Non-equilibrium phase transitions in hybrid Voronoi models of cell colonies

Giancarlo Ruocco; Matteo Paoluzzi; Mattia Miotto

arxiv: 2411.08012 · v2 · pith:W46P6R4Dnew · submitted 2024-11-12 · ❄️ cond-mat.soft · cond-mat.stat-mech· physics.bio-ph

Non-equilibrium phase transitions in hybrid Voronoi models of cell colonies

Mattia Miotto , Giancarlo Ruocco , Matteo Paoluzzi This is my paper

Pith reviewed 2026-05-23 17:38 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mechphysics.bio-ph

keywords Voronoi modelcell coloniesnon-equilibrium phase transitionsnuclear compressibilitymotility-induced phase separationmesenchymal transitionsteric repulsionself-propelled cells

0 comments

The pith

Adding short-range repulsions for nuclear compressibility to the self-propelled Voronoi model produces multiple non-equilibrium phase transitions controlled by nucleus size.

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

The paper examines how a stiff nucleus affects collective cell behavior in a model of cell colonies. It adds short-range repulsive forces to the standard Voronoi tessellation to represent nuclear and cellular compressibility, then shows that these forces compete with the vertex interactions that stand for cell-cell adhesion and cytoskeleton effects. This competition produces transitions among motility-induced phase separation, mesenchymal-like states, and disordered confluent configurations. Adjusting the effective size or compressibility of the nucleus moves the system across these phase boundaries, reproducing trends seen in experiments.

Core claim

In the hybrid Voronoi model, steric repulsions representing nuclear compressibility compete with vertex interactions that mimic adhesion and cytoskeletal organization; the resulting non-equilibrium dynamics yield phase transitions from motility-induced phase separation through mesenchymal-like phases to disordered confluent states, with nucleus effective size providing an independent control parameter that crosses phase boundaries in agreement with experimental observations.

What carries the argument

Hybrid self-propelled Voronoi model with added short-range repulsive forces that encode nuclear compressibility.

If this is right

Cells with larger or stiffer nuclei remain in confluent disordered states over wider ranges of motility and adhesion parameters.
Lowering nuclear compressibility allows the system to enter mesenchymal-like phases even at moderate adhesion strengths.
The same repulsion term suppresses motility-induced phase separation when nucleus size is increased.
Phase diagrams in the space of repulsion strength, motility, and adhesion strength contain at least three distinct non-equilibrium regimes.

Where Pith is reading between the lines

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

Nuclear mechanics could serve as a tunable handle in tissue engineering to steer collective cell migration without altering adhesion molecules.
The model suggests that nuclear size variation within a single tissue could create spatial heterogeneity in cell packing and motility.
If the repulsion term is made dependent on local cell density, the transitions might sharpen into first-order lines rather than crossovers.

Load-bearing premise

The short-range repulsive forces added to the Voronoi tessellation accurately capture the quantitative effects of nuclear compressibility without needing extra subcellular details or direct experimental calibration.

What would settle it

Measure the phase boundary locations in cell colonies while varying nuclear size or stiffness (for example via lamin mutations) and check whether the observed shifts match the locations predicted by changing the repulsion strength in the model.

Figures

Figures reproduced from arXiv: 2411.08012 by Giancarlo Ruocco, Matteo Paoluzzi, Mattia Miotto.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

Eukaryotic cells are characterized by a stiff nucleus whose effect in modeling the collective behavior of cell aggregates is usually underestimated. However, increasing experimental evidence links nuclear modifications with phenotypic transition, like the one between epithelial and mesenchymal states. In this work, we explore the effect of short-range repulsive forces in the non-equilibrium dynamics of the self-propelled Voronoi model. We show that the competition between steric repulsions (representing nuclear/cellular compressibility) and Vertex interactions (mimicking cell-cell adhesion/interaction and cytoskeleton organization) generate a variety of non-equilibrium phase transitions from Motility-Induced Phase Separation to mesenchymal-like phases up to disordered confluent configurations. Notably, we found that tuning the nucleus's effective size/compressibility provides an additional way to cross the boundary between the different possible phases in line with experimental observations.

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

The paper adds short-range repulsions to the self-propelled Voronoi model to represent nuclear compressibility and reports that this tunes several non-equilibrium phases, but the mapping stays asserted rather than calibrated.

read the letter

The core move is straightforward: take the existing self-propelled Voronoi setup and insert short-range steric repulsions that stand for nuclear or cellular compressibility. The authors find that varying the effective size or strength of these repulsions shifts the system across motility-induced phase separation, mesenchymal-like states, and disordered confluent packs, and they note the sequence matches some experimental trends during epithelial-mesenchymal transitions. That supplies one extra control parameter inside a familiar modeling framework, which is the main concrete addition here. The competition between the new repulsions and the standard vertex terms is a plausible mechanism on paper, and the claim that nuclear parameters can cross phase boundaries is at least consistent with the direction of recent experiments on nuclear mechanics in tissues. The limitation is that the abstract supplies no implementation details, no parameter sweeps, no error bars, and no direct comparison of the repulsion amplitude or range to measured nuclear stiffness or volume changes. Without those steps it is difficult to judge whether the reported boundaries are robust or whether the force term actually encodes the biological effect the authors intend. The work is aimed at groups already running Voronoi or vertex simulations of cell colonies who want a minimal way to include nuclear effects. A reader looking for new phase diagrams in active-matter cell models could extract something usable if the numerics hold up in the full text. I would send it for peer review because the modeling extension is simple enough to check and the biological motivation is current, even though the validation gap needs to be addressed.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces a hybrid self-propelled Voronoi model augmented with short-range repulsive forces intended to represent nuclear/cellular compressibility. It claims that competition between these repulsions and standard vertex interactions produces a sequence of non-equilibrium phase transitions, from motility-induced phase separation through mesenchymal-like states to disordered confluent configurations, and that varying the effective nuclear size or compressibility provides an additional control parameter that crosses these boundaries in a manner consistent with experimental observations on nuclear modifications during epithelial-mesenchymal transitions.

Significance. If the mapping from the added repulsion to nuclear mechanics can be placed on a quantitative footing and the phase boundaries shown to be robust, the work would supply a computationally tractable way to incorporate nuclear stiffness into vertex-based models of cell colonies and would identify nuclear compressibility as a tunable parameter for collective transitions. The simulation framework itself appears straightforward to implement and could be useful for exploring parameter space once calibrated.

major comments (1)

[Model definition and results (abstract and main text)] The central claim that tuning the nucleus's effective size/compressibility crosses phase boundaries 'in line with experimental observations' rests on an uncalibrated identification of the short-range repulsive term with nuclear compressibility. No derivation relating the repulsion amplitude or range to measured nuclear Young's modulus, lamin stiffness, or nuclear volume data is supplied, nor are simulated transition loci compared quantitatively to experimental parameter ranges for EMT-related nuclear changes. This mapping is load-bearing for the biological interpretation but remains an assumption without supporting evidence or sensitivity analysis.

minor comments (1)

[Abstract] The abstract states that 'a variety of non-equilibrium phase transitions' are generated but provides no quantitative metrics (order parameters, transition loci, error bars, or system-size dependence) that would allow a reader to assess robustness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major concern regarding the mapping of the repulsive term to nuclear compressibility below, clarifying the phenomenological nature of the model while agreeing that additional discussion is needed.

read point-by-point responses

Referee: The central claim that tuning the nucleus's effective size/compressibility crosses phase boundaries 'in line with experimental observations' rests on an uncalibrated identification of the short-range repulsive term with nuclear compressibility. No derivation relating the repulsion amplitude or range to measured nuclear Young's modulus, lamin stiffness, or nuclear volume data is supplied, nor are simulated transition loci compared quantitatively to experimental parameter ranges for EMT-related nuclear changes. This mapping is load-bearing for the biological interpretation but remains an assumption without supporting evidence or sensitivity analysis.

Authors: We agree that the identification of the short-range repulsion with nuclear compressibility is phenomenological rather than derived from a first-principles mapping to Young's modulus or lamin stiffness. The term is introduced as a minimal representation of nuclear excluded volume and stiffness within the hybrid Voronoi framework, motivated by the established role of nuclear mechanics in cell aggregates. The central result is that varying the effective nuclear size and repulsion strength provides an additional control parameter that induces the reported sequence of non-equilibrium transitions; the statement that this occurs 'in line with experimental observations' refers to the qualitative direction of EMT-related nuclear changes (e.g., softening or volume alteration facilitating mesenchymal states), not a quantitative match. We have performed extensive parameter sweeps on repulsion amplitude and range that demonstrate robustness of the phase boundaries, but we acknowledge the absence of direct quantitative comparison to experimental nuclear parameter ranges. In the revised manuscript we will add an expanded discussion section that (i) explicitly states the phenomenological character of the mapping, (ii) includes sensitivity analysis on the repulsion parameters with the resulting phase diagrams, and (iii) places the chosen parameter values in the context of available literature values for nuclear stiffness, while noting the limitations and the need for future calibration. revision: partial

Circularity Check

0 steps flagged

No circularity; phases emerge from explicit simulation of added model terms

full rationale

The paper defines a hybrid self-propelled Voronoi model by adding short-range repulsive forces as a modeling choice to represent nuclear compressibility, then runs simulations to observe emergent non-equilibrium phases from competition with vertex interactions. No equations or results reduce a claimed prediction or phase boundary to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation chain that itself assumes the target result. The work is a self-contained simulation study whose outputs are not forced by redefinition of inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only; ledger populated from stated modeling assumptions. The central claim rests on the Voronoi representation plus one added repulsion term whose mapping to nuclear biology is asserted but not derived.

free parameters (1)

nuclear repulsion strength and range
Controls effective nuclear size/compressibility and is tuned to cross phase boundaries; value not specified in abstract.

axioms (2)

domain assumption Voronoi tessellation plus vertex interactions adequately capture cell-cell adhesion and cytoskeleton effects
Standard modeling choice invoked to represent collective cell behavior.
domain assumption Short-range repulsions map directly to nuclear/cellular compressibility
Central modeling step stated in abstract without further justification.

pith-pipeline@v0.9.0 · 5677 in / 1216 out tokens · 21066 ms · 2026-05-23T17:38:58.902637+00:00 · methodology

discussion (0)

Reference graph

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4: Nucleus size as a driver for the Epithelial-to-Mesenchymal transition in cell colonies

Geometrical force The geometrical force acting on the nucleus center of cell i is obtained deriving the total Vertex energy: ⃗F i v = − dEv d⃗ ri = − dEi v d⃗ ri − X j∈N (i) dEj v d⃗ ri (5) 7 /uni00A0=/uni00A00.05 /uni00A0=/uni00A00.25 /uni00A0=/uni00A00.5 /uni00A0=/uni00A00.75 /uni00A0=/uni00A00.85 /uni00A0=/uni00A00.9 /uni00A0=/uni00A01.0 (i) (ii) (iii)...

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Repulsive force The repulsive force acting on the nucleus center of cell i is obtained by deriving the total repulsive energy ⃗F i r = − dϕr d⃗ ri = X j∈N (i) dϕj r d⃗ ri (22) and dΦj r drα i = −12 σ12 0 r13 ij ! (rα i − rα j ) rij (23) B. Observables As order parameters describing the global proper- ties of the system, we compute (i) the average long- ti...

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