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REVIEW 3 major objections 4 minor 58 references

Relative Binding Free Energy Estimation of Congeneric Ligands and Macromolecular Mutants with the Alchemical Transfer with Coordinate Swapping Method

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2412.19971 v1 pith:WKMQF5D2 submitted 2024-12-28 physics.chem-ph

classification physics.chem-ph
keywords alchemicaltransfermethodcoordinateswappingrelativebindingfreeenergyR-grouptransformationprotein-peptidemutantsestimationmoleculardynamicssimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [Appendix, Eqs. (19)–(21)] 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.
  2. [Table 1] 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.
  3. [Table 2 and Figure 5] 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.
minor comments (4)
  1. [Abstract and Introduction] The phrase 'the the bound and unbound ligands' appears twice; please correct the duplication.
  2. [Appendix, final paragraph] 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.
  3. [References] Reference 49 is incomplete; it lists only 'Tan, Z.; Gallicchio, E.' with no title, journal, year, or DOI. Please supply the full citation.
  4. [Theory and Methods] 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.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the ATS RBFE estimator is a derived ensemble average with no fitted parameters; the Appendix's approximate indicator matching is a rigor gap, not a circular reduction.

full rationale

The central ATS free energy expression, Eq. (8), is obtained by a change of variables in the ratio of binding-constant partition functions (Eqs. 12-21). The perturbation energy u in Eq. (9) is defined as the potential difference after coordinate swapping and displacement, and the final ensemble average follows algebraically from multiplying and dividing by the denominator Boltzmann factor. No parameter is fitted to the benchmark results; soft-core and restraint parameters are taken from prior work and the AToM-OpenMM defaults, not tuned to the TYK2 or PDZ data. The comparison to ATM-RBFE is a consistency check between two methods by the same author, but the central validation also includes experimental comparisons and external single-topology values from Panel et al. Self-citations (Refs. 15, 28, 30-35) support implementation choices and prior ATM machinery rather than supplying the ATS exactness claim. The one substantive concern is not circularity: the Appendix's exactness proof contains the statement 'approximately I*(cA) -> I*(cA+d)=I(cA)' and relies on indicator regions being large enough, so the claimed mathematical exactness is not rigorously established and the bias from fluctuating anchor displacement is unquantified. This is an accuracy/rigor limitation to be weighed separately, not a case where the prediction reduces to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central derivation is a change of variables in a partition function ratio. It introduces no new physical entities or fitted constants. The main burden is the indicator-function matching approximation, which is flagged as 'approximately' in the Appendix.

free parameters (3)
  • Soft-core perturbation parameters (umax, uc, a) = 200 kcal/mol, 100 kcal/mol, 1/16
    Chosen from prior ATM work (refs 34, 35); not fitted to this paper's benchmarks, but they control the alchemical interpolation and convergence.
  • Flat-bottom restraint tolerance and force constant = 3-5 A tolerance, 25 kcal/mol/A^2
    Setup parameters that determine the size of the indicator regions; the proof's assumption that indicator functions map exactly relies on these regions being large enough.
  • Ligand displacement distance d = 45 A (TYK2), 40 A (peptide)
    Fixed displacement of the unbound ligand; the proof's approximate mapping I*(cA + d) uses this d.
assumptions (5)
  • standard math Statistical mechanics partition functions and Boltzmann ensemble averages
    The derivation starts from Eq. (12) for binding constants.
  • standard math Change of variables and Jacobian determinant in configuration integrals
    Used in Appendix to transform Eq. (18) to Eq. (21).
  • domain assumption Common regions of the two ligands have a bijective atom mapping with identical chemical types
    Required for swapping coordinates without changing the common-region internal energy; introduced in the Appendix before Eq. (19).
  • domain assumption The coordinate transformation maps the binding-site indicator function to the bulk indicator function exactly (or the regions are large enough that the approximation is negligible)
    The proof states 'approximately I*(cA) -> I*(cA + d)' and relies on I() being large enough; this is an approximation, not an exact identity.
  • ad hoc to paper The anchor displacement vector dBA equals the fixed bulk displacement d
    The transformation displaces variable atoms by dBA, while the indicator I* is centered at d; the proof assumes they match.

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Cite this review

Pith. "Pith review of Relative Binding Free Energy Estimation of Congeneric Ligands and Macromolecular Mutants with the Alchemical Transfer with Coordinate Swapping Method." pith.science (2026). https://pith.science/paper/WKMQF5D2

@misc{pith2026241219971,
  author       = {Pith},
  title        = {Pith review of: Relative Binding Free Energy Estimation of Congeneric Ligands and Macromolecular Mutants with the Alchemical Transfer with Coordinate Swapping Method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WKMQF5D2}},
  note         = {Machine review of arXiv:2412.19971}
}
read the original abstract

We present the Alchemical Transfer with Coordinate Swapping (ATS) method to enable the calculation of the relative binding free energies between large congeneric ligands and single-point mutant peptides to protein receptors with the Alchemical Transfer Method (ATM) framework. Similarly to ATM, the new method implements the alchemical transformation as a coordinate transformation, and works with any unmodified force fields and standard chemical topologies. Unlike ATM, which transfers the whole ligands in and out of the receptor binding site, ATS limits the magnitude of the alchemical perturbation by transferring only the portion of the molecules that differ between the the bound and unbound ligands. The common region of the two ligands, which can be arbitrarily large, is unchanged and does not contribute to the magnitude and statistical fluctuations of the perturbation energy. Internally, the coordinates of the atoms of the common regions are swapped to maintain the integrity of the covalent bonding data structures of the molecular dynamics engine. The work successfully validates the method on protein-ligand and protein-peptide RBFE benchmarks. This advance paves the road for the application of the relative binding free energy Alchemical Transfer Method protocol to study the effect of protein and nucleic acid mutations on the binding affinity and specificity of macromolecular complexes.

Figures

Figures reproduced from arXiv: 2412.19971 by the authors.

Figure 1
Figure 1. Schematic diagram illustrating the ATS coordinate transformation for the estima [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. A representative ligand pair from the TYK2 RBFE benchmark set. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Illustration of the ATM and ATS simulation setups for the protein-ligand RBFE [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Illustration of the ATS simulation setup for the protein-peptide RBFE calculations. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Diagram of the ATS-RBFE estimates from Table 2. The values are in kcal/mol, [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.