eLife Assessment

With the goal of investigating the assembly and fragmentation of cellular aggregates, this work investigates cyanobacterial aggregates in a laboratory setting. Investigating the conditions and mechanisms behind aggregation is an important contribution as it yields basic understanding of natural processes and offers potential strategies for control. The combination of computational and experimental investigations in this manuscript provides solid support for the proposed processes for aggregation and fragmentation, with some concerns about the strength of evidence for a subset of claims.

Reviewer #1 (Public review):

This work has significant relevance to the field, both practically and naturally. Combatting or preventing toxic cyanobacterial blooms is an active area of environmental research that offers a practical backbone for this manuscript's ideas. Additionally, the formation and behavior of cellular aggregates, in general, is of widespread interest in many fields, including marine and freshwater ecology, healthcare and antibiotic resistance research, biophysics, and microbial evolution. In this field, there are still outstanding questions regarding how microbial aggregates form into communities, including if and how they come together from separate places. Therefore, I believe that researchers from many distinct fields would find interest in the topic of this paper, particularly Figure 5, in which a phase space that is meant to represent the different modes of aggregate formation and destruction is suggested, dependent on properties of the fluid flow and particle concentration.

Altogether, the authors were mostly successful in their investigation, and I find most of their claims to be justified. In particular, the authors achieve strong results from their experiments regarding aggregate fragmentation. However, readers could benefit from some clarification in a couple of key areas. Additionally, I found that some of the authors' claims were based on weak or nonexistent data. Below, I outline the key claims of the paper and indicate the level to which they were supported by their data.

- Their first major claim is that fluid flows alone must be quite strong in order to fragment the cyanobacterial aggregates they have studied. With their rheological chamber, they explicitly show that energy dissipation rates must exceed "natural" conditions by multiple orders of magnitude in order to fragment lab strain colonies, and even higher to disrupt natural strains sampled from a nearby freshwater lake. This claim is well-supported by their experiments and data.
- The authors then claim that the fragmentation of aggregates due to fluid flows occurs through erosion of small pieces. Because their experimental setup does not allow them to explicitly observe this process (for example, by watching one aggregate break into pieces), they implement an idealized model to show that the nature of the changes to the size histogram agrees with an erosion process. However, in Figure 2C there is a noticeable gap between their experiment and the prediction of their model. Additionally, in a similar experiment shown in Figure S6, the experiment cannot distinguish between an idealized erosion model and an alternative, an idealized binary fission model where aggregates split into equal halves. For these reasons, this claim is weakened.
- Their third major claim is that fluid flows only weakly cause cells to collide and adhere in a "coming together" process of aggregate formation. They test this claim in Figure 3, where they suspend single cells in their test chamber and stir them at moderate intensity, monitoring their size histogram. They show that the size histogram changes only slightly, indicating that aggregation is, by and large, not occurring at a high rate. Therefore, they lend support to the idea that cell aggregation likely does not initiate group formation in toxic cyanobacterial blooms. Additionally, they show that the median size of large colonies also does not change at moderate turbulent intensities. These results agree with previous studies (their own citation 25) indicating that aggregates in toxic blooms are clonal in nature. This is an important result and well-supported by their data, but only for this specific particle concentration and stirring intensity. Later, in Figure 5 they show a much broader range of particle concentrations and energy dissipation rates that they leave untested.
- The fourth major result of the manuscript is displayed in Equation 8 and Figure 5, where the authors derive an expression for the ratio between the rate of increase of a colony due to aggregation vs. the rate due to cell division. They then plot this line on a phase map, altering two physical parameters (concentration and fluid turbulence) to show under what conditions aggregation vs. cell division are more important for group formation. Because these results are derived from relatively simple biophysical considerations, they have the potential to be quite powerful and useful and represent a significant conceptual advance. However, there is a region of this phase map that the authors have left untested experimentally. The lowest energy dissipation rate that the authors tested in their experiment seemed to be \dot{epsilon}~1e-2 [m^2/s^3], and the highest particle concentration they tested was 5e-4, which means that the authors never tested Zone II of their phase map. Since this seems to be an important zone for toxic blooms (i.e. the "scum formation" zone), it seems the authors have missed an important opportunity to investigate this regime of high particle concentrations and relatively weak turbulent mixing.

Other items that could use more clarity:
- The authors rely heavily on size distributions to make the claims of their paper. Yet, how they generated those size distributions is not clearly shown in the text. Of primary concern, the authors used a correction function (Equation S1) to estimate the counts of different size classes in their image analysis pipeline. Yet, it is unclear how well this correction function actually performs, what kinds of errors it might produce, and how well it mapped to the calibration dataset the authors used to find the fit parameters.
- Second, in their models they use a fractal dimension to estimate the number of cells in the group from the group radius, but the agreement between this fractal dimension fit and the data is not shown, so it is not clear how good an approximation this fractal dimension provides. This is especially important for their later derivation of the "aggregation-to-cell division" ratio (Equation 8).

Reviewer #2 (Public review):

Summary:

In this work, the authors investigate the role of fluid flow in shaping the colony size of a freshwater cyanobacterium Microcystis. To do so, they have created a novel assay by combining a rheometer with a bright field microscope. This allows them to exert precise shear forces on cyanobacterial cultures and field samples, and then quantify the effect of these shear forces on the colony size distribution. Shear force can affect the colony size in two ways: reducing size by fragmentation and increasing size by aggregation. They find limited aggregation at low shear rates, but high shear forces can create erosion-type fragmentation: colonies do not break in large pieces, but many small colonies are sheared off the large colonies. Overall, bacterial colonies from field samples seem to be more inert to shear than laboratory cultures, which the authors explain in terms of enhanced intercellular adhesion mediated by secreted polysaccharides.

Strengths:

-This study is timely, as cyanobacterial blooms are an increasing problem in freshwater lakes. They are expected to increase in frequency and severeness because of rising temperatures, and it is worthwhile learning how these blooms are formed. More generally, how physical aspects such as flow and shear influence colony formation is often overlooked, at least in part because of experimental challenges. Therefore, the method developed by the authors is useful and innovative, and I expect applications beyond the presented system here.
-A strong feature of this paper is the highly quantitative approach, combining theory with experiments, and the combination of laboratory experiments and field samples.

Weaknesses:

-Especially the introduction seems to imply that shear force is a very important parameter controlling colony formation. However, if one looks at the results this effect is overall rather modest, especially considering the shear forces that these bacterial colonies may experience in lakes. The main conclusion seems that not shear but bacterial adhesion is the most important factor in determining colony size. As the importance of adhesion had been described elsewhere, it is not clear what this study reveals about cyanobacterial colonies that was not known before.
-The agreement between model and experiments is impressive, but the role of the fit parameters in achieving this agreement needs to be further clarified.
-The article may not be very accessible for readers with a biology background. Overall, the presentation of the material can be improved by better describing their new method.

Author response:

We thank the reviewers and the editor for the detailed and constructive feedback provided. We look forward to submitting a revised version of the manuscript that addresses their comments. We acknowledge that further clarification is needed about the novelty brought by our experimental setup and model in comparison to previous studies using different methodologies. We also acknowledge that more details can be included about the calibration steps and sensitivity of the model parameters. Below we detail the planned changes for the revised version regarding the points raised by the reviewers.

Reviewer #1 (Public review):

- The authors then claim that the fragmentation of aggregates due to fluid flows occurs through erosion of small pieces. Because their experimental setup does not allow them to explicitly observe this process (for example, by watching one aggregate break into pieces), they implement an idealized model to show that the nature of the changes to the size histogram agrees with an erosion process. However, in Figure 2C there is a noticeable gap between their experiment and the prediction of their model. Additionally, in a similar experiment shown in Figure S6, the experiment cannot distinguish between an idealized erosion model and an alternative, an idealized binary fission model where aggregates split into equal halves. For these reasons, this claim is weakened.

The two idealized models of fragment distribution, namely erosion and binary fission, lead to distinguishable final size distributions. We believe that our experiments support the hypothesis of the erosion mechanism. Please note that Figure 2 is concerned with the fragmentation of large colonies, whereas Figure 3 and associated Figure S6 are concerned with very small colonies of a few cells formed by aggregation of single-cell suspension. Indeed, for very small colonies of a few cells, our experimental results cannot distinguish between a binary fission model and an erosion model (Figure S6).

The situation is very different for large colonies. To address the reviewer’s concern, we will add a new figure in the Supplementary Information (SI), similar to our Figure 2C, where we will compare the erosion model with a binary fission model for large colonies fragmented under ε = 5.8 m²/s³. We already did this exercise. The results in this new supplementary figure will show that the idealized binary fission model (i.e., where every fracture event produces exactly two fragments) does not capture the experimental fragmentation behaviour of large colonies. In contrast, the idealized erosion model provides a much better prediction of the experimental results, within the experimental uncertainty and variability in colony strength, and has the notable advantage of a straightforward computational implementation.

- The fourth major result of the manuscript is displayed in Equation 8 and Figure 5, where the authors derive an expression for the ratio between the rate of increase of a colony due to aggregation vs. the rate due to cell division. They then plot this line on a phase map, altering two physical parameters (concentration and fluid turbulence) to show under what conditions aggregation vs. cell division are more important for group formation. Because these results are derived from relatively simple biophysical considerations, they have the potential to be quite powerful and useful and represent a significant conceptual advance. However, there is a region of this phase map that the authors have left untested experimentally. The lowest energy dissipation rate that the authors tested in their experiment seemed to be \dot{epsilon}~1e-2 [m^2/s^3], and the highest particle concentration they tested was 5e-4, which means that the authors never tested Zone II of their phase map. Since this seems to be an important zone for toxic blooms (i.e. the "scum formation" zone), it seems the authors have missed an important opportunity to investigate this regime of high particle concentrations and relatively weak turbulent mixing.

We agree with the reviewer that Zone (II) of Figure 5 is of great importance to dense bloom formation under wind mixing and that this parameter range was not covered by our experiments using a cone-and-plate shear flow. The measuring range of our device was motivated by engineering applications such artificial mixing of eutrophic lakes using bubble plumes, as well as preliminary experiments which demonstrated that high levels of dissipation rate were required to achieve fragmentation. The dissipation rates of our cone-and-plate experiments capture Zones (III) and (IV) and the higher end of Zone (I). However, the cone-and-plate experiments are less suitable for the lower dissipation rates of Zone (II), as indicated by the red bars in Figure 5, due to the accumulation of colonies in stagnation points.

Instead, in our revision we will more extensively discuss recent results published in the literature for evidence of aggregation-dominance at Zone (II). The experimental studies of Wu et al. (2019) and Wu et al. (2024) (full citation below) investigated the formation of Microcystis surface scum layers at high colony concentrations (high biovolume fraction) in wind-mixed mesocosms. These studies identified aggregation of colonies at rates faster than cell division, while the stable colony size decreased with mixing rate.  The parameter range of these studies fall within Zone II, and their experimental results agree with our model predictions. We will include in the reviewed version these references and a detailed discussion elucidating the parameter range covered in our experiments and the findings of other studies.

Wu, X., Noss, C., Liu, L., & Lorke, A. (2019). Effects of small-scale turbulence at the air-water interface on Microcystis surface scum formation. Water Research, 167, 115091.

Wu, H., Wu, X., Rovelli, L., & Lorke, A. (2024). Dynamics of Microcystis surface scum formation under different wind conditions: the role of hydrodynamic processes at the air-water interface. Frontiers in Plant Science, 15, 1370874.

Other items that could use more clarity:

- The authors rely heavily on size distributions to make the claims of their paper. Yet, how they generated those size distributions is not clearly shown in the text. Of primary concern, the authors used a correction function (Equation S1) to estimate the counts of different size classes in their image analysis pipeline. Yet, it is unclear how well this correction function actually performs, what kinds of errors it might produce, and how well it mapped to the calibration dataset the authors used to find the fit parameters.

We agree with the reviewer that more details of the calibration processes should be included. We will include in the revised version of the SI more details of the calibration steps and direct comparison of raw and corrected histograms of the size distribution and its associated uncertainty.

- Second, in their models they use a fractal dimension to estimate the number of cells in the group from the group radius, but the agreement between this fractal dimension fit and the data is not shown, so it is not clear how good an approximation this fractal dimension provides. This is especially important for their later derivation of the "aggregation-to-cell division" ratio (Equation 8)

We agree with the reviewer that more details on the estimation of fractal dimension are needed. The revised version of the SI will include the estimation procedure, the number of colonies analysed, and the associated uncertainty.

Reviewer #2 (Public review)

- Especially the introduction seems to imply that shear force is a very important parameter controlling colony formation. However, if one looks at the results this effect is overall rather modest, especially considering the shear forces that these bacterial colonies may experience in lakes. The main conclusion seems that not shear but bacterial adhesion is the most important factor in determining colony size. As the importance of adhesion had been described elsewhere, it is not clear what this study reveals about cyanobacterial colonies that was not known before.

As we explain in the Introduction, it is a major open question whether cyanobacterial colonies are formed mainly by cell division (after which the dividing cells remain attached to each other by the EPS layer) or mainly by the aggregation of independent cells & colonies. See for example the highly cited review of Xiao & Reynolds 2018 (our ref 17), and references therein. This question has not been resolved and is investigated in our study. We would like to emphasize several key findings that our study reveals about the mechanical behaviour of cyanobacterial colonies under flow:

(i) Quantification of mechanical strength in cyanobacterial colonies: Our results demonstrate the high mechanical strength of cyanobacterial colonies (much higher than previously thought in references 32 and 39 of the manuscript), as evidenced by the requirement of very high shear rates to achieve fragmentation. To this end, our study highlights their resilience against naturally occurring flows and bridges the gap between theoretical assumptions about colony strength and experimentally measured mechanical properties.

(ii) Validation of a hypothesis regarding colony formation: Using a fluid-mechanical approach, we confirm the findings of recent genetic studies (references 25 and 64 of the manuscript) which indicated that colony formation of cyanobacteria under natural conditions occurs predominantly via cell division rather than via the aggregation of individual cells. Only in very dense blooms and surface scums, colony formation by the aggregation of smaller colonies likely plays a role.

(iii) Practical guidelines for cyanobacterial bloom control: Our findings provide valuable insights into the design of artificial mixing systems that are used to suppress surface blooms of buoyant cyanobacteria in lakes. In these lake applications, in which we have been involved, the aim of the mixing is to disperse the colonies over the water column so that they cannot form a surface layer (i.e., the mixing intensity should overcome the flotation velocity of the colonies), which takes away the competitive advantage of buoyant cyanobacteria over nonbuoyant phytoplankton species. However, it has always been an open question whether the high shear of artificial mixing would cause colony fragmentation. An understanding of changes in colony size is relevant for the design of artificial mixing, because smaller colonies have a lower flotation velocity. Our results show that the dissipation rates that are generated by artificial mixing are sufficient to prevent aggregation of large colonies, but not high enough to induce fragmentation of division-formed colonies.

In the revised version of the manuscript, we will improve the writing to better clarify these three novel insights obtained from our study.

- The agreement between model and experiments is impressive, but the role of the fit parameters in achieving this agreement needs to be further clarified.

The influence of the fit parameters (namely the stickiness α1 and the pairs of colony strength parameters S1,q1,S2,q2) is discussed in the sections “DYNAMICAL CHANGES IN COLONY SIZE MODELED BY A TWO-CATEGORY DISTRIBUTION” and “MATERIALS AND METHODS.” We kept the discussion concise to maintain readability. However, we agree with the reviewer that additional details about the importance of the fit parameters and the sensitivity of the results to these parameters could be beneficial. In the revised version of the SI, we will include a more detailed discussion of the fit parameters.

- The article may not be very accessible for readers with a biology background. Overall, the presentation of the material can be improved by better describing their new method.

We apologize for the limited readability of the description of the experimental setup and model used. In the revised version of the manuscript, we aim to expand the description of the new methods presented here for a broader audience of biology.