Maxwell Relaxation Time Aging Exponent beta_M in FUS-P525L Condensates

Maxwell Relaxation Time Aging Exponent beta_M in FUS-P525L Condensates

Verification of MAGELLAN Hypothesis E2-H4 (session 2026-04-19-scout-027)

Verdict: INCONCLUSIVE (arithmetic + methodology confirmed; core empirical

claim NOT directly verifiable from publicly accessible data; primary

disease-discriminator prediction is UNTESTED in the literature)

1. Hypothesis

E2-H4 proposes that condensate viscosity follows a power law in aging time:

    eta(t_age) = eta_0 * t_age^beta_M

and that the exponent beta_M discriminates healthy (FUS-WT) from

disease-associated (FUS-P525L) condensates, with:

• FUS-WT: beta_M in [0.5, 0.8]
• FUS-P525L: beta_M in [0.9, 1.5]
• Discriminator: beta_M^P525L - beta_M^WT > 0.3 (primary endpoint)

The hypothesis anchors the WT value to Jawerth 2020 Science 370:1317

(PMID 33303613) with the specific claim: "eta increases approximately 10x

from t_age=1h to t_age=24h, giving beta_M = log(10)/log(24) approximately 0.72".

2. Data Sources

Primary (paywalled, not directly accessible)

• Jawerth et al. 2020 Science 370:1317 "Protein condensates as aging

Maxwell fluids" PMID 33303613. This paper contains the raw eta(t_age) data

the hypothesis cites. Full PDF is paywalled and the supplementary tables are

not mirrored in the open literature.

Secondary (open-access, used for verification)

• Alshareedah et al. 2022 JACS Au, PMC9326828. Table 1 reproduces Jawerth

numerical values: FUS eta_early = 4 Pa.s, eta_late = 50 Pa.s (ratio 12.5x);

PGL-3 at 75 mM KCl, eta_early = 4.4 Pa.s, eta_late = 40 Pa.s (ratio 9.09x).

The time points corresponding to "early" and "late" are NOT explicitly

reported in the accessible text.

• PRX Life 1:013006 (2023) "Theory of Rheology and Aging of Protein

Condensates". Reports aging exponent mu where tau_c ~ t_w^mu, fit to the

Jawerth data: mu = 6.4 at 150 mM KCl and mu = 2.1 at 100 mM KCl for PGL-3.

The authors note that these values exceed what their theoretical model

can explain (would require negative alpha).

• arXiv:2303.18028 identical theoretical re-analysis in preprint form.
• Nat Commun 2025 PMID 40473633 (6xPSD multivalent protein) reports

rheological power-law exponent alpha approximately 0.5, attributed to

weak-bond binding/unbinding.

• Nat Phys 2024 PMID 39464253 (hnRNPA1 LCD variants) reports

sequence-specific aging rates but no single exponent.

• Patel et al. 2015 Cell, PMID 26317470. Original study establishing

FUS-P525L as an ALS-linked mutant with accelerated liquid-to-solid

transition in condensates. Contains 24h/48h/72h viscosity and elasticity

measurements but does NOT report a power-law aging exponent.

3. Methodology

3.1. Arithmetic check (Part 1)

Direct computation:

    log(10) / log(24) = 0.724527

The hypothesis's stated value of approximately 0.72 is correct (to two

decimal places: 0.7245 rounds to 0.72).

3.2. Power-law fit (Part 2)

A log-log linear fit, log(eta) = log(eta_0) + beta_M * log(t_age), was

applied to synthetic data with known beta_M = 0.72 and 5% Gaussian noise.

Recovered beta_M = 0.7087 +/- 0.0207 (95% CI:

[0.6682, 0.7493]),

R^2 = 0.9955. The methodology recovers the true exponent

within statistical error.

3.3. Jawerth 2020 Table 1 reanalysis (Part 3)

Because the exact time points in Jawerth 2020 Table 1 are not accessible in

secondary literature, we computed beta_M under several plausible time

assignments using the published (eta_early, eta_late) values:

protein scenario t_early_h t_late_h eta_early eta_late beta_M

FUS 1h -> 24h 1.0 24.0 4.0 50.0 0.794741

FUS 0.5h -> 24h 0.5 24.0 4.0 50.0 0.652441

FUS 1h -> 10h 1.0 10.0 4.0 50.0 1.096910

FUS 1h -> 48h 1.0 48.0 4.0 50.0 0.652441

PGL-3 1h -> 24h 1.0 24.0 4.4 40.0 0.694537

PGL-3 0.5h -> 24h 0.5 24.0 4.4 40.0 0.570178

PGL-3 1h -> 10h 1.0 10.0 4.4 40.0 0.958607

PGL-3 1h -> 48h 1.0 48.0 4.4 40.0 0.570178

3.4. Monte Carlo uncertainty propagation (Part 5)

With a 10% relative uncertainty on each of eta(1h) and eta(24h) (a typical

microrheology noise floor), the 95% CI on beta_M is:

[0.637, 0.814] (width

0.177, median

0.725). This implies a single two-point measurement cannot

resolve a beta_M difference of 0.3 between WT and P525L without substantial

replication; the hypothesis's specified n>=5 per genotype is appropriate.

3.5. P525L discriminator analysis (Part 6)

If WT beta_M = 0.72 and the discriminative threshold is beta_M^P525L -

beta_M^WT > 0.3, then P525L beta_M >= 1.0200. This implies

the P525L viscosity at 24h is at least 25.6x the 1h

value, i.e., SUPER-LINEAR aging. This is a well-defined, testable prediction

but the required P525L time-resolved viscosity data have NOT been published

at the time of this verification.

4. Results

Core arithmetic CONFIRMED

The formula beta_M = log(eta_ratio) / log(t_ratio) is correct, and the

specific numerical claim log(10)/log(24) = 0.7245 approximately 0.72

is arithmetically correct.

Methodology CONFIRMED

The log-log fitting procedure recovers a known exponent from noisy data

within statistical error.

Jawerth Table 1 magnitude PARTIALLY CONSISTENT

Under the 1h -> 24h time assumption:

• FUS (4 -> 50 Pa.s, 12.5x): beta_M = 0.795
• PGL-3 (4.4 -> 40 Pa.s, 9.09x): beta_M = 0.695

Both values are consistent with the hypothesis's WT range [0.5, 0.8], IF

and only if the early/late Jawerth measurements correspond to 1h and 24h.

The hypothesis does not prove this time assignment.

Published reanalysis INCONSISTENT with hypothesis

An independent theoretical fit to the same Jawerth data (PRX Life 2023)

reports mu = 2.1 to 6.4 for PGL-3 (tau_c ~ t_w^mu). Under the hypothesis's

constant-G' Maxwell assumption, mu is equivalent to beta_M. These values

are MUCH LARGER than the hypothesis's WT range [0.5, 0.8] and would

imply P525L must have beta_M > mu + 0.3 > 2.4, far beyond physical

power-law aging.

The authors of that reanalysis note their theoretical model cannot

accommodate mu > 1 without unphysical parameters, suggesting that either

(a) the Jawerth aging is NOT a single power law (might be stretched

exponential or crossover behaviour) or (b) the relevant exponent depends

on which observable (viscosity vs relaxation time) is fit.

FUS-P525L differential UNTESTED

No published study reports time-resolved viscosity aging of FUS-P525L at

the resolution required (multiple time points, 1h-24h) to extract beta_M.

Patel 2015 measures viscosity at 24, 48, 72h but uses different protocols

(micropipette aspiration) and does not compute an aging exponent.

5. Convergent Evidence Table

id study system exponent_name value ci_low ci_high compares_to_beta_M note

hyp Hypothesis E2-H4 (MAGELLAN) FUS-WT, 1h->24h, 10x eta beta_M 0.72 None None True log(10)/log(24) assumed magnitude

jawerth_fus Jawerth 2020 FUS Table 1 (as cited, 1h->24h) FUS, early->late beta_M 0.79 None None True ln(50/4)/ln(24) under 1h->24h assumption

jawerth_pgl Jawerth 2020 PGL-3 Table 1 (as cited, 1h->24h) PGL-3 75 mM KCl beta_M 0.69 None None True ln(40/4.4)/ln(24) under 1h->24h assumption

prxlife_150 PRX Life 1:013006 theoretical re-fit PGL-3, 150 mM KCl mu (tau_c~tw^mu) 6.40 None None True Relaxation-time aging, equivalent to beta_M when G' constant

prxlife_100 PRX Life 1:013006 theoretical re-fit PGL-3, 100 mM KCl mu (tau_c~tw^mu) 2.10 None None True Weaker aging at lower salt

natcomm2025 Nat Commun 2025 PMID 40473633 6xPSD multivalent network alpha (G(t) power law) 0.50 None None False Weak-bond binding dynamics - DIFFERENT quantity

natphys24 Nat Phys 2024 PMID 39464253 hnRNPA1 LCD variants aging rate (qualitative) NaN None None False Sequence-specific; not a single exponent

wang2021 Wang 2021 Nat Phys (RGX polypeptides) [RGYGG]5 vs [RGFGG]5 etc. eta range (Pa.s) NaN None None False 0.1 to 40 Pa.s at fixed age; not an aging exponent

6. FUS-P525L Open Question (CORE UNVERIFIED PREDICTION)

The hypothesis's testable prediction - that FUS-P525L condensates exhibit

beta_M > beta_M^WT + 0.3 - has NOT been tested in the published literature.

Required experimental design:

• n >= 5 FUS-WT and n >= 5 FUS-P525L condensate preparations, identically

processed (Jawerth 2020 protocol: 200 uM protein, 5% dextran-70, 150 mM

NaCl, 25 C).

• Passive microrheology with 200-nm beads, measuring eta(t_age) at

t_age = 1, 2, 4, 8, 12, 18, 24 h.

• Log-log fit to extract beta_M per preparation; two-sample t-test.
• Independent control: ThT + G'(t_age) to verify Maxwell regime holds for

P525L (not pure fiber formation).

This is the CORE EMPIRICAL TEST of the hypothesis and it has not yet been

run. It is executable with standard equipment on a roughly 1 month

timescale.

7. Verdict: INCONCLUSIVE

Breakdown:

• Arithmetic: CONFIRMED. log(10)/log(24) = 0.7245 approximately 0.72.
• Methodology (log-log fit): CONFIRMED. Recovers known exponents.
• Hypothesized WT beta_M approximately 0.72: PARTIALLY CONFIRMED under

a 1h -> 24h time assignment of the Jawerth Table 1 values.

• Published alternative fit (mu = 2.1 to 6.4): INCONSISTENT with the

hypothesis, but not necessarily a refutation because the fits are to

different observables (eta vs tau_c) and the theoretical framework

disagrees with experimental magnitudes.

• P525L discriminator prediction: UNTESTED. The experimental design

is sound and executable; the data do not exist.

The hypothesis is NOT refuted. Its core predictions are testable but the

data to discriminate are not yet published. This places the hypothesis in

a genuinely productive zone: a clean, well-defined experiment would either

confirm or refute it.

Suggested computational follow-ups for future verification

1. Request raw Jawerth 2020 data from corresponding author (Alf Honigmann

or Frank Juelicher) or check Zenodo/Dryad mirrors. If available, directly

fit eta(t_age) and G'(t_age) power laws.

1. Contact the PRX Life 2023 authors for their digitized version of the

Jawerth figures; they did the fit that gave mu = 6.4 / 2.1.

1. Survey recent preprints for FUS-P525L time-resolved microrheology

(bioRxiv, specifically Honigmann, Juelicher, Pappu groups 2024-2026).

1. Re-examine Patel 2015 supplementary for any hint of viscosity vs age

beyond 24h that could be retrofitted to a power law.

8. Figures

• fig1_eta_vs_age.png/pdf: Synthetic + canonical + Jawerth Table 1

points in log-log.

• fig2_convergent_exponents.png/pdf: Bar chart of published aging

exponents vs hypothesis WT/P525L ranges.

• fig3_monte_carlo_beta.png/pdf: Monte Carlo uncertainty on beta_M.
• fig4_p525l_discriminator.png/pdf: Implied P525L viscosity trajectories.

9. Verification provenance

• Session: 2026-04-19-scout-027
• Hypothesis ID: E2-H4 (composite 7.85, PASS)
• Verified: 2026-04-19
• Verification mode: arithmetic + methodology + literature-grounded

power-law fit on Jawerth 2020 Table 1 values as cited in

PMC9326828; Monte Carlo uncertainty; convergent-exponent survey.

• Data limitations: Jawerth 2020 raw figure data are paywalled; we

rely on secondary quotations. All inferences are clearly labelled as

assumptions.