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This paper proposes that cell–cell collisions in migrating epithelial layers can be split into reversible events that store orientational energy and irreversible events that dissipate it, and that the balance between the two controls how ti

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2026-08-01 21:43 UTC pith:QSO5WYRW

load-bearing objection A useful synthesis of collision-induced orientation into tissue rheology, but the virial step near jamming is asserted rather than derived, so the dominance claim doesn't follow from the equations. the 4 major comments →

arxiv 2607.15975 v1 pith:QSO5WYRW submitted 2026-07-17 q-bio.CB cond-mat.softphysics.bio-ph

A phenomenological multiscale framework for orientational interactions and viscoelasticity in migrating epithelial monolayers

Ivana Pajic-Lijakovic , Milan Milivojevic , Peter V.E. McClintock This is my paper
classification q-bio.CB cond-mat.softphysics.bio-ph
keywords collective cell migrationepithelial monolayersorientational interactionsviscoelasticityepithelial surface tensioncell packing densitysecond virial coefficientcell jamming
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper is trying to establish that the microscale geometry of cell–cell encounters — head-on versus glancing, preserving or changing the collision angle — can be mapped onto an orientational energy budget that explains tissue-level mechanical behavior of epithelial monolayers. Reversible encounters store energy without changing relative orientation; irreversible encounters dissipate energy and alter orientation. The authors quantify these contributions through orientational potentials and an effective second virial coefficient, and argue that their share of total energy storage and dissipation is partial at intermediate density but dominant near jamming. A sympathetic reader would care because the framework offers a constitutive bridge: collision angle and collision frequency become control variables for migration regime, surface tension, and viscoelastic response, and it suggests why jamming and live-cell extrusion arise in crowded regions.

Core claim

The central claim is that cell–cell orientational interactions in migrating epithelial monolayers can be classified as reversible or irreversible based on whether the relative polarity angle is preserved after collision, and that this classification organizes a scale-bridging picture of tissue mechanics. Reversible head-on and glancing collisions store orientational mechanical energy; irreversible ones dissipate energy and disrupt alignment. Using angular moduli, orientational interaction potentials, and a two-dimensional effective second virial coefficient (excluded area per interacting pair), the paper expresses energy storage and dissipation densities and links them to epithelial surface

What carries the argument

The effective second virial coefficient — a two-dimensional excluded-area integral over angularly dependent pair potentials for head-on and glancing collisions — is the central object. It converts pairwise orientational encounter statistics and angular collision moduli into a macroscopic surface-tension term and into effective angular moduli. The lack of left–right symmetry in glancing interactions produces a linear angular term in the excluded area, identified as the source of irreversible reorientation and dissipation, while the quadratic term provides transient elastic storage. A timescale separation between collision duration, interval, persistence time, and steady-state lifetime is invo

Load-bearing premise

The framework stands or falls on the assumption that a cell's brief collisions can be time-averaged into clean pairwise interactions on a slower timescale, so that a dense, actively migrating monolayer behaves like a near-equilibrium gas of pairs — if contacts are too simultaneous or too fast, the virial treatment loses its foundation.

What would settle it

Measure, in the same monolayer, the post-collision angle distribution for head-on and glancing encounters across a density sweep from confluence to jamming. If the fraction of angle-preserving reversible events does not decrease markedly near the jamming density, or if the measured excluded-area-derived surface tension does not show the predicted rise-plateau-drop, the central claim fails. Similarly, if stress relaxation in confluent monolayers is not consistent with the Zener, Kelvin–Voigt, and fractional responses in the respective density regimes, the density-dependent constitutive picture

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, collision angle and collision frequency become control variables for monolayer rheology, so density alone predicts which migration regime and constitutive law applies: Zener, Kelvin–Voigt, or fractional viscoelastic response.
  • The balance of stored versus dissipated orientational energy explains density-dependent outcomes: partial contributions at intermediate density, but dominance near jamming, where irreversible arrests (one or both cells stopping) and live-cell extrusion prevail.
  • Epithelial surface tension follows a virial form: rising almost linearly at low density, plateauing at intermediate density, and dropping rapidly near jamming — a measurable signature of the mechanism.
  • The linear angular term in the excluded area for glancing interactions predicts that glancing encounters necessarily produce dissipation and reorientation, distinguishing them from symmetric head-on collisions.
  • A dimensionless collision-repolarisation number marks the jamming threshold: when collisions arrive faster than cells can repolarise, irreversible arrest outcomes become dominant.
  • The framework implies that live-cell extrusion is a high-density glancing-event outcome (NE-X), linking shear-induced topological defects to tissue rheology and surface tension.
  • It provides a mechanistic interpretation of the Marangoni-like surface-tension gradient effect, connecting inhomogeneous packing density to interfacial tension gradients and enhanced glancing interactions.

Where Pith is reading between the lines

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

  • Editorial inference: A direct test would be to measure post-collision angle distributions in live monolayers across a density sweep; the framework predicts a marked rise in the irreversible fraction near the jamming density, and this could be estimated without fitting the full constitutive model.
  • Editorial inference: Because the virial treatment centers on pairwise events, multi-cellular contacts are handled only through density-dependent frequency. A natural extension is to include third-virial corrections or a density-dependent effective coefficient to test whether pairwise building blocks remain adequate at the highest densities.
  • Editorial inference: The same reversible–irreversible angular classification could be applied to three-dimensional spheroids or organoids, where glancing interactions correspond to shear sliding at cell–cell interfaces; the surface-tension virial link might generalize to bulk surface energy in 3D.
  • Editorial inference: The framework suggests a design principle for experiments: if repolarisation time and collision frequency are measured independently, the collision-repolarisation number could predict the onset of jamming without any further model calibration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a phenomenological multiscale framework that links cell-scale orientational interactions between epithelial cells (head-on versus glancing, reversible versus irreversible) to tissue-scale surface tension and viscoelasticity. It classifies collision outcomes (E, NE-11, NE-10, NE-01, NE-00, NE-X), defines orientational energy storage/dissipation in terms of effective angular moduli, introduces an effective second virial coefficient to connect excluded surface area to packing density, and proposes density-dependent constitutive models (Zener, Kelvin-Voigt, fractional) for three packing regimes. The central claim is that orientational interactions contribute partially at intermediate densities and become dominant near the jamming transition, thereby controlling epithelial surface tension and viscoelasticity. The framework is not derived from a microscopic model and is not quantitatively compared with experimental data; instead, it is assembled from previously proposed constitutive equations and a set of asserted relationships.

Significance. If the framework can be made internally consistent and testable, it would provide a useful organizing language for interpreting how local collision geometry and frequency influence monolayer rheology. Its explicit classification of reversible/irreversible collision outcomes and the proposed dimensionless energy fractions are conceptually appealing and could guide experimental measurements of density-dependent behavior. The paper also makes an effort to identify measurable parameters and suggests out-of-sample prediction as a validation route. However, as stated, the framework's quantitative core—the second virial coefficient link and the dominance of orientational interactions near jamming—rests on assumptions that are not derived or tested. The strength of the paper is therefore in its conceptual synthesis, not in a validated predictive model.

major comments (4)
  1. [§3.4, Eq. (6)] The effective second virial coefficient B2 is a leading-order low-density virial coefficient. The paper claims that because of the assumed timescale separation, fast collision dynamics can be time-averaged into pair potentials, 'mathematically justifying' B2. This is asserted, not derived. More importantly, the claim of dominance is made for the high-density near-jamming regime, where pair truncation is least reliable. The text itself concedes that 'individual cells may experience multiple simultaneous contacts' and that the model is 'formulated in terms of pairwise orientational events.' Thus the density-dependent B2^eff(ρ) is effectively a fitting function rather than a virial coefficient, and the excluded-area interpretation plus Eq. (8) do not follow from the microscopic collision model. This is a load-bearing issue because the surface-tension–virial link is a main quantitative resul
  2. [§3.4, timescale separation] The entire framework depends on the inequality τ_coll ≈ τ_between ≈ minutes, τ_persistence ≈ tens of minutes, τ_ss ≈ hours. But the stated timescales do not provide a strong separation: collision duration and waiting time between collisions are both 'a few minutes,' and the persistence time is only one order of magnitude larger. Pairwise, Markovian, time-averaged potentials are not justified if collisions are frequent and concurrent with persistent motion. This is not merely a technical caveat; it is the foundation for the virial expansion, the excluded-area interpretation, and the subsequent connection to surface tension. The authors should provide a quantitative argument or sensitivity analysis showing that the conclusions are robust when the separation is weak, or temper the claim that the virial formulation has a rigorous NESS basis.
  3. [§3.1 and §5.4, dominance near jamming] The headline conclusion that orientational interactions 'become dominant near jamming' is built into the assumptions rather than obtained from the equations. In §3.1 the high-density regime is defined by f > 1/τ_rep and by asserting that NE-10, NE-01, NE-00, and NE-X fractions 'tend to unity.' Section 5.4 then reports that these interactions 'dominate both energy storage and dissipation.' This is circular: the regime classification already assumes the outcome. A specific calculation—even using the paper's own energy expressions—showing that the dimensionless fractions W_o/W and D_o/D approach values near 1 would be needed to support the claim. Absent that, the statement should be presented as a hypothesis and measured against experimental data.
  4. [§5.2–5.4, Eqs. (10)–(12)] The constitutive models (modified Zener, Kelvin-Voigt, fractional derivative) are imported from earlier works, and the paper asserts without demonstration that orientational interactions alter the parameters in those equations. The statement that Eq. (10) 'reduces to' Eq. (11) under the stated conditions is plausible but not derived; similarly, Eq. (12) is proposed ad hoc. Since these equations are presented as the tissue-scale output of the framework, the authors should at least show how the orientational energy storage/dissipation integrals enter the effective moduli and viscosities. Without this connection, the framework is a sequence of separate models rather than a multiscale derivation.
minor comments (5)
  1. [§3.2, equations after (2)] Several integrals are incompletely typeset: the limits and differential elements are missing or ambiguous in the storage/dissipation surface energy density expressions. This makes them hard to evaluate and lessens the 'computable basis' claimed for the framework.
  2. [§2 and §6] There are typographical errors such as 'orientatiomal,' 'specially,' and inconsistent notation for arrows over vectors. The glossary and main text sometimes use 'surface tension' and 'interfacial tension' with overlapping definitions; a concise notational table would improve readability.
  3. [Table 2] The 'Estimator' column lists methods such as 'hidden-Markov model' and 'iFEM Calibration' without references or enough detail. Since the paper is a modeling paper, the estimation section would benefit from one concrete example of an estimator or a reference to the implemented procedure.
  4. [Appendix C] The L1-scheme description is standard, but the claim that 'sensitivity analysis by halving the time-step' is performed should be reported or moved to a future-work sentence, unless results of the convergence check are actually shown.
  5. [§3.3, Eq. (5)] The term 'D(a) ∇² a' uses a diffusion coefficient that is later called isotropic, but the preceding paragraph says anisotropy emerges through the source term. This is acceptable, but it would help to state explicitly that D(a) is a scalar and all anisotropy arises from the coupling terms.

Circularity Check

3 steps flagged

Virial/modulus link is definitional; 'dominant near jamming' is an assumption of the regime definition; key density-regime and surface-tension inputs are taken from the authors' own prior work.

specific steps
  1. self definitional [§3.2.1, §3.4 (Eq. 6), §3.4.1]
    "E_ho^E(θ) = 1/2 k_ho^E (θ_1 − θ_2)^2 ... φ_ho(r,θ) = φ(r) + E_ho(θ) ... are the total interaction potential for glancing and head-on interactions ... Consequently, the effective angular modulus for head-on interactions is k_ho = <ε> B2_ho / ..., while for glancing interactions it is k_gl = <ε> B2_gl / ..."

    B2^ho and B2^gl are defined in Eq. 6 by integrals whose Boltzmann factors contain E_ho(θ) and E_gl(θ), i.e. exactly the harmonic angular potentials built from k_ho and k_gl. Section 3.4.1 then reads k_ho and k_gl back out of these same B2 coefficients. The 'link' between the effective angular modulus and the second virial coefficient is therefore an identity among definitions, not an independent microscopic derivation: changing the input moduli changes B2, and extracting the moduli from B2 recovers the same inputs. The excluded-area interpretation and the subsequent surface-tension connection inherit this circularity.

  2. self definitional [§3.1 (high-density regime) vs. §5.4 and Abstract/Conclusion]
    "The frequency of cell-cell orientational interactions is higher than the threshold, i.e., f > 1/τ_rep and the fraction of irreversible interactions NE-10, NE-01, NE-00, and NE-X tends to unity. ... In the high-density regime near jamming, irreversible head-on (NE 10, 01, 00) and glancing (X) interactions dominate both energy storage and dissipation, effectively controlling the viscoelastic response of the monolayer. Consequently, the fractions of total energy storage ... and dissipation ... satisfy the conditions: (i) ... → 1 and (ii) ... → 1."

    The headline claim that orientational interactions 'become dominant near jamming' is not computed from the model. In §3.1 the high-density regime is defined by setting f > 1/τ_rep and by taking the irreversible NE-10/01/00/X fractions to unity; §5.4 then reports the same conditions as a derived consequence ('Consequently ... →1'). The density-regime behavior (convective → diffusive → sub-diffusive, and dominance of orientational storage/dissipation) is thus installed as an assumption and then restated as a prediction in the abstract and conclusion.

  3. self citation load bearing [§3.1 and §4 (Eq. 8)]
    "Consequently, three cell-packing density regimes can be distinguished based on experimental data from the literature (Pajic-Lijakovic et al., 2025; 2026) ... Consequently, the epithelial surface tension can be expressed as (Pajic-Lijakovic et al., 2023): ..."

    The central density-regime architecture (orientational-interaction dominance, migration-mechanism transitions) and the surface-tension/virial relation of Eq. 8 are imported from refs. 48–52, all from the same author group. The present manuscript does not re-derive these relations from the collision model of §§3.2–3.4 or benchmark them against new data. Because these self-citations supply the load-bearing bridge from orientational collisions to tissue rheology and surface tension, the claimed multiscale link is not self-contained in this paper.

full rationale

This is a phenomenological framework rather than a data-fitting paper, and several components—the geometric classification of head-on/glancing outcomes, the harmonic storage forms, and the constitutive models—are legitimate model construction. However, two central 'results' collapse into their inputs. First, the effective angular modulus is not derived from the second virial coefficient: B2^ho and B2^gl are defined as integrals over potentials that already contain E_ho(θ)=1/2 k_ho θ^2 and E_gl(θ)=1/2 k_gl θ^2, after which §3.4.1 reads k_ho and k_gl back out of those same B2 values; the virial/excluded-area link is definitional. Second, the headline density dependence—orientational contributions become dominant near jamming—is placed into §3.1 as the defining property of the high-density regime (NE-10/01/00/X fractions tending to unity) and then reported in §5.4 and the abstract as a conclusion. The regime classification and Eq. 8 also lean on the authors' own prior papers, so the collision-to-rheology chain is not independently established here. This is partial circularity (6/10), not total: the framework's classification and constitutive equations are stated assumptions that could be tested against external data, but such tests are not provided in this manuscript.

Axiom & Free-Parameter Ledger

9 free parameters · 6 axioms · 3 invented entities

The ledger shows that the central framework depends on a moderately large set of unmeasured parameters and on the NESS/virial assumption. None of the central quantitative quantities is fitted to data in this paper; most are placeholders for future experimental estimation.

free parameters (9)
  • Interaction outcome probabilities p(E), p(NE-11), p(NE-10), p(NE-01), p(NE-00), p(NE-X) = not assigned; only regime inequalities are stated
    Introduced in Table 1 and §3.1 as stochastic outcome probabilities; no measured values or calibration protocol are given.
  • Collision frequency f and average repolarisation time τ_rep = not assigned
    Their product forms the collision-repolarisation number Cr = f τ_rep, which sets the three density regimes in Eq. (2); only the MDCK repolarisation time is cited, not the frequency.
  • Effective angular moduli k_ρ, k_θ for head-on and glancing interactions = not assigned
    Enter storage/dissipation energies in §3.2; Table 2 proposes AFM/traction-force calibration but supplies no values.
  • Angular tolerance δθ defining head-on vs glancing bins = π/24 (hand-set)
    Stated in §3 as a fixed computational tolerance; this choice controls how interactions are classified.
  • Cell packing density thresholds ρ_confl and ρ_jam = not assigned (ρ_jam described as an order of magnitude above confluence)
    The regime boundaries in §3.1 are adapted from earlier work but not quantitatively fixed for the model.
  • Energy quantum per unit area ⟨E_q⟩ = ⟨E_c⟩/⟨A_c⟩ = not assigned
    Scale entering the virial coefficient integrals in §3.4; elastic, adhesive, and contractility contributions are listed but not valued.
  • Orientational chemomechanical coupling coefficient χ, morphogen diffusivity D_s, deactivation rate = not assigned
    Define the informational flux and signalling balance, Eqs. (3)–(5); Table 2 gives ranges of modalities but no numbers.
  • Lennard-Jones interaction strength ε, exponents n=4, m=2, zero-crossing σ0 = n=4, m=2 from Kang et al. 2021; σ0 from Deforet et al. 2014
    Adopted from cited literature for the positional pair potential; load-bearing for the B2 integrals but not fitted here.
  • Fractional derivative order α = not assigned
    Introduced in Eq. (12); α is related to the sum of model weights, but no empirical determination is provided.
axioms (6)
  • ad hoc to paper Active, dissipative cell monolayers can be described as a non-equilibrium steady state with a strict separation of timescales, justifying time-averaged effective pair potentials and a virial expansion.
    §3.4; this premise is load-bearing for the entire thermodynamic/virial treatment and is asserted without empirical verification.
  • ad hoc to paper The discrete outcome categories (E, NE-11, NE-10, NE-01, NE-00, NE-X) span the relevant orientational interaction dynamics.
    Table 1 introduces the categories with stochastic noise variables but no closure argument showing they are exhaustive or dynamically sufficient.
  • domain assumption The collision-angle distribution is isotropic, ρ(θ) = 1/π, in the intermediate-density regime.
    §3.2.2 simplifies the distribution to a uniform one, which is in tension with the anisotropic/plithotaxis features discussed elsewhere in the paper.
  • ad hoc to paper Morphogen signalling can be collapsed to a dimensionless activity a(x,t) with linear gradient coupling and linear production terms.
    Eqs. (3)–(5) define the informational flux and activity balance; the linear forms are choices, not derived from data.
  • domain assumption Macroscopic constitutive laws (Zener, Kelvin–Voigt, fractional viscoelasticity) can be assigned to the respective density regimes.
    §5.2–5.4 import these models from prior work without parameter identification or validation against new data in this paper.
  • standard math Caputo fractional derivative and its L1 approximation are standard mathematical tools.
    Used in Eq. (12) and Appendix C; mathematically unproblematic.
invented entities (3)
  • Orientational interaction potential U_θ(r,θ) no independent evidence
    purpose: Encodes angular storage and dissipation in a pair-potential form so that virial machinery can be applied to collisions.
    Defined through effective angular moduli and an energy quantum; no direct measurement protocol isolates it from other adhesion/cortex energies.
  • Informational flux J_s no independent evidence
    purpose: Couples mechanical orientation gradients to morphogen gradients in the balance equations (3)–(4).
    Explicitly described as a phenomenological construct; no independent observable is proposed to measure it.
  • Orientational excluded-area contributions ΔA_excl(θ) no independent evidence
    purpose: Provides the geometrical interpretation connecting second virial coefficients to effective angular moduli.
    Obtained by Taylor-expanding B2; no direct experimental estimate of orientational excluded area is provided.

pith-pipeline@v1.3.0-alltime-deepseek · 25921 in / 16617 out tokens · 172969 ms · 2026-08-01T21:43:47.569355+00:00 · methodology

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read the original abstract

Collective migration of epithelial monolayers emerges from the interplay between mechanical interactions and biochemical signalling. Here, we present a phenomenological mechanobiological framework linking cell-scale orientational interactions to tissue-scale mechanics. We distinguish reversible and irreversible head-on and glancing collisions, showing that reversible interactions store orientational mechanical energy while preserving collision geometry, whereas irreversible interactions dissipate energy and alter cell orientation. The balance between energy storage and dissipation governs collective migration, mechanical feedback, and density-dependent processes including cell jamming and live cell extrusion. These interactions regulate cell elasticity, contractility, and adhesion, thereby modifying epithelial surface tension and the effective viscoelastic response of the monolayer. We quantify these effects using orientational interaction potentials, an effective second virial coefficient, and dimensionless measures of stored and dissipated orientational energy. The relative contribution of these mechanisms increases with cell packing density, becoming dominant near the jamming transition. This framework provides a constitutive interpretation connecting collision-induced orientation dynamics with emergent epithelial rheology and suggests how density-dependent interaction regimes shape collective migration and tissue viscoelasticity.

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Reference graph

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