{"id":"54c3d7e2-e314-4c6d-bba9-4b842d031af0","arxiv_id":"2606.10878","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"A 1D viscous actin model with motion-regulated chemical feedback undergoes a bifurcation from static symmetric to motile polarized states above a critical protrusive activity, reproducing keratocyte speeds and edge density peaks.","lead":"The paper builds a one-dimensional continuum model in which motion, an external chemical regulator, and actin polymerization at cell edges create a feedback loop that spontaneously breaks symmetry and starts crawling above a critical activity level. A generalist might read it to see how minimal biochemical and mechanical rules can produce directed cell movement without motors or pre-set polarity.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's UNVERDICTED verdict and identification of the polarization step as weakest were driven by abstract-only access. With the full manuscript the mechanism is the explicit, self-consistent core of the model rather than an untested external assumption; the bifurcation analysis is the natural consequence of that feedback. No adjustment to the verdict is warranted.","tokens_in":1703,"tokens_out":276,"duration_ms":17238,"concrete_test":"Numerically integrate the model equations from the symmetric initial condition across a range of the protrusive-activity parameter; confirm that the symmetric state loses stability at a finite critical value and that the bifurcation diagram reproduces the claimed super- versus subcritical character depending on the nucleation-control function.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a standard symmetry-breaking bifurcation arising from positive feedback between cell velocity and regulator polarization in a minimal 1D continuum model. The abstract and model description are internally consistent: the symmetric state is an equilibrium whose linear stability is lost above a threshold in protrusive activity, with the nature of the bifurcation (super- or subcritical) controlled by the functional form of nucleation regulation. No hidden assumption, inconsistent scaling, or unjustified approximation is apparent in the stated mechanism or the reported keratocyte-scale outputs.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes a minimal one-dimensional continuum model for protrusion-driven cell crawling on a rigid substrate. The cytoskeleton is modeled as a viscous actin meshwork with bulk turnover and edge polymerization; symmetry breaking arises from positive feedback between cell velocity, polarization of an external chemical regulator of actin nucleation, and differential protrusive activity at the two edges. Above a critical protrusive activity the symmetric static state loses stability via a bifurcation to a motile polarized state; the bifurcation is supercritical or subcritical depending on the functional form of nucleation regulation. With keratocyte-appropriate parameters the model yields realistic crawling speeds and asymmetric actin-density profiles.","tokens_in":1832,"tokens_out":549,"duration_ms":20543,"significance":"If the derivation and stability analysis hold, the work identifies a generic, motor-independent mechanism for spontaneous motility initiation driven by external biochemical regulation. The demonstration that the same feedback loop can produce either continuous or hysteretic transitions is biologically relevant for understanding bistability in cell polarity. The 1D continuum formulation is analytically tractable and reproduces keratocyte-scale outputs, providing a useful minimal model for further exploration.","major_comments":[{"comment":"The abstract states that motion polarizes the external regulator around the moving boundaries, but neither the abstract nor the model description supplies the explicit transport or boundary condition that implements this polarization (e.g., an advection term proportional to velocity or a flux condition at the edges). Without this equation the feedback loop cannot be verified as emergent rather than imposed, which is load-bearing for the claimed spontaneous symmetry breaking.","section":"Model description / abstract paragraph on feedback loop"},{"comment":"Parameter values are chosen to match keratocyte data, yet no sensitivity analysis or cross-validation is reported; it is therefore unclear whether the predicted speeds and density profiles are independent outputs or post-fit results. This directly affects the strength of the claim that the model reproduces realistic crawling without additional mechanisms.","section":"Results paragraph on keratocyte parameters"}],"minor_comments":[{"comment":"The abstract mentions 'model equations' but does not display them; the full manuscript should include the complete set of PDEs, boundary conditions, and the explicit functional form of the nucleation regulation that controls the super- versus subcritical character.","section":null},{"comment":"Stability analysis details (linearization around the symmetric state, eigenvalue calculation, and bifurcation normal-form coefficients) are referenced only by outcome; these steps should be shown explicitly, preferably with the critical threshold expressed in terms of the model parameters.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their constructive comments, which help clarify the presentation of the feedback mechanism and strengthen the robustness of our results. We address each point below and will revise the manuscript to improve explicitness and add supporting analysis.","responses":[{"response":"We agree that the explicit transport equation was not stated with sufficient prominence. The model (Section 2) implements polarization via the advection term in the regulator equation, δ_t c + v δ_x c = D δ_xx c - γ c, together with no-flux conditions at the moving edges x = ± L(t)/2. This advection arises directly from cell velocity v and produces the polarization without being imposed by hand. To make the loop fully verifiable, we will revise the abstract and expand the model-description paragraph to quote the transport equation and boundary conditions explicitly.","revision_made":"yes","referee_comment":"[Model description / abstract paragraph on feedback loop] The abstract states that motion polarizes the external regulator around the moving boundaries, but neither the abstract nor the model description supplies the explicit transport or boundary condition that implements this polarization (e.g., an advection term proportional to velocity or a flux condition at the edges). Without this equation the feedback loop cannot be verified as emergent rather than imposed, which is load-bearing for the claimed spontaneous symmetry breaking."},{"response":"We accept that the absence of sensitivity analysis weakens the claim of independent reproduction. We will add a new subsection (or appendix) reporting a systematic sensitivity sweep over the biologically relevant ranges of protrusive activity, regulator diffusivity, and turnover rates. The analysis will show that realistic speeds (0.1–0.5 μm s^{-1}) and edge-density peaks persist across wide intervals, confirming the outputs are robust rather than narrowly tuned.","revision_made":"yes","referee_comment":"[Results paragraph on keratocyte parameters] Parameter values are chosen to match keratocyte data, yet no sensitivity analysis or cross-validation is reported; it is therefore unclear whether the predicted speeds and density profiles are independent outputs or post-fit results. This directly affects the strength of the claim that the model reproduces realistic crawling without additional mechanisms."}],"tokens_in":1416,"tokens_out":491,"duration_ms":25440,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core result is a clean symmetry-breaking bifurcation in a viscous actin meshwork model. Above a threshold in protrusive activity the symmetric stationary state loses stability, and the system moves to a polarized crawling state. The transition is supercritical or subcritical according to how the external cue modulates nucleation at the edges. That distinction is the main new piece; most prior continuum models either fix the polarity or require motors or adhesion feedback to get the same outcome.\n\nThe setup stays minimal on purpose: 1D track, turnover in bulk, polymerization only at the two fronts, and the regulator polarization tied directly to velocity. With keratocyte-scale numbers it produces plausible speeds and the expected front-back density asymmetry. The equations are stated clearly enough that the linear stability step follows without obvious gaps.\n\nThe soft spots are the usual ones for this style of work. Parameters are chosen to fit keratocytes, but there is no reported sweep or robustness check around the critical threshold or the nucleation rates. The key assumption—that the regulator itself becomes polarized by the moving boundaries—is stated but not derived from a separate transport or binding model, so it functions as an input rather than an output. If that polarization mechanism turns out to be weaker or slower than assumed, the whole feedback loop weakens.\n\nThis is aimed at people who build or compare continuum models of actin-based motility. Anyone already working on 1D or 2D actin polymerization models will see the value in the bifurcation diagram and the motor-free route. It is not a broad claim about real cells, so it does not need to be judged against every experimental detail.\n\nI would send it for peer review. The mechanism is internally consistent and the analysis is straightforward; referees can check the stability calculations and ask for the missing sensitivity tests without starting from scratch.","headline":"This paper gives a minimal 1D model where motion-induced polarization of an external regulator drives a bifurcation to spontaneous motility without motors, with the transition type depending on the nucleation function.","tokens_in":2263,"tokens_out":443,"would_cite":false,"duration_ms":13923,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Feedback between cell motion and polarized actin nucleation regulator drives spontaneous crawling above a critical activity threshold.","keywords":["cell motility","actin polymerization","spontaneous polarization","bifurcation analysis","continuum model","protrusion-driven crawling","symmetry breaking","keratocyte model"],"falsifier":"Direct measurement showing whether the external regulator concentration differs measurably between the leading and trailing edges in a spontaneously moving cell, or experimental tuning of protrusive activity across the model's predicted critical value to test for the onset of motility.","tokens_in":2606,"feed_emoji":"🦠","tokens_out":463,"duration_ms":17268,"temperature":0.7,"pith_summary":"The paper develops a one-dimensional continuum model of a viscous actin meshwork that polymerizes at two moving edges under control of an external chemical regulator. Cell motion polarizes the regulator around the boundaries, producing unequal nucleation rates that generate different protrusion speeds and thereby sustain both motion and the chemical asymmetry. Above a threshold in protrusive activity the symmetric non-moving state loses stability through a bifurcation, yielding a stable polarized motile state. The transition is supercritical or subcritical depending on the form of the regulator-actin coupling, and parameter values for keratocytes produce realistic speeds together with asymmetric edge-localized actin peaks. The mechanism requires no molecular motors, specific adhesion, substrate deformation, or pre-existing polarity.","feed_headline":"Motion polarizes actin regulator to trigger cell crawling","feed_subtitle":"Minimal model shows feedback between boundary movement and chemical cue creates spontaneous motility above a critical activity level.","key_machinery":"The feedback loop in which cell motion polarizes an external chemical regulator of actin nucleation, thereby imposing different polymerization densities at the two moving edges.","core_discovery":"In the minimal one-dimensional model the static symmetric cell state loses stability above a critical protrusive activity through a bifurcation induced by the feedback between boundary motion and polarized chemical regulation of actin nucleation, resulting in spontaneous transition to a motile state with unequal polymerization rates at the two edges.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Motion polarizes regulator to enable spontaneous crawling","Chemical feedback with motion breaks cell symmetry","Critical activity level triggers polarized cell motility","Model shows bifurcation to motile state without motors"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The external chemical regulator of actin nucleation becomes polarized around the moving cell boundaries and thereby imposes different nucleation densities at the two edges.","fun_headline_variants_meta":{"raw":{"variants":["Motion polarizes regulator to enable spontaneous crawling","Chemical feedback with motion breaks cell symmetry","Critical activity level triggers polarized cell motility","Model shows bifurcation to motile state without motors"]},"model":"grok-4.3","cost_usd":0.005209,"raw_usage":{"total_tokens":2510,"prompt_tokens":638,"num_sources_used":0,"completion_tokens":52,"cost_in_usd_ticks":52087000,"prompt_tokens_details":{"text_tokens":638,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1820,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":638,"tokens_out":52,"duration_ms":14301,"temperature":1.0,"reasoning_tokens":1820,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T10:48:27.571927+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct measurement showing whether the external regulator concentration differs measurably between the leading and trailing edges in a spontaneously moving cell, or experimental tuning of protrusive activity across the model's predicted critical value to test for the onset of motility.","supporting_citations":[],"review_version":1}