1. Author Response:

    Reviewer #1 (Public Review):

    [...] In terms of weaknesses, I did not see any technical problems. One question that remains for me is how this model would apply in a more diverse gut microbiome. Specifically, do the authors envision single species aggregates in the human gut? How would the model be applied when there are ~1000 species? Do multispecies aggregates form by the same principle? I would expect this to be addressed in future work.

    Reply, regarding multiple species: This is a great question, and one that we’re already starting to get data on! Because this reply will likely be posted online, we won’t describe the preliminary observations.

    Reviewer #2 (Public Review):

    [...] Weaknesses:

    • The authors present data from 8 different bacterial strains but do not investigate how their model explains differences in bacterial aggregate distribution between these strains. This data would provide biological intuition about the specific different strains and their modes of aggregation.

    We have added text to the discussion to clarify this, noting especially plateau differences.

    • The manuscript would gather a broader readership were the model more thoroughly explained. For example, how are the parameters considered? E.g., is growth rate constant across a single aggregate? As written, the model can be difficult to understand conceptually to non-theoretical readers and the concepts would be more accessible if key details were explicitly communicated.

    We have added a paragraph introducing the modeling approach to a more general audience, and clarified the growth rate.

    • Greater discussion and prediction of how effective the model of aggregation may be in guts of different physical or chemical conditions would be valuable towards developing general biophysical principles. For example, is the spatial dependence of fragmentation rate dependent on the type of fluid flow field that exists in the gut?

    This is definitely interesting, generally unknown, and something we wonder about (whether there is a fluid dynamical explanation for the aggregation scaling). We have raised this as an interesting future direction in the Discussion.

    Reviewer #3 (Public Review):

    [...] Overall, the the model sufficiently explains the important features of the gut bacterial aggregate size distribution, namely, the initial power law and the final plateau.

    That said, a minor issue is that the initial motivation behind building the model in this way seems somewhat unnecessary. The authors motivated the basis for the model by claiming P(size > n) ∼ n−1, using Fig. 2. But the model seems to work for any slope (depending on fragmentation rates etc). So why is the slope of -1 special?

    We have clarified this in the Results, explaining that the slope of -1 (only) robustly emerges from growth/fragmentation

    Also, in Fig. 2, since the dashed line is separated from the actual data, it is tricky to visually compare them, and some experimental plots appear to have quite different slopes. It would be helpful if the best fit slope for the small n part is also reported.

    We now include all the slope values in a table.

    Another minor issue: they claim that the decrease in size due to fragmentation is linked to cell division at the surface. However, after the cell divides, if only one daughter leaves the cluster then it shouldn't change the cluster's size (since size is measured in terms of numbers of cells rather than total volume). But if both daughters leave the surface, then what does it have to do with division?

    We have revised the text to clarify what is meant by fragmentation.

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  2. Evaluation Summary:

    This manuscript provides an innovative merging of biophysical models with imaging data to explain the physical structure of microbial communities in the gut of zebrafish. Using imaging data to examine cluster sizes for eight different bacterial strains in the larval zebrafish gut, the authors report a common family of size distributions and show that these distributions arise naturally from a simple biophysical model of aggregation that tends to condense the system to a single massive cluster, reminiscent of gel formation observed in non-living systems. Within-host microbial dynamics represent an area of tremendous interest, as the microbiome is increasingly recognized to play a role in host physiology. This work contributes to a new perspective by elucidating physical mechanisms driving spatial segregation of these communities, opening the door to future studies that incorporate traditional genomic and microbiological insight with the physical and mechanical dynamics of microbial communities in living hosts.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #3 agreed to share their names with the authors.)

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  3. Reviewer #1 (Public Review):

    Spatial structure of bacterial communities in the gut microbiome can influence the species composition, which influences host health. Yet how the structure arises in the dynamic gut environment is poorly understood. Schlomann and Parthasarathy investigate a mechanism for spatial structure in bacterial communities using mathematical modeling and live imaging of bacterial aggregates in the zebrafish gut. This model predicts the size distribution of bacterial aggregates.

    In terms of strengths, the model fits the data remarkably well and also gives mechanistic insights into how the various rates of fragmentation, growth, aggregation, and expulsion can affect the distribution of bacterial aggregates. The authors base their model on a preferential attachment process and provide biological intuition for how the preferential attachment process, which was formulated to study evolution of phylogenies, applies to the ecological process of bacterial cluster formation.

    In terms of weaknesses, I did not see any technical problems. One question that remains for me is how this model would apply in a more diverse gut microbiome. Specifically, do the authors envision single species aggregates in the human gut? How would the model be applied when there are ~1000 species? Do multispecies aggregates form by the same principle? I would expect this to be addressed in future work.

    In my opinion, the authors have done a nice job of framing a rather nebulous problem and putting some quantitative theory to it. To start with the model system is elegant, and such dynamical spatial data would be exceedingly difficult to come by in other systems such as humans or mice. The methods have been refined over many years, and provide a new perspective on the spatial dynamics of the gut microbiome. Next, the theory is well applied to this new problem of how spatial dynamics of bacterial populations arise in the gut. Finally, the authors lay out a coherent plan for how their theory might be applied to study other systems, such as humans and mice, for which the data is harder to come by.

    I found the paper well-written and think that a general audience will appreciate the key message that a simple aggregation process can explain the spatial size distribution of bacterial populations in the gut.

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  4. Reviewer #2 (Public Review):

    In this manuscript, the authors investigate the biological parameters affecting bacterial aggregation by developing a mathematical model and simulating the formation and decay of bacterial clusters. Through this mechanistic description of bacterial aggregate growth (and decay) in the larval zebrafish gut, they conclude that cell division, cell loss from aggregates, aggregate fusion, and aggregate expulsion are critical parameters controlling the distribution of bacterial aggregates.

    Dynamic observations of intestinal bacteria in situ are valuable and rare, particularly observations that capture single-cell dynamics across the whole gut. This manuscript leverages an exceptionally unique dataset to gain mechanistic insights on how single-cell growth and movement can produce distributions of bacteria across the larval zebrafish intestine. Determining what situations in other guts (i.e., mouse or human) or other systems with bacterial aggregates (i.e., biofilm streamers) could be described by the model presented in this manuscript represents an exciting direction enabled by this work.

    Strengths:

    • The authors draw from a unique image dataset that is among the most complete visualizations of bacterial distribution within the entire gut of a living organism.

    • The proposed model is compelling and builds from a growing interest in biophysical characterizations of the gut environment.

    • The code is well documented, compact, easily accessible.

    • The model makes clear predictions for further tests in the authors system as well as other gut systems.

    • The model is practical with tangible parameters that directly relate to biological processes or entities.

    Weaknesses:

    • The authors present data from 8 different bacterial strains but do not investigate how their model explains differences in bacterial aggregate distribution between these strains. This data would provide biological intuition about the specific different strains and their modes of aggregation.

    • The manuscript would gather a broader readership were the model more thoroughly explained. For example, how are the parameters considered? E.g., is growth rate constant across a single aggregate? As written, the model can be difficult to understand conceptually to non-theoretical readers and the concepts would be more accessible if key details were explicitly communicated.

    • Greater discussion and prediction of how effective the model of aggregation may be in guts of different physical or chemical conditions would be valuable towards developing general biophysical principles. For example, is the spatial dependence of fragmentation rate dependent on the type of fluid flow field that exists in the gut?

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  5. Reviewer #3 (Public Review):

    To address the goal of characterizing the distributions of gut bacterial aggregate sizes, the authors have motivated, from the ground up, an excellent first-principles-based model, and have added in complexity in layers. The model is capable of describing the aggregate size dynamics for a wide variety of gut bacteria in zebrafish. Given the specifics of the first-principles based approach used, it is plausible that it's directly applicable to gut bacteria in other animals too. Sufficient complexity is systematically added, clearly distinguishing the individual effects of each added factor on the model. Overall, the the model sufficiently explains the important features of the gut bacterial aggregate size distribution, namely, the initial power law and the final plateau.

    That said, a minor issue is that the initial motivation behind building the model in this way seems somewhat unnecessary. The authors motivated the basis for the model by claiming P(size > n) ∼ n−1, using Fig. 2. But the model seems to work for any slope (depending on fragmentation rates etc). So why is the slope of -1 special?

    Also, in Fig. 2, since the dashed line is separated from the actual data, it is tricky to visually compare them, and some experimental plots appear to have quite different slopes. It would be helpful if the best fit slope for the small n part is also reported.

    Another minor issue: they claim that the decrease in size due to fragmentation is linked to cell division at the surface. However, after the cell divides, if only one daughter leaves the cluster then it shouldn't change the cluster's size (since size is measured in terms of numbers of cells rather than total volume). But if both daughters leave the surface, then what does it have to do with division?

    These are minor issues which can be readily addressed through clear prose and presentation in the manuscript. They do not affect the model or the overall results.

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