Diffusional Interactions among Marine Phytoplankton and Bacterioplankton: Modelling H2O2 as a Case Study

Marine phytoplankton vary widely in size across taxa, and in cell suspension densities across habitats and growth states. Cell suspension density and total biovolume determine the bulk influence of a phytoplankton community upon its environment. Cell suspension density also determines the intercellular spacings separating phytoplankton cells from each other, or from co-occurring bacterioplankton. Intercellular spacing then determines the mean diffusion paths for exchanges of solutes among co-occurring cells. Marine phytoplankton and bacterioplankton both produce and scavenge reactive oxygen species (ROS), to maintain intracellular ROS homeostasis to support their cellular processes, while limiting damaging reactions. Among ROS, hydrogen peroxide (H2O2) has relatively low reactivity, long intracellular and extracellular lifetimes, and readily crosses cell membranes. Our objective was to quantify how cells can influence other cells via diffusional interactions, using H2O2 as a case study. To visualize and constrain potentials for cell-to-cell exchanges of H2O2, we simulated the decrease of [H2O2] outwards from representative phytoplankton taxa maintaining internal [H2O2] above representative seawater [H2O2]. [H2O2] gradients outwards from static cell surfaces were dominated by volumetric dilution, with only a negligible influence from decay. The simulated [H2O2] fell to background [H2O2] within ~3.1 µm from a Prochlorococcus cell surface, but extended outwards 90 µm from a diatom cell surface. More rapid decays of other, less stable ROS, would lower these threshold distances. Bacterioplankton lowered simulated local [H2O2] below background only out to 1.2 µm from the surface of a static cell, even though bacterioplankton collectively act to influence seawater ROS. These small diffusional spheres around cells mean that direct cell-to-cell exchange of H2O2 is unlikely in oligotrophic habits with widely spaced, small cells; moderate in eutrophic habits with shorter cell-to-cell spacing; but extensive within phytoplankton colonies.


Marine Phytoplankton
Phytoplankton are a polyphyletic functional grouping of~275,000 species of oxygenic photosynthetic microorganisms that grow while suspended in marine or freshwater habitats [1,2]. Phytoplankton interact with their aqueous environment [3], and with cooccurring bacterioplankton cells, through diffusion of nutrients, toxic compounds and signaling molecules, notably including reactive oxygen species (ROS). Phytoplankton span a wide size range [4] (Table 1), which directly affects their diffusional interactions. Larger cells have longer paths for intracellular diffusion or transport paths for solutes, and can therefore potentially impose larger concentration gradients between their internal cell contents and the local microenvironment. Larger cells also have lower surface to volume ratios which impose limits on their trans-membrane transport per biovolume of the cell [5].  [8] These wide ranges of cell suspension densities for phytoplankton and bacterioplankton across habitats strongly influence the extent to which the growth and activity of a phytoplankton population or community alters, or even governs, solute concentrations in the local habitat [15][16][17][18]. Beyond the bulk activities of the phytoplankton population or community, differences in cell suspension densities mean the diffusional path lengths for solutes separating individual cells vary by orders of magnitude across habitats and taxa. Intercellular distances then influence whether the activity of an individual cell can directly influence the microenvironment of neighboring cells [19].
Our understanding of the taxa-and habitat-specific effects of cell-to-cell separation is then influenced by schematic visualizations of phytoplankton communities with implied cell suspension densities far higher than is realistic, or with cell symbol sizes scaled differently than the scaling of the spatial axes [20]. Symbol size scaling exaggerated relative to the scaling of the spatial axes allows schematic visualizations of cells, but can give a visual impression of a community with fairly close cell-to-cell interactions. In our visualizations, we maintain cell symbol size at the same size scaling as the spatial axes ( Figure 1).

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Microorganisms 2022, 10, x FOR PEER REVIEW 4 of 22 Figure 1. Phytoplankton and heterotrophic bacteria spacing from eutrophic or oligotrophic environments, with cell size on the same scaling as the 1 mm XY spatial axes. A 1 mm Z spatial axis is coded with fainter points farther back.

Reactive Oxygen Species
Electrons can transfer from photosynthetic or respiratory electron transport to reduce O2 to form the superoxide radical, a reactive oxygen species (ROS) [21,22] (Reaction (1)).

Reactive Oxygen Species
Electrons can transfer from photosynthetic or respiratory electron transport to reduce O 2 to form the superoxide radical, a reactive oxygen species (ROS) [21,22] (Reaction (1)).
ROS include both radicals (superoxide, nitric oxide and hydroxyl radicals) and nonradicals (hydrogen peroxide, singlet oxygen and peroxynitrite), which are more reactive than ground state di-oxygen molecules [23,24]. Reduction of O 2 to H 2 O requires the sequential addition of four electrons, and therefore progresses through three ROS intermediates: superoxide (O 2 •− ), hydrogen peroxide (H 2 O 2 ) and hydroxyl radical (OH • ) (Reaction (1)) [25]. ROS are by-products of both photosynthetic and heterotrophic metabolism, but are also generated abiotically in seawater [26].
ROS are important at low concentrations due to their role in cell signaling [36][37][38][39][40][41][42] and lipid accumulation [43]. In order to benefit from ROS, organisms must maintain ROS levels above the cytostatic threshold, the minimum concentration of ROS required to maintain normal cellular processes, as well as below the cytotoxic threshold, the level at which the negative effects of ROS outweigh the positives [44].

Concentrations and Properties of H 2 O 2
H 2 O 2 is an uncharged compound documented in the ocean at concentrations of 10 −9 to 10 −6 mol L −1 [29,45] depending upon location and conditions. These [H 2 O 2 ] are high enough to significantly contribute to the redox cycling of copper [46,47]. [H 2 O 2 ] in seawater increases after precipitation, including rain and snowfall [18,26,48]. [H 2 O 2 ] in seawater also follows a diurnal cycle with a peak at mid-day [18,49,50], which suggests significant direct or indirect photochemical or photobiological generation of H 2 O 2 . [H 2 O 2 ] also exhibits latitudinal variation at the surface, higher in the brighter, warmer, mid to low latitudes compared to the colder, darker, higher latitudes [50]. The authors of [50] suggest that regional variation in [H 2 O 2 ] may be caused by the depth of the mixed layer and the concentration of total dissolved organic carbon. Abiotic production rates of H 2 O 2 vary from 0.28 to 4.2 pM s −1 in near surface open ocean waters vs. 1.0 to 84.4 pM s −1 in coastal sites [26].
The diffusion coefficients (a measure of how quickly a molecule travels via diffusion), and therefore the diffusional mobilities, of ROS through seawater vary widely. Diffusion coefficients in water decrease with increasing molecular mass, and from uncharged to charged compounds. Diffusion coefficients are strongly influenced by temperature and slightly influenced by pressure. For H 2 O 2 at~20 • C the diffusion coefficient is~1500 µm 2 µs −1 (note conversion of units from more typical reporting of cm 2 s −1 ) [51]. In aquatic systems, H 2 O 2 has extracellular lifetimes of hours to days [29,52] before decay.
H 2 O 2 is acutely toxic to most cells in the range of 10 −5 to 10 −4 mol L −1 range [53], about 10-fold higher than seawater concentrations [29,45]. We found few quantitative estimates of the intracellular concentrations of H 2 O 2 within cells [54][55][56][57][58][59][60], with a particular lack of measurements from phytoplankton. Limited data, from mammalian cells, support an intracellular H 2 O 2 concentration of 10 −6 M [61]. Although only weakly directly reactive, H 2 O 2 can react with thiols and methionine [62] and thereby modulate gene expression and transcription [63,64] ] background also depends upon extracellular destruction and diffusion rates. The extent of this altered zone will then influence downstream processes. For specific cell-cell interactions or responses, a cell has to change the [H 2 O 2 ] in the local microenvironment sufficiently to provoke a response in neighboring cells. Beyond this local sphere of influence around an individual cell, the collective activity of cells in a community contributes to generating a general seawater [H 2 O 2 ], which in turn influences cellular gene expression and metabolism.

Goals
Microbes consume and produce H 2 O 2 , thereby potentially helping, or at least influencing, other microbes. We sought to quantify the influences of cell density and cell size on these potential microbial interactions.

Cell to Cell Spacing across Habitats and Taxa
Possible cell-to-cell exchanges of H 2 O 2 are mediated by diffusions through intercellular path lengths, varying by orders of magnitude across habitats and taxa. To understand such diffusional exchanges we need realistic visualizations of cell spacings, achieved by maintaining cell symbol size at the same size scaling as the spatial axes ( Figure 1). In the visualization of randomized cell spacing under oligotrophic conditions, we see wide spacing among cells, because the small cell symbols are on the same size scaling as the spatial axes. In the visualization of randomized cell spacing under eutrophic conditions, some cells are in close proximity. Note that this standardized scaling visualization approach is only feasible with highly expanded spatial axes such as the 1 mm axis used in Figure 1, equivalent to simulation of only 1 µL. Attempting to visualize 10 mm axes, equivalent to a 1 mL volume, causes the cell symbol size to shrink below visibility (data not presented). A further nuance not captured in these visualizations and subsequent simulations is nonrandom clustering of cells, as perhaps around particles of marine snow.   Figure 2) dominates the concentration gradient moving out from the cell. Including the influence of the decay term (red points, Figure 2) has only a negligible influence on [H 2 O 2 ] moving out from the phytoplankton cell over simulated timescales of <100 µs and distances of~100 µm. For other, less stable ROS, decay would become a significant influence, acting to narrow the local concentration gradients around cells.

H 2 O 2 Concentration Gradients around Cells
Seawater   (Figure 4). Such a colony could also be usefully simulated as a single homeostatic sphere of [H 2 O 2 ], with a significant local sphere of influence beyond the colony. Although we did not include bacteria in Figure 4, in fact Phaeocystis antarctica colonies have rich bacterial components [73], which may greatly alter the local H 2 O 2 environment within the colony, beyond the activities of the Phaeocystis cells.

Threshold Distances for Cell to Cell Exchange of [H2O2]
We find that cell size, cell suspension density, cellular [H2O2] and seawater [H2O2] interact to influence the potential for direct cell-to-cell diffusional interactions. We sought to generalize the estimations presented earlier for combinations of taxa x habitat ( Figure  3) to summarize how these variables potentially affect cell-to-cell interactions via H2O2 ( Figure 5).

Threshold Distances for Cell to Cell Exchange of [H 2 O 2 ]
We find that cell size, cell suspension density, cellular [H 2 O 2 ] and seawater [H 2 O 2 ] interact to influence the potential for direct cell-to-cell diffusional interactions. We sought to generalize the estimations presented earlier for combinations of taxa x habitat (Figure 3) to summarize how these variables potentially affect cell-to-cell interactions via H 2 O 2 ( Figure 5). Figure 5 plots combinations of cell suspension density (X axis, governing cell-to-cell distance), and the radii of the cell-specific sphere of influence . We see that a homogeneous population of large cells of 40 µm radius would maintain overlapping cell-specific spheres of influence down to cell suspension densities of 2.7 × 10 9 cells m 3 ( Figure 5). In contrast, a homogeneous population of cells of 0.5 µm radius would only achieve directly interacting cell-specific spheres of influence at a hypothetical 1.9 × 10 15 cells m 3 , far above cell suspension densities for most marine habitats (Table 1). For comparison, in Figure 5 we overlay symbols for representative taxa from different habitats ( Table 1) showing that for hypothetical homogeneous populations the cell-specific spheres of influence are generally far below the expected cell-to-cell spacing.      Figure 6). Thus, the cell-specific effects of bacterioplankton upon local [H 2 O 2 ] are unlikely to overlap at reasonable cell suspension densities. seawater [H2O2] given the likely roles of H2O2 in cell signaling [36], and the need to maintain a basal [H2O2] [44]. The authors of [58] predict an intracellular steady-state [H2O2] of 20 nM in heterotrophs in the absence of extracellular H2O2, which would suggest that at low extracellular [H2O2], the intracellular:extracellular [H2O2] ratio would be >0.1, and the spheres of lowered local [H2O2] would not overlap ( Figure 6). Thus, the cell-specific effects of bacterioplankton upon local [H2O2] are unlikely to overlap at reasonable cell suspension densities.

Conclusions
Our approximations of cell-to-cell spacing are applied to each taxa x habitat combination separately, based upon published measures of cell suspension densities in marine systems. We then overlaid the taxa-specific simulations from a given habitat to give a visualization of community level cell-to-cell spacings, across taxa within a habitat (Figure 1). As a next step we aim to implement probability distributions of cell-to-cell spacings across all cells from a mixed community in the habitat, to more accurately capture the likelihood of cell-to-cell interactions. Our work used available cell suspension density data exclusively from marine habitats. In general, we would assume that if cell densities and [H 2 O 2 ] in freshwater systems are similar to that of marine systems, the diffusional patterns described for marine habitats would be comparable to freshwater systems, but future studies would need to confirm this.
Our simple approximations of diffusion gradients out from cells are limited by a dearth of published information on the intracellular concentrations of H 2 O 2 , and other ROS, in phytoplankton or bacterioplankton cells. There are published estimates of intracellular and extracellular H 2 O 2 production and decay rates in seawater, which could support more sophisticated reaction/diffusion simulation approaches.
The threshold lines for interacting cell-specific spheres of influence as functions of cell radii and cell suspension densities are generated for individual 'taxa' from marine environments with uniform intracellular [H 2 O 2 ] (Figure 5), rather than for a mixed community of different cell sizes and physiologies. These fixed threshold lines also apply to a fixed ratio of internal to external [H 2 O 2 ], whereas this ratio could vary rapidly with changes in cell physiology and external conditions, causing the threshold for direct cell-to-cell interactions to shift. Our models suggest that it is unlikely that H 2 O 2 diffusing out of a phytoplankton cell directly interacts with another phytoplankton cell at natural seawater cell densities ( Figure 5), with the exception of Phaeocystis, whereby H 2 O 2 diffusing out of a cell would directly interact with other cells if the intracellular:extracellular [H 2 O 2 ] ratio is greater than 100. A future approach aims to generate probability distributions for direct cell-to-cell interactions, since even populations with widely spaced cells occasionally generate close cell-to-cell distances. Analyses show higher rates of cell-normalized H 2 O 2 production in bloom-forming phytoplankton taxa, providing support for the selective influence of cell suspension density upon ROS dynamics [29].
It is likely that extracellular ROS play a role in the growth and development of phytoplankton, given that [74] found that the addition of superoxide dismutase and catalase inhibited the growth of Chattonella marina. Our models suggest that H 2 O 2 diffusing out of phytoplankton cells reaches external [H 2 O 2 ] before interacting with other cells (Figures 3 and 5), and are primarily driven by the influence of diffusion, and with negligible contribution from the decay of H 2 O 2 ( Figure 2). Indirect interaction of H 2 O 2 diffusing out of cells is also possible as H 2 O 2 can affect biogeochemical cycles and bioavailability of nutrients [75].
The simple estimates presented herein using H 2 O 2 as a case study are generalizable to other, less stable ROS where decay will be a more immediate influence. For example, O 2 •− itself is not cell membrane permeable and so forms separate intra-and extracellular pools. However, O 2 •− is metabolized to H 2 O 2 , both inside and outside cells, and so could indirectly influence [H 2 O 2 ], and thereby alter cell-to-cell interactions beyond the simple diffusion-dominated simulations we present. For example, extracellular production of O 2 •− by heterotrophic bacteria can significantly alter O 2 •− concentrations in the dark ocean [28]. Heterotrophs might also produce enough O 2 •− to indirectly influence concentrations of O 2 •− in the photic zone of the ocean. The phytoplankter T. weissflogii [34] generates ranges of~8 × 10 −16 mol O 2 •− cell −1 hr −1 , while four raphidophytes show production ranges of 0.45 to 4 × 10 −12 mol O 2 •− cell −1 hr −1 [76], illustrating the wide range of extracellular production which can differentially influence extracellular [ROS] across communities or conditions. The approaches presented here are a step towards visualizing and constraining estimates of cell-to-cell interactions in plankton communities. We next need to validate these approaches with quantitative estimates of intracellular [H 2 O 2 ], and other [ROS], within phytoplankton and bacterioplankton cells.

Estimation of Cell to Cell Spacing
A simplistic estimator of cell-to-cell spacing is the reciprocal of the cube root of the cell suspension density. For example, if cell suspension density is expressed as cells µL −1 (equivalent to cells mm −3 ), the reciprocal of the cube root gives a cell-to-cell spacing estimate in mm. This cube root estimate assumes equally spaced cells, which somewhat overestimates average cell-to-cell spacing, since equally spaced cells give a maximum spacing, not the average spacing of randomly located cells. An arithmetic correction based upon the gamma function of 4/3 generates a numeric correction to multiply the reciprocal of the cube root of the cell suspension density by 0.55 to approximate average spacing of cells [77] (Equation (2)).
We generated simulated cell suspension densities for each taxa and habitat by generating points separated by the average cell spacing between cells, along each of the X, Y, Z spatial axes. We then added random variation to the values of the evenly spaced points (R jitter, factor = 2), to generate a XYZ coordinate cloud. In a parallel approach (data not presented) we directly generated normally distributed random distributions around the average cell spacings, but that approach was computationally slow for denser cell suspension densities. Overlaying the results from co-occurring taxa then gives a visualization of the community in a habitat ( Figure 1). Although overlaying data from separately simulated taxa is adequate for visualization, a more sophisticated model would be required to explicitly generate and retrieve the distributions of cell-to-cell distances within, or across, taxa. Furthermore, even in oligotrophic habitats with low average cell suspension densities the few cells present may be clustered non-randomly, an ecological nuance not captured in our approach.

Simulating Concentration Gradients
To simulate H 2 O 2 concentration gradients generated around a given cell, we consider the cell as a fixed spherical volume which maintains a steady, homeostatic intracellular Using the H 2 O 2 diffusion co-efficient in water, and time increments from 0 µs with a log 10 series upwards to 100 µs, we calculate the progressive net diffusional displacement of H 2 O 2 outward from the cell surface. We then estimate dilution of [H 2 O 2 ] with diffusion outwards from a source 'Phytoplankton' cell or diffusion inwards towards a sink 'Heterotrophic' cell. In addition to the simple volumetric dilution as ROS diffuses outwards from 'Phytoplankton' cells, we add a time-dependent decay term based upon measured lifetimes of H 2 O 2 in seawater, which also vary widely. We use nominal time increments to generate the diffusion distances of H 2 O 2 outward from the cell and to simulate the concurrent effect of pseudo-first order decay as H 2 O 2 moves outward from the cell with time, but this simple simulation assumes a steady state, without considering local mixing or fluctuations in cellular or environmental H 2 O 2 .