{"id":"ab533fdc-7935-4ea1-b4da-110f4ea08ecc","arxiv_id":"2502.03927","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A non-motile growing colony develops tensile stress because rim growth drives an inward cell flux whose friction stretches the tissue; analytic stress profiles and a phase diagram are provided.","lead":"Growing cell colonies can be placed under tension even when the cells exert no outward motility force. The paper shows, by simulation and a simple mechanical theory, that growth itself, combined with friction against the substrate, pulls colonies into tension and predicts a measurable inward flow of cells.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The expansion-speed prediction is partly circular: Eq. (11)'s ΔkΔx is fitted from the measured front speed it is then said to predict; an independent measure of surface growth would settle it.","rationale":"Reader's conditional verdict identifies exactly the same weak point: the surface-growth amplitude is an input calibrated from the data the model predicts. I agree with that assessment. The central conceptual claim—that a colony growing under negative homeostatic pressure with a proliferating rim can be tensile even without motility—is directly evidenced by the simulation snapshots and stress profiles, and the analytic mechanism (boundary growth → inward flux → friction → tension) is internally consistent. What is not established is the quantitative predictive power. Since ΔkΔx is obtained from the expansion speed, comparing Eq. (11) with the same expansion speed is tautological. The paper's statement that 'all parameters measured independently' is too strong for this term. A local division-rate measurement would settle whether the fitted ΔkΔx is physically real or an effective fit parameter. If the local measurement reproduces the expansion speed, the concern disappears and the quantitative claim can stand. If not, the paper should either present Eq. (11) as a consistency relation or re-fit with parameter uncertainty. No more severe flaw is apparent; the existence claim and phase diagram are supported by simulation. Therefore the verdict should remain CONDITIONAL, not be raised or lowered.","tokens_in":14590,"tokens_out":6356,"duration_ms":67924,"concrete_test":"In a non-motile quasi-1d simulation (e.g. ε*=1, G*=11.4, v0*=0), bin division events in the comoving frame and integrate the local growth-rate excess over the boundary layer to obtain ΔkΔx directly, without using the measured front speed. Use that value with independently measured PH, κ, ρ, γ in Eq. (11) and compare with the measured v(x0) for G*=8.6, 10, 11.4, 12.8. Also compare the measured width of the enhanced-growth region with the assumed Δx*=0.7. If the predicted speeds deviate by more than ~10% from the simulated v(x0), the fitted ΔkΔx was absorbing model error and the expansion-speed prediction is not demonstrated; if they match, the circularity concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The non-motile tensile mechanism rests on the surface-growth term ΔkΔx in Eq. (1). For PH<0 and v0=0, this term is the source of the inward cell flux whose friction builds the tensile stress; without it Eq. (11) gives a negative expansion speed and no phase II. The key quantitative claim is v(x0)=PH sqrt(κ/(4ργ))+ΔkΔx. The paper says after Eq. (11): 'We use this constant expansion speed to obtain ΔkΔx.' SI Fig. S7 confirms that the surface contribution is obtained as the difference between the directly measured front speed and the independently computed bulk term PH sqrt(κ/(4ργ)). Thus the agreement between Eq. (11) and the simulated front speeds used for calibration is a consistency check, not an independent prediction. The pressure and velocity profile comparisons in Fig. 3 are less circular—PH, κ, ρ, γ are measured separately and Δx is estimated—but Δk also enters the piecewise profile (Eq. S6), so fixing it through v partially constrains those profiles too. The physical motivation for boundary-enhanced growth is plausible, and the tensile stress in non-motile colonies is a direct simulation observation, so the existence claim survives. The load-bearing weakness is quantitative: the central expansion-speed prediction is calibrated in-sample on the quantity it claims to predict.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript combines 2PG-type agent-based simulations and a one-dimensional continuum theory to argue that cell colonies expanding on a substrate can be under tensile stress even in the absence of motility forces. The proposed mechanism is that cells near the free boundary grow faster than the bulk, producing an inward cell flux; substrate friction opposes this flux and generates tension when the homeostatic pressure is negative. The authors derive exponential pressure profiles, a constant expansion speed v(x0) = PH sqrt(kappa/(4 rho gamma)) + Delta k Delta x, and a phase boundary between finite and indefinitely growing colonies. They extend the model to motile colonies, where boundary polarization adds a motility tension term, and compare the resulting profiles and speeds with simulations.","tokens_in":14893,"tokens_out":2768,"duration_ms":28984,"significance":"If the central claim holds, the paper offers a mechanistically distinct route to tensile stress in freely expanding monolayers, complementing the established motility-alignment and confinement-sorting explanations. The analytical model is transparent, the simulation method is standard, and the predicted retrograde flow in non-motile tensile colonies is a concrete, falsifiable experimental target. The comparison between analytic pressure profiles and simulations in Fig. 3 is largely convincing for the shape of the profiles. However, the quantitative predictive claim for the expansion speed is weakened by the in-sample calibration of the surface-growth parameter Delta k Delta x from the very speed the theory is said to predict, as discussed below. The existence of tension in non-motile colonies is a direct simulation observation and is not undermined by this calibration issue.","major_comments":[{"comment":"The central quantitative claim v(x0) = PH sqrt(kappa/(4 rho gamma)) + Delta k Delta x is presented as a prediction, but the text states 'We use this constant expansion speed to obtain Delta k Delta x.' SI Fig. S7(b) confirms that the surface-growth contribution is obtained as the difference between the total measured front speed and the independently computed bulk term. Therefore the agreement between Eq. (11) and the simulated front speed used for calibration is a consistency check, not an independent prediction. The linearity in G of the simulated speed is also not an independent test, because Delta k Delta x is derived from that speed and could absorb the same linear dependence. Please either measure Delta k locally in the simulations, provide a microscopic derivation of its value, or explicitly re-frame Eq. (11) as a parameterized relation rather than a parameter-free prediction.","section":"Section I, after Eq. (11) and SI Fig. S7"},{"comment":"The Fig. 3 caption claims that the theory curves are 'calculated from the piecewise solution with all parameters measured independently (i.e. not fitted)' and that only Delta x is estimated. This conflicts with the main-text statement that Delta k Delta x is obtained from the constant expansion speed. Since Delta k enters the piecewise pressure profile in Eq. (S6), the pressure and velocity comparisons in Fig. 3 are partially constrained by the fitted quantity, not fully independent. The manuscript should clearly list, for every parameter entering Eqs. (S6)-(S7), whether it is measured in a separate simulation, estimated from a structural assumption, or calibrated from the expansion speed.","section":"Main text Fig. 3 caption vs. Section I, after Eq. (11)"},{"comment":"The existence of indefinite tensile growth for PH < 0 rests entirely on the surface-growth term Delta k Delta x in Eq. (1): without it, Eq. (11) gives a negative expansion speed and no phase II. The physical motivation for boundary-enhanced growth is plausible, but the manuscript does not provide a direct measurement of the local growth rate k(x) in the simulation rim, nor a derivation of Delta k from the 2PG microscopic rules. Given that this term is load-bearing, please report the measured k(x) profile in the boundary layer and compare it with the assumed step/delta form, or state clearly that the surface growth amplitude is an inferred effective parameter.","section":"Section I, Eq. (1) and phase-II mechanism"}],"minor_comments":[{"comment":"The manuscript contains many typographical errors, including 'optianed', 'boudnary', 'therory', 'shortcommings', 'enabeled', 'reaveals', 'arrise', 'mechanims', 'accrding', 'consitituting', and 'partcile'. A thorough proofreading pass is needed.","section":"Throughout"},{"comment":"The text refers to 'Main text Fig.7(a)' when comparing quasi-1d and 2d expansion speeds, but the main text has Fig. 6(a) for this comparison; please correct the cross-reference.","section":"SI Section S2"},{"comment":"The caption uses 'B^* = 11.4' where the context indicates this should be 'G^* = 11.4'.","section":"SI Fig. S10 caption"},{"comment":"The description of the pressure peak for expanding fronts with PH < 0 is qualitatively clear, but the figure inset is too small to see the predicted boundary pressure peak; a larger inset or an explicit zoom would help the reader verify this nontrivial prediction.","section":"Main text Fig. 3(b) and Section I, paragraph after Eq. (11)"}],"recommendation":"major_revision","confidential_remarks":"The paper's core observation — that non-motile expanding colonies can be under tension — is robust and interesting, and the analytical framework is a useful contribution. The main concern is the calibration of Delta k Delta x from the expansion speed, which should be addressed by an independent measurement or by an honest reframing of the quantitative claim. I do not see this as requiring rejection; the phenomenological mechanism and the experimental retrograde-flow prediction retain value even if the expansion-speed comparison is downgraded from a prediction to a consistency check."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, what you should know: this paper shows that non-motile growing colonies develop tensile stress, purely from boundary-enhanced growth plus substrate friction. That is a new result relative to the cited literature, which ties tension to outward-oriented motility. The authors build a simple continuum model that reproduces the simulation pressure and velocity profiles with mostly independently measured parameters, and they make a sharp, testable prediction: tensile non-motile colonies should show retrograde cell flow. The two-particle growth simulation is standard, and the stress measurement technique is reasonable. Credit is due: the central existence claim is direct simulation observation, and the analytic derivation is clear and internally consistent. The paper honestly flags its own limitations, including the absence of motility alignment and the reliance on linear friction. Now the soft spot, confirmed on reading: the quantitative expansion-speed prediction in Eq. (11) is partly calibrated in-sample. The paper states, after Eq. (11), \"We use this constant expansion speed to obtain ΔkΔx.\" So the surface-growth amplitude, which is the key input for the tensile phase, is fitted to the very front speed the model then claims to predict. The agreement is a consistency check, not a fully independent validation. That said, the pressure and velocity profile comparisons (Fig. 3) are less circular—PH, κ, ρ, γ are measured separately, and Δx is estimated—so the mechanism itself is not in doubt. The matching to Trepat et al. is also parameter-choice dependent, without robustness analysis. What would settle it: an independent measurement or derivation of ΔkΔx, plus release of simulation code and data. The paper is worth engaging seriously; the physics is plausible, the writing is honest, and the retrograde-flow prediction is falsifiable in experiments. I would accept it for peer review and ask for the calibration issue to be addressed, not because the result is wrong, but because the headline quantitative claim currently overstates its predictive status. For a reading group it would spark good discussion. I would not cite it for the expansion-speed formula without caveat, but I would cite it for the mechanism.","headline":"A genuinely new mechanism for tensile stress in growing colonies without motility, with a clean analytic model and honest calibration; the expansion-speed prediction is partly self-consistency but the existence claim holds.","tokens_in":15354,"tokens_out":530,"would_cite":true,"duration_ms":7034,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A cell colony can develop tensile stress with no motility force at all, driven by growth plus substrate friction.","keywords":["tissue mechanics","homeostatic pressure","tensile stress","cell colony growth","substrate friction","retrograde flow","two-particle growth model","active matter"],"falsifier":"Measure the velocity field inside a non-motile expanding colony that is under tension: the model predicts a retrograde inward flow of cells throughout the interior, so the absence of such a flow would falsify the mechanism.","tokens_in":14390,"feed_emoji":"🧫","tokens_out":6191,"duration_ms":55933,"temperature":0.7,"pith_summary":"The paper sets out to show that the tensile stress observed in expanding cell colonies does not require cells to push outward. In its model, cells proliferate faster in a thin rim at the free boundary; those extra cells flow inward, and substrate friction resists that flow, stretching the tissue into tension. The authors derive analytic pressure and velocity profiles, a constant expansion speed, and a phase diagram in which colonies can grow indefinitely while under tension even when the homeostatic pressure is negative. Adding random motility strengthens the tension and reproduces the stress profile reported in [7]. If correct, the work gives a purely mechanical origin for tissue tension and makes a testable prediction of retrograde cell flow.","feed_headline":"Growth plus friction, not motility, can put cell colonies under tension","feed_subtitle":"Boundary growth plus substrate friction generates tensile stress, and predicts a testable inward cell flow.","key_machinery":"The load-bearing object is the growth law $k = \\kappa(P_H - P) + \\Delta k\\Delta x\\,\\delta(x - x_0)$, which couples proliferation to mechanical stress through a bulk response coefficient $\\kappa$ and a surface term $\\Delta k\\Delta x$: cells near the free boundary proliferate faster because growth there is mechanically cheaper. From that law, the continuity equation $\\partial_x v = k$, and force balance with linear substrate friction, the argument reduces the stress field to the screened Poisson equation $\\partial_x^2 P_x = (P_x - P_H)/\\lambda^2$, whose solution is the hyperbolic-cosine pressure profile of Eq. (7). The same growth law, with a motility traction term added to the force balance, yields the motile pressure profile and the generalized expansion speed. The crucial entity is therefore the combination of negative homeostatic pressure and rim growth: the rim produces an inward flux, friction converts that flux into tension, and the tension suppresses growth in the bulk.","core_discovery":"The central discovery is that tension arises from the interplay of a negative homeostatic pressure and boundary-enhanced growth. The growth rate is written as $k = \\kappa(P_H - P) + \\Delta k \\Delta x\\,\\delta(x - x_0)$, with the surface term representing faster growth in a thin layer at the free edge. Combining this with force balance, where substrate friction is the only external force, $\\partial_x\\sigma_{xx} = 2\\rho\\gamma v$, gives a screened Poisson equation for the pressure, $P_x = P_H\\bigl(1 - \\cosh(x/\\lambda)/\\cosh(x_0/\\lambda)\\bigr)$ with $\\lambda^2 = (\\rho\\kappa\\gamma)^{-1}$. For homeostatic pressures between a critical negative value $P_H^c = -\\Delta k\\Delta x\\sqrt{4\\rho\\gamma/\\kappa}$ and zero, colonies expand indefinitely at constant speed $v(x_0) = P_H\\sqrt{\\kappa/(4\\rho\\gamma)} + \\Delta k\\Delta x$ while their interior is tensile; the tension is balanced by friction against an inward retrograde flow of cells. Motility adds a boundary-localized traction that generates additional tension and extends the tensile-growth phase, and the two-dimensional circular case reduces to the same physics with growth proportional to the perimeter.","pith_inferences":["The same mechanism should apply to other proliferating tissues or colonies on frictional substrates, wherever growth is enhanced at free edges and friction resists inward flow; this is an extension the paper does not develop.","Because the surface growth term $\\Delta k\\Delta x$ is partly calibrated from the expansion speed it later predicts, a full test of the theory would require measuring $\\Delta k$ and $\\Delta x$ independently; absent that, the quantitative match is less decisive.","A simultaneous measurement of stress and velocity fields in an expanding monolayer would separate this growth-friction mechanism from motility-alignment mechanisms: the former predicts inward flow correlated with tension, while alignment models predict outward-oriented traction.","The predicted exponential buildup length $\\lambda$ could be extracted experimentally from stress and velocity profiles and compared with the bulk response coefficient $\\kappa$ measured by independent deformation experiments."],"forward_implications":["Non-motile tensile colonies should show a retrograde flow: cells move inward from the proliferating rim toward the center, except in a thin layer at the boundary; this is directly measurable by particle image velocimetry.","The expansion speed of an indefinitely growing colony is constant and independent of colony size; it is linear in the growth force for non-motile colonies and quadratic in the motility speed for motile ones.","Motility generates its own boundary tension $T$ that is quadratic in $v_0$ and linear in $G$, and it widens the range of negative homeostatic pressures for which a colony can grow indefinitely under tension.","In two dimensions, growth is perimeter-controlled: cell number grows as $t^2$, radius grows linearly, and fingers at the frontier do not lead to fractal boundaries.","The analytical profiles allow experimental stress profiles to be decomposed into friction and motility contributions, providing a procedure for inferring the underlying mechanics from traction measurements."],"supporting_citations":[{"why":"Experimental stress measurements in expanding monolayers that the model matches and explains.","marker":"[7]"},{"why":"The two-particle growth (2PG) simulation method used for all tissue simulations.","marker":"[8]"},{"why":"Establishes negative homeostatic pressure and the notion of a tensile homeostatic state that the model builds on.","marker":"[25]"},{"why":"Mechanical control of cell flow in spheroids; basis of the pressure-dependent growth law.","marker":"[2]"},{"why":"Supplies the adhesion and active Brownian motility model that is merged with 2PG growth.","marker":"[16]"},{"why":"Gives the screening length $\\lambda^2 = (\\rho\\kappa\\gamma)^{-1}$ and interface dynamics formalism used for the stress profile.","marker":"[26]"},{"why":"Stress clamp experiments showing that pressure slows growth, motivating the homeostatic-pressure growth law.","marker":"[1]"}],"fun_headline_variants":["Friction, not crawling, explains tension in growing cell colonies","Boundary growth plus friction yields tension and inward flow","Tension in colonies without motility: a simple mechanical model","Growing tissue tension from boundary growth and substrate friction","Tensile stress in colonies arises from growth and friction, not cell motion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole mechanism depends on the assumption that cells in a thin rim at the colony boundary proliferate faster than cells in the bulk; if that surface growth advantage disappeared, no inward flux would form and tension would not arise.","fun_headline_variants_meta":{"raw":{"variants":["Friction, not crawling, explains tension in growing cell colonies","Boundary growth plus friction yields tension and inward flow","Tension in colonies without motility: a simple mechanical model","Growing tissue tension from boundary growth and substrate friction","Tensile stress in colonies arises from growth and friction, not cell motion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000252,"raw_usage":{"total_tokens":1560,"prompt_tokens":946,"completion_tokens":614,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":531}},"tokens_in":562,"tokens_out":614,"duration_ms":5845,"temperature":1.0,"reasoning_tokens":531,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T00:12:45.819507+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the velocity field inside a non-motile expanding colony that is under tension: the model predicts a retrograde inward flow of cells throughout the interior, so the absence of such a flow would falsify the mechanism.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Experimental stress measurements in expanding monolayers that the model matches and explains."},{"cited_title":"& Elgeti, J","cited_arxiv_id":null,"evidence_quote":"The two-particle growth (2PG) simulation method used for all tissue simulations."},{"cited_title":"& Elgeti, J","cited_arxiv_id":null,"evidence_quote":"Establishes negative homeostatic pressure and the notion of a tensile homeostatic state that the model builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Mechanical control of cell flow in spheroids; basis of the pressure-dependent growth law."},{"cited_title":"& Elgeti, J","cited_arxiv_id":null,"evidence_quote":"Supplies the adhesion and active Brownian motility model that is merged with 2PG growth."},{"cited_title":"& Elgeti, J","cited_arxiv_id":null,"evidence_quote":"Gives the screening length $\\lambda^2 = (\\rho\\kappa\\gamma)^{-1}$ and interface dynamics formalism used for the stress profile."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Stress clamp experiments showing that pressure slows growth, motivating the homeostatic-pressure growth law."}],"review_version":1}