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Extracting host-specific developmental signatures from longitudinal microbiome data

PLOS Computational Biology

Dear Dr. Erdős,

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Vicky Yao

Academic Editor

PLOS Computational Biology

Marc Birtwistle

Section Editor

PLOS Computational Biology

Additional Editor Comments:

Both reviewers found the application of PARAFAC2 to longitudinal microbiome data timely and the manuscript well-organized, but also have raised concerns that must be addressed. The most critical issue is the one raised regarding methodological novelty, especially Reviewer 2's comment regarding substantial overlap with Ramirez et al. Clearly articulating what adaptations were required for microbiome data and what distinguishes the methodological contribution of this work is essential. Both reviewers also raise concerns regarding validation, including improvements to simulations, etc. The clarifications suggested by reviewers should all be addressed through revisions to the text and explained in the response.

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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: This manuscript extends standard matrix factorization ideas to longitudinal microbiome studies by working in a tensor setting (subject by taxa by time), where each latent component can be interpreted as a microbial signature, together with its temporal progression and its expression across individuals. The authors built on the widely used CP tensor decomposition, which assumes a single shared time factor across all subjects, and propose using PARAFAC2 to relax this assumption by allowing subject-specific time factors. PARAFAC is not new in itself; it is an existing tensor factorization algorithm that predates this paper by decades. The paper’s novelty is in adapting PARAFAC2 as an analysis framework for longitudinal microbiome data, and in showing that it can capture subject-specific temporal shifts/delays that CP-based tensor methods miss. Conceptually, this is a valuable extension for longitudinal microbiome research because many biological processes (maturation, perturbation, recovery, dietary response, etc.) share similar overall patterns but with heterogeneous timing and pace across individuals.

Overall, I find the contribution timely and potentially very useful, and I appreciate the careful comparisons between CP and PARAFAC2 on simulations and real-world microbiome cohorts, as well as the attention to replicability. I have several major points that hopefully would strengthen the manuscript’s clarity and impact:

Parameterization/Model complexity: Since PARAFAC2 is more flexible than CP (subject-specific time factors rather than a shared time factor), it would help readers to understand the cost of this flexibility. Could the authors describe how many additional free parameters PARAFAC2 uses compared to CP? How is this flexibility related to sample size (both number of subjects and time points) and overfitting risk?

Biological meaning of the constant cross-product constraint: This constraint is mathematically well-motivated to solve the parameter identification challenge, but it is less clear what it implies biologically. Could the authors provide an intuitive biological interpretation of this constraint, and discuss when it might be biologically unreasonable for microbiome time series?

Validation and extraction of group-level trajectories: I agree with the current approach of comparing inferred trajectories across predefined groups as an indirect validation and interpretation strategy. However, I wonder whether the framework could more directly extract group-level temporal patterns, instead of either a single shared pattern (CP) or fully subject-specific patterns (PARAFAC2). A clinically relevant middle ground would be a model with group-specific time factors, which could be useful for stratified medicine applications. Even if not implemented, it would strengthen the paper to discuss this as a natural extension and its potential clinical applications.

Non-negativity and interpretability of taxa signatures: In Fig. 3, the displayed microbial signatures show entirely positive values, which makes me wonder whether non-negativity is imposed on taxa loadings (like in non-negative matrix factorization). It seems that the authors apply a CLR transformation before tensor decomposition and signed values are expected. I would appreciate some clarification on whether negative values are allowed.

If negative values are possible, I am worried that negative loadings can be challenging for biological users to interpret and may reduce their enthusiasm to use if not explained carefully. Please provide a clear interpretation of what positive vs. negative loadings mean and consider showing an example where negative loadings occur (or explicitly state if they do not).

Make biological assumptions more explicit/Reduce technical barrier: The writing is sometimes quite technical, which is good for a solid paper but may compromise readability. It would help to more explicitly state the biological assumptions behind the modeling choices. For example: what is the biological assumption underlying the mathematical approximation of longitudinal microbiome variation by a sum of rank-1 outer products? Similarly, terms like loadings are standard in dimensionality reduction but can be unintuitive for many microbiome readers. A short plain language explanation would make the manuscript more accessible to broader readership.

In addition to these points, I think the work is promising and could become a useful tool for detecting and characterizing heterogeneous, time-dependent microbiome shifts across patients if these clarifications and biological interpretations are strengthened.

Reviewer #2: In this study authors apply PARAFAC2 tensor factorization framework to several microbiome datasets, and an additional simulated dataset to showcase the ability of the framework to model within subject longitudinal variability in microbial composition patterns. The application of PARAFAC2 to longitudinal microbiome data is novel, and well-positioned with respect to the prior CP applications in microbiome research. Authors also note a recent application of PARAFAC2 to single-cell RNA-seq data (Ramirez et al., 2025). However, it’s not clearly stated what is the major methodological novelty which distinguishes this work from Ramirez et al. In particular, it’s unclear what adaptations unique to microbiome data were needed or whether the framework is largely unchanged, which in turn would hinder the methodological novelty. Additionally, the simulated data experiment is interesting, but might be insufficient to capture more realistic dynamics within a microbial community. Overall, the manuscript is well structured and written, but needs strengthening of methodology and additional validation.

Major comments:

* While I agree with authors that in real world biological samples the true underlying population dynamics of constituent microbes are unknown, multiple models of population dynamics are widely used in literature. In particular Lotka-Volterra and generalized Lotka-Volterra models can be tuned to yield reasonable dynamics for infant gut colonization. Showing the ability of PARAFAC2 to capture such dynamics and variability in those that can be attributed to individuals would significantly strengthen the simulated data results.

* The data analyzed in the study had a good degree of completeness, with only the FARMM dataset showing some (<15%) missing entries. Unfortunately, this level of data completeness is not common in many microbiome studies, especially those focused on more challenging environmental samples. Ablation experiments investigating to what degree artificial zero-inflation (observed taxa count is 0 due to sampling/mis-classification) and missing data affect method’s convergence and results. This is particularly relevant, as longitudinal regularization employed in the study could help mitigate occasional data dropout, but more systematic evaluation is required to draw such conclusion.

References

Ramirez, Andrew, Brian T. Orcutt-Jahns, Sean Pascoe, Armaan Abraham, Breanna Remigio, Nathaniel Thomas, and Aaron S. Meyer. "Integrative, high-resolution analysis of single-cell gene expression across experimental conditions with PARAFAC2-RISE." Cell Systems 16, no. 6 (2025).

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: No

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Dear Erdős,

We are pleased to inform you that your manuscript 'Extracting host-specific developmental signatures from longitudinal microbiome data' 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,

Vicky Yao

Academic Editor

PLOS Computational Biology

Marc Birtwistle

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: All my comments have been properly addressed and congratulations for the successful revision!

Reviewer #2: The authors provided thoughtful responses to the comments and have adequately addressed the feedback both at the level of the manuscript edits, and additional ablations. As presented the manuscript is well positioned and presents a good argument for the proposed novel methodology.

A minor suggestion for the authors would be to carefully review the language on p. 17 (lines 504--555), as several paragraphs repeatedly use "[Statement A]. Nevertheless, ..." construction. This is a style rather than content concern, but I believe that a minor revision of the phrasing can reduce repetitiveness and improve the flow.

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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: No