Should I stay or should I go? Spatiotemporal dynamics of bacterial biofilms in confined flows

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1. 

   Version published to 10.7554/elife.98292.2 on eLife

   Mar 6, 2026
2. 

   Version published to 10.7554/elife.98292 on eLife

   Mar 6, 2026
3. 

   eLife

   Mar 5, 2026

   eLife Assessment

   This important study combines microfluidic experiments with mathematical modeling to elucidate the reciprocal interplay between flow dynamics and biofilm growth and detachment. Using Pseudomonas aeruginosa as a model organism, the authors identify several key regimes and stages of biofilm development. Overall, the comparison between experimental observations of biofilm behavior under varying flow conditions and corresponding theoretical predictions forms a compelling understanding of the processes involved in biofilm dynamics. The results will be of interest to researchers studying biofilms and their technological and biological applications.

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4. 

   eLife

   Mar 5, 2026

   Reviewer #1 (Public review):

   Summary:

   The paper investigates the interplay between fluid flow and biofilm development using Pseudomonas aeruginosa PAO1 in microfluidic channels. By combining experimental observations with mathematical modeling, the study identifies the significant impact of nutrient limitation and hydrodynamic forces on biofilm growth and detachment. The authors demonstrate that nutrient limitation drives the longitudinal distribution of biomass, while flow-induced detachment influences the maximum clogging and temporal dynamics. The study highlights that pressure buildup plays a critical role in biofilm detachment, leading to cyclic episodes of sloughing and regrowth. A stochastic model is used to describe the detachment process, capturing the apparent randomness of sloughing events. The findings offer insights into …

   Reviewer #1 (Public review):

   Summary:

   The paper investigates the interplay between fluid flow and biofilm development using Pseudomonas aeruginosa PAO1 in microfluidic channels. By combining experimental observations with mathematical modeling, the study identifies the significant impact of nutrient limitation and hydrodynamic forces on biofilm growth and detachment. The authors demonstrate that nutrient limitation drives the longitudinal distribution of biomass, while flow-induced detachment influences the maximum clogging and temporal dynamics. The study highlights that pressure buildup plays a critical role in biofilm detachment, leading to cyclic episodes of sloughing and regrowth. A stochastic model is used to describe the detachment process, capturing the apparent randomness of sloughing events. The findings offer insights into biofilm behavior during clogging and fouling, potentially relevant to infections, environmental processes, and engineering applications.

   Strengths:

   This paper demonstrates a strong integration of experimental work and mathematical modeling, providing a comprehensive understanding of biofilm dynamics in a straight microfluidic channel. The simplicity of the microchannel geometry allows for accurate modeling, and the findings have the potential to be applied to more complex geometries. The detailed analysis of nutrient limitation and its impact on biofilm growth offers valuable insights into the conditions that drive biofilm formation. The model effectively describes biofilm development across different stages, capturing both initial growth and cyclic detachment processes. While cyclic pressure buildup has been studied previously, the incorporation of a stochastic model to describe detachment events is a novel and significant contribution, capturing the complexity and randomness of biofilm behavior. Finally, the investigation of pressure buildup and its role in cyclic detachment and regrowth enhances our understanding of the mechanical forces at play, making the findings applicable to a wide range of technological and clinical contexts.

   Weaknesses:

   The study achieves its primary objective of combining experiments and modeling to elucidate the coupling between flow, biofilm growth, and detachment in a confined microfluidic channel. In the revised manuscript, the authors have clarified several methodological choices and underlying assumptions. The points below are best viewed not as weaknesses, but as aspects that define the scope of the approach.

   • Biofilm porosity and permeability. The authors now discuss biofilm porosity and provide a clear rationale for neglecting permeability effects in their system, arguing that flow around dense biofilm structures dominates over flow through the matrix. While this assumption appears reasonable for the conditions explored, permeability effects are not explicitly modeled and could become relevant in less compact or more heterogeneous biofilms.

   • Characterization of the EPS matrix. The role of the extracellular matrix is convincingly addressed using polysaccharide‑deficient mutants, which provides a strong and causal link between EPS composition and mechanical stability. At the same time, the absence of complementary biochemical or imaging‑based characterization means that spatial or temporal variations in EPS distribution are not directly resolved, limiting the level of structural details.

   • Three‑dimensional interpretation of biofilm development. The authors clarify that three‑dimensional information is primarily obtained from pressure‑based measurements, with two‑dimensional imaging serving as a validation tool. This approach is coherent and supported by scaling arguments and reproducibility across experiments.

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5. 

   eLife

   Mar 5, 2026

   Author response:

   The following is the authors’ response to the original reviews.

   We sincerely thank the reviewer for the thorough and constructive evaluation of our manuscript. We greatly appreciate the recognition of our work's strengths, particularly the integration of experiments and mathematical modeling, the stochastic framework for describing sloughing events, and the insights into pressure-driven detachment dynamics.

   We have carefully considered each point raised and provide detailed responses below. In response to the reviewer's comments, we have revised the Methods section to better clarify our approach to three-dimensional assessment. We believe these revisions have improved the clarity of the manuscript.

   Below, we address each of the specific concerns raised by the reviewer:

   Public Reviews:

   Reviewer #1 (Public review):

   Weakne…

   Author response:

   The following is the authors’ response to the original reviews.

   We sincerely thank the reviewer for the thorough and constructive evaluation of our manuscript. We greatly appreciate the recognition of our work's strengths, particularly the integration of experiments and mathematical modeling, the stochastic framework for describing sloughing events, and the insights into pressure-driven detachment dynamics.

   We have carefully considered each point raised and provide detailed responses below. In response to the reviewer's comments, we have revised the Methods section to better clarify our approach to three-dimensional assessment. We believe these revisions have improved the clarity of the manuscript.

   Below, we address each of the specific concerns raised by the reviewer:

   Public Reviews:

   Reviewer #1 (Public review):

   Weaknesses:
   The study achieves its primary goal of integrating experiments and modeling to understand the coupling between flow and biofilm growth and detachment in a microfluidic channel, but it should have highlighted the weaknesses of the methods. I list the ones that, in my opinion, are the main ones:

   The study does not consider biofilm porosity, which could significantly affect the flow and forces exerted on the biofilm. Porosity could impact the boundary conditions, such as the no-slip condition, which should be validated experimentally.

   Porosity is indeed a key component of biofilm structures, resulting from the polymeric nature of the EPS matrix, mechanical forces, and biological processes such as cell death or predation. When considering flow-biofilm interactions, this porosity may allow fluid flow through the biofilm, with reported permeability values spanning an extremely broad range from 1015 to 10-7 m2 (Kurz et al., 2023).

   However, we argue that biofilm permeability is not the primary driver in our system:

   (1) In microscopy visualization, our biofilms form dense structures where flow around the biofilm through narrow channels dominates over flow through the porous biofilm matrix.

   (2) We performed microrheology experiments in these biofilms by imaging the Brownian motion of nanoparticles in the biofilm. Their trajectories indicate that, in our conditions, the viscoelastic flow of the biofilm itself largely dominates over the flow of culture medium through the biofilm matrix.

   (3) We argue that the extreme variability in reported permeability values (spanning several orders of magnitude, Kurz et al., 2023) reflects not only differences in experimental systems, but also fundamental challenges in defining and measuring permeability for viscoelastoplastic biofilms (the biofilm itself is actually flowing). Given this uncertainty, incorporating permeability into our model would introduce parameters that cannot be reliably constrained from literature or independently measured in our setup. Our approach (i.e. treating the biofilm as impermeable and focusing on flow obstruction) avoids this parametrization complexity while successfully capturing the observed dynamics.

   (4) Our model successfully predicts the observed scaling laws (φmax ∝ Q1/2, Fig. 7f) and hydraulic resistance dynamics (Fig. 3) without invoking permeability, suggesting that flow obstruction rather than flow penetration is the dominant mechanism.

   Reference: Kurz, D. L.; Secchi, E.; Stocker, R.; Jimenez-Martinez, J. Morphogenesis of biofilms in porous media and control on hydrodynamics. Environ. Sci. Technol. 2023, 57 (14), 5666−5677.

   The research suggests EPS development as a stage in biofilm growth but does not probe it using lectin staining. This makes it impossible to accurately assess the role of EPS in biofilm development and detachment processes.

   We respectfully disagree that lectin staining is necessary to assess the role of EPS in our system, and we argue that our approach using genetic mutants is superior for the following reasons. Lectin staining has significant limitations. While widely used, lectin staining (e.g., concanavalin A) is non-specific (binding not only to EPS polysaccharides but also to bacterial cell surfaces) and is non-quantitative. It can confirm the presence of polysaccharides but cannot establish causal relationships between specific EPS components and mechanical properties or detachment dynamics. We performed preliminary experiments with ConA-rhodamine (data not shown), which showed widespread presence of polysaccharides. However, this provided limited insight beyond confirming EPS production, which is well-established for P. aeruginosa PAO1 biofilms. We employed a more rigorous genetic approach to directly assess the role of EPS composition. We used Δpel and Δpsl mutants (strains lacking key exopolysaccharides that are the primary structural components of the PAO1 matrix). Our results demonstrate that both mutants show significantly reduced maximum clogging compared to wild-type. The Δpsl mutant is particularly affected, with near-complete detachment at certain flow rates. These differences directly link EPS composition to mechanical stability and detachment dynamics. This genetic approach provides causal, quantitative evidence for the role of specific EPS components in biofilm development and detachment, information that lectin staining cannot provide. We believe this addresses the reviewer's concern more rigorously than lectin staining would.

   While the force and flow are three-dimensional, the images are taken in two dimensions. The paper does not clearly explain how the 2D images are extrapolated to make 3D assessments, which could lead to inaccuracies.

   We thank the reviewer for this important observation. We would like to clarify our methodological approach. Our primary three-dimensional measurement is the hydraulic resistance R(t), obtained from pressure drop measurements across the biofilm-containing channel section. This pressure-based measurement inherently captures the three-dimensional flow obstruction caused by the biofilm. We then employ a geometric model (uniform biofilm layer on all channel walls) to convert R(t) into volume fraction φ(t).

   The two-dimensional fluorescence imaging serves to validate this model-based approach rather than being the basis for three-dimensional extrapolation. The uniform layer assumption is supported by three independent lines of evidence: (i) the excellent quantitative agreement between predicted and measured scaling laws (φmax ∝ Q1/2, Fig. 7f), obtained without adjustable parameters; (ii) the high reproducibility of φmax values across different flow rates and replicates; and (iii) the strong correlation between model-derived φ(t) from pressure measurements and integrated fluorescence intensity (Fig. 3b-d).

   We have added clarifying text in the Methods section (subsection "Data analysis for the calculation of the hydraulic resistance and volume fraction") to better explain this approach and emphasize that pressure measurements provide the three-dimensional information, with the geometric model serving as the link to volume fraction.

   Although the findings are tested using polysaccharide-deficient mutants, the results could have been analyzed in greater detail. A more thorough analysis would help to better understand the role of matrix composition on the stochastic model of detachment.

   We thank the reviewer for this suggestion. Our mutant analysis demonstrates that Δpsl and Δpel strains have significantly reduced φmax and altered detachment dynamics compared to wild-type (Fig. 8), directly linking EPS composition to mechanical stability as predicted by our model. A rigorous quantitative connection between matrix composition and the stochastic parameters (interevent times, jump amplitudes) would require: (i) substantially more sloughing events for statistical power, (ii) independent mechanical characterization of each mutant, and (iii) a mechanistic model linking EPS composition to detachment parameters. We are currently developing microrheology approaches to characterize mutant mechanical properties, which could enable such refinement in future work.

   However, this represents a substantial study beyond the scope of the current manuscript, which establishes the self-sustained sloughing-regrowth cycle and its stochastic nature. The mutant results serve their intended purpose: demonstrating that EPS composition affects detachment, consistent with our model's framework.

   Reviewer #2 (Public review):

   This manuscript develops well-controlled microfluidic experiments and mathematical modelling to resolve how the temporal development of P. aeruginosa biofilms is shaped by ambient flow. The experiment considers a simple rectangular channel on which a constant flow rate is applied and UV LEDs are used to confine the biofilm to a relatively small length of device. While there is often considerable geometrical complexity in confined environments and feedback between biofilm/flow (e.g. in porous media), these simplified conditions are much more amenable to analysis. A non-dimensional mathematical model that considers nutrient transport, biofilm growth and detachment is developed and used to interpret experimental data. Regimes with both gradual detachment and catastrophic sloughing are considered. The concentration of nutrients in the media is altered to resolve the effect of nutrient limitation. In addition, the role of a couple of major polysaccharide EPS components are explored with mutants, which leads results in line with previous studies.

   There has been a vast amount of experimental and modelling work done on biofilms, but relatively rarely are the two linked together so tightly as in this paper. Predictions on influence of the non-dimensional Damkohler number on the longitudinal distribution of biofilm and functional dependence of flow on the maximum amount of biofilm (𝜙max) are demonstrated. The study reconfirms a number of previous works that showed the gradual detachment rate of biofilms scales with the square root of the shear stress. More challenging are the rapid biofilm detachment events where a large amount of biofilm is detached at once. These events occur are identified experimentally using an automated analysis pipeline and are fitted with probability distributions. The time between detachment events was fitted with a Gamma distribution and the amplitude of the detachment events was fitted with a log-normal distribution, however, it is not clear how good these fits are. Experimental data was then used as an input for a stochastic differential equation, but the output of this model is compared only qualitatively to that of the experiments. Overall, this paper does an admirable job of developing a well-constrained experiments and a tightly integrated mathematical framework through which to interpret them. However, the new insights this provides the underlying physical/biological mechanisms are relatively limited.

   We thank the reviewer for the thorough evaluation of our work and for highlighting the tight integration between experiments and modeling. We appreciate the constructive feedback regarding the goodness-of-fit for the probability distributions.

   To address the concern that "it is not clear how good these fits are," we have added quantile-quantile (Q-Q) plots for the Gamma distribution fits of inter-event times to the Supplementary Materials (Supplementary Figure S20). These plots demonstrate that the sample quantiles track the theoretical Gamma quantiles across all flow rates (0.2, 2, and 20 μL/min), indicating that the Gamma distribution provides a reasonable approximation of the overall distributional behavior. For detachment amplitudes, we selected the lognormal distribution based on the observed high skewness and kurtosis in the data, which are characteristic signatures of lognormal processes.

   Formal goodness-of-fit tests (chi-square, Kolmogorov-Smirnov) yielded mixed results across datasets, passing for some while failing for others. This variability reflects inherent noise from measurements, discrete temporal sampling, automated detection thresholds, and intrinsic biological variability. Importantly, our goal is to capture essential distributional characteristics for input into the stochastic model, not to achieve perfect statistical fit across all individual datasets. The Q-Q plots confirm that these distributions provide reasonable approximations, and the qualitative agreement between model predictions and experimental observations validates this modeling approach. We have revised the Methods section to clarify this rationale.

   We respectfully disagree that “new insights this provides the underlying physical/biological mechanisms are relatively limited.” Beyond confirming previous findings (e.g., scaling for gradual detachment), we believe our work provides several novel mechanistic insights. First, the Pe/Da criterion enables quantitative prediction of nutrient limitation regimes, allowing systematic decoupling of nutrient effects from other phenomena in biofilm studies. Second, we demonstrate that pressure, not shear, drives sloughing detachment events, a mechanism overlooked in previous studies where the notion of “shear-induced detachment” clearly dominates. Third, we show that sloughing-regrowth cycles occur even in single channels, establishing pressure-driven fluctuations as a signature of confined biofilm growth, independent of geometric complexity. Finally, the stochastic description of sloughing demonstrates that, while instantaneous biofilm states are irreproducible, the underlying randomness is predictable, therefore addressing a fundamental challenge in biofilm research.

   Recommendations For The Authors:

   Reviewer #1 (Recommendations For The Authors):

   (1) In the abstract, I suggest clarifying the term "bacteria development." It is unclear if it refers to bacterial growth, biofilm formation, or biofilm detachment. The concept is expressed more clearly at the end of the Introduction.

   We have modified the entire abstract to make it clearer. The abstract now explicitly establishes the key processes - growth ('nutrients necessary for growth', 'growing bacteria obstruct flow paths') and detachment ('mechanical stresses that cause detachment', 'flow-induced detachment', 'sloughing') - before using 'bacterial development' as a collective term to refer to these coupled spatiotemporal dynamics. We believe the abstract is now clear as written.

   (2) Findings from Sanfilippo et al. (2019) were slightly questioned by Padron et al. (PNAS, 2023), who discovered that H2O2 transport is responsible for fro operon upregulation.

   Thanks for the clarification, which is indeed significant. The new sentence now reads: Pseudomonas aeruginosa has been found to regulate the fro operon in response to flow-modulated H2O2 concentrations (Sanfilippo et al. 2019, Padron et al. 2023).

   (3) Additionally, Kurz et al. (2022) account for pressure buildup as the mechanism controlling sloughing.

   We respectfully disagree and note that Kurz et al. (2022) identify shear stress, not pressure buildup, as the primary mechanism controlling sloughing. Besides the title, key sentences include “opening was driven by a physical process and specifically by the shear forces associated with flow through the biofilm”, “The opening of the PFPs is driven by flow-induced shear stress, which increases as a PFP becomes narrower due to microbial growth, causing biofilm compression and rupture.” While pressure differences are measured as indicators of system state and do contribute to normal compression stresses, their mechanistic explanation emphasizes that narrowing PFPs experience increased shear rates that eventually exceed the biofilm's yield stress, triggering viscoplastic deformation and detachment. The pressure buildup is a hydraulic consequence of narrowing rather than the direct cause of sloughing. In contrast, our work demonstrates that in confined geometries, pressure differences generate tangential stresses at the biofilm-solid interface that directly drive detachment.

   (4) The flow control strategy represented in Fig. 1 is not explained and should be detailed in the Methods section.

   The methods section reads as follows. Inoculation and flow experiments BHI suspensions were adjusted at optical density at OD640nm= 0.2 (108 CFU/mL) and inoculated inside the microchannels from the outlet, up to approximately ¾ of the channel length in order to keep a clean inlet. The system was let at room temperature (25°C) for 3h under static conditions. Flow experiments were then performed at 0.02, 0.2, 2, 20 and 200 μL/min constant flow rates for 72h in the microchannels at room temperature. For the experiments at 0.2, 2, 20 and 200 μL/min, the fluidic system was based on a sterile culture medium reservoir pressurized by a pressure controller (Fluigent FlowEZ) and connected with a flow rate controller (Fluigent Flow unit). The flow rate was maintained constant by using a controller with a feedback loop adjusting the pressure in the liquid reservoir. The reservoir was connected to the chip using Tygon tubing (Saint Gobain Life Sciences Tygon™ ND 100-80) of 0.52 mm internal diameter and 1.52 mm external diameter, along with PEEK tubing (Cytiva Akta pure) with 0.25 mm inner diameter adapters for flow rate controller. The waste container was also pressurized by another independent pressure controller to reduce air bubble formation in the inlet part. For the experiments at 0.02 μL/min, we used an Harvard Phd2000 syringe pump for the flow.

   (5) Including images of the actual biofilms formed in a portion of the channel would aid in understanding the analysis presented in Fig. 2.

   Images are introduced later on (eg Figure 5). There is also supplementary material showing videos.

   (6) The boundary conditions used to calculate the stress in the developed model should be discussed. The authors should specify why biofilm porosity is neglected.

   We have added a detailed discussion in the supplementary (Section I.2).

   (7) In the first section of the Results, the authors hypothesize that heterogeneity in biofilm development could be due to oxygen limitation. However, given the high oxygen permeability of PDMS, this hypothesis is later denied by their data. It would be prudent to avoid this hypothesis initially to streamline the presentation. Additionally, the authors should specify how oxygen levels at the inlet and outlet are measured.

   We appreciate this comment and agree that streamlining would simplify the presentation. However, after careful consideration, we have chosen to retain the oxygen limitation hypothesis for the following reasons: (1) oxygen limitation is a frequently invoked mechanism in biofilm systems and deserves explicit consideration, (2) it is not immediately obvious that oxygen remains non-limiting in larger microchannels where transverse gradients could develop, and (3) systematically eliminating this plausible alternative hypothesis strengthens our mechanistic conclusion that BHI drives the observed heterogeneity. Regarding oxygen measurements: we did not directly measure dissolved oxygen concentrations. Our approach is only indirect.

   (8) What is the standard deviation of the doubling time measured at different flows (page 9)?

   We have indicated the standard deviation in the text. Note that the graph shows the SEM.

   (9) What is the "zone of interest" in the channel mentioned on page 9?

   We have added the following sentence to clarify: To further understand this effect, let us consider the mass balance of biofilm in the zone of interest -- the zone where biofilm grows in between the two UVC irradiation zones -- in the channel.

   (10) Minor and major detachment events should be classified based on a defined threshold or criteria, and their frequency should be measured.

   We appreciate the reviewer's concern about quantitative rigor. However, we respectfully disagree that imposing arbitrary thresholds to classify 'minor' vs. 'major' events would improve our analysis. Detachment events in our system span a continuum of magnitudes, and any threshold would be artificial and potentially misleading. Our quantitative characterization of detachment dynamics is provided through the statistical analysis of interevent times, which we show follow a gamma distribution. This stochastic framework captures the full spectrum of detachment behavior without requiring arbitrary binning. The terms 'minor' and 'major' in our manuscript are used qualitatively to illustrate the range of observed phenomena, not as formal classifications.

   (11) Have the authors identified a reason for the peaks in the volume fraction in the Δpsl mutants at the highest flow rate?

   The biofilm thickness following these sloughing events is below our detection limit, consistent with a residual layer of cells. However, these cells grow, leading to a time window where the fraction is measurable, before a new detachment event occurs. Our understanding is that the psl mutant forms a weaker matrix with a much lower threshold for sloughing.

   (12) The fit of the probability density function for the relative density function does not match the data well. The authors should comment on this.

   We have added quantile-quantile (Q-Q) plots for the Gamma distribution fits of inter-event times to the Supplementary Materials (Supplementary Figure S20). These plots demonstrate that the sample quantiles track the theoretical Gamma quantiles across all flow rates (0.2, 2, and 20 μL/min), indicating that the Gamma distribution provides a reasonable approximation of the overall distributional behavior. For detachment amplitudes, we selected the lognormal distribution based on the observed high skewness and kurtosis in the data, which are characteristic signatures of lognormal processes. Formal goodness-of-fit tests (chi-square, Kolmogorov-Smirnov) yielded mixed results across datasets, passing for some while failing for others. This variability reflects inherent noise from measurements, discrete temporal sampling, automated detection thresholds, and intrinsic biological variability. Importantly, our goal is to capture essential distributional characteristics for input into the stochastic model, not to achieve perfect statistical fit across all individual datasets. The Q-Q plots confirm that these distributions provide reasonable approximations, and the qualitative agreement between model predictions and experimental observations validates this modeling approach. We have revised the Methods section to clarify this rationale.

   (13) Additionally, the simulated fraction appears very flat, with limited detachments compared to experiments. Why?

   The model captures the essential dynamics of growth-detachment cycles, including the characteristic timescales and volume fraction ranges. Some event-to-event variability in the experimental data likely reflects biological stochasticity not captured by our current approach—for example, variations in local biofilm mechanical properties or matrix composition that affect the precise stress at which sloughing occurs. While incorporating such biological variability as a stochastic parameter would improve detailed agreement, it would require extensive additional characterization beyond the scope of this study. The current model successfully reproduces the key qualitative and semi-quantitative features of the system.

   (14) The methods section should include a more detailed explanation of how the model was validated against experimental data.

   Model validation was performed by comparing predicted biofilm volume fraction time series and sloughing event statistics against experimental observations across multiple flow rates. The model reproduces the characteristic growth-sloughing cycles, timescales, and steady-state volume fractions without additional parameter fitting beyond the experimentally measured distributions.

   (15) It would be useful to include information on the reproducibility of the experiments and any variations observed between replicates.

   Experiments were performed in N=3 biological replicates. Individual time series for all replicates are shown in Supplementary Figures, demonstrating consistent behavior across replicates.

   (16) A discussion of the limitations of the study, particularly regarding the assumptions made in the modeling and their potential impact on the results, would strengthen the paper.

   We have added a discussion on why we chose to neglect the porosity of the biofilm, and strengthened parts on the uniform biofilm layer assumption.

   Reviewer #2 (Recommendations For The Authors):

   Page 2: "A vast" —> "The vast"

   Changed.

   The text and line widths on many of the figures are far too small. I printed it out at normal size, but had to look at a PDF and magnify to actually see what the graphs are showing. Fig. 9c is particularly illegible.

   Changed.

   Fig. 1 caption "photonic" —> "optical"?

   Changed

   Can you spell out the actual mathematical definition of 𝜙 on page 5 when it is introduced? Currently it just says the "cross section volume fraction of the biofilm", but that seems potentially ambiguous. It is valid to say that this is "fraction of the cross section occupied by the biofilm"?

   Changed

   Bottom of page 5: can you state the physical interpretation of the assumption that M is bounded between 0 and 1. i.e. that growth is larger than detachment?

   There is a comment on that in the paper. It reads “In assuming that M ∈ ]0, 1] and eliminating cases where M > 1, we have not considered situations of systematic detachment 𝜙equ = 0 for any value of the concentration, since this is not a situation that we encountered experimentally.” This comes just after presenting the expression on the only non-trivial steady-state, as it becomes easier to explain the consequences of the initial choice at this point.

   Currently the choice of detachment initially used in the model is a bit confusing. You say that you are going to assume a (1-𝜙)-1 model for simplicity (bottom of page 5), but then later you find that the (1-𝜙)3/4 model is more accurate (page 16). Since the latter has already been confirmed in numerous other studies, why not start with that one from the beginning?

   We thank the reviewer for this important question, which highlights an area where our presentation could be clearer. We did not find that the (1-φ)-3/4 model is "more accurate." Rather, we deliberately chose the (1-φ)-1 scaling because it captures pressure-induced detachment, which we hypothesized would dominate in confined flows where biofilms clog a large portion of the channel. The (1-φ)-3/4 scaling, widely used in previous studies, describes shear stress at the biofilm/fluid interface and was developed primarily for reactor systems where pressure effects are negligible. Our analysis on page 16 validates this choice by demonstrating that pressure stress indeed exceeds shear stress when volume fraction is large, which corresponds to late Stage I and all of Stage II precisely where our model is applied. The excellent quantitative agreement between predicted and measured φmax values across flow rates (Fig. 7f, Table 1) further supports the (1-φ)-1 scaling. We recognize that our initial presentation may have suggested the (1-φ)-1 choice was merely for "simplicity." We have revised this section to emphasize that this scaling was chosen specifically to capture pressure-driven detachment in confined geometries, with the physical justification provided by the stress analysis that follows. We have also clarified our ideas on page 16 to express clearly that (1-φ)-3/4 is never used. We could alternatively use a multi-modal detachment function combining both scalings, but the data do not require this additional complexity.

   In general, the models you derived in this study could be better contrasted with that from previous works. e.g. can you compare your Eqn (4) with the steady-state solutions obtained by other previous studies? Is this consistent with previous works or different? (aside from framing the biofilm thickness in terms of 𝜙)

   We are currently working on a paper dedicated to modeling biofilm development in confined flows, which will do a better job at comparing approaches.

   Top of page 6 - you assume K* = 0.1 - Does this assume that cells grow at half the rate in 0.1X BHI as they do in 1X BHI? Has this been confirmed experimentally or is this just a guess?

   This was estimated rather than measured directly. Model predictions were a lot more sensitive to the Damköhler number, than to the value of K.

   "radial" is used widely in this paper, but you are using a square geometry. Is "transverse" a better choice?

   Yes it clearly is. It’s been changed.

   Fig 3. Are panels (a) and (b) showing different bioreps of the same condition? If so, please spell that out in the caption.

   There was an error here in the caption of fig a. This has been changed. The correspondence is between a and c, and these are exactly the same, not bioreps.

   In multiple places it noted that the change in hydraulic resistance is correlated with the "change in biofilm colonization." Why not demonstrate this directly using a cross correlation analysis? How is the latter connected to the 𝜙 parameter? (e.g. is this d(𝜙)/dt?)

   We thank the reviewer for this suggestion. To clarify: φ(t) represents the volume fraction of biofilm in the channel. We measure this in two independent ways: (1) φ(t) from hydraulic resistance (black line in Fig. 3) i.e. calculated from pressure measurements using φ = 1 - √(R₀/R(t)), assuming uniform layer growth (see Methods section "Data analysis for the calculation of hydraulic resistance and volume fraction") and (2) φ(t) from fluorescence (green squares in Fig. 3) i.e. estimated from integrated GFP intensity or image segmentation of the glass/liquid interface. The reviewer is correct that we should quantify this relationship directly. We have now added correlation analysis between these two independent measurements of φ (new Supplementary Figure S21). The analysis shows strong positive correlation, with r-values ranged from 0.68 to 0.77 across all flow rates. This validates two key aspects of our approach: (1) the uniform layer assumption used to convert R(t) to φ(t) is reasonable, and (2) the pressure-based measurements accurately capture the dynamics visible in fluorescence imaging, including both growth phases and sloughing events. The strong agreement is particularly notable given that these measurements probe different aspects of the biofilm: hydraulic resistance is sensitive to the three-dimensional obstruction of flow, while fluorescence captures primarily the biofilm attached to the glass surface within our focal plane. Their correlation supports the model assumptions. We have revised the manuscript to clarify this relationship and present the correlation analysis.

   Top of page 9 - a doubling time of 110 mins is reported in liquid culture - is this in shaken or static conditions? Can you provide some data on how this was calculated? (e.g. on a plate reader?) Do you think your measurements in the microfluidics could be affected by attachment/detachment of cells, rather than being solely driven by division. It is curious that your apparent growth rate varies by a factor of two across the different flow rates and there is not a monotonic dependency. Both attachment and detachment would depend on the flow rate (with some non-trivial dependencies).e.g. https://www.pnas.org/doi/10.1073/pnas.2307718120 https://doi.org/10.1016/j.bpj.2010.11.078

   Given that your doubling time in the microfluidics is sole based on changes in cell number (rather than directly tracking cell divisions) it seems possible your results here are measuring the combined effect of growth, attachment and detachment, rather than just growth.

   We agree with those comments regarding the doubling time measurement. We have added a description of how we performed the doubling time measurement in the Methods section.

   Page 9 - you discuss the role of EPS here, but the effect of EPS is not demonstrated here and this is muddled with a discussion about the non-linearity of the putative dependency. Maybe this would be on a firmer footing if you save the discussion of EPS for the section on the Psl and Pel mutants?

   Changed.

   Middle of page 9: Please define what "smooth detachment" means and contrast it with catastrophic sloughing. Also, please define what you mean by "flow, seeding, and erosion" detachment are and how these three things differ from one another.

   We have clearly defined each term in the revised version.

   The results from wavelet scalograms seem to be underutilised and not well described. Can you clearly say what time series this analyses has been calculated on the caption? e.g. hydraulic resistance? Other than simply pointing out the "blue stripes", what can be gained from this analyses that could not be obtained with another method? It would be great if the basic features of this plot could more fully discussed (e.g. is the curved envelope at the bottom caused by edge effects?)

   We have improved the text, captions and method section following the reviewer’s comment.

   Fig. 5 a and b - please list the time at which each of these images were taken. Do these have the same dt between the two sets of images?

   Yes the dt is the same (30 minutes). It’s been indicated in the caption.

   Fig. 6: you have significant 2D variation in the biofilm width along the length of the channel. The relative contribution of pressure and shear based detachment will be different at different positions along the length. However, this variation is ignored in your model. Can you please comment on this in our manuscript and how it might affect the interpretation of your results? e.g. would the longitudinally averaged description yield the same result as one that takes the geometry into account (on average)?

   Our model indeed assumes longitudinally averaged properties. A more detailed spatially resolved model would be valuable for capturing heterogeneities and will be explored in future work.

   Bottom of page 11: you say standard deviations are in the range of 10-3. How does this jibe with the error bars on the middle flow rate in Fig. 7e?

   This extremely low standard deviation only applies to the maximum value of 𝜙 and is a completely different measurement from the whisker boxes presented in fig7e.

   Fig. 7: You are calculating the "Fraction" here. Is this "𝜙"? If so, can you put that on the y-axis instead? You calculate the volume fraction two different ways e.g. with hydraulic resistance and with imaging. Is only one of these shown in (e)? Is the same powerlaw dependence shown in (f) conserved when the other measurement of the "fraction" is used? Can you include both in Fig. 7e?

   We have modified the axis and indicated 𝜙.

   (e) is calculated only from hydraulic resistance. This is the most precise measurement to evaluate 𝜙 quantitatively.

   Related to the previous comment: Some of the estimates of 𝜙max in Table 1 are obtained by fitting the model to integrated fluorescence data (Fig. 2b), while others are estimated from measurements of the hydraulic resistance. The former yields non-unique sets of parameters. Can the biofilm fraction instead actually be estimated directly from fluorescent imaging by segmenting biofilm and directly calculating how much of the cross section is occupied by cells on average across the length? This seems like a more direct measure of this quantity. Given there are multiple ways of estimating the same parameter, it would be better consistency checking to make sure that different methods actually yield the same result.

   We have now added in Fig S21 a direct comparison of these two measurement methods. These are strongly correlated. Microscopy is more direct but only provides 2D pictures. Hydraulic resistance provides a 3D measurement, but relies on a model of biofilm distribution. Both are imperfect, but correlate well. In particular, we see that the 2D measurement does capture sloughing.

   You cite a large number of supplemental figures (e.g. Fig. S21 on page 12), but the figures in your SI only go up to 11.

   We have revised references to supplementary figures.

   Bottom of page 11: Your data from liquid culture suggests that your psl mutant grows at half the rate of WT cells. Is that consistent with your microfluidic data (e.g. Fig. 8)? If not, might this be a sign that your growth rate analyses from the microfluidics might be affected by attachment/detachment? (see comment above) Psl cells should detach much more easily.

   The approach taken to measure doubling times in the microfluidic system does not rely on the macroscopic measurements presented in figure 8, but rather on the approach presented in fig 4. These measurements require specific imaging (different magnification and time stepping) and we did not perform such experiments for the mutants.

   In analyses of sloughing, you fit the times between the jumps and the relative amplitude. Are these two random variables correlated with one another? Might that influence your results? Your methods say that "jumps were identified through through the selection of local maxima" of the derivative. Do you to say "minima" here? Did you keep all local maxima/minima or did you have a threshold?

   These are two random variables, not correlated with another. This is an assumption, and it would be interesting to analyze whether these are correlated. To perform this analysis, we believe that we would first need to acquire even more data and more replications to improve the statistical analysis.

   Yes, it was minima (in the code we make everything positive, hence the confusion).

   Yes, there is a threshold on the value of the jump itself. This value is extremely low and essentially filters out noise.

   Fig. 9 - can you make it clearer in the caption what timeseries you are analysing here? I understand from the methods this that is the "volume fraction." The data/fits are difficult to see in Fig. 9 b and impossible to see in Fig. 9c because the green bars get in the way of the other two data sets. Can this visualisation be improved? It is not clear to me how good of a job the Gamma and log-normal fits are actually doing.

   We have clarified that histograms are calculated from all experiments/replicates.

   We have slightly modified the graph to make it clearer. This comparison is intrinsically hard, partly because it compares discrete data with continuous PDFs.

   Aside from noting the results from the stochastic sloughing model are 'strikingly similar to experimental data', which seems to be based on a qualitative analysis of the lines in Fig. 7 d, e, and f. However, experimental data is not plotted in the same graph nor is the experimental data that we should be comparing this to cited in the text/caption.

   We have added a note in the caption to indicate which figure it can be compared to.

   Read the original source
6. 

   Version published to 10.7554/elife.98292.1 on eLife

   Sep 10, 2024
7. 

   eLife

   Aug 29, 2024

   eLife assessment

   This important study integrates microfluidic experiments and mathematical modeling to investigate how flow dynamics and biofilm growth and detachment influence each other. Using Pseudomonas aeruginosa as a model organism, the study identifies several key effects and stages in biofilm development, albeit with some weaknesses in clearly defining the setup and some of their interpretations. The comparison between experimental results and theoretical models is convincing, providing a robust analysis of the biofilm's behavior under varying flow conditions. The findings will be helpful for researchers working on biofilms and their applications.

   Read the original source
8. 

   eLife

   Aug 29, 2024

   Reviewer #1 (Public Review):

   Summary:
   The paper investigates the interplay between fluid flow and biofilm development using Pseudomonas aeruginosa PAO1 in microfluidic channels. By combining experimental observations with mathematical modeling, the study identifies the significant impact of nutrient limitation and hydrodynamic forces on biofilm growth and detachment. The authors demonstrate that nutrient limitation drives the longitudinal distribution of biomass, while flow-induced detachment influences the maximum clogging and temporal dynamics. The study highlights that pressure buildup plays a critical role in biofilm detachment, leading to cyclic episodes of sloughing and regrowth. A stochastic model is used to describe the detachment process, capturing the apparent randomness of sloughing events. The findings offer insights into …

   Reviewer #1 (Public Review):

   Summary:
   The paper investigates the interplay between fluid flow and biofilm development using Pseudomonas aeruginosa PAO1 in microfluidic channels. By combining experimental observations with mathematical modeling, the study identifies the significant impact of nutrient limitation and hydrodynamic forces on biofilm growth and detachment. The authors demonstrate that nutrient limitation drives the longitudinal distribution of biomass, while flow-induced detachment influences the maximum clogging and temporal dynamics. The study highlights that pressure buildup plays a critical role in biofilm detachment, leading to cyclic episodes of sloughing and regrowth. A stochastic model is used to describe the detachment process, capturing the apparent randomness of sloughing events. The findings offer insights into biofilm behavior during clogging and fouling, potentially relevant to infections, environmental processes, and engineering applications.

   Strengths:
   This paper demonstrates a strong integration of experimental work and mathematical modeling, providing a comprehensive understanding of biofilm dynamics in straight microfluidic channel. The simplicity of the microchannel geometry allows for accurate modeling, and the findings have the potential to be applied to more complex geometries. The detailed analysis of nutrient limitation and its impact on biofilm growth offers valuable insights into the conditions that drive biofilm formation. The model effectively describes biofilm development across different stages, capturing both initial growth and cyclic detachment processes. While cyclic pressure buildup has been studied previously, the incorporation of a stochastic model to describe detachment events is a novel and significant contribution, capturing the complexity and randomness of biofilm behavior. Finally, the investigation of pressure buildup and its role in cyclic detachment and regrowth enhances our understanding of the mechanical forces at play, making the findings applicable to a wide range of technological and clinical contexts.

   Weaknesses:
   The study achieves its primary goal of integrating experiments and modeling to understand the coupling between flow and biofilm growth and detachment in a microfluidic channel, but it should have highlighted the weaknesses of the methods. I list the ones that, in my opinion, are the main ones:

   • The study does not consider biofilm porosity, which could significantly affect the flow and forces exerted on the biofilm. Porosity could impact the boundary conditions, such as the no-slip condition, which should be validated experimentally.
   • The research suggests EPS development as a stage in biofilm growth but does not probe it using lectin staining. This makes it impossible to accurately assess the role of EPS in biofilm development and detachment processes.
   • While the force and flow are three-dimensional, the images are taken in two dimensions. The paper does not clearly explain how the 2D images are extrapolated to make 3D assessments, which could lead to inaccuracies.
   • Although the findings are tested using polysaccharide-deficient mutants, the results could have been analyzed in greater detail. A more thorough analysis would help to better understand the role of matrix composition on the stochastic model of detachment.

   Read the original source
9. 

   eLife

   Aug 29, 2024

   Reviewer #2 (Public Review):

   This manuscript develops well-controlled microfluidic experiments and mathematical modelling to resolve how the temporal development of P. aeruginosa biofilms is shaped by ambient flow. The experiment considers a simple rectangular channel on which a constant flow rate is applied and UV LEDs are used to confine the biofilm to a relatively small length of device. While there is often considerable geometrical complexity in confined environments and feedback between biofilm/flow (e.g. in porous media), these simplified conditions are much more amenable to analysis. A non-dimensional mathematical model that considers nutrient transport, biofilm growth and detachment is developed and used to interpret experimental data. Regimes with both gradual detachment and catastrophic sloughing are considered. The …

   Reviewer #2 (Public Review):

   This manuscript develops well-controlled microfluidic experiments and mathematical modelling to resolve how the temporal development of P. aeruginosa biofilms is shaped by ambient flow. The experiment considers a simple rectangular channel on which a constant flow rate is applied and UV LEDs are used to confine the biofilm to a relatively small length of device. While there is often considerable geometrical complexity in confined environments and feedback between biofilm/flow (e.g. in porous media), these simplified conditions are much more amenable to analysis. A non-dimensional mathematical model that considers nutrient transport, biofilm growth and detachment is developed and used to interpret experimental data. Regimes with both gradual detachment and catastrophic sloughing are considered. The concentration of nutrients in the media is altered to resolve the effect of nutrient limitation. In addition, the role of a couple of major polysaccharide EPS components are explored with mutants, which leads results in line with previous studies.

   There has been a vast amount of experimental and modelling work done on biofilms, but relatively rarely are the two linked together so tightly as in this paper. Predictions on influence of the non-dimensional Damkohler number on the longitudinal distribution of biofilm and functional dependence of flow on the maximum amount of biofilm (phi_max) are demonstrated. The study reconfirms a number of previous works that showed the gradual detachment rate of biofilms scales with the square root of the shear stress. More challenging are the rapid biofilm detachment events where a large amount of biofilm is detached at once. These events occur are identified experimentally using an automated analysis pipeline and are fitted with probability distributions. The time between detachment events was fitted with a Gamma distribution and the amplitude of the detachment events was fitted with a log-normal distribution, however, it is not clear how good these fits are. Experimental data was then used as an input for a stochastic differential equation, but the output of this model is compared only qualitatively to that of the experiments. Overall, this paper does an admirable job of developing a well-constrained experiments and a tightly integrated mathematical framework through which to interpret them. However, the new insights this provides the underlying physical/biological mechanisms are relatively limited.

   Read the original source
10. 

    Version published to 10.1101/2024.06.07.597893 on bioRxiv

    Jun 9, 2024