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Bacterial clustering amplifies the reshaping of eutrophic plumes around marine particles: A hybrid data-driven model [1]

['George E. Kapellos', 'Department Of Chemical Engineering', 'Massachusetts Institute Of Technology', 'Cambridge', 'Massachusetts', 'United States Of America', 'University Of Patras', 'Rion Achaia', 'Hermann J. Eberl', 'Department Of Mathematics']

Date: 2024-12

Multifaceted interactions between marine bacteria and particulate matter exert a major control over the biogeochemical cycles in the oceans. At the microbial scale, free-living bacteria benefit from encountering and harnessing the plumes around nutrient-releasing particles, like phyto-plankton and organic aggregates. However, our understanding of the bacterial potential to reshape these eutrophic microhabitats remains poor, in part because of the traditional focus on fast-moving particles that generate ephemeral plumes with lifetime shorter than the uptake timescale. Here we develop a novel hybrid model to assess the impacts of nutrient uptake by clustered free-living bacteria on the nutrient field around slow-moving particles. We integrate a physics-based nutrient transport model with data-derived bacterial distributions at the single-particle level. We inferred the functional form of the bacterial distribution and extracted parameters from published datasets of in vitro and in silico microscale experiments. Based on available data, we find that exponential radial distribution functions properly represent bacterial microzones, but also capture the trend and variation for the exposure of bacteria to nutrients around sinking particles. Our computational analysis provides fundamental insight into the conditions under which free-living bacteria may significantly reshape plumes around marine aggregates in terms of the particle size and sinking velocity, the nutrient diffusivity, and the bacterial trophic lifestyle (oligotrophs < mesotrophs < copiotrophs). A high potential is predicted for chemotactic copiotrophs like Vibrio sp. that achieve fast uptake and strong clustering. This microscale phenomenon can be critical for the microbiome and nutrient cycling in marine ecosystems, especially during particulate blooms.

Recent lines of evidence highlight the pronounced impact of slow-moving particles on the oceanic carbon cycle and associated ecosystem functions (e.g., CO 2 removal, oxygenation, acidification). In contrast to fast ones, slow-moving particles generate large and persistent eutrophic plumes of dissolved organic matter (DOM) and host intense interactions between surface-attached and free-living bacteria. However, significant aspects of the multifaceted biochemical coupling in these eutrophic microhabitats remain largely unexplored. Here we elucidate the potential of free-living bacteria to reshape microscale eutrophic plumes with a particle-level model that combines a physics-based description of the chemical field with a data-based description of bacterial clusters. This hybrid framework captures salient features and impacts of bacterial clustering in a simple and efficient manner, while bypassing inherent uncertainties of more sophisticated bacterial transport models. Our computational analysis delineates the conditions and types of particles, bacteria, and DOM for which plume reshaping is expected to be important.

Funding: This work received funding from the European Union’s Horizon 2020 research and innovation programme under a Marie Skłodowska-Curie grant agreement (No. 741799, "OILY MICROCOSM" to GEK). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2024 Kapellos et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Particle-based models provide a link between microbial-scale processes and ocean-level dynamics of carbon cycling and microbial growth. Significant modeling work has been done on the potential of particle-associated bacteria to subsidize eutrophic DOM plumes through the enzymatic hydrolysis of POM [ 33 – 36 ], and the concomitant chemotactic response of free-living bacteria to track the plumes [ 20 , 37 ]. However, the potential of free-living bacteria to reshape the plumes has been largely overlooked because of the traditional focus on fast-moving particles that create short-lived plumes and, also, due to a lack of simple mathematical descriptions of bacterial clustering [ 16 ]. Nonetheless, recent lines of evidence leverage the significance of suspended and slow-moving particles that generate large persistent plumes [ 38 – 41 ], amenable to transformation by planktonic bacteria when the uptake timescale is shorter than the plume lifetime. In that vein, we recently suggested that even uniformly distributed bacteria may substantially reshape nutrient plumes around individual phytoplankton and marine aggregates, when the particles sink slowly at less than 40 m/d [ 9 ]. Here, we develop a hybrid microscale model to quantitatively assess the impacts of bacterial clustering on the reshaping of eutrophic plumes around marine particles. The model formulation combines a physics-based description for the nutrient field with a data-based description for the bacterial distribution at the single-particle level.

Microscale experiments have demonstrated the capacity of chemotactic marine bacteria to tune their navigation mode and develop high swimming speeds (10−1000μm/s) so as to track and rapidly colonize both ephemeral and persistent plumes [ 17 – 23 ]. For instance, the prototypical plume trackers Shewanella putrefaciens and Pseudoalteromonas haloplanktis have been found to successfully pursue motile algae [ 18 ], to form microzones around nutrient-releasing beads [ 19 ], and to massively accumulate within plumes of algal exudates [ 20 ]. Similar observations have been made with computer simulations [ 24 – 29 ]. Efficient plume trackers benefit from harnessing eutrophic plumes and secure high growth rates in the presence of organic particles, plumes and associated nutrient gradients. Plume tracking and feeding play a critical role in the response of local microbiomes to sporadic or seasonal releases of POM, like after phytoplankton blooms [ 30 ] and oil spills [ 31 ]. For example, the Deepwater Horizon oil spill caused a subsea hydrocarbon plume that stimulated the growth of bacteria in the Oceanospirillales order with genes for chemotaxis and alkane degradation [ 32 ], thus indicating that these bacteria are capable of tracking and exploiting oil droplets.

Marine particles generate microscale eutrophic plumes of dissolved organic matter (DOM) with products from the enzymatic hydrolysis of particulate ingredients and the metabolic activities of microbial particle-dwellers [ 4 – 7 ]. The volume of a plume may be 10−100 times the particle volume [ 8 , 9 ], with nutrient concentrations from one to three orders of magnitude higher than ambient levels [ 10 – 12 ], thereby offering a unique nutritional opportunity to planktonic microbes. Chemotactic bacteria, in particular, may actively track plumes by detecting fluctuations in the concentration of the emitted chemical cues. However, plume tracking can be successful only if the chemotaxis timescale is shorter than the plume lifetime. The chemotaxis timescale is determined by the bacterial systems of chemosensing (i.e., palette and thresholds of detected solutes) and seascape navigation (i.e., tuning of swimming speed and direction) [ 13 , 14 ]. The plume lifetime may range from several seconds to tens of minutes depending on the size and velocity of the particle, the flow regime, the mechanisms of nutrient release, the spreading due to advection and diffusion, and the consumption by planktonic bacteria [ 9 , 15 , 16 ].

In vast oligotrophic oceans, organic particles offer oases full of resources to marine bacteria. Multifaceted physical and biochemical interactions between the bacteria and particulate organic matter (POM) underpin the health and essential functions of oceanic ecosystems by modulating the cycles of carbon and inorganic elements (N, P, Fe, S), the marine primary production and food webs, the removal of atmospheric CO2, the levels of seawater oxygenation and acidification, and the efficiency of the biological carbon pump (i.e., vertical transport and storage of organic carbon into the deep ocean) [ 1 – 3 ]. Advanced mechanistic understanding of microscale oceanic processes between microorganisms and POM is a major enabler towards a sustainable development in marine environments.

Results and discussion

Chemotaxis and RDF parameters Bacterial chemotaxis is included in Eq (1) through the values of the RDF parameters. Although rather limited and from disparate sources/systems, the available datasets support the following observations. First, the good fit to the data by simple exponential functions with maximum at the particle surface suggests that there is no inhibition by the chemoattractant or any competing gradients from other chemoattractants or repellants that could result in more complex patterns, such as band formation [19]. Furthermore, the RDF parameters from the first three datasets in Table 1, show that an increase of the normalized peak concentration (β m ) is accompanied by a decrease of the accumulation length (d s ). This trend may be attributed to two different chemotactic mechanisms. For chemotactic bacteria with run-and-tumble motility, lower swimming speeds result in elevated peak concentrations and shorter accumulation lengths, i.e., thinner and denser microzones (Fig 2). In this mode of motility, any gain in the run of long distances by swimming fast, comes at the cost of reduced ability to maneuver and focus close to confined nutrient sources [14]. By contrast, for chemokinetic bacteria with run-reverse motility and modulation of their swimming speed, the opposite trend has been reported [47]. That is, the microzone becomes thinner and denser as the average swimming speed increases because chemokinetic bacteria fine tune their speed and, thus, increase their ability to maneuver as they approach a chemoattractant source. PPT PowerPoint slide

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TIFF original image Download: Fig 2. Correlation of bacterial swimming to RDFs. Impact of the bacterial swimming speed on the accumulation of marine bacteria with run-and-tumble motility around nutrient-exuding algae. (A) The data points originate from individual-based simulations by Bowen et al. (Fig 2A in [25]) and the continuous lines represent optimal fit of our exponential RDF (see section S1.5 in S1 Appendix). The bacterial peak concentration (B) and the chemotactic accumulation length (C) are negatively and positively correlated to the bacterial swimming speed, respectively, for this mode of motility. https://doi.org/10.1371/journal.pcbi.1012660.g002 Although the above trend for {β m , d s } is confirmed by simulations of Bowen et al. [25] (see Fig 2), their parameter values stand out due to differences in the underlying mechanisms and experimental setups (Table 1 and S1 Appendix). In particular, the high values of normalized peak and ambient concentrations (β m and β 0 ) are partly attributed to the large observation window used by Bowen et al. [25]. Moreover, the striking difference in the accumulation length (d s ), which is 2–5 times larger for the algal cell than other datasets, is rooted in chemotactic features (swimming speed, average run time, chemoreceptor saturation) that favor the formation of wider microzones by bacteria with run-and-tumble motility. For instance, in the individual-based simulations of Bowen et al. [25], bacteria run about 40μm between tumbles (i.e., one particle diameter). The respective average run length is only 6μm in the simulations of Desai et al. [29]. The role of the RDF exponent (n) is somewhat more intricate. For n = 1, the derivative of the exponential RDF at the particle surface is B’(1) = β m ⁄d s and, as discussed above, sharp RDFs (high β m , low d s ) correspond to thin and dense microzones. For n > 1, the derivative becomes B’(1) = 0 and implies relation to wide microzones. For n < 1, the derivative becomes B’(1) → ∞ and suggests association with very confined microzones. In the literature, the value of n = 1 is established [47], as it appears in the steady state solution of the Keller-Segel model of chemotaxis. In this work, we examined Gaussian and fractional RDF exponents and found that fractional exponents provide best-fit in certain cases (S1 Appendix). For example, the optimal exponent is n = 4/5 for a synthetic dataset and the oil droplet, and n = 3/5 for the fecal pellet. However, for consistency, we used the near-optimal integer exponent n = 1 throughout the subsequent analysis of plume quenching. Finally, our analysis of bacterial RDFs from computer simulations by Bowen et al. [25], suggests that the RDF exponent (n) depends strongly on the interplay between chemoattractant exudation and bacterial chemotaxis (Fig U in S1 Appendix). The chemoattractant exudation rate affects the thickness of the concentration boundary layer around the particle, while the chemotactic response weighs in the ability of the bacteria to maneuver and focus within the nutrient-rich layer. Thus, under a given flow regime, thicker boundary layers may support thicker and denser microzones (high β m , high d s ). Moving forward, a systematic correlation between RDF parameters and underlying mechanisms presents an exciting avenue for future research, as complex cell-scale processes are parameterized in simple models on the particle scale.

A hybrid model of microscale plume (re)shaping The chemical field around marine organic particles is shaped by the interplay between advection, diffusion and microbial transformation. The relative importance of these processes is quantified by the dimensionless Péclet and Damköhler numbers, which can be expressed in terms of fundamental timescales as and , respectively. Here, is the diffusion timescale, is the advection timescale, is the uptake timescale, is the ambient water velocity, and is the nutrient diffusivity. In the particle frame of reference, the advection-diffusion-bioreaction equation that describes the formation of quasi-steady DOM plumes around the particle can be expressed in dimensionless generic form as follows: (2) Here, C is the nutrient concentration, and v is the fluid velocity. For the dimensional analysis, the concentration at the particle surface (e.g., solubility) is the reference concentration, and the ambient water velocity is the reference velocity. The product a(x)C(x) is the nutrient uptake rate per single cell and the affinity factor, a(x), accounts for nonlinear effects of physical and biochemical stressors, such as saturation, inhibition and multi-substrate limitation. For instance, a = 1 for unsaturable uptake and a = K S ⁄(K S + C) for Michaelis-Menten kinetics [48], where K S is the dimensionless half-saturation constant. Furthermore, the product B(x)C(x) represents the encounter rate between bacteria and DOM and, accordingly, the average nutrient exposure of a bacterial population in a specified volume of seawater (e.g., the microzone volume, V M ) is calculated as: (3) As shown in Fig 3, the amplification in nutrient exposure due to bacterial clustering around slow-moving particles is particularly pronounced. By contrast, fast-sinking particles create slender eutrophic plumes, characterized by high Péclet numbers, and offer reduced nutrient exposure to free-living bacteria, albeit substantially higher than ambient levels (c* > 0.001). PPT PowerPoint slide

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TIFF original image Download: Fig 3. Nutrient exposure. The bacterial microzone model captures in silico observations for the nutrient exposure of free-living bacteria in the undisturbed nutrient field (Da = 0) around a sinking particle. The solid lines correspond to bacterial distributions described by the exponential RDFs used in this work with red color for strong clustering, green color for weak clustering, and blue for a uniform distribution. The shaded areas correspond to results from computer simulations by Desai et al. [37] for chemotactic bacteria with (◊) or without (□) hydrodynamic interactions, and non-chemotactic bacteria with (Δ) or without (○) hydrodynamic interactions. https://doi.org/10.1371/journal.pcbi.1012660.g003 In terms of fundamental timescales, plume colonization is plausible if the bacterial chemotaxis is faster than plume dissipation due to advection and diffusion, , and plume depletion due to uptake, . The undisturbed plume lifetime, , may range from several seconds to tens of minutes [15,16], while the chemotaxis timescale, , is on the order of a few seconds [13,14]. Consequently, chemotactic marine bacteria may always achieve a degree of clustering in the presence of particles, plumes and associated chemical gradients. One step further, plume reshaping is expected to be significant when and, in accordance with dimensional analysis, the degree of reshaping depends on the Péclet and Damköhler numbers. In the special case of , the steady-state solution of Eq (2) is null and the transient fully-coupled analysis of nutrient and bacteria transport is required [49,50]. The uptake timescale depends on the bacterial abundance and the nutrient affinity, . The average bacterial abundance, , ranges from 104 cells/mL in the deep ocean to 107 cells/mL in coastal waters [51], and the bacterial affinity for organic and inorganic nutrients, , ranges from tens of femtoliters up to a few picoliters per second per cell (Table 2 in [9]). In the presence of organic particles, the bacterial abundance and nutrient affinity are expected on the high end of their ranges, that is and . Hence the uptake timescale may range from tens to hundreds of seconds [16,28]. For uniformly distributed bacteria, we have recently shown that the timescale condition is satisfied if Pe/Da<100 and Da > 10−4 [9]. Given the rapid chemotactic response of marine bacteria ( ) [14,28], here we examine the effects of bacterial clustering and uptake strength on the pattern and characteristic metrics of the nutrient field, under realistic conditions for marine aggregates and phytoplankton.

Implications of plume quenching on the oceanic microbiome Marine waters host diverse bacterial communities with trophic lifestyle ranging over the spectrum from oligotrophy to copiotrophy [61]. Typical oligotrophs, like Pelagibacter and Sphingopyxis species, are small (<0.1 μm3) non-motile cells, well adapted for slow growth in nutrient-poor waters [61–63]. Their uptake systems have high affinity and broad substrate specificity, but saturate at elevated nutrient concentrations [64,65]. Although non-motile oligotrophs are thought to drift along seawater and be homogeneously distributed around POM [21], weak clustering may occur when the hydrodynamic interactions with the particle surface are strong [37]. At the other end, copiotrophic bacteria, like Marinobacter and Vibrio species, are large cells (>1 μm3) capable of motility, environmental sensing, and thriving growth in nutrient-rich waters [61,66]. They possess multiple systems for nutrient uptake with variable affinity and substrate specificity [64,65]. Copiotrophs adapt to the changing nutrient availability in marine waters through a feast-and-famine strategy [64,66,67]. Under prolonged scarcity of nutrients (famine), copiotrophs become idle and enter into a non-proliferating state of reduced cell size and functions (e.g., spend more than 80% of their time without swimming [68]). By contrast, during an extensive POM release (feast), copiotrophs are enabled with functions for tracking and exploiting eutrophic patches in the heterogeneous microscale seascape (e.g., rapidly boost their uptake affinity when detecting nutrient surges [52]). The energetic cost associated with the chemosensory and swimming functions of copiotrophs is compensated by the benefit of harvesting eutrophic microhabitats [28,69]. Genomic analyses have revealed that Pelagibacters of the SAR11 clade are prevalent in the epipelagic microbiome of the oceans [70], while the fraction of motile chemosensing bacteria is usually low (<10%) [68]. However, extensive POM releases, like algal blooms and oil spills, increase the overall bacterial abundance (>107 cells/mL) and induce the ephemeral dominance of selected copiotrophic lineages with genes for chemotaxis and energy-based uptake systems [30–32]. Microscale and trade-off analyses suggest that such transformations of the marine microbiome are sustained by the ability of copiotrophs to sense their microenvironment and outcompete oligotrophs in harvesting nutrients under the presence of particles, plumes and associated chemical gradients [21]. In this context, our results for uniformly distributed bacteria with normal uptake are relevant to Pelagibacters and other oligotrophs, whereas Vibrios and other chemotactic copiotrophs could achieve strong clustering, fast uptake and pronounced plume reshaping. Interim effects of weak clustering may be achieved by mesotrophic bacteria with reduced chemotactic attributes (e.g., the motile species Deleya marina is chemotactically attracted to casein, but not to valine [19]). Accordingly, copiotrophs may achieve at least 4x higher nutrient exposure than oligotrophs and 2x higher than mesotrophs (Fig 3). When the saturation effect on oligotrophic uptake is taken into account, the advantage in nutrient uptake by copiotrophs is multiplied by another 2–4 factor [9], and becomes significantly higher than previously thought. The potential impact of bacteria with different trophic lifestyles on the trailing 3D plume behind a slow-sinking particle is illustrated in Fig 8. Plume quenching may also trigger a competition of the type "first come, first served while supplies last", as successful plume trackers reduce the extent of the plume and the probability of other, less competitive, chemosensing bacteria to detect the nutrient source. To fully unravel the impacts of plume reshaping on bacterial succession dynamics during particulate blooms, our analysis could be coupled to population-based models [49]. PPT PowerPoint slide

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TIFF original image Download: Fig 8. Three-dimensional plume quenching. Volumetric representation of the undisturbed nutrient plume in the wake of a slow-sinking particle (Pe = 20, Da = 0) and, also, as reshaped by oligotrophs with uniform distribution and normal uptake (Da = 0.16), mesotrophs with weak clustering and upregulated uptake (Da = 0.8), and copiotrophs with strong clustering and fast uptake (Da = 1.6). Clustering parameters are given in Table 1. Nested isoconcentration surfaces are shown at selected values of nutrient concentration (C = 0.1, 0.2, 0.5 and 0.7). The Péclet number corresponds to an alginate particle of radius , sinking velocity , and oligo-alginate diffusivity [7]. https://doi.org/10.1371/journal.pcbi.1012660.g008

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