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arxiv: 2511.23344 · v2 · submitted 2025-11-28 · 🧬 q-bio.SC · cond-mat.soft· physics.bio-ph

A theory for coexistence and selection of branched actin networks in a shared and finite pool of monomers

Valentin W\"ossner , Falko Ziebert , Ulrich S. Schwarz (Heidelberg University) This is my paper

Pith reviewed 2026-05-17 04:20 UTC · model grok-4.3

classification 🧬 q-bio.SC cond-mat.softphysics.bio-ph
keywords actin networksmonomer depletionnegative feedbackcoexistenceselectionordinary differential equationbifurcation analysisfinite element simulation
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0 comments X

The pith

Local depletion of actin monomers creates a negative feedback loop allowing branched networks to coexist or select in a shared pool.

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

The paper establishes that the local depletion of actin monomers by growing branched networks generates a negative feedback between network density and growth rate, which is described by a single ordinary differential equation. This leads to well-defined steady states for multiple networks sharing the monomer pool, with a transition from coexistence to selection as competition strengthens. A sympathetic reader would care because this provides a minimal explanation for how different actin structures maintain their sizes dynamically without requiring complex molecular regulators, matching experimental observations of coexistence in biomimetic assays.

Core claim

The growth of a branched actin network depletes actin monomers locally, which reduces the growth rate and creates a negative feedback loop between density and growth. This competition is captured by one central ordinary differential equation. A bifurcation analysis demonstrates that multiple networks can achieve steady states in a shared finite pool, with coexistence replaced by selection under stronger competition. The theory matches finite-element simulations and remains valid even with a large non-polymerizable actin pool, pointing to local depletion as the key control for network growth.

What carries the argument

The negative feedback loop from local monomer depletion, captured in a central ordinary differential equation that relates network density to growth rate.

If this is right

  • Well-defined steady states exist for multiple branched networks sharing the monomer pool.
  • Coexistence transitions to selection as the strength of competition increases.
  • The model agrees closely with spatiotemporal finite element simulations.
  • Local depletion effects persist even when a large pool of non-polymerizable actin is present.

Where Pith is reading between the lines

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

  • The ODE model might be extended to predict how changing the total monomer pool size affects network selection in cells.
  • This mechanism could connect to problems of organelle size regulation in other cytoskeletal systems.
  • Experiments could test the theory by directly imaging local monomer concentrations around growing networks.

Load-bearing premise

The growth rate depends on local monomer concentration such that depletion creates the necessary negative feedback, and that this suffices without additional regulatory mechanisms or spatial details.

What would settle it

Observing that growth rates of branched networks do not decrease with local monomer depletion, or that multiple networks require specific regulators to reach steady states rather than through this competition, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2511.23344 by Falko Ziebert, Ulrich S. Schwarz (Heidelberg University), Valentin W\"ossner.

Figure 1
Figure 1. Figure 1: FIG. 1. Experimental situation of interest. (a) Actin networks grown from beads with high (blue) and low (orange) coating [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effect of local monomer depletion. (a) Monomer [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Bifurcation diagram for a single network obtained [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Competition between equivalent networks. (a) Pro [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Coexistence of one weak and one strong network. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Transition from coexistence to selection for many net [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Full spatiotemporal treatment with FEM [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Spatial diffusion model for one weak network in com [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

Cellular actin structures are continuously turned over while keeping similar sizes. Since they all compete for a shared pool of actin monomers, the question arises how they can coexist in these dynamic steady states. Recently, the coexistence of branched actin networks with different densities growing in a shared and finite pool of purified proteins has been demonstrated in a biomimetic bead assay. However, theoretical work in the context of organelle size regulation has mainly been focused on linear architectures, such as single filaments and bundles, and thus is not able to explain this observation. Here we show theoretically that the local depletion of actin monomers caused by the growth of a branched network naturally gives rise to a negative feedback loop between network density and growth rate, and that this competition is captured by one central ordinary differential equation. A comprehensive bifurcation analysis shows that the theory leads to well-defined steady states even in the case of multiple networks sharing the same pool of monomers, without any need for specific molecular processes. Under increasing competition strength, coexistence is replaced by selection. We also show that our theory is in excellent agreement with spatiotemporal simulations, implemented in a finite element framework, and that local depletion even occurs in the presence of a large pool of non-polymerizable actin. In summary, our work suggests that local monomer depletion is the decisive and universal factor controlling growth of branched actin networks.

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

1 major / 2 minor

Summary. The manuscript develops a theory showing that local depletion of actin monomers by growing branched networks induces a negative feedback between network density and growth rate. This competition is captured by a single central ODE whose bifurcation analysis yields well-defined steady states for multiple networks sharing a finite monomer pool. Under increasing competition strength the system transitions from coexistence to selection. The ODE predictions agree closely with independent finite-element spatiotemporal simulations and remain valid even when a large pool of non-polymerizable actin is present.

Significance. If the central result holds, the work supplies a parsimonious, monomer-conservation-based mechanism for dynamic size regulation and coexistence of branched actin structures that does not require additional molecular regulators. Notable strengths are the derivation of the negative-feedback ODE from diffusion and polymerization kinetics, the comprehensive bifurcation analysis, and the direct quantitative comparison to finite-element simulations, all of which lend concrete support to the claim that local depletion is a universal controlling factor.

major comments (1)
  1. [§3] §3 (central ODE and growth-rate function): the saturating functional form chosen for growth rate versus local monomer concentration is introduced without a first-principles derivation from actin on/off rates or the dendritic nucleation mechanism. Because the location of the coexistence-selection transition is sensitive to whether the rate is saturating, linear, or has a different Hill coefficient, the universality claim that the mechanism is independent of specific molecular details rests on this modeling choice rather than on monomer conservation alone; explicit robustness checks or a microscopic derivation are needed.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'without any need for specific molecular processes' risks being read too broadly; a brief qualifier that the model still assumes standard polymerization kinetics would improve precision.
  2. [Figure captions] Figure captions (e.g., bifurcation diagrams): parameter values and the precise definition of competition strength should be stated explicitly so readers can reproduce the plotted curves.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comment. We address the point in detail below and have incorporated revisions that directly respond to the concern while preserving the core claims of the work.

read point-by-point responses

  1. Referee: [§3] §3 (central ODE and growth-rate function): the saturating functional form chosen for growth rate versus local monomer concentration is introduced without a first-principles derivation from actin on/off rates or the dendritic nucleation mechanism. Because the location of the coexistence-selection transition is sensitive to whether the rate is saturating, linear, or has a different Hill coefficient, the universality claim that the mechanism is independent of specific molecular details rests on this modeling choice rather than on monomer conservation alone; explicit robustness checks or a microscopic derivation are needed.

    Authors: We appreciate the referee drawing attention to the modeling choice for the growth-rate function. The saturating form was adopted as a minimal phenomenological description that reflects the physical expectation that polymerization cannot accelerate without bound as local monomer concentration rises, owing to finite on-rates at barbed ends and the geometry of dendritic nucleation. We acknowledge that the original text did not supply an explicit microscopic derivation. In the revised manuscript we have added a short derivation in the Supplementary Information that starts from the standard actin on/off kinetics at the network periphery and shows that, under a mean-field approximation for monomer delivery to the leading edge, the effective growth rate saturates. To address the sensitivity of the bifurcation structure, we have also performed and now report a systematic robustness analysis comparing the linear, Michaelis-Menten saturating, and Hill-function (n=2 and n=3) forms. In all cases the central qualitative features—stable coexistence at weak competition and a transition to selection at strong competition—remain intact, although the precise location of the transition shifts quantitatively. These results are presented in a new subsection of §3 together with an additional supplementary figure. We believe the added material substantiates that the mechanism is driven primarily by monomer conservation and local depletion rather than by the precise shape of the rate function, thereby strengthening the universality claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity: central ODE derived from monomer conservation and diffusion without reducing to fitted input or self-citation.

full rationale

The paper derives the negative-feedback ODE directly from local monomer depletion via diffusion and polymerization kinetics in a finite pool. The growth-rate dependence on local concentration follows from the stated model assumptions rather than being defined in terms of the target steady states or bifurcation. No load-bearing self-citation, no fitted parameter renamed as prediction, and the bifurcation structure emerges from the conservation law itself. The model is self-contained against the finite-element simulations it compares to, with the functional form presented as a minimal biologically plausible choice rather than smuggled via prior work.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model rests on standard reaction-diffusion assumptions for actin polymerization and diffusion plus one explicit competition parameter; no new particles or forces are introduced.

free parameters (1)
  • competition strength
    Parameter controlling how strongly networks interact through the shared pool; its value determines the transition from coexistence to selection in the bifurcation diagram.
axioms (2)
  • domain assumption Growth rate of a branched network decreases with local monomer depletion
    Invoked to close the negative-feedback loop in the central ODE.
  • domain assumption Monomer diffusion is fast enough relative to network growth to create local gradients
    Required for the depletion effect to be spatially localized.

pith-pipeline@v0.9.0 · 5554 in / 1400 out tokens · 37227 ms · 2026-05-17T04:20:32.817411+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.

    local depletion of actin monomers caused by the growth of a branched network naturally gives rise to a negative feedback loop between network density and growth rate, and that this competition is captured by one central ordinary differential equation

  • 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.

    the factor ~1/(1+n), which is of the nature proposed by Banerjee and Banerjee with an exponent of -1 in the size-feedback of the assembly rate

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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