{"id":"a492bab4-28f5-4751-87e3-a8ec4f22b08d","arxiv_id":"2603.23856","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Coupled conserved protein and lipid dynamics produce multiscale membrane patterns with traveling protein domains and arrested lipid coarsening, captured by two non-reciprocally coupled Cahn-Hilliard equations.","lead":"A continuum model couples membrane proteins and lipid composition and produces multiscale patterns: traveling protein domains alongside smaller stationary lipid domains with arrested coarsening. It offers a minimal physical picture of how conserved protein and lipid dynamics can organize cell membranes.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"Abstract-only review leaves the continuum coupling form and the claimed reduction to two non-reciprocal Cahn-Hilliard equations uncheckable; the multiscale/arrested-coarsening claim therefore cannot be stress-tested beyond the abstract.","rationale":"The Reader correctly flags that an abstract-only review cannot audit soundness or reproducibility and therefore returns UNVERDICTED with low confidence. The single most load-bearing concern is precisely the one the Reader isolates: the continuum coupling form itself (including non-reciprocity and unequal interface tensions) is introduced by definition and underpins every reported phase. No stronger internal inconsistency can be demonstrated without the equations; manufacturing a different concern would violate the good-faith rule. The concrete test simply operationalizes the missing audit: re-derive the dispersion and re-run the coarsening diagnostics once the free energies are known. Because that check is unavailable, the verdict remains UNVERDICTED and agreement with the Reader is complete.","tokens_in":2154,"tokens_out":594,"duration_ms":5653,"concrete_test":"Obtain the full manuscript (or arXiv source) and extract the free-energy functionals and the precise non-reciprocal coupling terms that reduce the three-variable model to the two-CH system. Independently recompute the linear-stability spectrum of the homogeneous state for the reported parameter set; if the long-wavelength oscillatory protein mode and the classical lipid spinodal do not coexist in the claimed region, or if the numerical coarsening of lipid domains continues without arrest once the protein domains travel, the multiscale/arrested-coarsening claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that a three-variable continuum model (membrane-bound protein, cytosolic protein, binary lipid composition) with two global conservations, when coupled via a specific active phase-separation + Cahn-Hilliard form, produces multiscale traveling/rotating protein domains coexisting with smaller-scale stationary lipid domains and, above a critical coupling, arrested lipid coarsening; and that this is captured by two non-reciprocally coupled Cahn-Hilliard equations with unequal interface tensions. Because only the abstract is available, neither the explicit free-energy densities, the non-reciprocal coupling terms, the mobility/tension parameters, the linear-stability dispersion relations, nor the numerical evidence for arrested coarsening can be inspected. The load-bearing premise is therefore identical to the reader's weakest_assumption: that the chosen continuum coupling is a faithful minimal representation rather than an artifact that manufactures the multiscale/arrested regime. Without equations or figures this premise cannot be confirmed or refuted; the claim remains coherent within the established non-reciprocal CH literature but is currently unsubstantiated by the available text.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript proposes a three-variable continuum model for near-membrane cell-polarity dynamics, coupling membrane-bound and cytosolic protein (globally conserved total protein) to binary lipid composition (globally conserved average lipid fractions). Protein dynamics are treated as conserved active phase separation; lipid dynamics follow a Cahn–Hilliard equation. From linear stability of the homogeneous state and direct numerical simulations, the abstract reports classical lipid demixing, oscillatory protein phase separation with a long-wavelength instability and traveling domains, multiscale coexistence of larger traveling/rotating protein domains with smaller stationary lipid domains, and arrested lipid coarsening above a critical coupling. The main instabilities and phase diagram are claimed to be captured by two non-reciprocally coupled Cahn–Hilliard equations with unequal interface tensions, framed as an extension of a conserved FitzHugh–Nagumo model for non-reciprocal pattern formation.","tokens_in":2398,"tokens_out":1126,"duration_ms":21233,"significance":"If the full analysis holds, the work would give a minimal, conservation-constrained continuum account of multiscale polarity patterns in which traveling protein domains coexist with arrested lipid coarsening, and would place that phenomenology inside the non-reciprocal Cahn–Hilliard framework with unequal tensions. That reduction, and the associated asymmetry between static lipid and traveling protein patterns, would be a useful theoretical contribution to non-reciprocal pattern formation and a concrete link to membrane polarity. Linear stability plus DNS and a reduced two-field model are the right tools for this claim class; the significance is therefore conditional on the coupling form and the arrested-coarsening evidence being as stated.","major_comments":[{"comment":"Only the abstract is available for this review, so the continuum free-energy densities, non-reciprocal coupling terms, mobilities, interface tensions, and the explicit reduction to two non-reciprocally coupled Cahn–Hilliard equations cannot be inspected. The central multiscale and arrested-coarsening claims are load-bearing on that coupling form; without equations or figures they remain unsubstantiated rather than refuted. A full-text review is required before any accept/reject decision.","section":null},{"comment":"Abstract claim of arrested coarsening of stationary lipid domains “above a critical coupling”: this is a strong dynamical statement (finite domain size, suppressed Ostwald ripening or equivalent). It needs a clear operational definition (e.g., domain-size time series, structure-factor peak saturation, comparison to uncoupled CH), the critical coupling value or scaling, and evidence that arrest is not a finite-size or mobility artifact. None of this is checkable from the abstract alone.","section":null},{"comment":"Abstract claim that the main instabilities and phase diagram are “well captured” by two non-reciprocally coupled Cahn–Hilliard equations with different interface tensions: the reduction from the three-variable (membrane protein, cytosolic protein, lipid) model to that two-field system must be stated (adiabatic elimination, projection, or phenomenological matching) and checked against the three-variable linear dispersion and DNS phase boundaries. Whether the reduction is controlled or only qualitative is load-bearing for the “explains the observed asymmetry” claim.","section":null},{"comment":"Weakest modeling premise (stated in the abstract’s model definition): that the chosen conserved active protein–lipid coupling is a faithful minimal representation of near-membrane polarity rather than an artifact that manufactures multiscale traveling-protein / arrested-lipid states. The free parameters listed (total protein, coupling strength, unequal interface tensions, mean lipid fractions) should be accompanied by a robustness check: which qualitative regimes survive under reciprocal coupling, equal tensions, or alternative mass-action binding kinetics.","section":null}],"minor_comments":[{"comment":"Abstract: “conserved FitzHugh–Nagumo model for non-reciprocal pattern formation” should cite the specific prior work being extended so the novelty of the unequal-tension extension is clear to non-specialists.","section":null},{"comment":"Abstract: “oscillatory phase separation for intermediate total protein contents, associated with a long-wavelength instability and traveling domains” mixes temporal oscillation, long-wave instability, and traveling domains; a single sentence clarifying which dispersion feature (e.g., complex eigenvalue at small k vs finite-k Hopf) drives each would help.","section":null},{"comment":"Abstract: “multiscale patterns with larger-scale traveling and rotating protein domains coexisting with smaller-scale stationary lipid domains” — once figures exist, report characteristic length-scale ratios and how they depend on the two interface tensions.","section":null}],"recommendation":"uncertain","confidential_remarks":"This is an abstract-only review (full text not provided). Soundness cannot be assessed beyond coherence with the non-reciprocal CH literature; confidence is low. I recommend obtaining the full manuscript (equations, linear-stability dispersions, DNS of domain-size vs time, and the reduced two-CH derivation) before assigning a definitive recommendation. Scope (cond-mat.soft / non-reciprocal pattern formation with a biological motivation) appears appropriate for a soft-matter or biophysics theory journal if the analysis checks out. No concerns about circularity from curve-fitting; residual risk is modeling-choice artifact, not data circularity."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is an abstract-only look at a continuum soft-matter / cell-polarity paper, so everything below is provisional.\n\nWhat they claim is clear and sits in a real program: a three-variable model (membrane protein, cytosolic protein, binary lipid composition) with two global conservations, coupling conserved active protein phase separation to Cahn–Hilliard lipid demixing. Linear stability plus numerics are said to give classical lipid phase separation, oscillatory protein phase separation with long-wavelength instability and traveling domains, multiscale coexistence of larger traveling/rotating protein domains with smaller stationary lipid domains, and—above a critical coupling—arrested lipid coarsening. They further reduce the main instabilities to two non-reciprocally coupled Cahn–Hilliard equations with unequal interface tensions (an extension of conserved FitzHugh–Nagumo / non-reciprocal CH ideas). That reduction, if it holds, is the cleanest part of the contribution: it explains the asymmetry between static lipids and traveling proteins without extra machinery.\n\nCredit where due: the setup is self-contained theory, not curve-fitting. Circularity burden is low. Conserved RD + CH + non-reciprocal coupling is a natural combination for near-membrane polarity, and reporting multiscale patterns plus arrested coarsening under traveling protein domains is useful if the numerics are solid. Free parameters (total protein, coupling strength, interface tensions, lipid fractions) are the expected ones.\n\nSoft spots, in proportion: we cannot see the free-energy densities, the precise non-reciprocal terms, the dispersion relations, or any figure showing arrested coarsening. The load-bearing premise is exactly that the chosen continuum coupling is a faithful minimal representation rather than an artifact that manufactures the multiscale/arrested regime. That premise is uncheckable from the abstract alone; the stress-test note is right on that point. Novelty is mid-range—known ingredients, new combination and reported phenomenology—not a conceptual break. Significance is likewise mid-range: useful within polarity and membrane soft-matter theory if robust, not a resolution of a long-open problem.\n\nWho it is for: people already working on non-reciprocal Cahn–Hilliard, conserved reaction–diffusion polarity models, or lipid–protein membrane patterning. A serious referee should see the full equations, parameters, and evidence for arrest; I would not desk-reject on the abstract. I would not cite it yet or bring it to reading group until the full text is available. If the reduction and the arrested-coarsening numerics check out, it is a clean, citable model paper.","headline":"Abstract-only: coherent conserved protein–lipid model claiming multiscale traveling protein domains and arrested lipid coarsening, reduced to two non-reciprocal Cahn–Hilliard equations; interesting but currently uncheckable.","tokens_in":3028,"tokens_out":645,"would_cite":false,"duration_ms":5902,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A conserved continuum model of protein and lipid dynamics produces multiscale patterns with traveling protein domains and arrested lipid coarsening.","keywords":["multiscale pattern formation","traveling protein domains","arrested coarsening","lipid domains","cell polarity","Cahn-Hilliard","non-reciprocal coupling","conserved reaction-diffusion"],"falsifier":"Simulations of the three-variable model or of the reduced two-equation Cahn-Hilliard system that, above the reported critical coupling, show unrestricted lipid coarsening instead of arrest, or that fail to produce coexisting larger traveling protein domains and smaller stationary lipid domains when both linear instabilities are simultaneously active.","tokens_in":2993,"feed_emoji":"🧬","tokens_out":881,"duration_ms":25577,"temperature":0.7,"pith_summary":"This paper models near-membrane cell polarity with a three-variable continuum description of membrane-bound protein, cytosolic protein, and binary lipid composition. Total protein and average lipid fractions are globally conserved. The model couples conserved active protein phase separation to a Cahn-Hilliard equation for lipid demixing. Linear stability analysis and simulations show classical lipid phase separation alongside oscillatory protein phase separation that produces traveling domains at intermediate protein content. When both instabilities act together, larger-scale traveling and rotating protein domains coexist with smaller-scale stationary lipid domains; above a critical coupling the protein motion arrests lipid coarsening. The same phase diagram is recovered from two non-reciprocally coupled Cahn-Hilliard equations that differ only in interface tension, which accounts for the static-lipid versus traveling-protein asymmetry.","feed_headline":"Traveling protein domains arrest lipid coarsening","feed_subtitle":"A conserved continuum model yields multiscale patterns of mobile proteins and frozen lipid domains near membranes.","key_machinery":"Two non-reciprocally coupled Cahn-Hilliard equations with unequal interface tensions, obtained as a reduction of a three-variable conserved continuum model that combines reaction-diffusion protein dynamics with lipid demixing; the non-reciprocal coupling and tension difference produce the observed multiscale traveling-protein versus static-lipid asymmetry.","core_discovery":"In a three-variable continuum model with globally conserved protein and lipid fractions, coupling conserved active protein phase separation to Cahn-Hilliard lipid demixing produces multiscale patterns of larger traveling or rotating protein domains coexisting with smaller stationary lipid domains; above a critical coupling, traveling protein domains coexist with arrested coarsening of the lipid domains. The main instabilities are captured by two non-reciprocally coupled Cahn-Hilliard equations with different interface tensions.","pith_inferences":["Non-reciprocal Cahn-Hilliard pairs with unequal tensions may organize other conserved near-membrane polarity systems without additional stabilizers.","Active protein domains could set a characteristic lipid domain size in living cells by arresting coarsening, a prediction testable by independent variation of protein load and lipid composition.","The same tension-asymmetry mechanism may decide which species travels in other non-reciprocally coupled conserved binary mixtures outside cell biology."],"forward_implications":["Multiscale patterns form whenever both the protein oscillatory instability and the lipid demixing instability are active.","Larger traveling and rotating protein domains can coexist with smaller stationary lipid domains.","Above a critical coupling strength, lipid coarsening arrests while protein domains continue to travel.","The phase diagram is quantitatively recovered by two non-reciprocally coupled Cahn-Hilliard equations that differ only in interface tension.","Distinct interface tensions alone select which field travels and which remains static under non-reciprocal coupling."],"fun_headline_variants":["Traveling proteins arrest lipid domain coarsening","Mobile protein domains freeze stationary lipids","Multiscale patterns: proteins travel, lipids stay put","Nonreciprocal coupling freezes lipids as proteins roam","Protein travel coexists with arrested lipid coarsening"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The particular continuum coupling chosen between conserved protein reaction-diffusion dynamics and binary lipid Cahn-Hilliard dynamics is a faithful minimal representation of near-membrane polarity, so the multiscale traveling-protein and arrested-lipid regime is not an artifact of that modeling choice.","fun_headline_variants_meta":{"raw":{"variants":["Traveling proteins arrest lipid domain coarsening","Mobile protein domains freeze stationary lipids","Multiscale patterns: proteins travel, lipids stay put","Nonreciprocal coupling freezes lipids as proteins roam","Protein travel coexists with arrested lipid coarsening"]},"model":"grok-4.5","effort":"low","cost_usd":0.006876,"raw_usage":{"total_tokens":1768,"prompt_tokens":837,"num_sources_used":0,"completion_tokens":71,"cost_in_usd_ticks":68760000,"prompt_tokens_details":{"text_tokens":837,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":860,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":837,"tokens_out":71,"duration_ms":7593,"temperature":1.0,"reasoning_tokens":860,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T19:15:52.573204+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Simulations of the three-variable model or of the reduced two-equation Cahn-Hilliard system that, above the reported critical coupling, show unrestricted lipid coarsening instead of arrest, or that fail to produce coexisting larger traveling protein domains and smaller stationary lipid domains when both linear instabilities are simultaneously active.","supporting_citations":[],"review_version":1}