Pseudo-chemotaxis of active Brownian particles competing for food

Abhinav Sharma; Hidde Derk Vuijk; Holger Merlitz; Jens-Uwe Sommer; Rene Wittmann

REVIEW 3 major objections 6 minor 27 references

Pseudo-chemotaxis of active Brownian particles competing for food

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In open, non-stationary systems with a food gradient, active Brownian particles that become motile on eating consume more food than passive ones, without any sensing.

desk verdict A clean simulation study that shows food-triggered activity can give a competitive advantage in transient gradients, but it needs a matched-diffusivity control and error bars to fully support the pseudo-chemotaxis claim. read the letter →

arxiv 1909.02779 v1 pith:4NH5L7E5 submitted 2019-09-06 physics.bio-ph cond-mat.soft

Holger Merlitz , Hidde Derk Vuijk , Rene Wittmann , Abhinav Sharma , Jens-Uwe Sommer This is my paper · ORCID

classification physics.bio-phcond-mat.soft

keywords activeBrownianparticlespseudo-chemotaxisanti-chemotaxisfoodcompetitionactivitygradientsdynamicssimulationself-propelledchemotaxiswithoutsensing

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 uses Brownian dynamics simulations to test whether self-propelled particles (active Brownian particles) that switch on motion only after eating can out-compete otherwise identical passive particles for a limited supply of food. In a closed, steadily fed system the active particles lose the competition: their activity depletes their density near the food source, the well-known anti-chemotaxis of active Brownian particles. In an open system where a short burst of food diffuses outward, the same particles gain a transient density advantage near the source and consume more food than their passive competitors, even though they have no sensor and no orientational bias. The paper calls this pseudo-chemotaxis and argues that it gives a purely physical, pre-sensory evolutionary benefit to early motile proto-lifeforms. The effect requires a spatial food gradient; with uniformly distributed food the active particles gain no advantage.

What carries the argument

The load-bearing element is the boost: each consumed food particle activates self-propulsion for a fixed time $\tau_B$, with the added active diffusion $D_a$ about three times the passive value, while rotational diffusion is assumed unchanged. This turns food intake into a local, time-delimited increase in mobility, and the resulting activity gradient reshapes the particle density: in steady state the density is depleted where activity is high, but in a transient burst the enhanced spreading makes the active front arrive at the food source before the passive front. The food concentration gradient is what converts this mobility contrast into a net intake advantage, since without a gradient the early spatial bias buys nothing.

What would settle it

A decisive check is to rerun the non-stationary burst competition with a refractory period after each boost equal to the 18-microsecond boost time, so no particle can chain activations, or with activity that shortens the rotational relaxation time; the claim would be refuted if the active particles' cumulative food consumption at $r_{\mathrm{ini}} = 200$ nm no longer exceeds that of passive particles. A complementary experiment would compare uptake of 30 nm catalytic enzymes versus inert tracers in a microfluidic substrate pulse and look for the predicted transient intake advantage.

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Extended reading notes

Core claim

Within the model, food consumption switches on self-propulsion for a fixed boost time $\tau_B = 2\tau_r \approx 18\,\mu\mathrm{s}$, and this temporary activity changes the transient concentration profile of the active species. Starting from a shell at distance $r_{\mathrm{ini}}$ from a sudden food burst, active Brownian particles spread faster once activated, so their front reaches the high-food region earlier; they therefore consume more food per particle than passive Brownian particles for $r_{\mathrm{ini}} = 200$ nm and, with increasing boost time, also at larger distances. In stationary confined systems the same mobility contrast produces the opposite result, a depletion of active particles near the food source and lower food consumption (anti-chemotaxis). The paper's claim is that the non-stationary advantage is a genuine chemotaxis-like bias, called pseudo-chemotaxis, that requires neither sensing of the gradient nor coupling of particle orientation to it, and that disappears when the food profile is made uniform.

Load-bearing premise

The model assumes that every collision with a food particle instantly turns on a fixed-duration speed boost, with no limit, pause, or stored energy, and that swimming does not change how quickly the particle forgets its direction; if real consumption involves any of those effects, the competitive advantage could shrink or reverse.

Editorial extensions

If this is right

In a non-stationary food burst, fuel-triggered activity alone, with no sensing and no orientation bias, is enough for one species to out-eat an identical passive species; the paper shows this directly for initial distances up to about 400 nm.
The advantage grows with boost time: longer $\tau_B$ lets active particles profit even at larger initial distances from the source.
Stationary, confined systems invert the outcome: activity becomes a handicap because active particles are depleted near the food source (anti-chemotaxis).
A food concentration gradient is necessary and sufficient for the pseudo-chemotactic advantage; with a uniform food profile the two species consume nearly equal amounts.
Pseudo-chemotaxis provides a mechanism by which a primitive organism could gain an evolutionary edge from self-propulsion before evolving chemosensory apparatus.

Reading between the lines

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

Beyond the paper: the same logic suggests a general foraging rule, that if resource encounters transiently raise mobility and resources arrive in patches, a forager can win without memory; a direct test would vary patch sharpness and food diffusivity and compare intake ratios.
Inference: because the advantage depends on chained boosts, a refractory period after consumption that exceeds the boost time should weaken or remove it; this is a testable modification of the model.
Inference: the evolutionary scenario could be tested dynamically by coupling food intake to reproduction and letting the two species compete over generations; the model predicts active-particle dominance in pulsed-food environments but not under steady feeding.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

This paper is a clean simulation study that takes an established mechanism—pseudo-chemotaxis in activity gradients—and puts it in an evolutionary food-competition setting. The new piece is the explicit coupling: particles get a fixed boost of activity when they consume food, and then compete against passive Brownian particles for a transient food burst. They show that in a confined stationary system, active particles lose (anti-chemotaxis), but in an open, non-stationary burst, they win. The density profiles in Fig. 4 show a clear asymmetry toward the food source, which is genuine evidence of a bias, not just faster spreading.

The paper does several things well. The model is simple and clearly stated, with parameters in Table I. The stationary/non-stationary contrast is a nice pedagogical point. Section III C's comparison between Gaussian and uniform food is a reasonable test of the gradient requirement. The biological speculation in the conclusion is explicitly labeled as speculation, which I appreciate.

The main soft spot is the one the stress test flags: there's no control that separates enhanced diffusivity from the pseudo-chemotactic bias. If you ran permanently active ABPs or passive particles with the same time-averaged diffusion coefficient and saw the same consumption curves, then 'chemotaxis' would be over-claiming. The Gaussian-vs-uniform comparison helps, but it's not enough, because it removes both the gradient and the spatial correlation between activity and food. A matched-diffusivity control would settle it. That said, the density bias in Fig. 4 already hints the mechanism is more than just speed, so this is a strengthening gap rather than a fatal flaw.

The second weakness is statistical: no error bars or significance tests on the key consumption curves (Figs. 3, 5, 7). The differences at larger initial distances look modest, and without error bars it's hard to tell how robust the effect is. This is a moderate concern for a simulation paper.

Overall, the central argument holds up qualitatively: activity that is triggered by food can confer a transient competitive advantage in a gradient. For a reader interested in active matter or early evolution scenarios, this is a useful and thought-provoking paper. It deserves serious peer review—the mechanism is plausible, the presentation is honest, and the missing control is an addressable request rather than a career-ender. I'd send it to review with a request for a matched-diffusivity control and error bars.

Referee Report

3 major / 6 minor

Summary. The manuscript reports Brownian dynamics simulations of two particle species, passive Brownian particles (BPs) and active Brownian particles (ABPs) that become self-propelled for a fixed boost time after consuming food, competing for a limited food supply. In confined stationary systems the ABPs are depleted near the food source and consume less food than BPs (anti-chemotaxis). In open, non-stationary systems with a localized food burst, the ABP density profile develops a tail toward the food source and the ABPs consume more food than the BPs; the authors attribute this to transient activity gradients and call it pseudo-chemotaxis. A comparison of Gaussian and step-like immobile food distributions is used to argue that a food-concentration gradient is required for the advantage. The paper concludes that food-triggered motility could confer an evolutionary advantage without any sensing mechanism.

Significance. If the central claim holds, the paper offers a minimal physical mechanism by which food-triggered motility, without sensing, can confer a competitive advantage in transient environments. The study is relevant for synthetic nanomotors and for speculations about early evolution. Strengths include a transparent simulation model with realistic particle dimensions, a direct competition setup between active and passive species, and a demonstration of the stationary anti-chemotaxis baseline that connects to prior work. The main limitation is that the non-stationary advantage is not separated from the trivial effect of enhanced diffusivity, and the statistical evidence is not quantified. These issues are addressable with additional simulations.

major comments (3)

[Sec. III B, Figs. 4 and 5] The observation that food-triggered ABPs consume more food than BPs after a burst is also consistent with a simple speed advantage: a particle with a larger diffusion coefficient explores space faster and reaches the food sooner. To support the claim that the food-triggered boost and the resulting activity gradient are the mechanism, the authors need a control in which enhanced motility is decoupled from food consumption, for example permanently active ABPs or passive particles with a fixed effective diffusion coefficient equal to the time-averaged value of the food-activated ABPs. If such a speed-matched, food-independent control reproduces the consumption curves, the data do not demonstrate pseudo-chemotaxis.
[Sec. III C, Figs. 6 and 7] The Gaussian-versus-step comparison does not isolate the role of the concentration gradient: the two profiles differ in shape, sharpness, and in the spatial correlation between activity and food, and the step profile is not 'uniform' but a finite spherical reservoir with a gradient at its boundary. To establish that gradients are necessary, additional controls are needed, such as a linear concentration ramp, a uniform food distribution over the whole accessible volume, or a step profile with matched smoothness. As it stands, the result demonstrates only that a smooth Gaussian reservoir favors ABPs.
[Figs. 3, 5, 7 and Sec. III] No error bars, number of independent runs, or significance tests are reported. The differences at rini = 300 and 400 nm in Fig. 5 appear small, and the statement in Sec. III C that BPs and ABPs receive 'close to identical results' has no statistical basis. The authors should report at least the number of realizations and standard deviations, and ideally a significance test, for the central consumption comparisons.

minor comments (6)

[Abstract] The phrase 'contrary to common believes' should be 'contrary to common beliefs'.
[Fig. 2 caption] The caption writes 'APBs' where it should write 'ABPs'.
[Conclusion] The phrase 'food of fuel intake' should be 'food or fuel intake'.
[Sec. III B] The phrase 'data not shown' should be replaced by a figure or table in a revised version.
[Sec. II and Table I] There are unit inconsistencies between the text and Table I: the text gives eta = 0.89 mPa·s and f = 1 pN, while Table I lists eta = 0.981 mPa·s and f = 1 ag·nm/ns^2, which corresponds to 1 nN. Please reconcile these values and verify the derived quantities such as the Stokes drag coefficient.
[Sec. III A] The phrase 'the quantity of the ABP-depletion' should be 'the magnitude of the ABP depletion'.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the food-competition result is a simulated output, not a fitted input; only minor background self-citations appear.

full rationale

The central claim that food-triggered ABPs outperform passive BPs in open, non-stationary systems with a food gradient is a direct simulation outcome (Figs. 5 and 7), with all parameters fixed in Table I and no fitting to the target result. The model encodes the mechanism (activity after food consumption) by construction, but the consumption advantage is an emergent, simulated quantity rather than a quantity defined to equal an input. The gradient requirement is supported by an internal control: a uniform food profile removes the ABP advantage (Sec. III C), showing that the result is not simply an artifact of enhanced diffusivity being inserted by definition. The paper's citations of prior work, including self-citations [9, 25], provide background and the pseudo-chemotaxis label, but they are not load-bearing: the implemented model itself contains no sensing and no food-gradient orientation coupling, so the absence of such coupling is a model input rather than an imported conclusion. No equation in the paper reduces to its inputs, no fitted parameter is renamed as a prediction, and no uniqueness theorem is invoked. The missing speed-matched control raised in review is a comparison/interpretation issue that could affect the mechanistic reading of the data, but it is not circularity of the derivation.

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

The central claim depends on several hand-chosen simulation parameters (boost time, driving force, food diffusivity, burst size, initial distance) and on modeling assumptions (no hydrodynamics, no pair interactions, fixed boost). None of these are fitted to reproduce the advantage; the advantage is an emergent output, so circularity burden is low. However, quantitative conclusions are tied to these choices.

free parameters (5)

Boost time τB = 2τr ≈ 18 µs (base case; varied in sweeps)
Duration of activity after food consumption; directly controls the magnitude of the ABP advantage and is chosen by hand.
Driving force f = 1 pN (1 ag·nm/ns²)
Self-propulsion force; sets active diffusivity Da = 0.048 nm²/ns, about three times passive diffusivity; chosen from enzyme estimates.
Food diffusion coefficient = 5 × Dt = 0.0815 nm²/ns
Ratio of food to particle diffusivity assumed; affects how quickly the food burst spreads and the gradient persists.
Food burst size = 5000 food particles
Amount of food released instantaneously in the non-stationary setup; chosen for simulation statistics.
Initial distance rini = 200, 300, and 400 nm
Starting distance of particles from food source; varied to demonstrate that the advantage shrinks with distance.

assumptions (5)

domain assumption Brownian dynamics with implicit solvent and no hydrodynamic interactions is an adequate model for 30 nm particles.
The simulation uses overdamped Langevin dynamics; hydrodynamic coupling, which could alter competition, is omitted.
domain assumption Self-propulsion does not affect rotational diffusion.
Stated explicitly in Sec. II and Table I; this affects persistence length and the degree of transient accumulation.
ad hoc to paper Food consumption immediately triggers a fixed-duration activity boost, with no accumulation or storage beyond a single quantum.
Model rule in Sec. II; the boost duration is a free parameter and central to the competitive advantage.
standard math The second-order Brownian dynamics integrator (ref. [23]) with dt = 10 ns accurately resolves the dynamics.
Numerical integration method is standard; authors do not provide convergence checks.
domain assumption Particles and food do not interact except for consumption upon overlap; competition is solely through depletion.
No pair potentials are used, so crowding and predator-prey-like interactions are absent.

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Cite this review

Pith. "Pith review of Pseudo-chemotaxis of active Brownian particles competing for food." pith.science (2026). https://pith.science/paper/4NH5L7E5

@misc{pith2026190902779,
  author       = {Pith},
  title        = {Pith review of: Pseudo-chemotaxis of active Brownian particles competing for food},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4NH5L7E5}},
  note         = {Machine review of arXiv:1909.02779}
}

read the original abstract

Using Brownian dynamics simulations, the motion of active Brownian particles (ABPs) in the presence of fuel (or 'food') sources is studied. It is an established fact that within confined stationary systems, the activity of ABPs generates density profiles that are enhanced in regions of low activity, which is generally referred to as 'anti-chemotaxis'. We demonstrate that -- contrary to common believes -- in non-stationary setups, emerging here as a result of short fuel bursts, our model ABPs do instead exhibit signatures of chemotactic behavior. In direct competition with inactive, but otherwise identical Brownian particles (BPs), the ABPs are shown to fetch a larger amount of food. From a biological perspective, the ability to turn active would, despite of the absence of sensoric devices, encompass an evolutionary advantage.

Figures

Figures reproduced from arXiv: 1909.02779 by the authors.

**Figure 3.** FIG. 3. Food consumption rates of particles for different siz [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** FIG. 4. Time evolution of the density distributions of BPs [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (2 more)

**Figure 6.** Figure 6: FIG. 6. Time evolution of the density distributions of BPs [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: FIG. 7. Consumed food under the condition that the food [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

15ms after setoﬀ

1 < t < 0. 15ms after setoﬀ. The system that features a food gradient (left panel) once again exhibits an increased concentration of ABPs close to the food source at which the food density is at its maximum. Contrary to that, the (initially) uniform food distribution leads to a diﬀer- ent situation (right panel): Although close to the center 5 FIG. 6. Tim...

work page

[2] [2]

Initial distance of the particles to the food source: rini = 200nm

15ms. Initial distance of the particles to the food source: rini = 200nm. Left panel: initial food proﬁle is Gaussian, right panel: Initial food proﬁle is a step-function. Food pa r- ticles are immobile. 0 0.5 1 time (ms) 0 5 10 15 20 25 30consumed food (per particle) BPs, food Gaussian ABPs, food Gaussian BPs, food uniform ABPs, food uniform FIG. 7. Cons...

work page

[3] [3]

Fenteany and M

G. Fenteany and M. Glogauer. Cytoskeletal remodeling in leukocyte function. Curr. Opin. Hematol. , 11:15, 2004

work page 2004

[4] [4]

Lokomotorische ric h- tungsbewegungen durch chemische reize

Wilhelm Friedrich Phillipp Pfeﬀer. Lokomotorische ric h- tungsbewegungen durch chemische reize. Untersuch. aus d. Botan. Inst. T¨ ubingen, 1:363, 1884

work page

[5] [5]

Howard C. Berg. E. coli in motion . Springer Verlag, Heidelberg, Germany, 2004

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[6] [6]

Howard C. Berg. Random Walks in Biology . Princeton University Press, Chichester, West Sussex, 1993

work page 1993

[7] [7]

Active particles in complex and crowded environ- ments

Clemens Bechinger, Roberto Di Leonardo, Hartmut L¨ owen, Charles Reichhardt, Giorgio Volpe, and Giovanni Volpe. Active particles in complex and crowded environ- ments. Rev. Mod. Phys. , 88:045006, 2016

work page 2016

[8] [8]

Self-propelled nano/micromotors with a chemical reaction: Underlying physics and strategies of motion control

Daigo Yamamoto and Akihisa Shioi. Self-propelled nano/micromotors with a chemical reaction: Underlying physics and strategies of motion control. KONA Powder Part. J. , 32:2, 2015

work page 2015