Centering and symmetry breaking in confined contracting actomyosin networks

Alex Mogilner; Angelika Manhart; Bruce L. Goode; Enas Abu-Shah; Kinneret Keren; Maya Malik-Garbi; Niv Ierushalmi

arxiv: 1907.10642 · v1 · pith:NJCG3JD5new · submitted 2019-07-24 · ⚛️ physics.bio-ph

Centering and symmetry breaking in confined contracting actomyosin networks

Niv Ierushalmi , Maya Malik-Garbi , Angelika Manhart , Enas Abu-Shah , Bruce L. Goode , Alex Mogilner , Kinneret Keren This is my paper

Pith reviewed 2026-05-24 16:31 UTC · model grok-4.3

classification ⚛️ physics.bio-ph

keywords actomyosin networkscell centeringsymmetry breakingDarcy frictionXenopus egg extractsartificial cellshydrodynamic mechanismcontractile networks

0 comments

The pith

Actomyosin networks in artificial cells center symmetrically via Darcy friction in large droplets but polarize via boundary attachments in small ones.

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

Artificial cells made by encapsulating Xenopus egg extracts into water-in-oil droplets contain persistently contracting actomyosin networks whose contraction center moves according to droplet size. Larger droplets produce a stable symmetric configuration with the center held in the middle, while smaller droplets produce a polar configuration with the center shifted near the boundary. The symmetric centering is produced by a hydrodynamic process in which Darcy friction between the contracting network and the surrounding cytoplasm generates restoring forces. Symmetry breaking happens when transient attachments form between the network and the droplet boundary and pull the center outward.

Core claim

In artificial cells formed by encapsulating Xenopus egg extracts into water-in-oil droplets, persistently contracting actomyosin networks exhibit size-dependent positioning of their contraction center. Larger droplets maintain a symmetric, centered configuration through active centering driven by Darcy friction between the network and surrounding cytoplasm. In smaller droplets, the center breaks symmetry and moves to a polar position near the boundary, facilitated by transient attachments to the cell boundary. This demonstrates a robust mechanism for subcellular localization that is tunable by cell size.

What carries the argument

Darcy friction between the contracting actomyosin network and the surrounding cytoplasm, acting together with transient attachments to the droplet boundary.

Load-bearing premise

The observed size-dependent localization patterns are produced specifically by the proposed Darcy friction and transient boundary attachments rather than by unmeasured factors such as extract variability or droplet interface properties.

What would settle it

If controlled experiments that vary only droplet volume while holding extract composition and boundary chemistry fixed show no consistent size threshold for the symmetric-to-polar transition, the hydrodynamic and attachment mechanism would be falsified.

read the original abstract

Centering and decentering of cellular components is essential for internal organization of cells and their ability to perform basic cellular functions such as division and motility. How cells achieve proper localization of their components is still not well-understood, especially in large cells such as oocytes. Here, we study actin-based positioning mechanisms in artificial cells with persistently contracting actomyosin networks, generated by encapsulating cytoplasmic Xenopus egg extracts into cell-sized water-in-oil droplets. We observe size-dependent localization of the contraction center, with a symmetric configuration in larger cells and a polar one in smaller cells. In the symmetric state, the contraction center is actively centered, via a hydrodynamic mechanism based on Darcy friction between the contracting network and the surrounding cytoplasm. During symmetry breaking, transient attachments to the cell boundary drive the contraction center to a polar location near the droplet boundary. Our findings demonstrate a robust, yet tunable, mechanism for subcellular localization.

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

Experimental size-dependent switch in droplet centering is the real observation here; the Darcy friction and attachment mechanism is an interpretation that needs controls the abstract does not show.

read the letter

The main point worth knowing is that the authors encapsulate Xenopus extracts in water-in-oil droplets and report a clear size dependence: larger droplets show a centered contraction zone while smaller ones go polar. They attribute the centered state to hydrodynamic Darcy friction between the network and cytoplasm, and the polar shift to transient boundary attachments. That size scaling is the concrete new result from the droplet assay. The setup itself is straightforward and lets them watch persistent contraction in a confined geometry that mimics large-cell conditions, which is a useful addition to the actomyosin literature. The abstract states the observations directly and ties them to a physical picture without obvious circularity in the reported data. The soft spot is the jump from pattern to mechanism. The stress-test concern holds: droplet interfaces can impose curvature-dependent boundary conditions and extract batches vary in contractility, yet the abstract gives no sign of quantified controls for either. Without those, it is difficult to know whether the proposed friction and attachment terms are doing the work or whether other unmeasured factors are. The paper is aimed at researchers in cell mechanics and active matter who care about subcellular positioning. A reader looking for experimental examples of size-dependent centering will find usable observations; someone needing a firmly supported hydrodynamic model will want the full methods and controls first. It is worth sending to referees because the experimental system is reproducible enough to test and the phenomenon is relevant, even if the mechanistic section will probably need strengthening.

Referee Report

2 major / 1 minor

Summary. The manuscript studies actin-based positioning in artificial cells created by encapsulating Xenopus egg extracts into cell-sized water-in-oil droplets, generating persistently contracting actomyosin networks. It reports size-dependent localization of the contraction center: symmetric centering in larger droplets attributed to an active hydrodynamic mechanism based on Darcy friction between the network and cytoplasm, and polar localization in smaller droplets driven by transient attachments to the droplet boundary. The work concludes that this constitutes a robust yet tunable mechanism for subcellular localization.

Significance. If substantiated, the findings would provide a physical, hydrodynamic explanation for centering and symmetry breaking in large cells such as oocytes, using a reconstituted confined system that isolates network-cytoplasm interactions. The droplet platform offers tunability via size and confinement, which could inform models of internal cellular organization. The paper does not report machine-checked proofs or parameter-free derivations, but the experimental approach to hydrodynamic friction is a potential strength if controls are added.

major comments (2)

[Abstract and Results] Abstract and Results (size-dependent localization): The central claim attributes symmetric centering specifically to Darcy friction and polar states to transient boundary attachments, yet the provided text contains no quantitative data, error bars, statistical tests, or controls for extract batch variability or droplet interface properties (e.g., curvature or surfactant effects). This interpretive mapping is load-bearing for the mechanism and requires direct evidence to rule out confounds.
[Mechanism section] Mechanism section (Darcy friction): The hydrodynamic centering mechanism is stated without accompanying measurements of friction coefficients, flow fields, or comparisons to alternative models (e.g., boundary curvature dominating in smaller droplets). The manuscript should include either direct friction quantification or simulations demonstrating that Darcy friction produces the observed size dependence independently of interface effects.

minor comments (1)

[Figures and Methods] Figure legends and methods: Ensure all panels include scale bars, droplet size distributions, and explicit description of how contraction center position is quantified to allow reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comments. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: [Abstract and Results] Abstract and Results (size-dependent localization): The central claim attributes symmetric centering specifically to Darcy friction and polar states to transient boundary attachments, yet the provided text contains no quantitative data, error bars, statistical tests, or controls for extract batch variability or droplet interface properties (e.g., curvature or surfactant effects). This interpretive mapping is load-bearing for the mechanism and requires direct evidence to rule out confounds.

Authors: We agree that the presentation would benefit from more explicit quantitative support. In the revised manuscript we have added error bars and statistical tests to the size-dependent localization data, along with controls addressing extract batch variability and droplet interface properties (including curvature and surfactant effects). These additions provide direct evidence for the mapping of symmetric centering to the Darcy friction mechanism and polar localization to boundary attachments. revision: yes
Referee: [Mechanism section] Mechanism section (Darcy friction): The hydrodynamic centering mechanism is stated without accompanying measurements of friction coefficients, flow fields, or comparisons to alternative models (e.g., boundary curvature dominating in smaller droplets). The manuscript should include either direct friction quantification or simulations demonstrating that Darcy friction produces the observed size dependence independently of interface effects.

Authors: We acknowledge the value of additional quantitative support for the proposed mechanism. While direct experimental measurement of friction coefficients within the confined droplet geometry remains technically challenging, the revised manuscript now includes simulations that explicitly demonstrate Darcy friction produces the observed size dependence. These simulations also compare against alternative models and show that boundary curvature effects do not dominate in the larger droplets where symmetric centering occurs. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations with interpretive mechanisms, no derivations or fitted predictions

full rationale

The paper reports direct experimental observations of size-dependent contraction center localization in Xenopus extract droplets. Proposed mechanisms (Darcy friction for centering in large droplets, transient boundary attachments for polar localization in small droplets) are presented as interpretations of the data rather than outputs of any mathematical derivation, parameter fitting, or self-citation chain. No equations, ansatzes, uniqueness theorems, or 'predictions' of closely related quantities appear in the provided text. The work is self-contained against external benchmarks as an observational study; the skeptic's concerns address causal attribution strength, not circular reduction of claims to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No mathematical model, free parameters, or new postulated entities are described in the abstract; the work is purely experimental observation and mechanistic interpretation.

pith-pipeline@v0.9.0 · 5709 in / 1111 out tokens · 19781 ms · 2026-05-24T16:31:18.039404+00:00 · methodology

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.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

hydrodynamic mechanism based on Darcy friction between the contracting network and the surrounding cytoplasm... transient attachments to the cell boundary drive the contraction center to a polar location
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

net centering force... behaves like a Hookean spring with a force that increases linearly as a function of the displacement

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.