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arxiv: 2509.00219 · v1 · submitted 2025-08-29 · 🧬 q-bio.CB · physics.bio-ph

Perfect adaptation in eukaryotic gradient sensing using cooperative allosteric binding

Vishnu Srinivasan , Wei Wang , Brian A. Camley This is my paper

Pith reviewed 2026-05-18 20:05 UTC · model grok-4.3

classification 🧬 q-bio.CB physics.bio-ph
keywords chemotaxisgradient sensingallosteric regulationreceptor adaptationeukaryotic cellsligand bindingdiffusion trade-off
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The pith

Eukaryotic cells adapt to wide ligand concentrations for near-optimal chemotaxis by tuning an allosteric factor to keep average receptor occupancy at one half.

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

The paper models how eukaryotic cells sense chemical gradients through ligand binding to membrane receptors, with an internal allosteric protein that raises binding affinity when it attaches to the receptor's cytosolic side. The cell regulates the availability of this allosteric factor through a reaction scheme that holds the average fraction of occupied receptors at exactly one half, independent of external ligand level. This adaptation mechanism yields bounds showing near-optimal chemotactic accuracy across a broad concentration range. Accuracy depends strongly on how fast the allosteric compound diffuses relative to other rates, producing a direct trade-off between adaptation speed and sensing precision.

Core claim

The cell reaches near-optimal chemotaxis over a broad range of concentrations by altering the allosteric factor's availability to adapt the average fraction of bound receptors to 1/2.

What carries the argument

The allosteric factor that binds the cytosolic side of the receptor to increase ligand affinity, together with the reaction scheme that tunes its availability to enforce one-half average receptor occupancy.

If this is right

  • Chemotactic accuracy depends strongly on the diffusion constant of the allosteric compound relative to binding and unbinding rates.
  • Faster adaptation to new concentrations reduces gradient-sensing accuracy.
  • The mechanism supports near-optimal performance over orders-of-magnitude changes in background ligand level.
  • Performance bounds can be calculated directly from the occupancy-maintenance condition and diffusion rates.

Where Pith is reading between the lines

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

  • Cells might evolve regulatory networks that set the diffusion rate of the allosteric protein to match typical environmental timescales.
  • The occupancy-at-one-half rule could be tested by measuring receptor states in cells with altered allosteric-protein expression.
  • Similar internal tuning might appear in other eukaryotic sensory systems that must operate across wide input ranges.

Load-bearing premise

The cell possesses a reaction scheme that can precisely tune allosteric factor availability to hold average receptor occupancy at exactly one half for any ligand concentration.

What would settle it

Measurements showing that the steady-state fraction of bound receptors deviates from one half across different ligand concentrations, or that disrupting allosteric binding abolishes adaptation while preserving baseline receptor function.

Figures

Figures reproduced from arXiv: 2509.00219 by Brian A. Camley, Vishnu Srinivasan, Wei Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. Reaction diagram showing all four states. Blue dots [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. How the Fisher information [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Reaction schematic for activation and inactivation [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Response curve illustrating the steady state receptor binding probability to a half-occupied state (gray line). Lower [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparing simulation results (blue circles) at high [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Comparisons between Fisher information of the adap [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: When KM is sufficiently small, we observe a rapid increase in gradient sensing accuracy near KD, af￾ter which the Fisher information seems to fall of like in the single-type model [Eq. (4)]. For larger KM, however, the sharp jump is smoothed out. This follows from the fact that smaller KM makes it easier to maintain the limit G, G∗ ≫ KM where near-perfect adaptation is possible (Sec. II C). E. Trade-offs i… view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Gradient sensing accuracy [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Ternary complex model diagram similar to Fig. [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
read the original abstract

Eukaryotic cells generally sense chemical gradients using the binding of chemical ligands to membrane receptors. In order to perform chemotaxis effectively in different environments, cells need to adapt to different concentrations. We present a model of gradient sensing where the affinity of receptor-ligand binding is increased when a protein binds to the receptor's cytosolic side. This interior protein (allosteric factor) alters the sensitivity of the cell, allowing the cell to adapt to different ligand concentrations. We propose a reaction scheme where the cell alters the allosteric factor's availability to adapt the average fraction of bound receptors to 1/2. We calculate bounds on the chemotactic accuracy of the cell, and find that the cell can reach near-optimal chemotaxis over a broad range of concentrations. We find that the accuracy of chemotaxis depends strongly on the diffusion of the allosteric compound relative to other reaction rates. From this, we also find a trade-off between adaptation time and gradient sensing accuracy.

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.

Referee Report

3 major / 2 minor

Summary. The paper presents a model of eukaryotic gradient sensing in which a cytosolic allosteric factor binds cooperatively to the intracellular domain of membrane receptors, thereby increasing ligand affinity. A reaction scheme is proposed that dynamically adjusts the availability of this factor so that the steady-state average receptor occupancy remains exactly 1/2 across a wide range of background ligand concentrations. Under this fixed-occupancy condition the authors derive analytic bounds on chemotactic accuracy, report near-optimal performance over broad concentration ranges, and identify a strong dependence of accuracy on the diffusion coefficient of the allosteric factor together with a trade-off between adaptation speed and sensing precision.

Significance. If the reaction scheme can be shown to achieve the required occupancy regulation robustly and without fine-tuning or extra noise sources, the work would supply a concrete, diffusion-dependent mechanism for perfect adaptation that could account for high chemotactic efficiency in fluctuating environments. The explicit trade-off between adaptation time and accuracy, together with the emphasis on intracellular diffusion, offers testable predictions for how cells might optimize gradient sensing.

major comments (3)
  1. [§3] §3 (reaction scheme for allosteric-factor control): the proposed reactions are introduced to enforce average occupancy = 1/2, yet the steady-state analysis does not demonstrate that this fixed point remains stable and parameter-insensitive when the diffusion coefficient of the allosteric factor and the background ligand concentration are varied simultaneously; this is load-bearing for the subsequent optimality bounds.
  2. [§5] §5 (accuracy bounds): the near-optimal chemotaxis claim is derived under the assumption that the adaptation loop maintains exactly 1/2 occupancy without introducing additional stochasticity or violating timescale separation; no explicit calculation shows that the control dynamics remain stable across the claimed concentration range when realistic values of the free diffusion parameter are inserted.
  3. [§4.2] §4.2 (trade-off between adaptation time and accuracy): the reported dependence on the allosteric diffusion rate is central, but the manuscript does not quantify how the required diffusion coefficient compares with measured cytosolic protein diffusivities or whether the implied reaction rates remain biologically plausible.
minor comments (2)
  1. Notation for the allosteric factor concentration and its binding states is introduced without a clear table or diagram summarizing the states and rate constants.
  2. Figure captions should explicitly state the parameter values used for the numerical illustrations of the accuracy bounds.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We respond to each major comment below, indicating the revisions that will be incorporated to address the concerns raised.

read point-by-point responses

  1. Referee: §3 (reaction scheme for allosteric-factor control): the proposed reactions are introduced to enforce average occupancy = 1/2, yet the steady-state analysis does not demonstrate that this fixed point remains stable and parameter-insensitive when the diffusion coefficient of the allosteric factor and the background ligand concentration are varied simultaneously; this is load-bearing for the subsequent optimality bounds.

    Authors: We agree that explicit demonstration of stability and parameter insensitivity under joint variation of the diffusion coefficient and ligand concentration is necessary to support the robustness of the fixed-occupancy condition. The manuscript derives the steady-state occupancy of exactly 1/2 from the proposed reaction scheme but does not include a full stability analysis across parameter ranges. In the revised version we will add a linear stability analysis of the fixed point, including evaluation of the Jacobian for representative values of the allosteric-factor diffusion coefficient and background concentrations, to confirm convergence without fine-tuning. revision: yes

  2. Referee: §5 (accuracy bounds): the near-optimal chemotaxis claim is derived under the assumption that the adaptation loop maintains exactly 1/2 occupancy without introducing additional stochasticity or violating timescale separation; no explicit calculation shows that the control dynamics remain stable across the claimed concentration range when realistic values of the free diffusion parameter are inserted.

    Authors: The accuracy bounds rest on the maintained occupancy of 1/2 and the separation of timescales. The current derivation is performed in the deterministic mean-field limit. To address the concern, the revised manuscript will include numerical simulations of the full reaction-diffusion system using realistic diffusion coefficients (on the order of 1–100 μm²/s) over the stated concentration range. These simulations will verify both stability of the control dynamics and preservation of timescale separation, thereby supporting the near-optimal chemotaxis result. revision: yes

  3. Referee: §4.2 (trade-off between adaptation time and accuracy): the reported dependence on the allosteric diffusion rate is central, but the manuscript does not quantify how the required diffusion coefficient compares with measured cytosolic protein diffusivities or whether the implied reaction rates remain biologically plausible.

    Authors: We acknowledge that the manuscript identifies the dependence on the allosteric diffusion rate and the associated trade-off but does not provide direct comparison to experimental values. In the revised discussion we will insert a paragraph comparing the diffusion coefficients required by the model to literature values for cytosolic proteins obtained by FRAP and FCS (typically 0.1–10 μm²/s). We will also reference typical biochemical rate constants for allosteric binding to assess plausibility of the implied reaction rates and discuss any limitations this comparison may reveal. revision: yes

Circularity Check

0 steps flagged

No significant circularity; adaptation scheme is an explicit modeling assumption

full rationale

The paper proposes a reaction scheme that tunes allosteric-factor availability to enforce average receptor occupancy of exactly 1/2, then derives chemotactic accuracy bounds under that fixed-occupancy condition. This is a standard modeling choice (input assumption) from which performance predictions follow; the bounds are not shown to reduce tautologically to the same fitted quantities or self-citations. No load-bearing self-citation chains, fitted-input predictions, or ansatz smuggling appear in the abstract or described derivation. The model is therefore self-contained against external benchmarks for the purpose of this circularity check.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The model rests on the introduction of an allosteric factor whose availability is actively controlled and on the assumption that this control can be tuned to enforce a fixed occupancy set-point; these elements are postulated rather than derived from upstream measurements.

free parameters (1)
  • diffusion coefficient of allosteric compound
    Accuracy is stated to depend strongly on this value relative to binding rates; the abstract implies it is chosen or varied to explore the trade-off.
axioms (1)
  • domain assumption The cell alters the allosteric factor's availability to adapt the average fraction of bound receptors to 1/2.
    This is the central proposed reaction scheme that enables adaptation.
invented entities (1)
  • allosteric factor (cytosolic protein) no independent evidence
    purpose: Binds receptor intracellularly to increase ligand affinity and thereby shift sensitivity.
    Postulated to implement the adaptation mechanism; abstract provides no independent experimental evidence for its existence or properties.

pith-pipeline@v0.9.0 · 5696 in / 1379 out tokens · 48843 ms · 2026-05-18T20:05:51.856658+00:00 · methodology

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Lean theorems connected to this paper

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

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    In the limit where G, G* ≫ KM, Eq. (11) reduces to ∂G/∂t = Vmax [−fb + fu] – so the system will reach a steady state where fu = fb = 1/2 – leading to perfect adaptation

  • IndisputableMonolith/Foundation/BranchSelection.lean branch_selection echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Iϕϕ = N g² C0 Keff / 8 (C0 + Keff)² ... maximized when C0 = Keff ... probability of binding is 1/2

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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