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Exploring the Structural Lexicon of the Proteome via Metric Geometry

PLOS Computational Biology

Dear Dr. Gonzalez Camara,

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PLOS Computational Biology

Ferhat Ay

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PLOS Computational Biology

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors introduce the methods/algorithms from the area of metric geometry to the study of protein structures. Problems involving protein structure comparisons can be formulated within a metric geometry framework (could probably be used for RNA/DNA and chemicals, too). Apparently some of the algorithms necessary to efficiently solve such problems from this realm were developed not too long ago, and the authors demonstrate the utility of these methods with a number of very interesting applications to computational structural biology.

Their applications include identifying the switch regions in an oncoprotein, functional domains in evolutionarily distant viral proteins, permuted motifs in a group of homologous proteins, recognizing RNA polymerases from different viral phyla, and looking for conserved small structural motifs across the human proteome.

A very nice feature of this approach is that the method does not rely on sequence order, so that structure similarity between motifs that may be sequence-wise permuted in different structures can still be recognized. They give a nice example of this with the RdRps (RNA polymerases).

The paper is very well written and the results appear to be reasonable. My comments are mainly concerned with adding a bit more of explanation to clarify a few things.

The introductory paragraph in Methods could use some clarification. The matrix T is supposed to be a 0/1-valued matrix and it is stated that each row sum should be equal to 1, as well as each column sum. But this requirement on the row and column sums implies that T must be a square matrix, i.e. m equal to n. I think that should be made clear at this point in the paper. This implies that one must be careful about choosing the subsets of atoms to compare. I think this is the simple reason for some of the limitations mentioned at the end of the Discussion.

For the problem of computing the matrix to optimize the GW cost, are there any computational complexity results for the approximation algorithms? I.e. how good are the approximations and what about the running times? Whatever is known would be good to mention; perhaps this could inspire improved algorithms to be developed.

On p. 19 they refer to ‘Duplonaviricota’, I think this is a little typo and should probably be ‘Duplornaviricota’.

For the RdRps test, it says on p. 20 that they “… augmented this dataset with 300 non-RdRp decoy structures that clustered at 97% amino acid sequence identity …” Do they mean the decoys by themselves formed a cluster at pairwise 97% sequence identity?

I am not an expert on viruses, but given that the results in Fig 2B look quite good, is it in fact true that the RdRps are a basis for the classification of these riboviral phyla to begin with? I think that is fine but think that it would be good to state this, to clarify for other non-experts.

Reviewer #2: This paper introduces GWProt, a computational framework that applies Gromov-Wasserstein (GW) and fused Gromov-Wasserstein (FGW) optimal transport to protein structure alignment. The authors propose a local geometric distortion measure derived from the GW objective to identify structurally conserved or variable regions. The approach is demonstrated on several biological applications, including detection of conformational switch regions in KRAS, identification of motifs in RdRps, and discovery of recurrent short structural fragments across human protein domains. While the approach is interesting, I have several concerns on the lack of algorithmic details, computational efficiency, stability of the GW/FGW outcomes, and the genuine benefit of solving such a computationally expensive problem over simple and cheap baselines.

Specific points:

1. The feasibility definition of T is problematic. When n does not equal m, it is impossible to enforce \sum_i T_{i,k}=\sum_k T_{i,k}=1. Depending on how the feasibility of T is defined, Eq. (3) may not be equivalent to the more commonly used formulation where the Wasserstein part is given by <\delta, T>.

2. Related to the previous point, if the feasible set is indeed the standard feasible set used in balanced OT with uniform initial and terminal distributions, how would one interpret the soft matching represented by T? For example, when n and m are significantly different (say n > m), balanced OT will force splitting mass of points in Y to X, causing large distortion values even if Y is identical to a subgraph of X. Could the authors discuss or explore the usage of unbalanced or partial OT setup in this application?

3. The algorithm used is unclear. Network simplex is for linear problems and GW and FGW are quadratic. Solving GW or FGW typically involves an outer loop with inner steps to iteratively solve linear problems. The full algorithm including the linearization, should be described.

4. The decomposition in Eqs. (4) and (5) are immediate algebraic restructuring of the loss term. I believe that this is rarely used in practice because GW and FGW are non-convex. Typical algorithms guarantee convergence of objective value to a local minimum but the coupling matrix is often only guaranteed to converge to a stationary point. Thus GW and FGW are more trustworthy as a global metric and for representing the global coupling structure. Zooming into distortions due to individual points could be highly unstable. Could the authors clarify this point, or at least demonstrate numerically that the residue level interpretation is stable when different initializations of GW/FGW algorithms are used?

5. Computing GW/FGW is often computationally costly, even with subsampling, when used to compute pairwise distances. Could the authors clarify the computational complexity and empirical computing time to conduct an analysis at such scale? The ~2000 proteins implies several million of FGW computations and the clips clustering analysis involves pairwise FGW computation for over 20000 samples. Could the authors clarify if any efficient approximation was used?

6. It is unclear how the many hyperparameters in the study were selected. For example, the \alpha in FGW, number of downsampling, 7-residue window, median distortion as a threshold, etc. A clarification of all the parameter choices and some sensitivity analysis study of the parameters would be helpful.

7. Related to the previous point, the clips are chosen by rolling a 7-residue window and thresholding the average distortion of the window by the median distortion of the domain. This median threshold is rather arbitrary. I suggest exploring some more rigorous statistical strategy.

8. In the only example with comparison to two existing methods (TM-align and Foldseek), GWProt is ranked the 3rd in 3 out of 5 and the 2nd in 2 out of 5 tasks. So the improvement over existing approaches is rather insignificant. I wonder how much benefit does solving original GW/FGW problem really bring. It would be interesting to see if a much simpler approach would achieve similar performance. For example, optimize a rigid-body motion and let I={(i_k,j_k)} be pairs of nearest neighbor points from the two proteins after performing the rigid-body motion on protein B, and minimize \sum_k \delta(i_k,j_k). A coupling T, if needed, can be recovered by just solving a Wasserstein OT using the optimal rotation+translation.

Reviewer #3: The work reported in this manuscript relies on extremely large all-vs-all GW computations. However, there is no report of the computational cost as a reference point for comparison, or for independent replication – ie. hardware resources used, runtimes. This would shed light as to how deployable the GW computations are across a wider variety of computing environments. This aspect is particularly important because GW is known to be computationally expensive and the authors do mention this fact. Therefore, I believe the authors should provide this context and reference to allow for readers to assess replicability or deployability in their own computing environments.

The section “GW distances enhance the discovery of previously unseen viral phyla” is potentially interesting, but the conclusions should be softened and be aligned to the fact that the reported performance differences between GWProt, TM-align, and Foldseek are relatively small. Furthermore, the authors explicitly acknowledge that GWProt is not the best performer in any individual phylum.

Although the embedding construction differs substantially between methods, no attempt was made to harmonize post-processing (e.g. distance normalization, embedding method).It is therefore unclear whether the observed differences are due to the alignment method itself, or the way the structural space is constructed. I recommend either providing a more careful normalization and calibration across methods, or reframing this section as a complementarity demonstration rather than a performance comparison. The majority-vote classifier result should be emphasized more.

The structural motif analysis is interesting, but remains largely descriptive. Beyond the two example motif clusters there is no direct demonstration that newly identified motifs correspond to known binding sites, known functional sites / functional microenvironments, or known fold-specific motifs. Given the existing literature on local structural motifs and microenvironments, a short comparative analysis (for example against existing motif libraries or known structural signatures) would substantially strengthen the biological interpretation. For example, have they considered looking at variations or conservations of 3D motifs/substructures, such as those that can be found by tools like Rasmot 3D Pro, ProBis, Pyscomotif, within the same clips or whether different clips can contain conserved 3D motifs?

The physical interpretation of local geometric distortion could be further clarified because readers might wonder how strongly it correlates with local RMSD or local distance-matrix deviations.

I accept that downsampling of RdRps to 200 residues is necessary for computational reasons, but the manuscript does not assess how much information is lost as a result of the downsampling. This could be a useful reference point for readers.

The term “clip” is intuitive but non-standard in structural bioinformatics. A short comparison with “fragments”, “structural motifs”, “local motifs”, or “tertiary/3D substructures” used in previous literature would improve clarity.

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Dear Dr. Gonzalez Camara,

We are pleased to inform you that your manuscript 'Exploring the Structural Lexicon of the Proteome via Metric Geometry' has been provisionally accepted for publication in PLOS Computational Biology.

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Section Editor

PLOS Computational Biology

Ferhat Ay

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #2: My comments have been addressed pretty well. I think the paper is suitable for publication.

Reviewer #3: The authors have satisfactorily responded to my queries and comments.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #2: No

Reviewer #3: No