arxiv: 2605.03632 · v1 · submitted 2026-05-05 · 🧬 q-bio.CB · q-bio.SC

Recognition: 3 theorem links

· Lean Theorem

Robust chemotaxis beyond sensing limits: signal, noise, and strategy

Robert G. Endres

Pith reviewed 2026-05-08 18:49 UTC · model grok-4.3

classification 🧬 q-bio.CB q-bio.SC

keywords chemotaxisrun-and-tumblenoise robustnesssensing limitstemporal averaginginformation efficiencybacterial motilityeukaryotic chemotaxis

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The pith

Bacterial chemotaxis stays robust to noise by using symmetric run-and-tumble motion and temporal averaging even when sensing efficiency is low.

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

The paper examines how bacteria achieve reliable directed movement toward chemicals despite capturing and processing only a small fraction of the information present in ligand arrival statistics. It shows that the run-and-tumble strategy itself supplies robustness through built-in symmetry that cancels random fluctuations and through averaging signals over successive runs. This perspective treats movement strategy as an equal partner with internal information processing rather than a downstream consequence of it. Comparisons to eukaryotic chemotaxis illustrate that different physical strategies convert the same sensing limits into distinct observable behaviors. A reader would care because the account suggests that biological systems often achieve functional performance through simple, noise-tolerant designs instead of maximal information efficiency.

Core claim

Chemotactic performance is shaped not only by information transmission and noise, but by the strategy of movement itself. Using simple scaling arguments and minimal models, run-and-tumble chemotaxis can remain robust to noise through symmetry and temporal averaging, even when internal information processing is inefficient. Comparing bacterial and eukaryotic chemotaxis highlights how different sensing strategies convert physical limits into observable behavior. These considerations suggest that low information efficiency need not imply poor performance, but may instead reflect an evolved balance between robustness, simplicity, and function.

What carries the argument

The run-and-tumble movement strategy, which exploits symmetry between runs and temporal averaging to suppress noise without requiring high internal information efficiency.

If this is right

Low information efficiency in sensing does not necessarily produce poor chemotactic performance.
The combination of movement symmetry and temporal averaging supplies robustness that sensing alone cannot provide.
Bacterial and eukaryotic cells convert the same physical sensing limits into different behaviors through their distinct movement strategies.
Evolution may select for strategies that trade information efficiency for robustness and mechanistic simplicity.

Where Pith is reading between the lines

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

The same symmetry-plus-averaging logic might stabilize other biological navigation tasks where cells or organisms must act on noisy spatial gradients.
Experiments that vary run duration while holding receptor noise fixed could isolate how much of observed robustness comes from movement strategy versus receptor kinetics.
In fluctuating or patchy environments, selection might favor longer averaging windows even if they slow response time, a trade-off not directly addressed in the minimal models.

Load-bearing premise

Simple scaling arguments and minimal models capture the essential features of real bacterial and eukaryotic chemotaxis without missing critical biological complexities or alternative mechanisms.

What would settle it

Measuring that run-and-tumble symmetry mutants lose noise robustness exactly as predicted by the scaling arguments under controlled high-noise ligand conditions would support the claim; large unexplained deviations would falsify it.

Figures

Figures reproduced from arXiv: 2605.03632 by Robert G. Endres.

**Figure 1.** Figure 1: Bacterial vs eukaryotic chemotaxis. (A) Drift velocity in bacterial chemotaxis, described by biased random walk up a chemical gradients based on run-and-tumble motion. (B) Chemotactic index in eukaryotic chemotaxis with θ the direction of movement relative to the gradient. Note drift and CI are closely related up to speed factor v. Combining the two information rates yields the information transmission eff… view at source ↗

**Figure 2.** Figure 2: Bacterial and eukaryotic chemotaxis compared to data. view at source ↗

**Figure 3.** Figure 3: Difference between spatial and temporal gradient sensing. view at source ↗

read the original abstract

Bacterial chemotaxis has long been viewed as operating near the physical limits of sensing, as originally articulated by Berg and Purcell. Recent information-theoretic analyses challenge this view, suggesting that Escherichia coli uses only a small fraction of the information available in ligand arrival statistics to bias its motion. How should such low information efficiency be interpreted at the level of behavior? Here, I argue that chemotactic performance is shaped not only by information transmission and noise, but by the strategy of movement itself. Using simple scaling arguments and minimal models, I show how run-and-tumble chemotaxis can remain robust to noise through symmetry and temporal averaging, even when internal information processing is inefficient. Comparing bacterial and eukaryotic chemotaxis highlights how different sensing strategies convert physical limits into observable behavior. These considerations suggest that low information efficiency need not imply poor performance, but may instead reflect an evolved balance between robustness, simplicity, and function.

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.

Desk Editor's Note private letter to a colleague

The paper reframes low information efficiency in bacterial chemotaxis as a consequence of run-and-tumble movement strategy rather than a sensing shortfall.

read the letter

The core point is that E. coli can keep chemotaxis working despite using only a small fraction of available ligand information because its run-and-tumble pattern builds in symmetry and temporal averaging that buffers noise. This is presented as an interpretive lens on top of Berg-Purcell and recent information-theoretic bounds, not as a new derivation of those bounds themselves. The comparison to eukaryotic chemotaxis is useful for showing how different movement rules turn the same physical limits into different observable behaviors. The scaling arguments and minimal models are kept simple enough to make the logic transparent without hidden parameters or curve-fitting. That keeps the piece readable and focused on the behavioral interpretation. The main limitation is that the models stay minimal, so they do not address how adaptation, receptor clustering, or spatial structure in real gradients might alter the picture. Those omissions are acknowledged in the framing, and they do not create internal contradictions with the stated claim. The argument stays consistent with the cited priors and does not over-reach into quantitative predictions. This is the kind of short conceptual piece that belongs in a journal that publishes perspectives or theory notes. Readers working on microbial navigation, information in biology, or synthetic circuit design would get the most out of it, because it gives a concrete way to think about why measured efficiencies look low without declaring the system broken. It is worth sending to referees; the synthesis is clear, the logic holds on its own terms, and the field benefits from explicit discussion of how movement rules interact with sensing limits.

Referee Report

2 major / 3 minor

Summary. The paper argues that low information efficiency in bacterial chemotaxis (as suggested by recent information-theoretic analyses) does not imply poor behavioral performance. Instead, the run-and-tumble strategy confers robustness to noise via symmetry and temporal averaging, even with inefficient internal processing. This is supported by simple scaling arguments and minimal models, with a comparison to eukaryotic chemotaxis illustrating how different sensing strategies shape observable behavior. The conclusion frames low efficiency as potentially reflecting an evolved balance between robustness, simplicity, and function rather than a limitation.

Significance. If the scaling arguments hold, this work provides a useful conceptual reframing of information limits in biological sensing, emphasizing the role of movement strategy in achieving robustness. It gives credit to parameter-free scaling relations and minimal models that avoid fitted parameters, offering an interpretive lens rather than new quantitative predictions. This could influence modeling of chemotaxis in both prokaryotes and eukaryotes by highlighting trade-offs between efficiency and noise resilience, and may inform synthetic biology designs for robust navigation.

major comments (2)

[Minimal models] Minimal models section: the central claim that symmetry and temporal averaging confer robustness relies on the assertion that run-and-tumble motion effectively averages ligand fluctuations over multiple runs. However, without an explicit scaling relation (e.g., how effective SNR improves with run number or tumble frequency) or a derivation showing noise variance reduction, it is difficult to evaluate whether this quantitatively offsets the stated information inefficiency.
[Scaling arguments] Scaling arguments paragraph: the statement that chemotactic performance remains robust 'even when internal information processing is inefficient' is load-bearing for the reinterpretation of Berg-Purcell limits. This requires a concrete comparison (perhaps via a table or equation) between the information used in the minimal model and the physical limit, to show the robustness is not an artifact of the model's assumptions.

minor comments (3)

[Abstract/Introduction] The abstract and introduction cite 'Berg and Purcell' but should include the full reference (Berg and Purcell, 1977) at first mention for clarity.
[Figures] Figure captions (if present) for the minimal models should explicitly define all parameters and state whether they are derived from scaling or chosen for illustration.
[Comparison section] The comparison to eukaryotic chemotaxis would benefit from a brief note on whether the same symmetry argument applies or is precluded by the different motility mechanism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation and constructive comments on our manuscript. We address each major comment below and have incorporated revisions to enhance the clarity of our scaling arguments and minimal models.

read point-by-point responses

Referee: Minimal models section: the central claim that symmetry and temporal averaging confer robustness relies on the assertion that run-and-tumble motion effectively averages ligand fluctuations over multiple runs. However, without an explicit scaling relation (e.g., how effective SNR improves with run number or tumble frequency) or a derivation showing noise variance reduction, it is difficult to evaluate whether this quantitatively offsets the stated information inefficiency.

Authors: We appreciate the referee pointing out the need for greater explicitness in our scaling arguments. While the manuscript presents scaling relations showing that temporal averaging over multiple runs reduces effective noise variance proportionally to the inverse square root of the number of independent samples, we agree that a dedicated derivation would improve accessibility. In the revised version, we have added a short derivation in the Minimal models section: the variance of the averaged signal scales as σ²/N, where N is the number of runs and σ² is the single-run variance, leading to an SNR improvement of √N. This quantitatively shows how the run-and-tumble strategy offsets internal inefficiencies. revision: yes
Referee: Scaling arguments paragraph: the statement that chemotactic performance remains robust 'even when internal information processing is inefficient' is load-bearing for the reinterpretation of Berg-Purcell limits. This requires a concrete comparison (perhaps via a table or equation) between the information used in the minimal model and the physical limit, to show the robustness is not an artifact of the model's assumptions.

Authors: We agree that an explicit comparison strengthens the central claim. The original manuscript uses parameter-free scaling to argue robustness below the Berg-Purcell limit, but to address this, we have added a new equation in the scaling arguments section that compares the effective information rate in the minimal model (derived from the bias in tumble probability) to the physical limit set by ligand diffusion and receptor occupancy. This comparison confirms that the model uses a small fraction of available information while maintaining performance through movement symmetry, indicating the result is not an artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity; conceptual scaling argument is self-contained

full rationale

The paper presents an interpretive argument using scaling relations and minimal models to show robustness of run-and-tumble chemotaxis via symmetry and temporal averaging. No equations or derivations are shown that reduce a claimed prediction to a fitted input or self-defined quantity by construction. Cited foundations (Berg-Purcell limits, information theory) are external classic and recent literature rather than self-citations that bear the central load. The contribution is framed as conceptual interpretation rather than quantitative prediction from fitted parameters, so the derivation chain does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on established domain knowledge from physics of sensing and information theory without introducing new free parameters or entities.

axioms (2)

domain assumption Bacterial chemotaxis has long been viewed as operating near the physical limits of sensing as articulated by Berg and Purcell
Explicitly stated as the long-held view being challenged.
domain assumption Recent information-theoretic analyses correctly show E. coli uses only a small fraction of available information
Basis for questioning how low efficiency should be interpreted at behavioral level.

pith-pipeline@v0.9.0 · 5448 in / 1268 out tokens · 92599 ms · 2026-05-08T18:49:36.074664+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Cost.FunctionalEquation / Foundation.LogicAsFunctionalEquation washburn_uniqueness_aczel (J(x)=½(x+x⁻¹)−1) unclear
SNR ∼ (gvτ)² · r₀τ = g²v²r₀τ³ ; v_drift ≤ √(2 D_eff · İ_behavior)
Cost (ratio-symmetric J-cost) Jcost_unit0 / Jcost_pos_of_ne_one unclear
Weber's law / log-sensing regime where v_drift ∼ g independent of c

Reference graph

Works this paper leans on

29 extracted references · 6 canonical work pages

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