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arxiv: 2604.26928 · v1 · submitted 2026-04-29 · 🧬 q-bio.TO · math.AP· physics.bio-ph

Recognition: unknown

Theory of adhesion-driven self-organisation in growing tissues

Carles Falc\'o, Mohit P. Dalwadi, Philip K. Maini, Samuel W. S. Johnson

Authors on Pith no claims yet

Pith reviewed 2026-05-07 09:53 UTC · model grok-4.3

classification 🧬 q-bio.TO math.APphysics.bio-ph
keywords cell adhesiontissue invasionpattern formationself-organisationcollective migrationmultiscale modelinggrowing tissuesdensity-dependent regulation
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The pith

Adhesion strength and its density-dependent regulation decide whether tissues invade cohesively or break into spatial patterns.

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

The paper builds a single mechanistic model that treats cell invasion and pattern formation as two outcomes of the same adhesion-driven process in growing cell populations. It uses multiscale analysis to link cell-cell adhesion, self-diffusion, and proliferation, showing that weak adhesion produces steady advancing fronts while stronger adhesion slows the front and triggers instability that generates aggregates and fingering patterns. The model further shows that making adhesion strength decrease with local cell density removes these instabilities and returns the tissue to uniform, cohesive expansion. This framework matters because it offers a single parameter set that can explain both normal morphogenesis and the dysregulated invasion seen in cancer.

Core claim

For weak adhesion, tissues advance via stable monotone fronts; increasing adhesion slows invasion, destabilizes the front, and produces aggregates and spatial patterns behind the edge, including two-dimensional fingering morphologies. Density-dependent downregulation of adhesion eliminates these instabilities and restores cohesive expansion. The transition between these regimes is controlled by the relative strengths of adhesion, diffusion, and proliferation.

What carries the argument

A continuum model obtained from multiscale analysis of adhesion-mediated cell interactions, in which adhesion strength is a density-dependent parameter that modulates front stability and pattern emergence.

If this is right

  • Tissues with low or regulated adhesion expand as stable, uniform fronts suitable for normal morphogenesis.
  • Higher unregulated adhesion produces fragmented invasion with patterns behind the front, resembling cancer invasion.
  • Density-dependent adhesion downregulation acts as a built-in stabilizer that suppresses pattern formation.
  • The same balance of adhesion, diffusion, and proliferation can switch a tissue between cohesive and fragmented states without changing other parameters.

Where Pith is reading between the lines

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

  • The model suggests that therapeutic targeting of adhesion regulation could restore cohesive growth in tumors exhibiting fingering invasion.
  • Similar density-dependent feedback might operate in other self-organizing systems such as bacterial colonies or regenerating tissues where adhesion strength varies with crowding.
  • Extending the framework to include explicit mechanical forces or extracellular matrix interactions could test whether the adhesion instability persists under more realistic mechanical constraints.

Load-bearing premise

The chosen mathematical forms for adhesion, self-diffusion, and proliferation accurately capture the biological mechanisms that operate in real tissues.

What would settle it

An experiment that increases adhesion uniformly without density dependence and checks whether invasion fronts destabilize and produce aggregates or fingering patterns in growing cell populations.

Figures

Figures reproduced from arXiv: 2604.26928 by Carles Falc\'o, Mohit P. Dalwadi, Philip K. Maini, Samuel W. S. Johnson.

Figure 1
Figure 1. Figure 1: Model schematic and interpretation. Left: continuum model showing the short-range interaction approximation from a non-local to a local formulation, with each numbered term corresponding to a distinct mechanism. Right: schematic representation of the three contributions: density-dependent self-diffusion, cell-cell adhesion, and density-modulated proliferation. Bottom left panels illustrate representative c… view at source ↗
Figure 2
Figure 2. Figure 2: Adhesion-based patterning. (A) Example of pattern formation in the conservative model without proliferation, illustrating the emergence of spatial structure driven purely by adhesion. Functions are chosen as m(ρ) = ρ, d(ρ) = αρ, with α − ω = −2, so that the pattern formation condition H′′(ϕ) < 0 is satisfied. (B) Dispersion relation λ(k; 1) at the saturated state ϕ = 1 for the model with logistic growth. B… view at source ↗
Figure 3
Figure 3. Figure 3: Cell invasion in the unsaturated adhesion model view at source ↗
Figure 5
Figure 5. Figure 5: Density-dependent adhesion gives rise to mono view at source ↗
read the original abstract

Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly different behaviours within a single mechanistic model for adhesion-mediated self-organisation in growing cell populations. Using a multiscale analysis, we show that the balance between cell-cell adhesion, self-diffusion, and proliferation controls the emergence of distinct collective dynamics. We find that for weak adhesion, tissues invade through stable monotone fronts. As adhesion increases, invasion slows, fronts become unstable, leading to aggregates and spatial patterns emerging behind the advancing edge. In two spatial dimensions, these instabilities generate fingering morphologies reminiscent of dysregulated invasion in cancer. Crucially, we show that density-dependent regulation of adhesion suppresses these instabilities and restores cohesive tissue expansion. Together, our results identify adhesion strength and its regulation as key determinants of whether tissues invade cohesively or fragment into patterns, and provide a unified framework for understanding collective migration, morphogenesis, and dysregulated growth.

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

0 major / 4 minor

Summary. The manuscript develops a multiscale theoretical framework linking cell-cell adhesion, self-diffusion, and proliferation in growing cell populations. It derives effective continuum PDEs and analyzes traveling-wave invasion fronts, showing that weak adhesion yields stable monotone fronts while increasing adhesion slows invasion and destabilizes fronts, producing aggregates and fingering patterns in 2D. Density-dependent regulation of adhesion is shown to suppress these instabilities and restore cohesive expansion.

Significance. If the derivations and stability analysis hold, the work provides a unified mechanistic account of how adhesion strength and its local regulation determine whether tissues expand cohesively or fragment into spatial patterns. This has clear relevance to morphogenesis, regeneration, and dysregulated invasion in cancer. The multiscale reduction from discrete to continuum descriptions and the explicit identification of a regulatory mechanism that damps front instabilities are strengths.

minor comments (4)
  1. The abstract and introduction refer to 'multiscale analysis' and 'continuum limit' without specifying the starting discrete model (lattice, agent-based, or off-lattice) or the precise averaging procedure used to obtain the effective diffusion, adhesion, and proliferation terms.
  2. Boundary conditions for the traveling-wave problem and the numerical scheme used to compute the monotone front profiles and their linear stability spectra should be stated explicitly, including how the far-field states are imposed.
  3. In the 2D fingering results, the wavelength selection mechanism and the role of the density-dependent adhesion function in shifting the most unstable mode should be quantified (e.g., via dispersion relations) rather than described qualitatively.
  4. A brief comparison with existing continuum models of adhesion-driven invasion (e.g., those based on nonlocal adhesion kernels) would help situate the novelty of the density-dependent regulatory term.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending minor revision. The summary correctly captures the central result that adhesion strength and its density-dependent regulation control the transition between cohesive invasion and fragmentation into aggregates or fingering patterns. We appreciate the recognition of the multiscale reduction and the mechanistic link to morphogenesis and cancer invasion.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from model assumptions

full rationale

The paper constructs a multiscale reduction from an underlying discrete or agent-based description to a continuum PDE system governing cell density, with effective terms for adhesion, self-diffusion, and proliferation. The subsequent traveling-wave analysis and linear stability of monotone fronts follow directly from standard linearization of the resulting PDE around the invasion profile. The density-dependent adhesion regulation is introduced explicitly as a modeling choice to damp instabilities, not as a fitted parameter whose value is then 'predicted' elsewhere. No load-bearing step reduces by construction to a self-citation, a pre-chosen ansatz renamed as output, or a statistical fit to the target phenomenon. The framework therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard continuum approximations for cell populations and specific functional forms for adhesion and proliferation; no new physical entities are introduced.

free parameters (2)
  • adhesion strength parameter
    Varied parametrically to delineate weak vs strong adhesion regimes
  • proliferation rate
    Controls growth behind the invasion front
axioms (2)
  • domain assumption Continuum limit of discrete cell model is valid at tissue scales
    Invoked by the multiscale analysis
  • domain assumption Adhesion, diffusion, and proliferation can be represented by local density-dependent functions
    Core modeling choice stated in the abstract

pith-pipeline@v0.9.0 · 5494 in / 1341 out tokens · 41892 ms · 2026-05-07T09:53:16.201870+00:00 · methodology

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Reference graph

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    and in [38] to describe long-range diffusion. The short-range approximation can be achieved, for instance, by rescaling the interaction kernel as W (x) = ε−dφ(x/ε), where r = |x| and 0 < ε ≪ 1 denotes a smallsensing radius. We further assume that adhesive interactions are symmetric, so φ(x) = φ(−x). With this rescaling, and omitting the time dependence in...

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    (D.11) 0 10 20 ζ −0.5 0.0 0.5 1.0 p q r s 0.00 0.25 0.50 0.75 1.00 p ( P) −0.4 −0.2 0.0 q ( P ′) Figure D.1: Non-zero contact angle travelling waves

    Hence we obtain the exact travelling wave solutions P(ξ) = 1 − eσ±ξ , for ξ ≤ 0 ; (D.10) c(µ) = 1 2 s 2 µ ± p µ2 − 2 , for µ > √ 2 . (D.11) 0 10 20 ζ −0.5 0.0 0.5 1.0 p q r s 0.00 0.25 0.50 0.75 1.00 p ( P) −0.4 −0.2 0.0 q ( P ′) Figure D.1: Non-zero contact angle travelling waves. Numerical solution of the system of ordinary differential equations given ...