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REVIEW 2 major objections 5 minor 52 references

Enzymatic activity can drive measurable diffusion and force fluctuations in micron-scale colloidal tracers, strongest when enzymes sit on the particle surface.

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2026-07-14 10:14 UTC pith:NBINBHA3

load-bearing objection Solid comparative experiment: 1 µm urease-decorated tracers show real dual-modality enhancement; the main soft spot is frozen κ/γ in OT, not a collapse of the claim. the 2 major comments →

arxiv 2607.10646 v1 pith:NBINBHA3 submitted 2026-07-12 cond-mat.soft physics.bio-phq-bio.BM

Enhanced diffusion of colloidal tracers due to enzymatic activity

Mauricio Gomez , Erick Leyva , Justine Miqueu-Petit , Dakota Feldcamp , Anthony Estrada , W. Benjamin Rogers , Jennifer L. Ross , Wylie W. Ahmed This is my paper
classification cond-mat.soft physics.bio-phq-bio.BM PACS 82.70.Dd87.16.Uv05.40.-a
keywords enhanced diffusionenzymatic activitycolloidal tracersdifferential dynamic microscopyoptical tweezersactive particlesureaseforce fluctuations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether molecular-scale enzymatic catalysis can be felt by larger colloidal tracers, and under what conditions that signal is detectable. The authors compare two setups: passive beads swimming in an enzyme-rich solution (active bath) versus beads that carry the enzyme on their own surface (active particles). They measure the same systems two ways: differential dynamic microscopy for long-time ensemble diffusion, and optical tweezers for short-time single-particle force fluctuations, using several different enhancement metrics. For 1 µm particles they find clear activity-induced increases in both diffusion and non-thermal forces, with the strongest and most persistent effects when urease is attached to the bead. For 200 nm particles the signals are weaker, method-dependent, and often clouded by aggregation. The central message is that enzyme activity can be transduced to microscale motion, but the size of the tracer, where the activity is located, and which timescale and metric you use all decide whether you see it.

Core claim

Enzymatic catalysis can be transduced from the molecular scale into measurable microscale tracer diffusion and non-thermal force fluctuations. The effect is real for 1 µm colloids in both active-bath and enzyme-decorated configurations, and is strongest and most persistent when urease is localized on the particle surface; for 200 nm tracers the enhancement is modest or unresolved and frequently limited by aggregation. Apparent magnitude and detectability therefore depend on tracer size, activity localization, the timescales probed, and the metric used to quantify enhancement.

What carries the argument

Complementary DDM and optical-tweezer force spectra, together with an Active Ornstein–Uhlenbeck model of nonthermal forcing whose persistence time τ sets the frequency window of the active force spectrum. Localizing enzymes on the colloid lengthens directional persistence, shifting active spectral power into experimentally accessible frequencies.

Load-bearing premise

The analysis assumes that trap stiffness and particle friction stay the same between passive and active conditions, so any spectral difference can be attributed to nonthermal enzymatic force rather than to chemistry- or aggregation-driven changes in hydrodynamics.

What would settle it

Repeat the 1 µm decorated-particle optical-tweezer measurements with independent, in-situ checks of trap stiffness and hydrodynamic radius under fuel-on versus fuel-off conditions; if the extracted nonthermal spectrum, integrated force, and diffusion enhancement disappear once those parameters are allowed to change, the activity-transduction claim collapses.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript reports that urease activity can enhance the diffusion and force fluctuations of colloidal tracers, with the strongest and most consistent effects for 1 µm enzyme-decorated particles. Two configurations are compared: bare tracers in an active enzyme bath and urease-decorated tracers with catalysis localized at the particle surface. Complementary DDM (long-time ensemble diffusion) and optical-tweezer force spectra (short-time fluctuations) are used, together with several enhancement metrics (ΔD/Dp, effective force F, AOUP parameters u^{2}τ, variance ratio Σ, integrated nonthermal spectrum √S, and dissipation-like J). For 1 µm particles both modalities detect enhancement, larger for decorated particles (DDM ΔD/Dp ≈ 14%; OT ΔD/Dp ≈ 29%, √S ≈ 154 fN); 200 nm results are weaker, method-dependent, and often aggregation-limited. An AOUP model is used to interpret how persistence time controls spectral observability.

Significance. If the dual-modality enhancements hold under tighter hydrodynamic controls, the work provides a useful experimental bridge between the contested enzyme-enhanced-diffusion literature and enzyme-powered colloid/micromotor studies. Strengths include the systematic bare-vs-decorated and size comparison, simultaneous DDM/OT on the same platform, multi-metric quantification (Tables I–II), activity-window controls via phenol-red assay, and a clear persistence-time interpretation (Fig. 8) that helps reconcile why free enzymes and decorated colloids look different. The force scales (√S ~ 96–154 fN) sit in a comparable range to prior OT work on enzyme motors, while using simpler polystyrene substrates. The candid treatment of aggregation for 200 nm decorated particles is also a strength.

major comments (2)
  1. [Sec. II.H, III.A–C, Eq. (2)] Sec. II.H and III.A–C (and Eq. 2): OT nonthermal metrics freeze κ and γ from passive Lorentzian fits and attribute residual spectral power entirely to enzymatic activity (effective temperature, AOUP u/τ, spectrum subtraction, Σ, √S). This is load-bearing for the strongest claim (1 µm decorated: low-frequency excess, ΔD/Dp ~ 29%, u^{2}τ/Dp ~ 33%, √S ~ 154 fN). The paper already notes aggregation-driven hydrodynamic shifts for 200 nm particles and reports slightly different trap stiffnesses for bare vs decorated 1 µm beads (83.6 vs 81.1 pN/µm), but does not independently re-measure κ or γ under active conditions for the decorated micron particles. Local chemistry, product gradients, or surface changes could alter effective friction or optical response and bias the nonthermal residuals. Please add active-condition trap calibrations (or an equivalent hydrodynamic control) for the 1 µm decora
  2. [Tables I–II; Sec. IV.B, V.A] Tables I–II and Sec. IV.B vs IV.A: DDM and OT ΔD/Dp disagree quantitatively for the same 1 µm decorated system (~14% vs ~29%), and model-free √S (~154 fN) is an order of magnitude larger than the diffusion-based F (~10 fN). The discussion (Sec. V.A) notes complementary timescales and cites Ma et al., but does not quantify how much of the gap is expected from free vs trapped dynamics, frequency windows, or the frozen-κ/γ assumption. A short consistency analysis (or explicit statement of which metric is primary for the force claim) is needed so the dual-modality result is not over-read as a single force scale.
minor comments (5)
  1. [Fig. 3A / Sec. IV.A] Fig. 3A caption reports passive mean 0.33±0.03 µm^{2}/s while the main text says 0.33±0.01 µm^{2}/s; align text and caption.
  2. [Fig. 6] Fig. 6B text has unit typos (µ^{2}m/s instead of µm^{2}/s).
  3. [Sec. IV.B] State explicitly how many independent sample preparations (not only n of FOVs/traps) underlie the 1 µm decorated DDM and OT distributions.
  4. [Sec. III.C; Fig. 8] Clarify whether the AOUP fit for 1 µm decorated particles yields a unique (u,τ) pair or only the product u^{2}τ, and report the fitted τ used in Fig. 8(b).
  5. [Sec. II.I] Buffer viscosity differs between DDM (10 imes DPBS, 1.4 mPa·s) and OT (1 M HEPES, 2.0 mPa·s); a brief note that absolute D values are not cross-compared would help readers.

Circularity Check

1 steps flagged

No significant circularity: enhancements are empirical active-vs-passive comparisons; AOUP is a fitting model, not a self-defining prediction.

specific steps
  1. self citation load bearing [Sec. II.J Theoretical model; Eq. (2); also Sec. III.C]
    "We therefore adopt a minimal mesoscopic Langevin description of colloidal dynamics [41, 42], modeling the nonthermal component as an Active Ornstein-Uhlenbeck process, as in our previous work [43]. ... This model yields an analytical form of the force spectrum, previously derived in [43], Sff(ω) = 2κ²D/(μ²+ω²) + 2κ²τ u²/((μ²+ω²)(1+ω²τ²))"

    The analytic nonthermal spectrum used to extract u and τ (and thus Da = u²τ) is taken from the authors' prior work rather than re-derived here. This is ordinary methodological self-citation and is not load-bearing for the experimental claim that active spectra exceed passive ones; the excess is measured by direct subtraction and by multiple model-free metrics (√S, Σ, J). It does not force the reported enhancements by construction.

full rationale

The paper's central claims are experimental: DDM and OT compare passive vs active baths and bare vs urease-decorated tracers, reporting measured shifts in diffusion and force spectra (Tables I–II, Figs. 3–6). Enhancement metrics (ΔD/Dp, F from long-time D, Σ, √S, J) are defined as differences or ratios of independently measured active and passive quantities, not as tautologies. The AOUP force spectrum (Eq. 2) is introduced as a minimal mesoscopic model to fit nonthermal residuals after passive baselines are measured and subtracted or held fixed; Da = u²τ is an output of that fit, not an input re-labeled as a prediction. Self-citations (e.g. prior AOUP force-spectrum work [43]) supply methodology and are not load-bearing uniqueness theorems that force the experimental result. Assumptions that κ and γ are unchanged between passive and active conditions are modeling choices that can bias interpretation if hydrodynamics change, but they do not make the reported spectral excess circular by construction. Score 1 reflects only minor self-citation of the authors' prior AOUP framework without circular reduction of the main claims.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim is empirical, so the ledger is dominated by standard soft-matter assumptions and analysis choices rather than new ontology. Load-bearing free parameters are the AOUP amplitude/timescale fits and experimental set-points (enzyme/fuel concentrations). Domain assumptions include Stokes friction, unchanged κ,γ between conditions, and that active−passive spectral differences isolate enzymatic nonthermal forcing. No new physical entity is postulated; AOUP is an imported mesoscopic model.

free parameters (4)
  • AOUP active speed u and persistence τ (via u²τ)
    Fitted to nonthermal OT force spectra using Eq. (2); used to report u²τ/Dp enhancements (e.g., ~33% for 1 µm decorated). Different metrics without these fits give different force scales.
  • Urease concentration 50 U/mL and urea 300 mM
    Chosen experimental set-points defining “active” conditions; activity window (10–20 min) is assay-dependent and bounds all enhancement claims.
  • Effective temperature / Da from OT Lorentzian-style fits
    Active spectra fit with effective temperature as free parameter after fixing passive κ,γ (Sec. III.A), producing ΔD/Dp values that can differ from DDM and from u²τ.
  • Integration band 1–25 kHz for √S and J
    Model-free force/dissipation scalars depend on the chosen frequency window of the OT measurement.
axioms (5)
  • domain assumption Colloidal friction follows Stokes drag γ = 6πηR in the buffers used; viscosity is constant and measured independently.
    Used for viscosity calibration, radius estimates from Lorentzian fits, and conversion between diffusion and force (Eq. 3).
  • domain assumption Nonthermal activity on a trapped tracer can be represented as an Active Ornstein–Uhlenbeck process yielding Eq. (2).
    Sec. II.J / III.C; justifies extracting u,τ and interpreting persistence-time shifts of spectral power (Fig. 8).
  • ad hoc to paper Trap stiffness κ and friction γ are unchanged between passive and active conditions, so spectral differences are nonthermal enzymatic forcing.
    Explicit analysis assumption in Sec. III.A–C; critical for OT ΔD, u²τ, nonthermal subtraction, and Σ comparisons.
  • domain assumption Long-time effective force from diffusion follows F = (3kBT/2R)√[2(Da/Dp−1)] for a sphere with two orientational degrees of freedom in a harmonic potential.
    Eq. (3), cited from active Brownian literature; used to convert ΔD into fN-scale forces for both DDM and OT.
  • domain assumption During the phenol-red assay window, bulk urease remains catalytically active and buffer changes do not dominate tracer dynamics beyond the intended activity.
    Sec. II.B; all “active” data are restricted to this window.

pith-pipeline@v1.1.0-grok45 · 21142 in / 3832 out tokens · 69792 ms · 2026-07-14T10:14:28.855746+00:00 · methodology

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read the original abstract

Enzymatic catalysis can generate nonequilibrium fluctuations, but how these couple to tracer motion at larger length scales depends on physical context. Here, we investigate colloidal tracers in two configurations: passive particles dispersed in an enzymatically active solution, and enzyme-decorated particles where catalysis occurs directly at the tracer surface. We combine differential dynamic microscopy (DDM), which probes ensemble-averaged long-time diffusion, with optical tweezer (OT) measurements of short-time force fluctuations, and compare several complementary metrics for quantifying activity-induced enhancement. For 1 $\mu$m tracers, we observe activity-induced enhancements in both configurations, with the strongest effects for enzyme-decorated particles, which exhibit enhanced diffusion and increased non-thermal force fluctuations. For 200 nm tracers, enhancements are more subtle and method-dependent: DDM detects modest increases in diffusion for bare particles, while corresponding signatures are not resolved by the OT. These results demonstrate that enzymatic activity can be transduced from molecular to microscale motion and forces, but that the apparent magnitude and detectability of enhancement depend strongly on tracer size, localization of activity, the timescales probed by the measurement, and the metric used to quantify enhancement. More broadly, understanding how enzyme activity modifies transport and fluctuations across scales is important for interpreting nonequilibrium dynamics in active soft matter, intracellular transport, and chemically crowded biological environments.

Figures

Figures reproduced from arXiv: 2607.10646 by Anthony Estrada, Dakota Feldcamp, Erick Leyva, Jennifer L. Ross, Justine Miqueu-Petit, Mauricio Gomez, W. Benjamin Rogers, Wylie W. Ahmed.

Figure 1
Figure 1. Figure 1: FIG. 1. (Left) In an active bath, passive colloidal tracers [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Representative images of urease-decorated active par [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. 200 nm decorated particles exhibit clumping. Left is [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: illustrates this effect across a broad range of persistence times, with three representative cases high￾lighted. For long persistence (τ ∼ 1 s; [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

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Reference graph

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