Topological potentials guiding protein self-assembly

Dear Dr. Spirandelli,

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Jianhan Chen, Ph.D.

Academic Editor

PLOS Computational Biology

Arne Elofsson

Section Editor

PLOS Computational Biology

Additional Editor Comments:

Apologies for the delay. We were waiting for a third reviewer who did not submit the report after the due date despite several reminders. Both reviewers clearly appreciate the innovation and importance of this work, while raising various minor and major concerns on a range of aspects. I will greatly appreciate a revised manuscript with all points thoroughly addressed. Thank you.

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At this stage, the following Authors/Authors require contributions: Ivan Lothar Arbo Spirandelli. Please ensure that the full contributions of each author are acknowledged in the "Add/Edit/Remove Authors" section of our submission form.

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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 study protein self-assembly using a computational approach that combines a morphometric geometric solvation model with a long-range topological potential derived from persistent homology. The central idea is to use weighted total persistence as an energetic bias to guide assembly pathways and reduce kinetic trapping in rugged energy landscapes. The authors apply the approach to several systems, including TMV dimers, hepatitis B core protein, SARS-CoV-2 ORF9b, and CD40 ligand, and report substantial improvements in assembly success rates compared to the geometric model alone.

The manuscript presents an interesting and potentially useful approach for improving simplified assembly simulations. The reported increases in assembly success rates are substantial, and the paper is generally clearly written. However, several points need to be addressed before publication.

1. The physical interpretation of the topological potential remains unclear. While the authors briefly relate a specific parameter choice to Gaussian curvature, the manuscript does not provide clear physical intuition regarding whether the topological term represents an effective approximation of omitted long-range interactions (e.g., electrostatic or hydrophobic effects) or functions primarily as an algorithmic bias that reshapes the energy landscape to reduce kinetic trapping. Relatedly, the manuscript frames protein assembly simulations as being dominated by short-range nonpolar interactions, whereas many assembly processes are strongly influenced by electrostatics, hydrogen bonding, and other longer-range effects. Since electrostatic interactions are omitted entirely, it remains unclear how the proposed topological potential compares to more conventional implicit-solvent or coarse-grained models that include electrostatics, and whether the topological term provides fundamentally new information or instead compensates for omitted physical interactions.

2. The manuscript focuses on relatively small homo-oligomeric systems, primarily dimers and trimers, rather than full viral capsids or larger supramolecular assemblies. Thus, the reported increases in “assembly success rates” correspond to improved formation of small native-like oligomeric complexes rather than full virus assembly. It would be useful for the authors to discuss more explicitly whether the proposed topological potential is expected to extend to larger-scale coarse-grained assembly simulations involving tens to hundreds of subunits, such as HBV or TMV capsid assembly. In particular, it remains unclear whether persistent homology can be computed efficiently using coarse-grained capsomers or bead-based representations rather than atomistic coordinates, whether the topological potential is expected to guide global shell closure or suppress malformed intermediates during capsid assembly, and how the computational cost is expected to scale with increasing system size.

3. Relatedly, the present model treats protein subunits as rigid bodies. In contrast, conformational flexibility often plays an important role in viral assembly pathways and polymorphism, including in coarse-grained models capable of assembling complete viral shells. See, for example, “From Disorder to Icosahedral Symmetry: How Conformation-Switching Subunits Enable RNA Virus Assembly,” Science Advances 11, eady7241 (2025). The authors should discuss whether the proposed topological framework could eventually be combined with flexible coarse-grained models and whether it is intended as a complementary guiding potential for improving existing coarse-grained assembly simulations rather than as a standalone assembly model.

4. The topological potential depends on weighting coefficients (λ0,λ1,λ2), which appear to be selected empirically through parameter scans, but the procedure used to choose these parameters remains somewhat unclear. The authors should clarify how the λi\lambda_iλi values are selected, whether they are optimized systematically or motivated by physical considerations, and how sensitive the results are to these choices. The apparent transferability across systems is interesting, but a more systematic robustness analysis would improve the conclusions.

Similarly, the implementation of Eq. (1) remains somewhat vague. The manuscript should more clearly state the numerical values used for the morphometric parameters, how these parameters are selected, and whether any of them are adjusted during the simulations. This clarification is particularly important for readers unfamiliar with morphometric approaches.

5. The reported improvements in assembly success rates (e.g., from 5% to 85%) are striking. However, the statistical interpretation of these values could be improved by including confidence intervals or uncertainty estimates, discussion of run-to-run variability, and additional context regarding the dependence on simulation parameters such as temperature and perturbation size. Since “success rate” is the primary performance metric of the manuscript, a more detailed quantitative discussion would improve the interpretation of the results.

Minor Comments

1. The description of persistent homology may be difficult for a broad audience. A more intuitive explanation in the main text would improve accessibility.

2. Figure 1 should more clearly explain the connection between the alpha filtration and the resulting topological potential.

3. The discussion of the morphometric solvation model should include a brief intuitive explanation of the integrated mean curvature C and integrated Gaussian curvature X of the solvent-accessible surface.

4. The manuscript states that simulations are driven by a Random Walk Metropolis algorithm, but the explanation in the main text is brief. Adding a short description of how moves are proposed and accepted/rejected would improve readability.

5. The definition of total persistence should include a simple illustrative example explaining the physical or geometric meaning of the birth (b) and death (d) values within the filtration.

6. The manuscript introduces Pearson correlation coefficients between different quantities. A short explanation of what the Pearson coefficient measures, and why it is informative in this context, would improve clarity for a broader audience.

7. The distinction between thermodynamic accuracy and kinetic accessibility is important and could be emphasized earlier in the manuscript.

8. Some notation associated with persistence measures and weighting coefficients could be simplified for readability.

Reviewer #2: the review is uploaded as an attachment

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: Yes: Vysakh Ramachandran

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Reproducibility:

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Dear Dr. Spirandelli,

We are pleased to inform you that your manuscript 'Topological potentials guiding protein self-assembly' has been provisionally accepted for publication in PLOS Computational Biology.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

Jianhan Chen, Ph.D.

Academic Editor

PLOS Computational Biology

Nir Ben-Tal

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 #1: The authors have addressed all my concerns and comments, and those of the other referee. Thus, I recommend the paper for publication.

Reviewer #2: All of my concerns have been addressed in the revised manuscript. The authors have responded appropriately to the reviewers' comments, and I believe the manuscript has improved significantly. I have no further concerns and recommend that the manuscript be accepted for publication.

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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 #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: Yes: Vysakh Ramachandran