{"id":"757ba116-8d6c-41e5-8134-7a95413380bd","arxiv_id":"2412.19971","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A new alchemical method, ATS, computes relative binding free energies for congeneric ligands and protein mutants by swapping coordinates of shared regions and transferring only the variable parts.","lead":"This paper introduces a new computational method, ATS, for estimating how mutations or small chemical changes to a drug molecule affect how tightly it binds to a protein. The method modifies an existing alchemical-free-energy approach so that only the changed part of the molecule is numerically perturbed, making calculations faster and applicable to large protein and peptide systems.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Appendix's exactness proof relies on 'approximately I*(cA) -> I*(cA + d) = I(cA)', so the claimed mathematical exactness of ATS is not established; the resulting bias from fluctuating dBA is unquantified.","rationale":"The central claim is the mathematical exactness of ATS. The only formal support is the Appendix proof, which contains an explicit 'approximately' step in mapping the indicator functions. This is the weakest load-bearing assumption: if the indicator mapping is not exact, the ensemble-average identity Kb(B)/Kb(A) = <exp(-beta u)>_RA+B does not follow exactly, and the RBFE estimator has an unquantified bias. The Jacobian determinant calculation is correct, and the rest of the derivation is standard once the indicator mapping is assumed, so the entire proof reduces to that mapping. The actual implementation defines the indicator on the anchor atom, which may make the mapping exact in practice, but the Appendix does not state or prove this; it uses a generic centroid and explicitly relies on large indicator regions. Thus the proof, as written, does not justify the 'exact' claim. The numerical benchmarks are supportive but not definitive: the TYK2 ATS-ATM RMSD of 0.37 kcal/mol is close to statistical uncertainty, yet a few pairs deviate by 0.5-0.8 kcal/mol, and the peptide benchmark shows a ranking reversal (A0M vs A0F) relative to experiment and to Panel et al., with WT-A0F overestimated by ~1.7 kcal/mol. These could reflect force-field inaccuracy, but they do not rule out a small methodological bias from the indicator approximation. Other issues, such as missing code/data, are real but secondary to the proof gap. A direct frame-by-frame test of the indicator mapping is a concrete way to determine whether the approximation is harmless for the tested systems; if it is, the conditional acceptance is justified, and if not, the exactness claim must be revised.","tokens_in":17995,"tokens_out":27109,"duration_ms":257097,"concrete_test":"Post-process an existing ATS trajectory of a TYK2 pair: for each saved frame, apply the ATS coordinate transformation (swap common-region coordinates and translate variable regions by the instantaneous anchor displacement dBA) and evaluate the indicator product I*(cA)I(cB) on the original frame and I(cA_transformed)I*(cB_transformed) on the transformed frame, using the same flat-bottom indicator centers and tolerance (5 A) as the simulation. If any frame yields different indicator product values, the exactness condition of Eq. (21) is violated for that frame; compute the fraction of violating frames and the reweighted change in <exp(-beta u)> to estimate the bias. If the fraction is zero for all frames, the indicator-mapping approximation is exact for that system and this concern does not land.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that ATS is 'mathematically exact' for R-group transformations, and this rests entirely on the Appendix proof. The proof performs the change of variables (19)-(20) and then asserts that the indicator product transforms as I*(cA)I(cB) -> I(cA)I*(cB). The text explicitly says 'approximately I*(cA) -> I*(cA + d) = I(cA)' and requires the indicator regions to be large enough. This is not an exactness proof. The transformed ligand centroid is a mass-weighted average of the common-region coordinates (swapped from the other ligand) and the variable-region coordinates (translated by the instantaneous anchor displacement dBA = rb - ra). This centroid equals the original centroid plus the fixed site-bulk displacement d only if dBA = d exactly and the mass distribution is favorable; in the dynamics dBA fluctuates because the anchors are restrained by flat-bottom potentials with 5 A tolerance. The deviation is approximately epsilon = (m_var/(m_com + m_var))(dBA - d), which can be several angstroms for large R-groups. When epsilon takes the transformed centroid outside the indicator region, the numerator integral after the change of variables is not equal to the denominator integral with the same indicator product, so Eq. (21) does not follow. The proof does not quantify this bias, and the paper's claim of mathematical exactness is therefore unsupported. The benchmarks do not resolve this: the TYK2 RMSD of 0.37 kcal/mol contains outliers (ejm42-ejm48: 0.82 vs 0.01; ejm42-ejm55: -0.86 vs -0.19), and the peptide A0M/A0F ranking is reversed relative to experiment and Panel et al. These are consistent with small systematic bias, though not conclusive.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces ATS-RBFE, an alchemical transfer variant for relative binding free energies in which only the variable R-groups of congeneric ligands (or mutated peptide side chains) are translated, while the coordinates of the common regions are swapped between the two ligands. The method is presented as a dual-topology scheme that retains ATM's compatibility with standard force fields while achieving the size-scaling advantages of single-topology approaches. The central theoretical claim is that the method is mathematically exact, with a proof in the Appendix. The paper reports benchmarks on the TYK2 inhibitor set, comparing ATS with standard ATM and with experiment, and on PDZ-domain/peptide mutants, comparing with literature single-topology calculations and experiment.","tokens_in":18364,"tokens_out":6503,"duration_ms":69329,"significance":"If the exactness claim were fully supported, ATS would be a valuable contribution: it extends the alchemical transfer framework to macromolecular R-group transformations, preserves standard chemical topologies, and avoids fitting any parameter to the benchmark results. The software is openly available, the benchmark systems are appropriate, and the comparison with ATM on TYK2 is a useful self-consistency check. However, the proof has an approximation at a load-bearing step, and several benchmark discrepancies are larger than the reported statistical uncertainties. The central claim that the method is 'mathematically exact' is therefore not established as written, and the validation evidence is more mixed than the text suggests.","major_comments":[{"comment":"The exactness proof requires that the change of variables maps the indicator product I*(cA)I(cB) exactly to I(cA)I*(cB). The text states, however, that 'approximately I*(cA) → I*(cA + d) = I(cA)', relying on the indicator regions being 'large enough'. This is an approximation, not an exact equality: dBA = rb − ra is an instantaneous, fluctuating quantity under the flat-bottom restraints used in the simulations, and the transformed centroid is a mass-weighted combination of swapped common coordinates and displaced variable coordinates, so the effective displacement is not exactly the fixed bulk displacement d. The resulting bias in Eq. (21) is not quantified. Please either prove an exact indicator mapping (for example by defining the bulk indicator relative to the instantaneous anchor displacement, or by constraining dBA to equal d) or explicitly restate the method's claim as approximate and provide a quantitative bound or estimate of the error.","section":"Appendix, Eqs. (19)–(21)"},{"comment":"The claim that the ATM and ATS estimates agree 'within statistical uncertainty' is not supported by the per-pair data. For ejm42–ejm48 the two estimates differ by 0.81 kcal/mol (0.82 ± 0.27 vs 0.01 ± 0.22), for ejm42–ejm55 by 0.67 kcal/mol, and for ejm31–ejm43 by 0.53 kcal/mol; in each case the difference exceeds the combined one-sigma uncertainty. Please report per-pair significance tests or otherwise reconcile these outliers with the statement that the 0.37 kcal/mol RMSD is within statistical uncertainty.","section":"Table 1"},{"comment":"The PDZ/peptide benchmark is described as confirming the correctness of ATS, but the quantitative agreement is limited. For WT–A0F the ATS value (2.17 ± 0.28 kcal/mol) differs from the Panel et al. value (0.50 ± 1.00) and from experiment (0.43) by well over 1 kcal/mol, and the A0M/A0F ranking is reversed relative to experiment, as the text acknowledges. These results do not demonstrate quantitative accuracy; the conclusions should be tempered accordingly, or additional analysis should be provided to separate model error from statistical error in these comparisons.","section":"Table 2 and Figure 5"}],"minor_comments":[{"comment":"The phrase 'the the bound and unbound ligands' appears twice; please correct the duplication.","section":"Abstract and Introduction"},{"comment":"The sentence 'Finally, Eq. (21) is recovered by multiplying and dividing the integrand in the numerator by the Boltzmann factor in the denominator, .' is incomplete and appears to be missing the Boltzmann factor expression; please complete it.","section":"Appendix, final paragraph"},{"comment":"Reference 49 is incomplete; it lists only 'Tan, Z.; Gallicchio, E.' with no title, journal, year, or DOI. Please supply the full citation.","section":"References"},{"comment":"The notation would be clearer if the text distinguished the fixed bulk displacement d from the instantaneous anchor displacement dBA throughout; the current usage of '≃' in the Appendix obscures this distinction, which is central to the exactness issue.","section":"Theory and Methods"}],"recommendation":"major_revision","confidential_remarks":"The exactness claim is repeated in the abstract, introduction, and conclusion; if the approximation in the Appendix is acknowledged, all of these statements need to be revised consistently. The journal scope is appropriate, and I see no citation or novelty concerns beyond the incomplete reference noted above."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The coordinate-swapping idea is the genuinely new thing here. Extending ATM so that only the variable R-groups are displaced, while the common core is swapped in place, is a clever way to make the perturbation scale with the difference between ligands rather than their size. That is worth something, especially since it opens the door to protein and peptide mutants, where dual-topology ATM was not practical. The paper also does solid work on the mechanics: the Jacobian argument in the Appendix is correct as far as it goes, the gradient formulas are clearly derived, and the TYK2 comparison against standard ATM (RMSD 0.37 kcal/mol) is a reasonable self-consistency check. The peptide benchmark, despite small system size, shows the method can be applied to a class of problems that was previously out of reach.\n\nNow the soft spot. The Appendix says the proof is \"mathematically exact,\" but the key step maps I*(cA) to I*(cA+d) = I(cA) with the qualifier \"approximately\" in the text. That qualifier is not decorative: dBA is the instantaneous anchor displacement, which fluctuates under the flat-bottom restraint, so the transformed centroid does not always land in the shifted indicator region. The bias from this is real and unquantified. You can see possible traces of it in the outliers (ejm42-ejm48 off by 0.8 kcal/mol, the A0M/A0F ranking reversal), though those are not conclusive. The authors should either prove that the indicator product is preserved exactly under the restraint, or state the method as asymptotically exact in the large-binding-site limit and quantify the error. That is an honest fix, not a fatal one.\n\nA secondary issue: no ATS-specific code or data are provided, only the general AToM-OpenMM package, so a reader cannot easily reproduce the ATS runs. This is a modest but legitimate referee request.\n\nWho gets value from this paper? Anyone working on alchemical RBFE methods or practical binding-affinity prediction, and researchers studying protein-protein or peptide interactions with alchemical protocols. The paper deserves a serious referee: the core idea is sound, the benchmarks are useful, and the proof gap is fixable. I would send it out, with the clear message that the exactness claim needs to be either defended rigorously or softened before acceptance.","headline":"The coordinate-swapping extension of ATM is a real and useful idea, but the claim of mathematical exactness goes beyond what the Appendix proof supports, and the authors should be pushed to either fix that gap or soften the claim.","tokens_in":18881,"tokens_out":1317,"would_cite":true,"duration_ms":15280,"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":"ATS computes exact relative binding free energies by transferring only the changed R-group and swapping common-region coordinates, so the cost scales with the mutation, not the ligand.","keywords":["alchemical transfer method","coordinate swapping","relative binding free energy","R-group transformation","protein-peptide mutants","binding free energy estimation","molecular dynamics simulation"],"falsifier":"Recompute a single ATS RBFE with progressively wider flat-bottom restraints on the anchor atoms; if the predicted value drifts by more than the statistical uncertainty, the indicator-mapping assumption is failing rather than being a benign approximation.","tokens_in":17803,"feed_emoji":"🧬","tokens_out":8781,"duration_ms":75629,"temperature":0.7,"pith_summary":"This paper introduces Alchemical Transfer with Coordinate Swapping (ATS), a method for computing relative binding free energies (RBFEs), the difference in binding strength between two similar ligands or between a protein and its mutant. Instead of alchemically transferring entire ligands between bulk solvent and a receptor binding site, ATS displaces only the atoms that differ between the two molecules and swaps the coordinates of the atoms they share. The paper argues that the perturbation energy and its statistical fluctuations then depend on the size of the changed region, not on the size of the whole ligand, which makes large and macromolecular partners tractable. It proves in an appendix that the estimator is mathematically exact, and validates the method on a protein-ligand benchmark and a protein-peptide mutant benchmark.","feed_headline":"Mutant binding predictions now scale with the mutation, not the ligand","feed_subtitle":"Alchemical Transfer with Coordinate Swapping freezes large common regions, making protein and peptide mutants tractable to compute.","key_machinery":"The load-bearing object is a coordinate transformation applied to the $RA+B$ configuration: coordinates of the mapped atoms in the common regions are exchanged, $r_{A'} \\leftrightarrow r_{B'}$, while the variable-region atoms are translated by the anchor displacement, $r_{A''} \\to r_{A''} + d_{BA}$ and $r_{B''} \\to r_{B''} - d_{BA}$. The perturbation energy is $u = U_{RB+A} - U_{RA+B}$, and the relative binding free energy is obtained from $\\Delta\\Delta G^\\circ_b = -(1/\\beta)\\ln\\langle e^{-\\beta u}\\rangle_{RA+B}$. The transformation's Jacobian determinant is 1, so no weight correction is needed, and its forces are assembled from gradients of the transformed potential. A soft-core alchemical interpolation $W_\\lambda[u]$ and a multi-state free energy estimator are used to converge the exponential average.","core_discovery":"The central claim is that the ratio of binding constants, $K_b(B)/K_b(A)$, equals the ensemble average $\\langle e^{-\\beta u}\\rangle_{RA+B}$ evaluated with ligand A bound and ligand B in bulk, where $u$ is the potential energy change caused by (i) translating the variable R-group of A by the anchor displacement $d_{BA}$ and that of B by $-d_{BA}$, and (ii) swapping the coordinates of the mapped atoms of the common region. Because the swapped atoms occupy each other's positions, the covalent structure of the common region is preserved and contributes almost nothing to the perturbation. The proof in the appendix shows the coordinate transformation has unit Jacobian, so no Jacobian factor enters the ensemble average, and relies on the binding-site and bulk indicator functions mapping onto each other under the displacement. On the TYK2 benchmark, ATS agrees with the standard whole-ligand ATM protocol within statistical error (RMSD 0.37 kcal/mol, correlation 0.91), and on the PDZ-peptide benchmark it yields converged RBFEs for single-point mutants that track the experimental ranking.","pith_inferences":["The exactness proof assumes the displaced coordinates land exactly inside the appropriate indicator region; because simulations use finite restraints, I would expect a small, unquantified bias that grows with anchor flexibility.","A direct way to test this is to recompute one mutation under several restraint tolerances: an exact estimator should be insensitive to the tolerance, so any systematic drift would expose the approximation.","The same swap-and-shift trick could be applied to other alchemical problems, such as hydration free energies or host-guest binding where only a small substituent changes on a large scaffold.","If the size-independence claim holds, ATS may open protein-protein and RNA-mutant RBFE calculations, where current whole-complex alchemy is dominated by the cost of the unchanged bulk of the molecule."],"forward_implications":["ATS makes RBFE calculations practical for congeneric ligands and macromolecular single-point mutants because enlarging the common region does not enlarge the alchemical perturbation.","For R-group transformations, ATS should converge as quickly as single-topology methods while keeping dual-topology simplicity: unmodified force fields and standard chemical topologies.","Because only the variable region is transferred, ATS extends alchemical RBFE to protein, peptide, and potentially nucleic acid mutations that whole-ligand transfer cannot handle.","The TYK2 benchmark shows ATS and standard ATM agree within statistical error (RMSD 0.37 kcal/mol, correlation 0.91), supporting the correctness of the new pathway.","ATS is compatible with any energy function, including neural-network, polarizable, and quantum-mechanical potentials, so its efficiency gain carries over to advanced models."],"supporting_citations":[{"why":"introduces the ATM-RBFE framework and dual-topology coordinate-transfer estimator that ATS extends.","marker":"[15]"},{"why":"supplies the statistical thermodynamics of binding constants and the indicator-function formulation used in the exactness proof.","marker":"[16]"},{"why":"provides the TYK2 benchmark set and experimental binding affinities used to validate ATS against ATM.","marker":"[38]"},{"why":"gives single-topology RBFE values for the PDZ-peptide mutants that ATS results are compared against.","marker":"[42]"},{"why":"supplies the molecular dynamics software implementation used to run the ATS simulations.","marker":"[30]"},{"why":"provides the multi-state free energy estimator used to analyze the perturbation energy samples.","marker":"[48]"}],"fun_headline_variants":["ATS freezes ligand common parts to speed mutant binding predictions","Swap-only alchemy predicts mutant binding with full-ligand accuracy","Coordinate swapping makes mutant binding free energy tractable","Frozen common regions, swapped coordinates: faster mutant RBFE","Alchemical swap method cuts mutant binding cost without accuracy loss"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof requires that after the displacement and swap each ligand lands exactly in the indicator region occupied by the other, which in practice is only approximated by finite restraints on the anchor atoms.","fun_headline_variants_meta":{"raw":{"variants":["ATS freezes ligand common parts to speed mutant binding predictions","Swap-only alchemy predicts mutant binding with full-ligand accuracy","Coordinate swapping makes mutant binding free energy tractable","Frozen common regions, swapped coordinates: faster mutant RBFE","Alchemical swap method cuts mutant binding cost without accuracy loss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000191,"raw_usage":{"total_tokens":1373,"prompt_tokens":1008,"completion_tokens":365,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":624,"completion_tokens_details":{"reasoning_tokens":282}},"tokens_in":624,"tokens_out":365,"duration_ms":4233,"temperature":1.0,"reasoning_tokens":282,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:42:36.703495+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute a single ATS RBFE with progressively wider flat-bottom restraints on the anchor atoms; if the predicted value drifts by more than the statistical uncertainty, the indicator-mapping assumption is failing rather than being a benign approximation.","supporting_citations":[{"cited_title":"K.; Given, J","cited_arxiv_id":null,"evidence_quote":"supplies the statistical thermodynamics of binding constants and the indicator-function formulation used in the exactness proof."},{"cited_title":"A.; Lu, C.; Scarabelli, G.; Albanese, S","cited_arxiv_id":null,"evidence_quote":"provides the TYK2 benchmark set and experimental binding affinities used to validate ATS against ATM."},{"cited_title":"J.; Simonson, T","cited_arxiv_id":null,"evidence_quote":"gives single-topology RBFE values for the PDZ-peptide mutants that ATS results are compared against."},{"cited_title":"https://github.com/Gallicchio-Lab/AToM-OpenMM, 2024","cited_arxiv_id":null,"evidence_quote":"supplies the molecular dynamics software implementation used to run the ATS simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the multi-state free energy estimator used to analyze the perturbation energy samples."}],"review_version":1}