{"id":"bac97734-3e0f-40c8-b648-4e29b95a4f3d","arxiv_id":"2412.04400","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A method to compute true reaction coordinates from energy relaxation simulations, claimed to accelerate protein conformational sampling by 10^5 to 10^15-fold and to reveal a mechanism for PDZ allostery.","lead":"This paper reports that the same collective coordinates govern both protein conformational changes and energy relaxation, so the authors compute optimal reaction coordinates from short energy relaxation simulations of a single structure. If correct, this would make enhanced molecular dynamics sampling of slow protein processes such as ligand binding and allostery far more practical.","discovery_kind":"unification","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Energy-relaxation SCs are identified as tRCs based on inner-product agreement in only one implicit-solvent system; the explicit-solvent and PDZ2 applications lack committor validation, so the claimed accelerations and natural-pathway property rest on an unverified assumption.","rationale":"The entire method—computing tRCs from energy relaxation and using them as bias CVs—hinges on the equivalence between the leading SCs of a short, strongly perturbed relaxation and the coordinates that dominate the rare activated transition. If that equivalence fails in explicit solvent, then the biased trajectories are just aggressively driven along generic coordinates; as the paper's own Fig. 6 shows for an empirical CV, strong biasing can produce fast but non-physical transitions. The reader flagged the same weakest assumption, and I agree with it. My analysis adds two concrete reasons to doubt the extrapolation beyond the single implicit-solvent test: (i) the 5 ps relaxation timescale is orders of magnitude shorter than the transition timescale, so the fast energy-flow channels need not coincide with the slow activated modes, especially when water provides a rapid dissipation sink; (ii) the shooting-move check with five trajectory pairs is far too weak to establish that a trajectory passes through the true transition state. The lack of committor data, combined with absent code/data availability and hand-tuned bias parameters (k = 500–30,000 kJ/mol, binning, epsilon), makes the CONDITIONAL verdict appropriate. My stress test does not alter that verdict; it reinforces the specific condition that must be met. Hence verdict_should_be = UNCHANGED.","tokens_in":20450,"tokens_out":11827,"duration_ms":118725,"concrete_test":"Perform a committor test on an explicit-solvent system, e.g., DRV-bound HIV-PR. Take 20–30 conformations spaced along an RC-uncovered trajectory from the bound/closed state (flap distance d_f ≈ 1.0 nm) to the open/unbound state (d_f ≥ 2.5 nm). From each, launch ≥100 unbiased NVE trajectories with Boltzmann-distributed momenta and compute pB = probability of reaching the product basin (d_f > 2.5 nm or ligand fully unbound) before returning to the reactant basin (d_f < 1.5 nm). If the leading SC u_1 is a true reaction coordinate, pB should increase monotonically and smoothly with u_1, and the distribution of pB within bins of width ~0.2 rad should be narrow (variance ≲ 0.05). Report the bin-wise pB histograms and a goodness-of-fit statistic against a binomial model with a single pB per bin.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the leading singular coordinates (SCs) computed from 5 ps energy relaxation are true reaction coordinates (tRCs) for the conformational transition is supported only by the inner-product agreement in Fig. 2a for ligand-free HIV-PR in implicit solvent. For the explicit-solvent systems (DRV- and MA/CA-bound HIV-PR) and for PDZ2, no committor test is performed; the PEF gap in Fig. 2b/S5a is taken as sufficient evidence that the chosen SCs are tRCs. The invoked Onsager regression hypothesis does not, by itself, transfer per-coordinate energy-flow rankings from a far-from-equilibrium, 5 ps, small-amplitude relaxation to the rare, large-amplitude, activated barrier crossing, especially in explicit solvent where fast dissipation into water can dominate the relaxation. The shooting-move 'validation' is not a committor substitute: with only five pairs of trajectories from visually selected conformations, a single successful reactive pair is consistent with pB anywhere in roughly 0.1–0.9, so it does not show that the biased coordinate predicts the committor or that the full biased trajectory follows the natural pathway. Consequently, the headline 10^5–10^15 acceleration factors and the PDZ allostery mechanism are contingent on an unverified identification.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that true reaction coordinates (tRCs) for protein conformational changes can be computed from short (5 ps) energy-relaxation simulations of a single protein structure, using the generalized work functional (GWF) method. The authors validate this for ligand-free HIV-PR in implicit solvent by showing that the leading singular coordinates (SCs) from energy relaxation have inner products close to 1 with previously identified tRCs. They then apply bias potentials along these SCs to accelerate flap opening and ligand dissociation in HIV-PR in explicit solvent, and to propose a mechanism for PDZ2 allostery. The reported accelerations are 10^5- to 10^15-fold, and shooting moves from the biased trajectories are used to argue that the biased trajectories pass through transition states and follow natural transition pathways.","tokens_in":20839,"tokens_out":4725,"duration_ms":45637,"significance":"If the central claim is correct, the method would break the long-standing circularity that tRCs are needed for enhanced sampling but are themselves identified only from natural reactive trajectories, which require enhanced sampling. The implicit-solvent validation in Fig. 2a is a quantitative, direct check and is the strongest evidence in the paper. The GWF formalism is an original theoretical contribution, and the paper makes a falsifiable prediction about PDZ2 allostery that is mechanistically interesting. However, the validation in explicit solvent and for PDZ2 is indirect, the acceleration factors are rough single-trajectory comparisons without error bars, and the PDZ mechanism is not a quantitatively falsifiable prediction. With additional validation the work could be highly impactful, but in its present form the evidence is not commensurate with the strength of the claims.","major_comments":[{"comment":"The shooting-move validation with only five pairs of trajectories per conformation is statistically underpowered. A single successful reactive pair out of five attempts is consistent with a wide range of committor values (e.g., p_B between roughly 0.1 and 0.9 at the 95% confidence level in a binomial model), so it does not establish that the chosen conformations are near p_B=0.5 or that the SCs are tRCs. The paper does not report the number of conformations attempted, the success rate, or the distribution of p_B. To support the claim that explicit-solvent RC-uncovered trajectories follow natural pathways, the authors should provide a committor histogram or at least a statistically meaningful count of shooting outcomes for at least one explicit-solvent system.","section":"RC-uncovered trajectories follow natural transition pathways (p.16)"},{"comment":"The foundational assumption that the leading SCs of energy relaxation are identical to the tRCs for the conformational transition is tested quantitatively only for one system (ligand-free HIV-PR in implicit solvent, Fig. 2a). For DRV-bound and MA/CA-bound HIV-PR in explicit solvent and for PDZ2, the tRC assignment is based on the PEF gap in Fig. 2b and Fig. S5a, but a gap in potential-energy-flow magnitudes does not establish that these coordinates determine the committor. The paper would be substantially strengthened by a committor test for at least one explicit-solvent system, even a small one, or by a systematic sensitivity analysis showing that the resulting SCs are robust to the choice of injection site, cluster selection, and the number of leading SCs.","section":"A hypothesis on activation and energy relaxation (p.9)"},{"comment":"The acceleration factors are not rigorously defined. Comparing the duration of a single biased RC-uncovered trajectory (200 ps) with an experimental half-life (8.9×10^? s) conflates a biased trajectory time with an unbiased mean first-passage time, and no error bars or replicate statistics are provided. The 10^15-fold factor appears to be obtained by multiplying a waiting-time reduction with a diffusive-motion reduction, but these are not measured on the same footing and are based on single trajectories (e.g., one NRT for DRV, one NRT for MA/CA). Please provide precise definitions of the acceleration factor, an ensemble average with uncertainty, and a discussion of the different physical meanings of biased trajectory time, NRT duration, and experimental lifetime.","section":"Efficiency of enhanced sampling by tRCs (p.18)"}],"minor_comments":[{"comment":"Many superscripted numbers and exponents are garbled (e.g., '10! to 10\"!-fold', '8.9×10! s', '10>-fold' in Sections 2, 13, and 18), making quantitative claims unreadable. The typesetting must be fixed.","section":"Throughout"},{"comment":"The inner products are described only as 'close to 1'; the numerical values and any uncertainty estimates should be reported in the text or a table so that the reader can judge the agreement.","section":"Fig. 2a (p.10)"},{"comment":"The stray text 'dfdf' appears immediately before Fig. 1 and should be removed.","section":"p.9, before Fig. 1"},{"comment":"The statement that testing ligand temperature increases of 150K and 800K gives 'the same results' is not substantiated with data. Please include a supporting figure or table in the Supplementary Information.","section":"Methods (p.25)"},{"comment":"Candidate TS conformations for shooting are selected 'based on visual inspection and intuition.' This is not a reproducible criterion; please provide a quantitative selection procedure or at least describe the visual criteria in detail.","section":"Methods (p.26)"},{"comment":"The metadynamics comparison uses Gaussian heights up to 10,000-fold the recommended value, which is an extreme bias regime. The non-physical features observed in Fig. 6e may be aggravated by this regime; the paper should acknowledge this limitation and ideally also show a comparison at a more moderate bias that still achieves dissociation.","section":"Comparison with empirical CVs (p.18, Fig. 6)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript relies heavily on the authors' own prior work (refs. 31, 34, 40-43) for the GWF formalism and the implicit-solvent tRCs. This is not by itself a problem, but the validation of the central claim for explicit solvent is indirect and the shooting statistics are thin. The authors should be encouraged to provide at least one committor-based validation for an explicit-solvent system and to report the exact numerical values of inner products. I would also check the claim of being the 'first successful attainment of NRTs for ligand dissociation from HIV-PR' against the literature, as this is a strong priority claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe one thing to know: this paper has a genuinely new idea—use 5 ps energy relaxation runs from a single structure to obtain singular coordinates that are then biased for enhanced sampling of rare conformational changes. If it works generally, it would effectively remove the CV-finding bottleneck. The paper earns credit for a rigorous check in one case: for ligand-free HIV-PR in implicit solvent, the leading SCs from relaxation have near-unit inner products with the tRCs previously validated by committor. That is direct evidence, not hand-waving.\n\nThe explicit-solvent HIV-PR and PDZ2 applications are where the argument gets wobbly. The PEF gap between leading and remaining SCs is suggestive, but it is not a committor test. The shooting-move validation is weak in the other direction: with only five pairs of trajectories, a single successful reactive pair does not constrain the committor tightly; success is expected for pB anywhere in roughly 0.1–0.9. So the claim that RC-uncovered trajectories follow natural pathways is only partially supported. The acceleration factors are rough—no error bars, comparisons to literature simulation times and a measured half-life. The PDZ allostery mechanism is a proposal, not a falsifiable prediction.\n\nOne more soft spot: the paper invokes Onsager regression to justify the central equivalence, but a 400 K excess-energy dump into the active site is not a small equilibrium fluctuation. The authors themselves note the differences in energy scale, timescale, and amplitude between relaxation and activation. The inner-product result for implicit solvent is real, but the leap to explicit solvent and to a new protein is exactly the place where a skeptical reader should ask for a committor or likelihood-based validation.\n\nI would still send this to peer review. The potential significance is high, and the core method is simple enough to be tested by others. A referee should ask for (1) a committor test in one explicit-solvent system, (2) error bars on the acceleration, and (3) a working link for the Code Ocean deposit. The paper is for people working on enhanced sampling methods and on the mechanism of PDZ allostery. It deserves a serious referee, though the verdict may be conditional.\n\nBest.","headline":"A genuinely new route to reaction coordinates from cheap relaxation runs, with one solid implicit-solvent check and an unverified leap to explicit solvent.","tokens_in":21276,"tokens_out":3456,"would_cite":false,"duration_ms":39851,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Relaxation-derived coordinates speed protein transitions by 10^5- to 10^15-fold","keywords":["true reaction coordinates","enhanced sampling","generalized work functional","energy relaxation","HIV-1 protease","PDZ domain allostery","transition path sampling","collective variables"],"falsifier":"Apply the same protocol to a protein whose true reaction coordinates are already known from unbiased transition path sampling: if the leading singular coordinates from energy relaxation have inner products far from 1 with the known tRCs, or if bias along them fails to produce trajectories that pass TPS shooting, the claimed identity between relaxation and activation coordinates is refuted.","tokens_in":1676,"feed_emoji":"⚡","tokens_out":2320,"duration_ms":92636,"temperature":0.7,"pith_summary":"This paper claims that the coordinates along which a protein dissipates excess energy are the same coordinates it must activate to change shape, so the true reaction coordinates (the few variables that predict which side of a barrier a trajectory will end on) can be obtained from a 5 ps energy-relaxation simulation of a single structure. If correct, this dissolves the paradox that optimal collective variables could only be found from unbiased reactive trajectories, which are exactly what good collective variables are needed to produce. The authors report that biasing these relaxation-derived coordinates opens HIV-1 protease flaps and dissociates DRV and MA/CA ligands within 200 ps, a claimed acceleration of $10^{5}$ to $10^{15}$ over unbiased simulation and experiment, and that the resulting trajectories pass through transition states and can seed natural reactive trajectories via transition path sampling. In a blind test on PDZ2, the same protocol predicts a transient cleft-opening mechanism for a decades-old allostery puzzle.","feed_headline":"Relaxation-derived coordinates speed protein transitions 10^15-fold","feed_subtitle":"A single structure's 5 ps relaxation predicts coordinates that open HIV-PR flaps and release ligands in 200 ps.","key_machinery":"The generalized work functional (GWF) is a tensor-valued generalization of mechanical work whose elements are products of force and displacement components; its singular value decomposition produces an orthonormal set of singular coordinates ranked by the potential energy flowing through each coordinate. The leading singular coordinates, carrying the largest potential energy flows during energy relaxation, are the paper's claimed true reaction coordinates. The physical bridge is Onsager's regression hypothesis: the same channels that dissipate deposited energy in a 5 ps relaxation are the channels that must absorb energy to cross a barrier during activation.","core_discovery":"The central discovery is that true reaction coordinates control both activation and energy relaxation. Using the generalized work functional, the authors compute singular coordinates ranked by potential energy flow through each coordinate during relaxation; the leading singular coordinates from a 5 ps ensemble match, to near unit inner product, the tRCs previously identified from natural reactive trajectories for flap opening in HIV-PR in implicit solvent. In explicit solvent, biases applied to these leading singular coordinates open the flaps and drive complete DRV and MA/CA unbinding in 200 ps, with the experimental DRV unbinding half-life as reference, while shooting from conformations on these trajectories produces unbiased natural reactive trajectories. The same procedure applied to PDZ2 yields natural trajectories showing transient opening of the alpha2-beta2 cleft and binding groove during ligand unbinding, which the authors propose as the physical basis of PDZ allostery.","pith_inferences":["Not in the paper: if relaxation and activation share tRCs in general, protein-level fluctuation-dissipation reasoning could extend to far-from-equilibrium energy injections, a generalization the authors only gesture at.","A reader could test the method against machine-learned slow-mode collective variables on the same proteins; where the two agree, energy-flow and statistical descriptions point to the same physics, and where they disagree the discrepancy would reveal which motions relaxation actually resolves.","The method's input is a single conformation, so a natural blind test is a protein with a known cryptic pocket or experimentally characterized allostery; success would mean tRCs can be predicted before any transition is observed.","The paper's tRCs are linear combinations of backbone dihedrals; whether linearity is generic remains open, and curved tRCs would require the piecewise linearization the authors note."],"forward_implications":["Biasing relaxation-derived tRCs should reproducibly open HIV-PR flaps and dissociate DRV and MA/CA ligands within about 200 ps, a claimed 10^5- to 10^15-fold acceleration over unbiased MD and experiment.","RC-uncovered trajectories should provide transition-state conformations that make transition path sampling practical, yielding the first natural reactive trajectories for ligand dissociation from HIV-PR.","Because tRCs come from a single structure, the method should predict functional conformational changes and ligand release for proteins with no prior reactive trajectory data.","For PDZ2, the predicted tRCs imply that allosteric effectors such as Cdc42 and the alpha_A helix alter ligand affinity by sterically interfering with transient cleft and groove opening during unbinding.","For multi-step reactions, repeating the relaxation-and-bias protocol basin by basin should build a network of natural reactive trajectories and rate constants."],"supporting_citations":[{"why":"Supplies the tRCs for flap opening in HIV-PR in implicit solvent that the relaxation-derived singular coordinates are compared against, and shows bias on tRCs opens flaps in 4 ps.","marker":"[34]"},{"why":"Provides the energy-relaxation simulation protocol and the GWF clustering analysis used to compute singular coordinates from relaxation.","marker":"[42]"},{"why":"Provides Onsager's regression hypothesis, the physical premise that relaxation and activation follow the same coordinates.","marker":"[45]"},{"why":"Defines transition path sampling and the shooting move used to validate that RC-uncovered trajectories pass through the transition state and generate natural reactive trajectories.","marker":"[10]"},{"why":"Introduces potential energy flow and the generalized work functional framework from which singular coordinates are derived.","marker":"[40]"},{"why":"Extends GWF to rigorous one-dimensional reaction-coordinate identification, including treatment of curved tRCs.","marker":"[43]"},{"why":"Supplies the empirical collective variable s_b and extensive metadynamics simulations whose dissociation trajectories are compared against RC-uncovered and natural trajectories.","marker":"[17]"},{"why":"Provides unbiased MD flap-opening rates for HIV-PR used to quantify the claimed acceleration factor.","marker":"[47]"},{"why":"Provides the experimental half-life of DRV unbinding used as the reference for the 200 ps dissociation claim.","marker":"[50]"}],"fun_headline_variants":["From one snapshot, 5 ps relaxation predicts 10^15-fold faster transitions","Relaxation-derived coordinates accelerate protein transitions up to 10^15-fold","Compute true reaction coordinates from energy relaxation alone, 10^15-fold speedup","5 ps relaxation yields coordinates for 10^15-fold faster conformational changes","Predictive sampling: relaxation coordinates give 10^15-fold speedups from one structure"],"cache_read_input_tokens":23424,"weakest_assumption_plain":"The load-bearing premise is that the channels a protein uses to shed a burst of excess energy in a few picoseconds are the same channels it must energize to cross a barrier in a rare conformational change, so ranking coordinates by relaxation energy flow reveals the coordinates that control the transition.","fun_headline_variants_meta":{"raw":{"variants":["From one snapshot, 5 ps relaxation predicts 10^15-fold faster transitions","Relaxation-derived coordinates accelerate protein transitions up to 10^15-fold","Compute true reaction coordinates from energy relaxation alone, 10^15-fold speedup","5 ps relaxation yields coordinates for 10^15-fold faster conformational changes","Predictive sampling: relaxation coordinates give 10^15-fold speedups from one structure"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000349,"raw_usage":{"total_tokens":1881,"prompt_tokens":895,"completion_tokens":986,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":511,"completion_tokens_details":{"reasoning_tokens":882}},"tokens_in":511,"tokens_out":986,"duration_ms":8533,"temperature":1.0,"reasoning_tokens":882,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:24:13.773917+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply the same protocol to a protein whose true reaction coordinates are already known from unbiased transition path sampling: if the leading singular coordinates from energy relaxation have inner products far from 1 with the known tRCs, or if bias along them fails to produce trajectories that pass TPS shooting, the claimed identity between relaxation and activation coordinates is refuted.","supporting_citations":[{"cited_title":"It remains to be seen whether this linearity is a general feature of tRCs in proteins and if there is a fundamental physical reason for it","cited_arxiv_id":null,"evidence_quote":"Extends GWF to rigorous one-dimensional reaction-coordinate identification, including treatment of curved tRCs."}],"review_version":1}