Dynamics-inspired Structure Hallucination for Protein-protein Interaction Modeling

• Lack of clarity: It remains unclear what the actual contribution is and what the main theme of the paper is. The title seems to indicate that one main component will be method that produces "halluzations", but later this is hardly picked on. Instead it appears that the masked mutation modeling is a core component, but a bit later again the PDC-Net is crucial. Similarly, the application area remains obscure: is it about predicting protein-protein-interactions or about changes in 3D conformation through mutation or is it about predicting free energies. The paper could be improved a lot by a consistent theme and improved writing.

• Significance: From the application perspective, this work appears very narrow: it can only be applied to antibody-antigen complexes, for which protein mutations are in question. Machine learning methods should be designed to solve a multitude of problems and even application papers should at least aim for broad application areas or point to similar problems in other domains. However, it appears that a very narrow problem is solved by stitching together a couple of machine learning components. The work is also of limited relevance because the performance difference to other methods could just arise by chance.

• Originality: It remains unclear what the novelty of this work is. The method has some novel components, such as the PCD-Net, and a somewhat novel objective. The application, however, is not novel and very narrow. The authors should clearly state what they see as their novelty and then embed it into related works. The authors should state if other methods arise as special cases of their method.

• Technical errors: a) It appears that Huber-loss breaks the equivariance of the method. Can the authors define Eq (2) clearer because Huber loss is not defined for vectors. Is it applied component wise. Can you theoretically show that equivariance is kept? b) Results are shown without error bars and confidence intervals (across re-trainings or training sets), Table 1, such that the difference between performance values could just arise by chance. Furthermore non-significant digits are likely shown in Table 1. The authors should perform nested cross-validation (if computationally feasible), or re-run the training multiple times. Ideally the method should also be applied to more than one dataset.

1. The paper may lack a clear justification for why incorporating dynamic properties into geometric GNNs enhances model performance relative to traditional static approaches. It would be helpful to demonstrate more about the motivations for using PDC-Net and its role in predicting changes in binding affinity.
2. There is a notable formatting issue near Figure 4 and the associated paragraph, where overlapping text obscures readability.
3. The definitions of various notations in Sections 2 and 3 could benefit from greater clarity. Certain variables are not explicitly defined, leading to potential ambiguity. A table summarizing the key notations and their meanings would improve comprehension and ensure that readers can follow the mathematical derivations without confusion.

The description of the Refine-PPI workflow is unclear at certain points. My best guess is that the authors suggest a denoising task (==MMM) on the wildtype structure for training. The motivation/post-analysis for MMM did not make it clear for me, why this might be especially useful for ddG prediction. Why do authors think that learning to denoise wildtype structures is advantagous for better ddG prediction?

Furhter presentation points unclear:

• Figure 3A: It seems that something is masked at the mutant and not at the wildtype. This is possibly in the inference mode. Is there no masking in the inference mode for wildtype, but instead only for mutant type?
• Looking at "Algorithm 1" it is completely unclear what $\mathcal G_t^{\text{WT/MT}}$ or $\tilde{\mathcal{G}}_t^{\text{WT/MT}}$ exactly should be? The link to equation (1) makes it even more confusing as this describes an initialization for coordinates, which in Algorithm 1 themselves also seem be denoted as $x_t^{\text{WT/MT}}$.
  ==> This is not only about "Algorithm 1" but also all the describing text in the main paper, which describes MMM. Notation is used in a confusing way.
  lines 839-840: Why are coordinate updates computed at all? I don't see them used anywhere later. Only after a long time of guessing how this algorithm might work, it seems that there might be a relationship to $\tilde{\mathcal{G}}^{\text{MT}}$. But this is nowhere made clear, which makes it hard to judge whether the author's contribution might be a meaningful contribution at all.
• One of the most confusing sentences in the paper to me: "It is worth noting that the resulting $x^{\text{WT}}$ does not carry gradients with no backpropagation at this phase". It's completely unclear what the authors want to say with this.
• What exactly is masking in the sense of the authors? Is it equivalent to denoising of coordinates or is the amino acid type somehow also masked by a mask token, which is trained to be predicted? To my opinion denoising should be denoted as denoising and masking should be denoted as masking, but to interchangeably use these terms is confusing. At least I don't see any masking in "Algorithm 1" which is in accordance to usual usage of masking in deep learning.

There seems to be an error in the equivariance proof (equation 11), which might be fixable, but some of the equalities in the equation are questionable. Or is $\Sigma$ always diagonal? ==> then the algorithm notation could be simplified and written without matrices possibly.

It is unclear how PDC integrates with MMM. What is the relationship to Algorithm 1? This is poorly explained.

Empirical evaluation:

• There is no reporting of the variance (error bars) in Table 1. This should be at least be possible for RMSE and MAE across the individual predictions. Even more interesting would the evaluation according to a cluster-cross-validation procedure to see variablity of correlation and AUROC. Further statistical tests showing whether Refine-PPI is superior to the other methods would be helfpul to judge whether Refine-PPI is a useful contribution.
• Why is Pearson correlation useful and one of the main metrics? Is there some indication of linear relationship between predictions and ground truth?

Typos: The paper needs a massive effort to improve writing/presentation and formatting. Here 3 other pieces that need to be made better:

• lines 416-417: Figure 5
• chapter A.3 empty: At this place there should be the algorithm.
• Figure 9: What is a seed-PDB? What is an "acceptable prediction error"?

Further Remark: Luo et al. (2023) was cited in an improper way in the main part of the manuscript. Large parts of Table 1 seem to be copies of their results.

1. Generalization of EGNN to the sets of gaussians is trivial, from the text of the paper it seems that according to the eq. 5, 6 the updates to the average and variance are not coupled, because phi_mu and phi_sigma are two independently learned functions. Appendix B.2 somewhat corrects this approach. However, on lines 250, 262 authors treat functions of gaussian distributions correctly. In general, the introduction of PDC-Net is unclear in whether it treats set of gaussians as probability density distribution or as the abstract mathematical objects transformed with rotations and translations as rigid bodies. In any case clarification is needed and if set of gaussians going into PDC-Net is indeed a probability distribution, it would be nice to have a full derivation of mean and variance updates upon transformation by the EGNN.
2. Proof in appedix D is given only for the case of main text variant of PDC-Net.
3. Lines 238-245 Analogy provided by the authors is rather awkward: atomic position uncertainty is negligible, compared to thermal fluctuations; Quantum numbers just enumerate solutions to the Shrodinger equations for steady state system consisting of electron and an atomic nucleus. I advise removing this analogy completely or asking for help someone more familiar with quantum mechanics/quantum chemistry.
4. The contribution of the PDC-Net itself to the final evaluation result is unclear. What if we substitute PDC-NET for EGNN + standard distances/angles encoding, how will it change the final result?