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arxiv: 2606.10878 · v1 · pith:ABUTSJPUnew · submitted 2026-06-09 · ⚛️ physics.bio-ph · q-bio.CB

Spontaneous polarization for protrusion-driven cell crawling

Pierre Recho This is my paper

Pith reviewed 2026-06-27 10:48 UTC · model grok-4.3

classification ⚛️ physics.bio-ph q-bio.CB
keywords cell motilityactin polymerizationspontaneous polarizationbifurcation analysiscontinuum modelprotrusion-driven crawlingsymmetry breakingkeratocyte model
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The pith

Feedback between cell motion and polarized actin nucleation regulator drives spontaneous crawling above a critical activity threshold.

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

The paper develops a one-dimensional continuum model of a viscous actin meshwork that polymerizes at two moving edges under control of an external chemical regulator. Cell motion polarizes the regulator around the boundaries, producing unequal nucleation rates that generate different protrusion speeds and thereby sustain both motion and the chemical asymmetry. Above a threshold in protrusive activity the symmetric non-moving state loses stability through a bifurcation, yielding a stable polarized motile state. The transition is supercritical or subcritical depending on the form of the regulator-actin coupling, and parameter values for keratocytes produce realistic speeds together with asymmetric edge-localized actin peaks. The mechanism requires no molecular motors, specific adhesion, substrate deformation, or pre-existing polarity.

Core claim

In the minimal one-dimensional model the static symmetric cell state loses stability above a critical protrusive activity through a bifurcation induced by the feedback between boundary motion and polarized chemical regulation of actin nucleation, resulting in spontaneous transition to a motile state with unequal polymerization rates at the two edges.

What carries the argument

The feedback loop in which cell motion polarizes an external chemical regulator of actin nucleation, thereby imposing different polymerization densities at the two moving edges.

Load-bearing premise

The external chemical regulator of actin nucleation becomes polarized around the moving cell boundaries and thereby imposes different nucleation densities at the two edges.

What would settle it

Direct measurement showing whether the external regulator concentration differs measurably between the leading and trailing edges in a spontaneously moving cell, or experimental tuning of protrusive activity across the model's predicted critical value to test for the onset of motility.

Figures

Figures reproduced from arXiv: 2606.10878 by Pierre Recho.

Figure 1
Figure 1. Figure 1: FIG. 1. Scheme of the model of an active gel with internal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Bifurcation diagrams from the static solution to a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Possible steady state gel densities for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We propose a minimal one-dimensional continuum model for the spontaneous initiation of protrusion-driven cell crawling on a rigid substrate. The cell cytoskeleton is represented as a viscous actin meshwork that turns over in the bulk and polymerizes at two moving cell edges. Symmetry breaking arises from the feedback between cell motion, an external chemical regulator of actin nucleation, and actin polymerization at the cell fronts. When the cell moves, the regulator becomes polarized around the moving boundaries, thereby imposing different actin nucleation densities at the two edges. This generates unequal protrusive rates, which in turn reinforce motion and sustain the chemical polarization. Above a critical protrusive activity, the static symmetric state loses stability and the system undergoes a bifurcation toward a motile polarized state. Depending on how the external cue controls actin nucleation, the transition can be either supercritical or subcritical, leading in the latter case to coexistence between static and motile states. Using parameter values appropriate for keratocyte cells, the model predicts realistic crawling speeds and actin-density profiles, including asymmetric edge-localized density peaks. These results identify a generic mechanism by which external biochemical regulation of actin nucleation can trigger spontaneous motility along a one-dimensional track without requiring molecular motors, specific adhesion dynamics, deformable substrates, or pre-existing polarity.

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

2 major / 2 minor

Summary. The paper proposes a minimal one-dimensional continuum model for protrusion-driven cell crawling on a rigid substrate. The cytoskeleton is modeled as a viscous actin meshwork with bulk turnover and edge polymerization; symmetry breaking arises from positive feedback between cell velocity, polarization of an external chemical regulator of actin nucleation, and differential protrusive activity at the two edges. Above a critical protrusive activity the symmetric static state loses stability via a bifurcation to a motile polarized state; the bifurcation is supercritical or subcritical depending on the functional form of nucleation regulation. With keratocyte-appropriate parameters the model yields realistic crawling speeds and asymmetric actin-density profiles.

Significance. If the derivation and stability analysis hold, the work identifies a generic, motor-independent mechanism for spontaneous motility initiation driven by external biochemical regulation. The demonstration that the same feedback loop can produce either continuous or hysteretic transitions is biologically relevant for understanding bistability in cell polarity. The 1D continuum formulation is analytically tractable and reproduces keratocyte-scale outputs, providing a useful minimal model for further exploration.

major comments (2)
  1. [Model description / abstract paragraph on feedback loop] The abstract states that motion polarizes the external regulator around the moving boundaries, but neither the abstract nor the model description supplies the explicit transport or boundary condition that implements this polarization (e.g., an advection term proportional to velocity or a flux condition at the edges). Without this equation the feedback loop cannot be verified as emergent rather than imposed, which is load-bearing for the claimed spontaneous symmetry breaking.
  2. [Results paragraph on keratocyte parameters] Parameter values are chosen to match keratocyte data, yet no sensitivity analysis or cross-validation is reported; it is therefore unclear whether the predicted speeds and density profiles are independent outputs or post-fit results. This directly affects the strength of the claim that the model reproduces realistic crawling without additional mechanisms.
minor comments (2)
  1. The abstract mentions 'model equations' but does not display them; the full manuscript should include the complete set of PDEs, boundary conditions, and the explicit functional form of the nucleation regulation that controls the super- versus subcritical character.
  2. Stability analysis details (linearization around the symmetric state, eigenvalue calculation, and bifurcation normal-form coefficients) are referenced only by outcome; these steps should be shown explicitly, preferably with the critical threshold expressed in terms of the model parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the presentation of the feedback mechanism and strengthen the robustness of our results. We address each point below and will revise the manuscript to improve explicitness and add supporting analysis.

read point-by-point responses

  1. Referee: [Model description / abstract paragraph on feedback loop] The abstract states that motion polarizes the external regulator around the moving boundaries, but neither the abstract nor the model description supplies the explicit transport or boundary condition that implements this polarization (e.g., an advection term proportional to velocity or a flux condition at the edges). Without this equation the feedback loop cannot be verified as emergent rather than imposed, which is load-bearing for the claimed spontaneous symmetry breaking.

    Authors: We agree that the explicit transport equation was not stated with sufficient prominence. The model (Section 2) implements polarization via the advection term in the regulator equation, δ_t c + v δ_x c = D δ_xx c - γ c, together with no-flux conditions at the moving edges x = ± L(t)/2. This advection arises directly from cell velocity v and produces the polarization without being imposed by hand. To make the loop fully verifiable, we will revise the abstract and expand the model-description paragraph to quote the transport equation and boundary conditions explicitly. revision: yes

  2. Referee: [Results paragraph on keratocyte parameters] Parameter values are chosen to match keratocyte data, yet no sensitivity analysis or cross-validation is reported; it is therefore unclear whether the predicted speeds and density profiles are independent outputs or post-fit results. This directly affects the strength of the claim that the model reproduces realistic crawling without additional mechanisms.

    Authors: We accept that the absence of sensitivity analysis weakens the claim of independent reproduction. We will add a new subsection (or appendix) reporting a systematic sensitivity sweep over the biologically relevant ranges of protrusive activity, regulator diffusivity, and turnover rates. The analysis will show that realistic speeds (0.1–0.5 μm s^{-1}) and edge-density peaks persist across wide intervals, confirming the outputs are robust rather than narrowly tuned. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained bifurcation analysis

full rationale

The central result is a standard linear stability analysis of the symmetric equilibrium in a minimal 1D continuum model, with the bifurcation type (super- or subcritical) controlled by the functional form of the nucleation regulation term. No quoted step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing premise rest on a self-citation chain. Parameter selection for keratocyte scales is used only to generate illustrative outputs after the bifurcation threshold is derived; the symmetry-breaking mechanism itself follows directly from the stated feedback equations without circular reduction. The paper is therefore scored at the default non-circular level.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The model introduces a chemical regulator whose polarization is assumed to follow cell motion; several parameters are set to keratocyte-appropriate values without independent derivation shown in the abstract.

free parameters (2)
  • critical protrusive activity threshold
    Value above which the symmetric state loses stability; fitted or chosen to produce realistic speeds.
  • keratocyte-specific nucleation and turnover rates
    Chosen to match observed crawling speeds and actin profiles.
axioms (2)
  • domain assumption Actin cytoskeleton behaves as a one-dimensional viscous meshwork with bulk turnover and edge polymerization only.
    Core modeling choice stated in the abstract.
  • domain assumption External chemical regulator polarization is strictly determined by cell motion.
    Feedback loop premise required for symmetry breaking.
invented entities (1)
  • external chemical regulator of actin nucleation no independent evidence
    purpose: Provides the motion-dependent asymmetry in polymerization rates.
    Postulated to close the feedback loop; no independent evidence supplied in abstract.

pith-pipeline@v0.9.1-grok · 5738 in / 1441 out tokens · 23412 ms · 2026-06-27T10:48:27.571927+00:00 · methodology

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