{"id":"7efa75c5-3e05-4e77-9a06-fa332fb51a76","arxiv_id":"2411.12325","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Derives an effective Fokker-Planck equation for Rouse modes of active-passive hybrid polymers in gradients and computes center-of-mass steady-state distributions plus mean first passage times, showing optimization via active-unit placement.","lead":"The paper models how polymers containing active segments can achieve directed transport along chemical gradients through polymerization, yielding an effective description of their center-of-mass motion. A smart generalist might read it to understand potential mechanisms for non-diffusive molecular delivery in cells or engineered systems.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Marginalization of active DOF may not close to an exact effective FP for Rouse modes under position-dependent gradients","rationale":"The reader's weakest_assumption correctly isolates the single step whose failure would invalidate the effective description and the subsequent COM/MFPT results. Because the original review was abstract-only, the concrete_test above directly checks whether the full manuscript supplies a rigorous or validated closure; agreement is therefore high and the verdict moves from UNVERDICTED to CONDITIONAL pending that check.","tokens_in":1675,"tokens_out":340,"duration_ms":16820,"concrete_test":"From the full model equations in the methods or SI, perform the marginalization step explicitly (e.g., via projection or adiabatic elimination) and verify whether the resulting FP operator for the Rouse modes is closed without residual active variables or gradient-induced couplings; if closure requires an approximation, recompute the COM MFPT both with the effective equation and with direct stochastic integration of the un-marginalized dynamics for the same linear gradient and compare the numerical values.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that integrating out the active degrees of freedom produces a closed Fokker-Planck operator acting only on the Rouse modes (including COM) whose steady-state and MFPT predictions remain quantitatively accurate when activity is spatially modulated by a chemical gradient. Because the gradient makes the active noise or drift term position-dependent, the marginalization generally generates non-local or higher-order terms in the polymer coordinates; the paper must demonstrate either that these terms vanish identically or that they are controlled by a small parameter whose validity is checked for the reported MFPT calculations.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes a mechanism for directed molecular transport in chemical gradients using active-passive hybrid polymers that polymerize. Active units are placed along the chain; their activity is modulated by the local chemical concentration. By marginalizing the active degrees of freedom, the authors derive an effective Fokker-Planck equation governing the Rouse modes of the hybrid polymer. They then compute the steady-state distribution of the center-of-mass coordinate and the mean first-passage time (MFPT) to a target location, and examine how the spatial arrangement of active monomers affects accumulation and motility.","tokens_in":1816,"tokens_out":607,"duration_ms":17181,"significance":"If the marginalization step is valid and the resulting effective dynamics remain quantitatively accurate, the work supplies a concrete, Rouse-mode-based route to optimize polymer design for gradient-driven transport. This could be relevant to models of intracellular transport and to the design of synthetic active filaments. The explicit focus on MFPT and on the effect of active-unit placement provides falsifiable predictions that can be tested in simulation or experiment.","major_comments":[{"comment":"§3 (or wherever the marginalization is performed): the central claim that integrating out the active degrees of freedom yields a closed Fokker-Planck operator acting only on the Rouse modes (including the center of mass) is asserted but the explicit steps are not shown. Under a spatially varying chemical gradient the active noise or drift term becomes position-dependent; the marginalization generally produces non-local or higher-order terms in the polymer coordinates. The manuscript must demonstrate either that these terms vanish identically or that they remain negligible for the reported MFPT values (e.g., by an explicit small-parameter expansion or by direct comparison with the un-marginalized dynamics).","section":"§3"},{"comment":"Results section on MFPT: the reported MFPT values are obtained from the effective Fokker-Planck equation. Because the validity of that equation under position-dependent activity has not been established, the quantitative dependence of MFPT on active-unit arrangement cannot yet be taken as a robust prediction. A direct numerical check (e.g., comparison of the effective-model MFPT against Brownian-dynamics trajectories of the full active-passive chain) is required before the optimization conclusions can be considered load-bearing.","section":"Results (MFPT)"}],"minor_comments":[{"comment":"Notation: the definition of the Rouse modes and the precise mapping from monomer activity to the effective drift/diffusion coefficients should be stated explicitly (including any averaging over the chemical gradient).","section":null},{"comment":"Figure captions: several panels compare different active-unit placements; the precise parameter values (gradient strength, activity magnitude, chain length) used in each panel should be listed in the caption or a table for reproducibility.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments on our manuscript. The points raised concerning the marginalization procedure and validation of the effective dynamics are well taken. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and checks.","responses":[{"response":"We agree that the explicit steps of the marginalization were not presented in sufficient detail. In the revised manuscript we will add a dedicated appendix that carries out the integration over the active degrees of freedom in full. Starting from the joint Fokker-Planck equation for the Rouse modes and the active variables, we will perform the marginalization under the assumption of fast active relaxation (separation of timescales) and a linear expansion in the chemical gradient. This yields an effective closed operator on the Rouse coordinates; the non-local and higher-order terms appear only at O(∇²) and higher and are shown to be negligible for the weak-gradient regime used in the MFPT calculations. We will also state the precise conditions under which the effective description holds.","revision_made":"yes","referee_comment":"[§3] §3 (or wherever the marginalization is performed): the central claim that integrating out the active degrees of freedom yields a closed Fokker-Planck operator acting only on the Rouse modes (including the center of mass) is asserted but the explicit steps are not shown. Under a spatially varying chemical gradient the active noise or drift term becomes position-dependent; the marginalization generally produces non-local or higher-order terms in the polymer coordinates. The manuscript must demonstrate either that these terms vanish identically or that they remain negligible for the reported MFPT values (e.g., by an explicit small-parameter expansion or by direct comparison with the un-marginalized dynamics)."},{"response":"We concur that a direct numerical validation is necessary to confirm the quantitative accuracy of the effective model. In the revision we will add a new subsection that compares the MFPT obtained from the effective Fokker-Planck equation against Brownian-dynamics trajectories of the full (un-marginalized) active-passive chain for several representative placements of active units. The comparison will be performed in the same parameter regime as the analytic results, thereby establishing the regime of validity of the effective description and supporting the reported optimization trends.","revision_made":"yes","referee_comment":"[Results (MFPT)] Results section on MFPT: the reported MFPT values are obtained from the effective Fokker-Planck equation. Because the validity of that equation under position-dependent activity has not been established, the quantitative dependence of MFPT on active-unit arrangement cannot yet be taken as a robust prediction. A direct numerical check (e.g., comparison of the effective-model MFPT against Brownian-dynamics trajectories of the full active-passive chain) is required before the optimization conclusions can be considered load-bearing."}],"tokens_in":1419,"tokens_out":604,"duration_ms":19755,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that marginalizing the active degrees of freedom yields an effective Fokker-Planck description for the Rouse modes, which they then use to compute the center-of-mass steady state and mean first passage times in a chemical gradient, plus an optimization over where to place the active units along the chain. That combination of polymerization-driven transport with tunable active-passive architecture is the concrete addition here. It is not a routine extension of standard Rouse or active-matter models, so the optimization results on accumulation versus motility stand out as the usable part. The paper does a straightforward job laying out the strategy and showing how different arrangements shift the steady-state distribution and passage times, giving modelers something specific to compare against. The soft spot sits in the marginalization itself. With activity modulated by a position-dependent chemical gradient, integrating out the active variables does not automatically produce a closed, local Fokker-Planck operator on the polymer coordinates; extra terms or non-Markovian effects can appear. The abstract states that a closed equation is obtained, but the derivation must show either that those terms vanish or that a controlled approximation holds for the reported MFPT values. The Rouse-mode reduction also carries its usual assumptions, which could be strained once the active noise is spatially varying. This work is aimed at people already modeling active polymers or gradient-driven transport in biophysics and soft matter. A reader who cares about Rouse chains with internal activity would get value from the placement optimization, even if they later redo the marginalization. The thinking is coherent on its own terms and the calculations are falsifiable, so it deserves a serious referee to check the closure step and the numerics. Send it to peer review.","headline":"The paper derives an effective FP equation for Rouse modes of hybrid polymers by marginalizing active DOF and optimizes active-unit placement for accumulation or motility, but the closure under position-dependent gradients needs explicit verification.","tokens_in":2324,"tokens_out":421,"would_cite":false,"duration_ms":35737,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"Standard Rouse-mode FP marginalization under activity gradients; no RS-shaped cost, ratio symmetry or forcing structure","alignment":"orthogonal","rationale":"The paper's core machinery (Langevin eqs. (1), Rouse transformation to modes χ_i, spherical-harmonics expansion of orientations, small-gradient closure to effective FP (3) for X_COM with V and D given by S1/S2 sums over eigenvectors, steady-state ρ ∝ [1 + τ S2 v²/(d D)]^{-ϵ/2}, MFPT ODE (10)) is conventional soft-matter coarse-graining. It contains none of the RS primitives: the reciprocal cost J(x) = ½(x + x^{-1}) − 1, its Aczél uniqueness (Cost/FunctionalEquation.lean), φ-ladder constants, 8-tick periodicity, or the distinction-to-spacetime forcing (Foundation/RealityFromDistinction.lean, AbsoluteFloorClosure.lean). The gradient-induced drift is phenomenological, not derived from any J-cost or ratio-symmetric functional equation. Hence the work lies outside the RS domain.","tokens_in":52739,"confidence":"high","tokens_out":248,"duration_ms":7119,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Active-passive hybrid polymers transport molecules directionally by polymerizing in chemical gradients.","keywords":["active-passive polymers","polymerization","chemical gradients","Rouse modes","Fokker-Planck equation","directed transport","mean first passage time","center of mass"],"falsifier":"Direct numerical simulation of the full active-passive polymer dynamics in a gradient showing that the center-of-mass steady-state distribution or mean first passage time differs from the predictions of the effective Fokker-Planck equation.","tokens_in":2589,"feed_emoji":"🧪","tokens_out":606,"duration_ms":21559,"temperature":0.7,"pith_summary":"The paper proposes directed molecular transport by attaching molecules to active-passive hybrid polymers whose growth is driven by polymerization in chemical or activity gradients. These gradients produce an effective drift that the authors capture by deriving a closed Fokker-Planck equation for the Rouse modes after the active degrees of freedom are integrated out. The resulting equation is solved for the steady-state distribution of the polymer center of mass and for its mean first passage time to a chosen destination. Different placements of active segments along the chain are examined to show how accumulation and transit speed can be tuned.","feed_headline":"Hybrid polymers drift in chemical gradients via polymerization","feed_subtitle":"Marginalizing active degrees gives exact center-of-mass distribution and passage times.","key_machinery":"Effective Fokker-Planck equation for the Rouse modes of active-passive hybrid polymers, obtained by marginalizing active degrees of freedom.","core_discovery":"By marginalizing out the active degrees of freedom, the system yields an effective Fokker-Planck equation governing the Rouse modes of active-passive hybrid polymers. This equation is solved to obtain the steady-state distribution of the center of mass and the mean first passage time to a destination under chemical/activity gradients. The arrangement of active units within the polymer is varied to optimize steady-state behavior and dynamic transport properties.","pith_inferences":["If the effective description holds, it could guide design of synthetic polymers for targeted delivery in varying chemical environments.","Similar marginalization might apply to other hybrid active systems where internal activity couples to external gradients.","Testing the dependence on active unit arrangement in experiments would validate the optimization strategy."],"forward_implications":["The steady-state distribution of the center of mass shifts due to the gradient-induced drift.","Mean first passage times to a target can be computed explicitly from the effective equation.","Optimizing the positions of active units enhances accumulation at preferred locations or reduces passage times.","Directed motility emerges without external forces, purely from the polymerization in gradients."],"fun_headline_variants":["Polymerization enables directed polymer transport in gradients","Hybrid polymers gain drift from chemical activity gradients","Effective equation reveals polymer passage times in gradients","Rouse modes dictate polymer accumulation under gradients"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The active degrees of freedom can be integrated out to produce a closed effective Fokker-Planck equation for the Rouse modes that remains valid for center-of-mass motion in gradients.","fun_headline_variants_meta":{"raw":{"variants":["Polymerization enables directed polymer transport in gradients","Hybrid polymers gain drift from chemical activity gradients","Effective equation reveals polymer passage times in gradients","Rouse modes dictate polymer accumulation under gradients"]},"model":"grok-4.3","cost_usd":0.004962,"raw_usage":{"total_tokens":2386,"prompt_tokens":587,"num_sources_used":0,"completion_tokens":53,"cost_in_usd_ticks":49624500,"prompt_tokens_details":{"text_tokens":587,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1746,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":587,"tokens_out":53,"duration_ms":16621,"temperature":1.0,"reasoning_tokens":1746,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-23T17:44:36.150200+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct numerical simulation of the full active-passive polymer dynamics in a gradient showing that the center-of-mass steady-state distribution or mean first passage time differs from the predictions of the effective Fokker-Planck equation.","supporting_citations":[],"review_version":1}