280 ms (or 240 ms in Methods), the reported corrected MFPTs of 1554 ms and 685 ms exceed the maximum possible values (NS/NO)*T, namely 1333 ms and 644 ms (or 1143 ms and 552 ms for T=240). This indicates a reproducibility error in the reported numbers, but it is a correctness problem, not a circularity in which a result reduces to its inputs by definition.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the SOP-IDP force field, the N* theory, AlphaFold-predicted core-3 structures, and a model-based correction for truncated FPT distributions. No new physical entities are postulated. The main free parameters are the chi_c thresholds (in SI) and the accelerated simulation conditions (T=209 K, 100x reduced viscosity).

free parameters (3)
  • Structural overlap thresholds chi_c.i for each core i = not specified in main text (SI Methods)
    The values of chi_c.i determine which monomer conformations are classified as N* fibril-like states, directly setting which events count as first-passage times. Threshold selection is described in SI, and the paper does not state sensitivity of the MFPT order to these values.
  • Multichain simulation temperature = 209 K
    Chosen 'to facilitate droplet formation under equilibrium conditions', well below the experimental room-temperature conditions. This could bias the dense-phase density and the nucleation kinetics.
  • Effective viscosity reduction factor = 100x reduced water viscosity
    Multichain simulations are run in the underdamped regime to accelerate sampling. The paper argues the kinetic picture is preserved with a follow-up Brownian dynamics run at real viscosity for 64 chains, but the main results use the reduced-friction ensemble.
assumptions (5)
  • domain assumption The SOP-IDP coarse-grained model reproduces the essential interactions of FUS-LC relevant to phase separation and fibril-like structure formation.
    All monomer and multichain results depend on this force field. It is a general model developed by the authors, not fitted to FUS-LC-specific core formation data, but its accuracy for subtle N* states is assumed.
  • domain assumption Monomers in isolation sample N* states that faithfully proxy for the conformations that nucleate fibrils in the multichain and droplet context.
    The MFPT analysis is performed on single chains. The paper argues this is valid (citing prior N* theory), but no direct multichain validation of the ordering is provided.
  • domain assumption AlphaFold3 predictions for the core-3 fibril provide a reliable reference structure, despite known limitations of AlphaFold for intrinsically disordered regions.
    Stated in the Discussion with caveats; the authors rely on it for core-3 MFPTs.
  • domain assumption The first-passage times to the N* states are exponentially distributed (two-state kinetics), enabling the MLE correction in Eq. 2.
    The paper cites the unimodality of ln FPT distributions and exponential survival probability as support, but the distributions are truncated, making the two-state assumption strong.
  • domain assumption In the chemical potential calculation, all chains outside the condensed droplet can be treated as a single dispersed phase species.
    Stated in the Results section: 'the variations in the oligomer sizes found in the dispersed phase are not treated as separate species.'

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Cite this review

Pith. "Pith review of Droplet growth, Ostwald's rule, and emergence of order in Fused in Sarcoma." pith.science (2026). https://pith.science/paper/NKE2M6EC

@misc{pith2026250621792,
  author       = {Pith},
  title        = {Pith review of: Droplet growth, Ostwald's rule, and emergence of order in Fused in Sarcoma},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NKE2M6EC}},
  note         = {Machine review of arXiv:2506.21792}
}
abstract

The low complexity domain of Fused in Sarcoma (FUS-LC consisting of 214 residues) undergoes phase separation, resulting in a dense liquid-like phase that forms early and slowly matures to reach ordered gel-like state on long time scales. Upon maturation, core-1, comprising of the 57 residues (39-95) in the N-terminus become structured, resulting in the formation of a non-polymorphic fibril. The truncated FUS-LC-C (residues 110-214) construct forms a fibril in which core-2 (residues 112-150) adopts a $\beta$-sheet structure. Using coarse-grained monomer SOP-IDP model simulations of FUS-LC, we predict that residues 155-190 in the C-terminal (core-3) form rapidly, followed by core-2, and finally core-1. The time scale of formation of the cores and their stabilities are inversely correlated, as anticipated by the Ostwald's rule of stages. Unbiased multichain simulations show that the chemical potentials in the two phases are equal and the calculated densities of the dense and dilute phases are in agreement with experiments. The dense phase, which forms by a nucleation mechanism, coarsens over time by a process that is reminiscent of Ostwald ripening. AlphaFold predictions of the core-3 structure and the simulations show that $\beta$-strand emerges in the core-3 region early during the droplet formation, and drives the initiation of FUS-LC assembly. The techniques introduced here are general and could be used to probe assembly of other IDPs such as TDP-43, which shares many features with FUS-LC.

Figures

Figures reproduced from arXiv: 2506.21792 by the authors.

Figure 1
Figure 1. Ostwald’s rule of stages: (A) The FUS-LC sequence using a one-letter code for the amino acids. Core-1 residues 39-95 are in red, core-2 residues are highlighted in purple, and those forming core-3 are in green. Panels B-D: Distributions of first-passage times (FPTs) for the transition from the disordered ground state to the fibril-like N∗ states in FUS￾LC (residues 1–214). Shown are the τF P T distributions sampled … view at source ↗
Figure 2
Figure 2. Phase separation in FUS-LC. (A) Representative snapshots illustrating the progression of phase separation in a system of 200 FUS-LC chains. The first panel shows the initial homogeneous configuration in the single dilute phase. Subsequent panels depict the emergence of small oligomeric nuclei, followed by their growth into a larger oligomer. This structure eventually matures into a droplet, representing the equilibr… view at source ↗
Figure 3
Figure 3. Equilibrium characteristics of FUS-LC condensates. (A) Small-angle X￾ray scattering (SAXS) profiles for FUS-LC polymers in the condensed phase (within the phase separated droplets) and the dilute phase (outside droplets). The scattering intensity I(q) as a function of the scattering vector q. The inset presents representative images from a simulation of 200 FUS-LC chains, illustrating the coexistence of dilute and c… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Conformations of monomers in dilute and dense phase are similar. Dis￾tance distributions between select residues (base on an experimental study [46]) within the same FUS-LC chain for chains in the dilute phase and those within the condensed droplet from simulations. Th…
Figure 5
Figure 5. Figure 5: Structural models of core-1 and core-3 fibrils predicted by AlphaFold3. (A) Structure of core-1 (residues 39–95) resolved by solid-state NMR [20]. Tyrosine (TYR) side chains are shown as sticks, with β-sheets colored brown and turn/coil regions in gray. (B, C) AlphaFol…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.