{"id":"8f56151f-f717-4b30-b366-2cdd7628ada6","arxiv_id":"2608.12691","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A single-trajectory lambda-dynamics protocol coupling OPES biasing with d-AFED conformational acceleration and octanol mass scaling yields solvation free energies and partition coefficients as accurate as replica exchange, with improved agreement with experiment for peptide-like solutes.","lead":"These authors combine three sampling accelerations (mass-scaled octanol, OPES-biased alchemical coordinate, and d-AFED torsional boosting) into one protocol for solvation free energies. The combined method reproduces replica-exchange benchmarks for rigid solutes and cuts the error against experiment for flexible peptide-like solutes from 0.75 to 0.30 log units in octanol-water partition coefficients.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The d-AFED 'negligible reweighting' claim is unquantified; with κ=1000 kJ/mol/rad^2 and 1000 K auxiliaries, the 0.30 MAE may reflect a 1000 K torsional ensemble rather than true 298 K conformational sampling.","rationale":"The paper's central claim is that λ-OPES-d-AFED reduces the logP MAE from 0.75 to 0.30 for seven acetyl amino-acid amides, implying that simultaneous alchemical and conformational enhanced sampling is necessary for accurate flexible-solute predictions. The load-bearing step is the assertion in Section II.A that the d-AFED high-temperature torsional bias does not require correction, backed only by \"negligible changes\" with no quantitative support. The reader's weakest assumption correctly identifies this as the key vulnerability. My analysis sharpens it: the harmonic coupling constant κ=1000 kJ mol^-1 rad^-2 and auxiliary temperature 1000 K (Section II.F) mean the physical torsions ξ_k are tightly slaved to their auxiliary variables s_k (conditional width ~0.05 rad at 298 K). The sampled conformational ensemble is therefore close to the 1000 K distribution of s_k, not the 298 K Boltzmann distribution of ξ_k. Since Figures 9A/B show that d-AFED changes ΔG by up to ~0.7 kcal/mol relative to λ-OPES, the solvation free energy is highly sensitive to the conformer distribution. It is inconsistent to claim both that the conformational bias matters (the MAE improvement) and that the reweighting correction is negligible (no effect), unless the mean force happens to be almost independent of the conformer populations within the visited states. That special coincidence needs to be demonstrated. The proposed test—recompute ΔG with the Cuendet-Tuckerman reweighted mean force and compare with Tables S3/S4—would settle the issue. If reweighted values differ significantly, the 0.30 MAE is not a valid 298 K result and the central claim fails. If they do not, the concern is resolved. This justifies the reader's CONDITIONAL verdict: the paper should be accepted only after this validation is reported. I therefore keep the verdict unchanged.","tokens_in":22554,"tokens_out":10535,"duration_ms":103640,"concrete_test":"Reanalyze the saved λ-OPES-d-AFED trajectories for the seven acetyl amino-acid amides: apply the Cuendet-Tuckerman reweighting (refs. 56, 73) to the binned mean force at each λ, using the appropriate weights, and recompute ΔG_water, ΔG_oct, and logP_oct/water. Compare with Tables S3 and S4. If any reweighted logP shifts by >0.1 log unit (or any ΔG by >0.1 kcal/mol), the \"negligible reweighting\" claim is falsified and the 0.30 MAE is not a validated 298 K conformational-sampling result. Also report effective sample sizes of the reweighted trajectories.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (MAE reduction 0.75→0.30 for logP of acetyl amino-acid amides) rests on the assumption in Section II.A that d-AFED auxiliary torsions at 1000 K leave the λ-conditional mean force unbiased. The paper states \"Applying this reweighting produced only negligible changes in the solvation free energies\" but reports no numbers. This is not a minor omission: with κ=1000 kJ mol^-1 rad^-2 (Section II.F), the 298 K conditional width of (ξ_k−s_k) is only ~0.05 rad, so each physical torsion ξ_k is slaved to its 1000 K auxiliary variable s_k. The sampled conformer populations are therefore the 1000 K populations, not the 298 K populations. Because Figures 9A/B show that conformational sampling shifts ΔG by up to ~0.7 kcal/mol, the solvation free energy is demonstrably sensitive to the torsional distribution. If the 1000 K population bias is not corrected, the improved agreement with Fauchere-Pliska logP values (Figure 10) could be a fortuitous consequence of sampling an elevated-temperature conformational ensemble, not evidence that simultaneous alchemical and conformational enhanced sampling at 298 K is required. The assertion that the conditional mean force is insensitive to the auxiliary temperature conflates the OPES bias (which depends only on λ and cancels in the conditional average) with the d-AFED coupling (which depends on ξ(r) and does not cancel).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an integrated enhanced sampling protocol for solvation free energy calculations. It combines (i) solvent mass scaling to accelerate relaxation in viscous phases such as octanol, (ii) a dual-bias lambda-dynamics scheme (“λ-OPES”) that applies OPES-Standard and OPES-Explore simultaneously on the alchemical coordinate, and (iii) driven adiabatic free energy dynamics (d-AFED) on selected solute dihedrals to accelerate conformational sampling. The manuscript reports that for seven rigid organic solutes, λ-OPES agrees with Hamiltonian replica exchange (HREX) and literature values (MAE below 0.06 kcal/mol in water and 0.17 kcal/mol in octanol), and that a tenfold reduction of octanol atomic masses accelerates convergence by more than fivefold without changing equilibrium free energies. For seven flexible N-acetyl amino-acid amides, the paper claims that coupling λ-OPES with d-AFED reduces the mean absolute error in octanol-water logP from 0.75 to 0.30 log units relative to experiment. The central methodological claims are the single-trajectory capability of λ-OPES and the necessity of simultaneous alchemical and conformational enhanced sampling for flexible solutes.","tokens_in":22952,"tokens_out":16841,"duration_ms":161587,"significance":"If the flexible-solute claim is correct, this is a practically valuable contribution: it offers a single-trajectory route to solvation free energies with coupled alchemical and conformational sampling, avoiding the need for predefined λ windows or replica coordination. The rigid-solute results are convincing and well controlled: λ-OPES reproduces HREX reference values and external literature values, and the mass-scaling acceleration in octanol is a broadly useful finding that is made credible by the consistent convergence data. The paper also provides open-source simulation scripts and a clear description of the LBF alchemical route, which strengthens reproducibility. However, the headline flexible-solute claim rests on a single, hand-picked set of d-AFED and OPES parameters for seven compounds, and on an unquantified statement that reweighting the d-AFED torsional ensemble changes solvation free energies negligibly. These points need to be substantiated before the central claim is established.","major_comments":[{"comment":"The assertion that reweighting the d-AFED torsional ensemble produces “only negligible changes in the solvation free energies” is unquantified and load-bearing. With κ = 1000 kJ mol^-1 rad^-2 and T_s = 1000 K (Section II.F), the conditional width of (ξ_k − s_k) at 298 K is about sqrt(k_B T/κ) ≈ 0.05 rad, so each physical dihedral is effectively slaved to its auxiliary variable, whose distribution is thermostatted at 1000 K. The sampled torsional population is therefore far from the 298 K physical population. Because Figures 9A/B show that ΔG changes by 0.5–1.2 kcal/mol when the torsional sampling protocol is changed, the mean force in Eq. (2) is demonstrably sensitive to the torsional ensemble. The statement in Section II.A that the conditional mean force is unaffected by the auxiliary temperature conflates the OPES bias (which depends only on λ and cancels in the conditional average) with the d-AFED coupling (which depends on r through ξ(r) and does not cancel). The authors must report a quantitative comparison of ΔG obtained with and without the Cuendet–Tuckerman reweighting for each of the seven solutes in water and octanol. If reweighting is not actually negligible, the MAE reduction from 0.75 to 0.30 log units (Figure 10) may reflect a high-temperature conformational ensemble rather than unbiased 298 K conformational sampling.","section":"Section II.A and Section III.D"},{"comment":"The flexible-solute result (MAE 0.30) is established for a single hand-picked parameter set: d-AFED masses of 50 Da nm^2 rad^-2, coupling constants of 1000 kJ mol^-1 rad^-2, auxiliary temperature 1000 K, and OPES barriers of 50 and 5 kcal/mol. No sensitivity analysis is presented for these parameters in the peptide-like systems. This matters because the authors themselves show in Section III.B (Figures S5 and S6) that the closely related λ-AFED results are sensitive to the extended-variable mass. A demonstration that the 0.75→0.30 improvement is robust to, e.g., varying T_s between 800 and 1200 K or κ by a factor of two, is needed to exclude the possibility that the improvement is a result of parameter tuning on a seven-compound set.","section":"Section II.F and Section III.D"}],"minor_comments":[{"comment":"The sentence describing the mirror-periodic representation of λ cites Wu, Hu, and Yang; a brief explanation of why the generalized force changes sign in the interval (1,2] would improve accessibility.","section":"Section II.A"},{"comment":"The superscripts in the tabulated ΔG values (presumably standard errors over the three runs) are not defined in the table caption or in the text; please add an explicit legend.","section":"Table S3"}],"recommendation":"major_revision","confidential_remarks":"The rigid-solute part of the paper is solid and likely publishable. The flexible-solute claim is the paper's headline advance, but it hinges on an unquantified reweighting assertion in Section II.A. I would ask the authors to provide the reweighted vs. unrewighted ΔG values and a minimal sensitivity analysis for the d-AFED parameters; these are feasible additions that would substantially de-risk the central claim. The seven-compound dataset is small, but a clear quantitative reweighting comparison would be more decisive than a larger dataset if the current effect is real."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's the quick read on arXiv:2608.12691. The paper does something genuinely useful: it combines octanol mass scaling, a dual-bias lambda-OPES, and d-AFED torsional acceleration into a single lambda-dynamics protocol. The rigid-solute benchmarks are convincing. HREX and lambda-OPES agree with each other and with Bannan et al. within 0.06 kcal/mol in water and 0.17 in octanol. The octanol mass-scaling result (5x faster convergence, same free energies) is clean and likely general.\n\nThe soft spot is the headline flexible-solute claim. The reduction in MAE for logP from 0.75 to 0.30 log units relative to experiment is based on seven N-acetyl amino-acid amides, with OPES and d-AFED parameters chosen without sensitivity analysis. More importantly, the d-AFED reweighting is dismissed as 'negligible' in Section II.A with no numbers. The stress-test note is right: with a 1000 K auxiliary thermostat and coupling constant 1000 kJ/mol/rad^2, the physical torsion is effectively slaved to the hot auxiliary variable. Under those conditions the sampled conformational ensemble is closer to 1000 K than 298 K, and if that population bias is not corrected, the improved agreement with experiment could be a fortuitous consequence of sampling elevated-temperature populations. The assertion that the conditional mean force is unaffected by the auxiliary temperature does not obviously hold, because the d-AFED coupling depends on the torsion coordinates and does not simply cancel in the conditional average the way an OPES bias along lambda does.\n\nNone of this is fatal. The rigid-solute work stands; the lambda-OPES dual-bias protocol is a real contribution; and the d-AFED coupling is a plausible way to accelerate torsional sampling. But the flexible-solute claim needs more than seven hand-picked cases. I'd ask for a quantification of the reweighting correction, a sensitivity scan over the d-AFED parameters (at minimum a lower coupling constant and a lower auxiliary temperature), and ideally a demonstration that the 298 K torsional distributions are recovered either through reweighting or through convergence of the mean force with respect to those parameters.\n\nThe paper is well written, the code and data are available, and the simulations are reproducible in principle. This deserves a serious referee. I'd send it to peer review with a request for revisions focused on the d-AFED reweighting and parameter sensitivity, not on the overall methodology.\n\nBring it to reading group? Yes, it will spark a good discussion about adiabatic separation and what counts as validation.","headline":"Solid lambda-OPES protocol with a convincing rigid-solute benchmark; the flexible-solute logP claim needs the d-AFED reweighting quantified before it can be trusted.","tokens_in":23495,"tokens_out":2592,"would_cite":true,"duration_ms":23781,"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":"The paper claims flexible-solute logP accuracy requires simultaneously enhanced sampling of the alchemical coordinate and solute conformations, which λ-OPES-d-AFED delivers, cutting mean absolute error from 0.75 to 0.30 log units.","keywords":["solvation free energy","lambda-dynamics","alchemical enhanced sampling","OPES","d-AFED","octanol-water partition coefficient","conformational sampling","mass scaling"],"falsifier":"A reader could settle the question by re-analyzing the stored d-AFED trajectories of the seven $N$-acetyl amino-acid amides with the explicit torsional reweighting procedure for d-AFED, and comparing the reweighted solvation free energies with the un-reweighted values reported here; if the differences exceed the reported statistical uncertainties, the 0.30 log-unit mean absolute error is contaminated by the auxiliary thermostat. A second decisive test is to repeat the $\\lambda$-OPES-d-AFED simulations at auxiliary temperatures of 500 K and 2000 K: if the predicted partition coefficients shift by more than the statistical error, the results depend on the nonphysical thermostat setting rather than on a converged conformational equilibrium.","tokens_in":22359,"feed_emoji":"🧪","tokens_out":21365,"duration_ms":166205,"temperature":0.7,"pith_summary":"This paper addresses a known bottleneck in molecular simulation: solvation free energies converge slowly because three families of motions—reorganization of the surrounding solvent, exploration of the alchemical coordinate $\\lambda$ that switches solute-solvent interactions on and off, and internal rotations of a flexible solute—relax on timescales far beyond ordinary simulation lengths. The authors claim all three can be handled in a single trajectory by combining solvent mass scaling, an adaptive OPES bias on $\\lambda$, and d-AFED, which drives selected dihedral angles by coupling them to hot auxiliary variables. For rigid solutes they show that cutting octanol atomic masses tenfold accelerates Hamiltonian replica exchange convergence by more than fivefold without changing the equilibrium free energy, and that a dual-bias $\\lambda$-OPES protocol matches replica exchange on comparable timescales without predefined $\\lambda$ windows. For seven flexible $N$-acetyl amino-acid amides, adding d-AFED to $\\lambda$-OPES lowers the mean absolute error of octanol-water partition coefficients from 0.75 to 0.30 log units relative to experiment, and shifts the predicted partitioning of Ac-Leu-NH$_2$ and Ac-Tyr-NH$_2$ into the experimentally observed water-favoring regime. The paper concludes that for flexible molecules, accurate partition coefficients require simultaneous alchemical and conformational sampling, and that the combined protocol provides a practical single-trajectory route to that goal.","feed_headline":"Torsion-boosted sampling halves logP prediction error","feed_subtitle":"Biasing alchemical and torsional coordinates together drops flexible-solute logP error from 0.75 to 0.30.","key_machinery":"The machinery is an extended Hamiltonian in which the alchemical coordinate $\\lambda$ is a dynamical variable propagated alongside the atomic coordinates, with a mirror-periodic mapping $\\theta \\in [0,2] \\to \\lambda \\in [0,1]$ that lets the trajectory traverse the alchemical pathway in both directions. The alchemical coupling uses the linear basis function (LBF) formulation, where $\\lambda$ enters only through switching functions $h_A(\\lambda)$ and $h_B(\\lambda)$ that smoothly turn on the full solute-solvent interaction and remove a softened Lennard-Jones capping potential, avoiding soft-core nonlinearities. OPES supplies the bias along $\\lambda$ as an adaptive potential built from a real-time kernel density estimate; the dual-bias variant applies OPES-Standard and OPES-Explore simultaneously, the former flattening the free energy profile and the latter driving barrier crossing between the end states. d-AFED accelerates conformational sampling by coupling each selected dihedral $\\xi_k$ to a harmonic auxiliary variable $s_k$ thermostatted at 1000 K with a large fictitious mass, chosen to preserve adiabatic separation from the physical degrees of freedom. The free energy is recovered by thermodynamic integration of the $\\lambda$-conditional mean force, which the paper argues is unaffected by the marginal sampling changes introduced by the biases and the auxiliary thermostat.","core_discovery":"The central claim is that the three coupled slow variables in solvation free energy calculations—solvent relaxation, the alchemical coordinate, and solute conformational modes—can be sampled simultaneously and accurately within one extended-dynamics simulation. The paper establishes this in stages: mass scaling of octanol by a factor of ten accelerates convergence of Hamiltonian replica exchange by more than fivefold while leaving equilibrium free energies unchanged; a dual-bias $\\lambda$-OPES protocol, in which OPES-Standard flattens the free energy profile along $\\lambda$ and a weaker OPES-Explore sustains transitions between the end states, reproduces HREX results in a single trajectory; and, for flexible $N$-acetyl amino-acid amides, coupling $\\lambda$-OPES with d-AFED on backbone and side-chain dihedrals lowers the mean absolute error of predicted octanol-water partition coefficients from 0.75 to 0.30 log units relative to experiment, including correcting the sign of partitioning for Ac-Leu-NH$_2$ and Ac-Tyr-NH$_2$. The paper interprets these results as demonstrating that simultaneous treatment of alchemical and conformational sampling is required for accurate partition coefficients of flexible molecules, and that the $\\lambda$-OPES-d-AFED protocol supplies that treatment in a single simulation.","pith_inferences":["If the pattern in this paper generalizes, a portion of the systematic error in computed octanol-water partition coefficients of flexible drug-like molecules that is currently blamed on force fields is really incomplete torsional sampling; comparing $\\lambda$-OPES-d-AFED against plain $\\lambda$-OPES on a diverse drug-like panel would test this directly.","The paper reports the d-AFED reweighting correction as negligible without quantitative support; a natural extension is to report reweighted and un-reweighted free energies explicitly for solutes with higher torsional barriers, where the 1000 K auxiliary population can deviate more strongly from the 298 K physical one.","The tenfold solvent mass-scaling result was established in octanol; applying the same rule to other viscous solvents (for example DMSO or ethylene glycol) would test whether the acceleration is robust beyond this one solvent."],"forward_implications":["If the central claim is right, solvation free energy and partition coefficient calculations on flexible solutes should treat conformational sampling as a first-class requirement; otherwise errors on the order of half a log unit may be misattributed to force-field inaccuracy.","The dual-bias $\\lambda$-OPES protocol matches Hamiltonian replica exchange results on comparable timescales while running as a single trajectory with no predefined $\\lambda$ windows and no replica coordination, which the paper notes is advantageous when replica-based approaches are computationally demanding.","Tenfold mass scaling of octanol speeds convergence more than fivefold without altering the equilibrium free energy, providing a cheap acceleration that can be combined with any sampling strategy in viscous organic solvents.","The protocol's validation on seven amino-acid amides establishes a foundation the paper proposes for applying alchemical free energy methods to larger and more conformationally complex solutes."],"supporting_citations":[{"why":"Supplies the reference solvation free energies and literature logP values against which the HREX and λ-OPES rigid-solute results are validated.","marker":"[8]"},{"why":"Provides the linear basis function alchemical model with the softened Lennard-Jones cap and switching functions on which the λ-dynamics protocol is built.","marker":"[21]"},{"why":"Defines the OPES adaptive bias framework used to construct the bias along the alchemical coordinate.","marker":"[34]"},{"why":"Defines the OPES-Explore variant that, combined with OPES-Standard, sustains barrier crossing in the dual-bias protocol.","marker":"[35]"},{"why":"Supplies the d-AFED reweighting procedure the paper applies and reports as producing negligible changes.","marker":"[56]"},{"why":"Introduces d-AFED, the method of coupling collective variables to high-temperature auxiliary variables used here to accelerate torsional sampling.","marker":"[63]"},{"why":"Provides the experimental octanol-water partition coefficients of N-acetyl amino-acid amides that define the 0.75-to-0.30 mean absolute error comparison.","marker":"[70]"},{"why":"Gives the extended Hamiltonian and the result that the λ-conditional mean force is unaffected by marginal sampling changes, the theoretical basis for reading free energies from the biased trajectory.","marker":"[71]"},{"why":"Provides the formula and criteria for choosing auxiliary masses and force constants to maintain adiabatic separation in d-AFED.","marker":"[73]"}],"fun_headline_variants":["Alchemical plus torsion sampling halves logP prediction error","Dual-bias λ-OPES with torsion biasing cuts logP error to 0.30","One trajectory for alchemical and torsional sampling in solvation","Integrated alchemical and conformational sampling improves logP accuracy","Single-run protocol for solvation free energies beats replica exchange"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the auxiliary torsional variables, thermostatted at 1000 K with large fictitious masses, leave the $\\lambda$-conditional mean force unbiased, so that solvation free energies can be read directly from the biased trajectory; the paper states that reweighting produced negligible changes without showing a quantitative comparison, and if that adiabatic-separation assumption silently fails, the improved mean absolute error of 0.30 log units could be an artifact of distorted torsional populations rather than a genuine conformational-sampling correction.","fun_headline_variants_meta":{"raw":{"variants":["Alchemical plus torsion sampling halves logP prediction error","Dual-bias λ-OPES with torsion biasing cuts logP error to 0.30","One trajectory for alchemical and torsional sampling in solvation","Integrated alchemical and conformational sampling improves logP accuracy","Single-run protocol for solvation free energies beats replica exchange"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00123,"raw_usage":{"total_tokens":5149,"prompt_tokens":1134,"completion_tokens":4015,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":750,"completion_tokens_details":{"reasoning_tokens":3925}},"tokens_in":750,"tokens_out":4015,"duration_ms":29868,"temperature":1.0,"reasoning_tokens":3925,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:28:26.124153+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A reader could settle the question by re-analyzing the stored d-AFED trajectories of the seven $N$-acetyl amino-acid amides with the explicit torsional reweighting procedure for d-AFED, and comparing the reweighted solvation free energies with the un-reweighted values reported here; if the differences exceed the reported statistical uncertainties, the 0.30 log-unit mean absolute error is contaminated by the auxiliary thermostat. A second decisive test is to repeat the $\\lambda$-OPES-d-AFED simulations at auxiliary temperatures of 500 K and 2000 K: if the predicted partition coefficients shift by more than the statistical error, the results depend on the nonphysical thermostat setting rather than on a converged conformational equilibrium.","supporting_citations":[{"cited_title":"2013 , journal =","cited_arxiv_id":null,"evidence_quote":"Supplies the reference solvation free energies and literature logP values against which the HREX and λ-OPES rigid-solute results are validated."},{"cited_title":"2015 , journal =","cited_arxiv_id":null,"evidence_quote":"Provides the linear basis function alchemical model with the softened Lennard-Jones cap and switching functions on which the λ-dynamics protocol is built."},{"cited_title":"2014 , journal =","cited_arxiv_id":null,"evidence_quote":"Defines the OPES-Explore variant that, combined with OPES-Standard, sustains barrier crossing in the dual-bias protocol."},{"cited_title":"2024 , journal =","cited_arxiv_id":null,"evidence_quote":"Supplies the d-AFED reweighting procedure the paper applies and reports as producing negligible changes."},{"cited_title":"2017 , journal =","cited_arxiv_id":null,"evidence_quote":"Provides the experimental octanol-water partition coefficients of N-acetyl amino-acid amides that define the 0.75-to-0.30 mean absolute error comparison."},{"cited_title":"2015 , journal =","cited_arxiv_id":null,"evidence_quote":"Gives the extended Hamiltonian and the result that the λ-conditional mean force is unaffected by marginal sampling changes, the theoretical basis for reading free energies from the biased trajectory."}],"review_version":1}