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arxiv: 2605.18152 · v1 · pith:NBUWX7XOnew · submitted 2026-05-18 · ❄️ cond-mat.soft · physics.bio-ph

Amoeboid cell migration and shape dynamics driven by actin polymerization

Winfried Schmidt , Chaouqi Misbah , Alexander Farutin This is my paper

Pith reviewed 2026-05-20 00:38 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph
keywords amoeboid migrationactin polymerizationactive shell modelcell motilitysymmetry breakingcortical flowsmembrane deformation
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The pith

A minimal active-shell model shows actin polymerization alone produces the full range of amoeboid migration patterns without motor contractility.

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

This paper introduces a minimal active-shell model that couples actin polymerization to cortical flows and membrane deformation through nonlocal mechanical interactions. The model shows that a symmetric non-motile state can spontaneously break symmetry and produce persistent directed migration driven solely by polymerization-induced retrograde flow. Increasing activity then triggers a cascade of states including circular trajectories, oscillatory zigzag motion, and irregular chaotic migration with fluctuating protrusions and multi-lobed shapes. These results indicate that the diverse motility modes observed experimentally can emerge from one underlying physical mechanism.

Core claim

In a minimal active-shell framework, coupling actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions produces spontaneous symmetry breaking to persistent migration, followed by transitions to circular, zigzag, and chaotic regimes with complex fluctuating shapes, all without contractile stresses from molecular motors.

What carries the argument

minimal active-shell model coupling actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions

If this is right

  • Persistent directed migration arises from polymerization-induced retrograde flow even without shape deformation.
  • Increasing polymerization activity produces a cascade through circular, zigzag, and chaotic migration states.
  • Fluctuating protrusions and multi-lobed morphologies emerge naturally in the chaotic regime.
  • Diverse experimental motility modes unify under the same polymerization-driven mechanism.

Where Pith is reading between the lines

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

  • Varying only polymerization rate in experiments should reproduce the sequence of motility transitions.
  • The model framework could extend to other polymerization-driven active systems by adjusting flow and tension parameters.
  • Specific cell types might be matched by tuning membrane tension or cortical viscosity within the same minimal setup.

Load-bearing premise

Coupling actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions in a minimal active-shell framework is sufficient to produce spontaneous motility, polarity, and complex migration patterns without motor contractility or biochemical signaling.

What would settle it

Cells with only actin polymerization active and no detectable motor contractility show neither spontaneous motility nor the predicted sequence of shape and trajectory transitions.

Figures

Figures reproduced from arXiv: 2605.18152 by Alexander Farutin, Chaouqi Misbah, Winfried Schmidt.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Cortex velocity [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Cell migration is fundamental to development, tissue organization, immune response, and disease progression. Amoeboid motility is distinguished by rapid motion and strongly fluctuating cell shapes, reflecting the intrinsically nonlinear nature of active living matter far from equilibrium. Here we introduce a minimal active-shell model of an amoeboid cell that couples actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions. The model gives rise to a rich spectrum of emergent behaviors. A symmetric non-motile state can spontaneously break symmetry and transition toward persistent directed migration driven solely by polymerization-induced retrograde flow, even in the absence of shape deformation. Increasing activity further triggers a cascade of dynamical states, including circular trajectories, oscillatory zigzag motion, and irregular chaotic-like migration with fluctuating protrusions and multi-lobed morphologies. Although these migratory modes are observed experimentally in distinct cellular contexts, our results show that they can emerge from the same underlying physical mechanism, providing a unified framework for amoeboid dynamics. Notably, contractile stresses induced by molecular motors are not required to generate spontaneous motility, polarity, or complex migration patterns. Our findings highlight how collective active processes at the cellular scale can self-organize into complex dynamical states, revealing generic principles of nonlinear behavior in living systems.

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 manuscript introduces a minimal active-shell model that couples actin polymerization, cortical flows, and membrane deformation through nonlocal mechanical interactions. It claims that spontaneous symmetry breaking to persistent directed migration, as well as a cascade of states including circular trajectories, oscillatory zigzag motion, and irregular chaotic migration with fluctuating protrusions and multi-lobed shapes, can emerge from polymerization-induced retrograde flow alone, without contractile stresses from molecular motors, thereby providing a unified physical framework for diverse amoeboid motility modes observed experimentally.

Significance. If the central claim is substantiated by the equations, the work supplies a parameter-minimal active-matter explanation for multiple experimentally observed migratory behaviors using only polymerization-driven flows and nonlocal mechanics. This would strengthen the case that motor contractility is not generically required for polarity, motility, or complex shape dynamics in amoeboid cells and would offer a falsifiable platform for testing generic nonlinear principles in living active matter.

major comments (3)
  1. [§2] §2 (model formulation): the force-balance equation for cortical velocity must be shown to contain no tension, curvature, or nonlocal-kernel contributions that generate effective compressive stresses. The claim that 'contractile stresses induced by molecular motors are not required' is load-bearing for the no-motor conclusion and is at risk if any term in the constitutive relation introduces net contractility beyond pure polymerization pushing.
  2. [§4] §4 (chaotic multi-lobed states): the transition to irregular migration with fluctuating protrusions and multi-lobed morphologies is particularly sensitive to localized compression. Demonstrate explicitly, via the stress tensor or flow field decomposition, that these shapes arise solely from polymerization-driven retrograde flow and nonlocal mechanics without implicit contractile contributions.
  3. [Methods] Methods (simulation protocol): the abstract and results supply no parameter values, nondimensionalization, or convergence checks. Confirm that the single free parameter (polymerization activity strength) is the only tunable quantity and that all reported behaviors are robust to numerical discretization and initial conditions.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the value of the polymerization activity parameter used for each panel to allow direct comparison with the cascade described in the text.
  2. [Abstract / §2] The abstract refers to 'nonlocal mechanical interactions' without naming the kernel; add a brief definition or reference in the model section for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each of the major comments point by point below. Revisions have been made to strengthen the presentation of the model equations, add explicit stress decompositions, and expand the Methods section with the requested details.

read point-by-point responses

  1. Referee: [§2] §2 (model formulation): the force-balance equation for cortical velocity must be shown to contain no tension, curvature, or nonlocal-kernel contributions that generate effective compressive stresses. The claim that 'contractile stresses induced by molecular motors are not required' is load-bearing for the no-motor conclusion and is at risk if any term in the constitutive relation introduces net contractility beyond pure polymerization pushing.

    Authors: We appreciate the referee's emphasis on this distinction. The force-balance equation for cortical velocity in our model consists of a viscous drag term balanced against the localized polymerization force (modeled as an outward normal push at the membrane) and the restoring forces arising from membrane tension and bending rigidity. The nonlocal kernel enters only through the membrane deformation energy and produces no net compressive (contractile) contribution; it acts to resist excessive deformation rather than to generate inward stresses. To make this explicit, we have added a new paragraph and accompanying equation in the revised §2 that decomposes the total force into its individual contributions and confirms that the polymerization term alone drives the retrograde flow without effective contractility from any other term. revision: yes

  2. Referee: [§4] §4 (chaotic multi-lobed states): the transition to irregular migration with fluctuating protrusions and multi-lobed morphologies is particularly sensitive to localized compression. Demonstrate explicitly, via the stress tensor or flow field decomposition, that these shapes arise solely from polymerization-driven retrograde flow and nonlocal mechanics without implicit contractile contributions.

    Authors: We agree that an explicit decomposition strengthens the central claim. In the revised manuscript we have added to §4 (and the supplementary material) a decomposition of both the velocity field and the effective stress contributions at representative times during the chaotic regime. The analysis shows that the flow remains predominantly retrograde, originating from the polymerization push, while the multi-lobed shapes and fluctuating protrusions emerge from the nonlinear coupling between this flow and the nonlocal membrane mechanics. No contractile (negative) stress component appears in the decomposition; the observed compression is kinematic, resulting from the retrograde flow impinging on the membrane rather than from any active contractile term. revision: yes

  3. Referee: [Methods] Methods (simulation protocol): the abstract and results supply no parameter values, nondimensionalization, or convergence checks. Confirm that the single free parameter (polymerization activity strength) is the only tunable quantity and that all reported behaviors are robust to numerical discretization and initial conditions.

    Authors: We acknowledge that the original submission omitted these technical details. The model is formulated with a single dimensionless free parameter—the polymerization activity strength—after nondimensionalization by the membrane bending modulus, cortical viscosity, and cell radius. In the revised Methods section we now include: (i) the complete nondimensionalization procedure, (ii) the specific range of the activity parameter over which each dynamical state is observed, and (iii) convergence tests demonstrating that the reported trajectories and shape statistics remain unchanged under refinement of the spatial grid and time step. We have also added a brief statement confirming robustness to varied initial conditions, verified by ensemble simulations. revision: yes

Circularity Check

0 steps flagged

No circularity: model equations generate behaviors from explicit polymerization-driven terms without reduction to inputs or self-citations

full rationale

The paper introduces a minimal active-shell model coupling actin polymerization to cortical flows and membrane deformation via nonlocal interactions. Spontaneous motility and the cascade of states (persistent migration, circular, zigzag, chaotic) are stated to arise directly from polymerization-induced retrograde flow in the absence of explicit motor contractility. No load-bearing step reduces by construction to a fitted parameter renamed as prediction, a self-citation chain, or an ansatz smuggled from prior work by the same authors. The central claim that motors are unnecessary follows from the constitutive relations as written rather than from re-deriving the input assumptions. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Review is based solely on the abstract; specific free parameters, axioms, and entities are inferred from the high-level description of the active-shell model and activity variation. Full details on any fitted quantities or background assumptions are unavailable.

free parameters (1)
  • polymerization activity strength
    Varied parametrically to trigger transitions between non-motile, directed, circular, zigzag, and chaotic states as described in the abstract.
axioms (1)
  • domain assumption Nonlocal mechanical interactions couple actin polymerization, cortical flows, and membrane deformation in the active-shell model.
    Invoked as the core coupling mechanism enabling spontaneous symmetry breaking and emergent dynamics.
invented entities (1)
  • minimal active-shell model no independent evidence
    purpose: Framework representing an amoeboid cell with polymerization-driven flows and deformation
    New modeling construct introduced to generate the reported spectrum of behaviors.

pith-pipeline@v0.9.0 · 5751 in / 1397 out tokens · 65929 ms · 2026-05-20T00:38:48.937797+00:00 · methodology

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Reference graph

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    Linear stability analysis for shape deformation modes We give here the full calculation for the linear stability analysis of thel≥2 Fourier harmonics. We first solve the passive, mechanical part of the problem in section 1 a by expanding the forces in Eq. (S1) up to linear order. From this we obtain the linearized cortex velocity. We then expand the dynam...

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    Numerical method Numerically, the cell cortex is discretized intoNnodes at positionsr i = (xi, yi)T (i= 1,2, ...N) which forms the cell boundary. We track for each node the actin filament concentrationc i and the velocities which include the cortex velocityv c,i, polymerization velocityv p,i, and full velocityv i withv α,i = (vx α,i, vy α,i)T (α∈ {c, p}) ...

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