Introduction

Interactions among microorganisms occur in every known ecosystem (recently reviewed by [1, 2]). Detailed studies of the interactions between selected model organisms (often in laboratory co-cultures) have begun to reveal the diversity of molecular mechanisms whereby organisms interact with each other [2,3,4]. However, it is currently unknown to what extent the studied interactions differ between organism pairs, growth stages, or environmental conditions. For example, while broad-scale phylogenetic patterns are often observed in microbial interactions, closely related bacteria may differ in the way they interact with other organisms, likely as a result of the significant genetic diversity observed in many microbial clades (e.g. [5, 6]). Additionally, the same pair of interacting organisms can synergize or compete depending on the composition of the culture media and the growth stage of (co)-culture (e.g. [7,8,9]). Finally, both the coarse-grained ecological classification of microbial interactions (e.g. positive/negative) and the high-resolution mechanistic view obtained using advanced physiology and ‘omics approaches are difficult to translate into quantitative, predictive models of organismal growth and decline [1, 10, 11].

Here we explore to what extent intra-clade diversity affects the outcome of microbial interactions, using growth curves as an information-rich view of microbial growth and mortality. Growth curves can be divided into discrete phases (lag, exponential, stationary, decline, and long-term stationary phases), and can be used to extract quantitative parameters such as growth rates and lag times [12, 13]. An extra layer of more subtle information may exist in the shapes of the growth curves, providing hints of important shifts in the physiology of the growing organisms, as classically demonstrated by Jacques Monod for diauxic growth in Escherichia coli [14]. While many studies of bacterial interactions focus on the exponential growth stage or on culture yield at a specific time-point (e.g. [15,16,17]), fewer studies look at the shape and dynamics of the decline phases, which can provide important hints regarding the effect of interactions on the process of microbial mortality (e.g. [18,19,20]).

Our model organisms are two globally abundant clades of marine bacteria: a cyanobacterial primary producer (Prochlorococcus) and a heterotrophic γ-proteobacterium (Alteromonas). Interactions between marine phototrophs (phytoplankton, including cyanobacteria) and heterotrophic bacteria have been studied intensively, as phytoplankton are responsible for about one-half of the photosynthesis on Earth (e.g. [21,22,23,24,25]). Thus, phytoplankton-bacteria interactions may strongly affect community structure and function on scales from microns to thousands of kilometers [26, 27]. Our model primary producer, Prochlorococcus, is found throughout the euphotic zone, the sunlit upper portion, of the oligotrophic (nutrient-poor) ocean. There are multiple Prochlorococcus clades, broadly partitioned into high-light (HL) and low-light (LL) adapted ecotypes, which differ in their photosynthetic parameters and occupy different niches in the ocean (e.g. surface verses deep water, reviewed by [28]). Strains differ also in traits such as the capacity to utilize different forms of inorganic nutrients and organic matter, as well as in their interactions with heterotrophic bacteria and phage. Alteromonas is a clade of free-living marine bacteria, which are also partitioned into surface and deep groups (A. macleodii and A. mediterranea, respectively) [29]. Alteromonas strains also exhibit diverse capabilities to utilize carbohydrates, to acquire iron, and in motility [30]. Interactions between individual strains of Prochlorococcus and Alteromonas have been characterized in some detail [12, 27, 31,32,33,34,35]. While the phenotype and gene expression patterns during interactions vary between strains, this variability has not been explored systematically ([12, 32, 36] and Supplementary Text S1). Strain- and condition-dependent phytoplankton-heterotroph interactions are observed also in other systems, including Synechococcus, a close relative of Prochlorococcus [18, 37, 38], as well as eukaryotic microalgae (e.g. coccolithophores and diatoms, [7,8,9, 39]).

We characterized the interactions between five strains each of Prochlorococcus and Alteromonas, from the first encounter between previously axenic strains (i.e., grown in mono-culture) and across ~1.2 years of co-culture (25 phototroph-heterotroph combinations). The culturing period spanned multiple cycles of exponential growth, culture decline and long-term nitrogen starvation [33]. Nitrogen limitation occurs across wide swaths of the global ocean, and affects a substantial proportion of Prochlorococcus diversity [40, 41]. We focused our analysis on Prochlorococcus growth and decline. Using this dataset of 429 growth curves, as well as associated cell counts, we ask: (i) How do the interactions between Prochlorococcus and Alteromonas vary across the diversity of each organisms? (ii) Do the interactions change over time (i.e. do the organisms adapt to “living together”)? (iii) When, during the life-cycle of a Prochlorococcus batch culture, do microbial interactions have the largest impact on growth, death, and overall culture carrying capacity, and can this impact be quantified?

Results and discussion

All Alteromonas strains support long-term survival of Prochlorococcus under N starvation

Previous research showed that Prochlorococcus, and to some extent Synechococcus depend on co-occurring heterotrophic bacteria to survive various types of stress, including nitrogen starvation [33, 34, 42, 43]. At the first encounter between previously axenic Prochlorococcus and Alteromonas (E1), all co-cultures and axenic controls grew exponentially (Fig. 1B, C). However, all axenic cultures showed a rapid and mostly monotonic decrease in fluorescence starting shortly after the cultures stopped growing, reaching levels below the limit of detection after ~20–30 days. None of the axenic Prochlorococcus cultures were able to re-grow when transferred into fresh media after 60 days (Fig. 1C). In contrast, the decline of co-cultures rapidly slowed, and in some cases was interrupted by an extended “plateau” or second growth stage (Fig. 1B). Across multiple experiments, 92% of the co-cultures contained living Prochlorococcus cells for at least 140 days, meaning that they could be revived by transfer into fresh media. Thus, the ability of Alteromonas to support long-term N starvation in Prochlorococcus was conserved in all analyzed strains.

Fig. 1: Experimental designs and overview of the dynamics of Prochlorococcus-Alteromonas co-cultures from first encounter and over multiple transfers.
figure 1

A Schematic illustration of the experimental design. One ml from Experiment E1 was transferred into 20 ml fresh media after 100 days, starting experiment E2. Experiment E2 was similarly transferred into fresh media after 140 days, starting experiment E3. Additional experiments replicating these transfers are described in Supplementary Fig. S1. B Overview of the growth curves of the 25 Prochlorococcus-Alteromonas co-cultures over three transfers spanning ~1.2 years (E1, E2 and E3). Results show mean + standard error from biological triplicates, colored by Prochlorococcus strain as in panel D. C Axenic Prochlorococcus grew exponentially in E1 but failed to grow when transferred into fresh media after 60, 100, or 140 days. Axenic Alteromonas cultures were counted after 60 and 100 days, as their growth cannot be monitored sensitively and non-invasively using fluorescence (optical density is low at these cell numbers). D High reproducibility and strain-specific dynamics of the initial contact between Prochlorococcus and Alteromonas strains (E1). Three biological replicates for each mono-culture and co-culture are shown. Note that the Y axis is linear in panels B, C and logarithmic in panel D. Au: arbitrary units.

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It has previously been shown that Prochlorococcus MIT9313 is initially inhibited by co-culture with Alteromonas HOT1A3, while Prochlorococcus MED4 is not [12, 32]. This “delayed growth” phenotype was observed here too, was specific to MIT9313 (not observed in other Prochlorococcus strains) and occurred with all Alteromonas strains tested (Fig. 1D). MIT9313 belongs to the low-light adapted clade IV (LLIV), which are relatively distant from other Prochlorococcus strains and differ from them in multiple physiological aspects including the structure of their cell wall [44], the use of different (and nitrogen-containing) compatible solutes [45], and the production of multiple peptide secondary metabolites (lanthipeptides, [46, 47]). LLIV cells also have larger genomes, and are predicted to take up a higher diversity of organic compounds such as sugars and amino acids [48]. It is intriguing that specifically this strain, which has higher predicted metabolic and regulatory flexibilities [49], is the only one initially inhibited in co-culture with Alteromonas.

Differences in co-culture phenotype are related to Prochlorococcus and not Alteromonas strains and occur primarily during the decline stage

While co-culture with all Alteromonas strains had a major effect on Prochlorococcus viability after long-term starvation, there was no significant effect of co-culture on traditional metrics of growth such as maximal growth rate, maximal fluorescence, and lag phase (with the exception of the previously described inhibition of MIT9313; Fig. 2A–C). However, a visual inspection of the growth curves suggested subtle yet consistent differences in the shape of the growth curve, and especially the decline phase, between the different Prochlorococcus strains in the co-cultures (Fig. 1D). To test this, we used the growth curves as input for a principal component analysis (PCA), revealing that the growth curves from each Prochlorococcus strain clustered together, regardless of which Alteromonas strain they were co-cultured with (Fig. 2D). The growth curves of all high-light adapted strains (MED4, MIT9312, and MIT0604) were relatively similar, the low-light I strain NATL2A was somewhat distinct, and the low-light IV strain MIT9313 was a clear outlier (Fig. 2D), consistent with this strain being the only one initially inhibited in all co-cultures. Random forest classification supported the observation that the growth curve shapes were affected more by the Prochlorococcus rather than Alteromonas strains, and also confirmed the visual observation that most of the features differentiating between Prochlorococcus strains occurred during culture decline (random forest is a supervised machine learning algorithm explained in more detail in Supplementary Text S2; see also Supplementary Fig. S2). Thus, co-culture with Alteromonas affects the decline stage of Prochlorococcus in co-culture in a way that differs between Prochlorococcus but not Alteromonas strains.

Fig. 2: Growth analysis and principal component analysis (PCA) of the growth curves from all co-cultures during 140 days of E1.
figure 2

A Growth rate, B Maximum fluorescence, and C duration of lag phase during experiment E1. Box-plots represent mean and 75th percentile of co-cultures, circles represent measurements of individual cultures of the axenic controls. The only significant difference between axenic and co-cultures is in the length of the lag phase for MIT9313 (Bonferroni corrected ANOVA, p < 0.001). D PCA ordination of the growth curves colored by Prochlorococcus (left) and by Alteromonas (right) strains. The growth curves cluster by Prochlorococcus strain (Adonis test, F(4,68) = 42.3, R2 = 0.71, p = 0.001) and only marginally by Alteromonas strain (Adonis test, F(4,68) = 2.29, R2 = 0.11, p = 0.017). Au arbitrary units.

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We next asked whether the phenotypes of interaction, which were observed when high cell densities of Prochlorococcus and Alteromonas interacted for the first time (E1), were maintained after the cells had lived together in co-culture for extended periods. We therefore continued to transfer the co-cultures into fresh media over multiple additional transfers, performed 40–200 days after the initial inoculations. In total, fluorescence measurements are available for a cumulative period of 380 days, which the cells spent in co-culture (Fig. 1A; Supplementary Fig. S1). The ability of Prochlorococcus to survive long-term N starvation, the clustering of the growth curves by Prochlorococcus but not Alteromonas strains, and the results of the random forest classification, were all reproduced in subsequent transfers (Fig. 1B; Supplementary Figs. S2, S3; Supplementary Text S3). These observations are thus robust to the cumulative time the organisms have been interacting and the cell densities of both organisms when transferred to new media (see below).

Differences in the carrying capacity suggest different modes of interaction

While Alteromonas clearly support Prochlorococcus, by enabling it to survive long-term N starvation, is the reciprocal interaction also synergistic? Do Prochlorococcus enhance the growth of Alteromonas, and does the interaction affect the overall carrying capacity of the system, defined here as the ability to efficiently utilize the limiting resource (nitrogen)? To answer these questions, we used the flow cytometry cell counts of Prochlorococcus and Alteromonas on days 60, 100, and 140 of experiment E1 to infer the nitrogen (N) biomass of each population grown alone or in co-culture (Fig. 3; Supplementary Table S1; see Methods and Supplementary Text S4 for the calculations and caveats).

Fig. 3: Carrying capacity and type of interactions.
figure 3

A Growth curves of experiment E1, arrows showing the days where cell numbers were counted by flow cytometry (see also Supplementary Table S1). Axenic curves shown are from all Prochlorococcus strains. Thick lines represent mean fluorescence. B Total calculated N biomass of the cultures in E1 on days 60 and 100 in μmol N/L. Dashed line indicates total available N in co-cultures. C Log2 Fold Change (log2FC) of Alteromonas N biomass relative to axenic Alteromonas controls on days 60 and 100. Asterisks indicate statistically significant FC (Bonferroni corrected ANOVA p < 0.05). ALT Alteromonas, PRO Prochlorococcus, Au arbitrary units.

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The overall carrying capacity of the co-cultures was higher than the axenic Alteromonas cultures, and much higher than the axenic Prochlorococcus (Fig. 3B). On day 60, the mean carrying capacity of the co-cultures was 2–3 times higher than that of the Axenic Alteromonas (69 ± 35 compared with 32 ± 22 μmol N/L), suggesting that the heterotroph benefited from carbon fixed by the phototrophic Prochlorococcus partner. Indeed, most of this cellular N was found in the Alteromonas cells (76 ± 13%, see Supplementary Text S4 for a sensitivity analysis). The ability of axenic Alteromonas to survive in the absence of organic matter from Prochlorococcus is not surprising, as an Alteromonas strain distantly related to the ones studied here, AltSIO, can utilize a large fraction of the labile organic material found in natural seawater used to make the growth media [50]. In contrast, in axenic Prochlorococcus cultures only a small fraction of N in the system was found in cell biomass (~0.01 μmol N/L). This likely reflects the inability of all Prochlorococcus strains to recycle organic nitrogen lost due to exudation or cell lysis (Fig. 3B).

Mutual synergism was not observed across all strain combinations. While some Prochlorococcus strains (MED4, MIT0604, and NATL2A) supported significantly higher Alteromonas N biomass compared to the axenic control (log2FC 1.3 ± 0.6), co-cultures with MIT9312 and MIT9313 resulted in similar or lower Alteromonas biomass (log2FC −0.2 ± 0.9) (Fig. 3C). Therefore, on day 60, some of the interactions were mutually synergistic whereas in other cases Prochlorococcus do not support Alteromonas and may even compete with it. The two “non-mutually-synergistic” Prochlorococcus strains belong to different ecotypes but were isolated from the same drop of water from the Gulf Stream [51]. In all co-cultures the Prochlorococcus population benefited from the presence of Alteromonas (log2FC 10 ± 4 in N biomass compared to axenic controls).

In contrast to day 60, after 100 days essentially all of the interactions were mutually synergistic, with Alteromonas supporting the growth of all Prochlorococcus strains (log2FC 10 ± 1) and Prochlorococcus increasing the Alteromonas biomass in all strains with the exception of BS11 (log2FC 3 ± 1.5) (Fig. 3C). This suggests that the mode of interaction (synergist verses competition) may change temporally during the extended period of N starvation.

On day 140 the carrying capacity of the co-cultures declined further (only 1% of the N was in biomass). This suggests that the system is not in steady state, with a slow yet constant reduction in carrying capacity. We speculate that this is driven by the loss of bioavailable N from the system (i.e., most of the nitrogen is in a recalcitrant form that cannot be utilized by either partner). This is further supported by the observation that while the co-cultures after 140 days were still alive and could be transferred to new media, in a subsequent experiment, only 16/30 cultures could be transferred after 195 days, and only 3/75 cultures could be transferred after 250 days (Supplementary Fig. S5). MIT0604 (HLII) was the strain most likely to survive transfer after these extended periods and was also the most abundant Prochlorococcus strain after 140 days (1.46 ± 1 μmol N/L MIT0604 biomass verses 0.26 ± 0.56 μmol N/L for all other strains). While we do not currently have an explanation for the higher survival of this strain, it is noteworthy that it is the only strain to utilize nitrate [52].

Modeling the effect of co-culture on Prochlorococcus mortality

Given that the clearest effect of co-culture was on the decline phase of the co-cultures, we asked whether we could quantify and model the effect of Alteromonas on Prochlorococcus mortality. While the growth of bacteria has been extensively studied and modelled, the decline of bacterial cultures is much less studied, and mortality is rarely represented in ecological or biogeochemical models of microbial dynamics [53]. Bacterial mortality has, however, often been modelled in the context of food safety and genome evolution, using either mechanistic or descriptive approaches [53,54,55,56,57]. We chose to focus on four of these previously described models which are relatively simple and have a clear biological interpretation (Table 1). The exponential model is the simplest and most commonly used one, where a constant portion of the population dies over time [58]. The bi-exponential model is slightly more complex, representing two separate subpopulations in the community, each with its own death rate [55]. The Weibull model is probabilistic, modeling a heterogeneous population with a diverse stress tolerance [53, 59], finally, the harmonic model employs a quadratic rate of decline which is often associated with predator-prey interactions or cellular encounter rates [58]. When fitting each of these models to the decline phase of the growth curves, the Weibull model stands out as it has a low error for both axenic and co-cultures (Table 1) as well as in consequent transfers (Supplementary Table S2), the bi-exponential model is a better fit for the co-cultures but does not represent well the axenic ones. Based on the Weibull model, and assuming that culture fluorescence is related to the number of non-lysed cells in the media (Fig. S7), axenic Prochlorococcus cells die more than ten-fold faster than cells in co-culture (2-decimal reduction time, td2, is 12.58 ± 3.85 days for axenic cultures and 316 ± 337 days for co-cultures). Similar results were obtained with the bi-exponential model (Supplementary Text S5).

Table 1 Mathematical description and biological interpretation of four models used to describe bacterial mortality.
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In the Weibull model, the “shape parameter” (n) represents the change over time (as the cultures decline) in the susceptibility of the bacterial community to stress. A shape parameter above one represents an increasing probability that cells will die as time increases (e.g. due to the accumulation of damage), whereas a shape parameter below one suggests that, as the culture declines, the cells become more resistant to damage. Axenic cultures have high mean shape value of 2.1 ± 0.9, suggesting an accumulation of cell damage leading to increasing death rate (Fig. 4A). In contrast, the mean shape value of co-cultures is significantly lower and below 1 (0.4 ± 0.2, student t-test, p < 0.001), suggesting that during N starvation in co-culture the Prochlorococcus cells are acclimating over time to the nutrient stress conditions.

Fig. 4: Weibull modeling of long-term starvation.
figure 4

A Weibull shape (n) in Axenic Prochlorococcus (PRO) and in Co-cultures. In all axenic samples n > 1, in most co-cultures n < 1 (students t-test, p < 0.001). B Scatter plot showing the reverse correlation between the total N biomass of the co-cultures on day 60 and Weibull shape (n). Pearson r = −0.33, p = 5e-3. Circles represent co-cultures with mutual synergistic interactions (i.e. Prochlorococcus strains MED4, MIT0604, and NATL2A), X represent potential competitive interactions (strains MIT9312, MIT9313). C Scatter plot showing the correlation between the total N biomass of the co-cultures on day 60 and Weibull root mean square error (RMSE). Pearson r = 0.64, p < 0.001. For the correlations with total N biomass on day 100 see Supplementary Fig. S6. D–F Weibull model fit for selected decline curves (FL). D Mutually synergistic co-culture of Prochlorococcus NATL2A and Alteromonas DE1. E Potentially competitive co-culture of Prochlorococcus MIT9312 and Alteromonas DE1. F Axenic Prochlorococcus NATL2A. FL fluorescence (arbitrary units). RMSE root mean square error.

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While the molecular and physiological mechanisms of Prochlorococcus adaptation are currently unclear, the Weibull shape parameter decreases as the total N in cellular biomass increases, suggesting that the Prochlorococcus acclimation process is related to the ability to recycle N between the specific Prochlorococcus and Alteromonas strains in co-culture (Fig. 4B). Thus, the rate of acclimation is higher in the co-cultures supporting high N biomass and mutually synergistic interaction (NATL2A, MED4, and MIT0604) compared to MIT9312 and MIT9313, where Alteromonas do not gain from the interaction (0.36 ± 0.14 verses 0.52 ± 0.16, student t-test p < 0.001).

While the Weibull model is useful in quantifying mortality rates and raising the hypothesis that Prochlorococcus cells are acclimating to starvation over time, none of the tested models was able to fully capture the intricate dynamics of culture decline (Fig. 4C, D). In most mutually synergistic co-cultures involving Prochlorococcus strains NATL2A, MED4, and MIT0604, culture decline was not monotonic, and was interrupted by additional growth phases about 40–50 and 100 days after the cultures started declining (Fig. 4D). These latter growth phases were mostly absent in co-cultures with MIT9312 and MIT9313 (RMSE 0.36 ± 0.1 verses 0.2 ± 0.1 in the other strains, student t-test p < 0.001). The correlation between N biomass and the secondary growth phases (i.e., higher deviation from simple Weibull model; Fig. 4C) suggest that these phases may also be related to the ability of the interacting partners to recycle N through mutually beneficial metabolic interactions.

Conclusions and future prospects

Elucidating the mechanisms of microbial interactions requires well-characterized model systems. However, extending the insights from such models across the diversity of organisms and environmental conditions remains challenging. Our results from the highly simplified system of multiple Prochlorococcus and Alteromonas strains provide an important step towards this goal. Using the rich information on interaction phenotypes present in the growth and decline curves, we identify conserved and strain-specific facets of these interactions. Despite the genetic diversity across the Alteromonas strains studied [30], it was primarily the identity of the Prochlorococcus strain that determined the interaction phenotype. This manifests in the growth and decline rates, in the shape of the curve (primarily the decline phase), in the amount of N retained in biomass, and in whether the co-cultures are mutually synergistic or, potentially, competitive.

Under our laboratory conditions, it is likely that the combined response of both interacting partners to nitrogen starvation underlies the dynamics of the long-term co-cultures, although other stressors such as the increase in osmolarity/salinity or the accumulation of waste products cannot be ruled out [18, 34, 60]. This response is dynamic, as illustrated by the reproducible deviations of the fluorescence curves from the monotonic decline predicted by all models tested (“second growth” stages; Fig. 4). Three different (non-mutually-exclusive) processes may underlie these dynamics. Firstly, it is likely that one or both organisms modify their physiology or metabolism over time, for example through the activation of stringent responses, utilization of N or C storage pools, rewiring of metabolism to utilize available N sources, or activation of mechanisms such as extracellular enzymes allowing the cells to access previously unusable substrates (e.g. [61, 62]). Secondly, it is possible that there are “invisible” ecological dynamics underlying the observed fluorescence curves, for example cyclic changes in the abundance of Alteromonas cells. Under such a scenario, rapid Prochlorococcus mortality could produce an increase in Alteromonas abundance, resulting in degradation and remineralization of dead Prochlorococcus biomass and the release of resources that can drive subsequent Prochlorococcus growth. Thirdly, both Prochlorococcus and Alteromonas populations may be evolving, for example through emergence of genetically distinct populations better adapted to nutrient starvation (reminiscent of the GASP phenotype described in E. coli and other bacteria [63]).

Why is it the identity of the primary producer (Prochlorococcus) rather than the heterotrophic “recycler” (Alteromonas) that determines the outcome of the co-culture? A-priori, it was reasonable to assume that the co-culture phenotype would be affected by the differences between the Alteromonas strains in their ability to degrade and utilize polysaccharides and a variety of other organic molecules [30, 64]. We speculate that the increased growth of Alteromonas in the co-cultures compared to the axenic ones is fueled primarily by the availability of major biomass components released by Prochlorococcus as they die, such as proteins, amino acids, and nucleotides. Such common macromolecules do not require highly specialized metabolic processes to degrade and utilize, and hence can be utilized by all of the Alteromonas strains [65]. It is possible that the differences between Alteromonas strains may manifest when more complex macromolecules are available, e.g. from plant material, or when all of the “easy to digest” (labile) organic matter has been utilized and only complex macromolecules remain [66]. These conditions may not have been met in our experiments. It is also possible that co-culture with a more diverse range of heterotrophic bacteria, including additional Alteromonas species, would reveal more pronounced differences in the effect of the heterotroph of the primary producer. Similarly, we currently do not know why some Prochlorococcus strains support a mutually synergistic interaction with Alteromonas relatively early during the long-term N starvation (day 60) whereas other strains do not, and why at a later stage (day 100) almost all interactions are mutually beneficial. We could not identify any metabolic traits [11] clearly differentiating MIT9313 and MIT9312 (the “competitive” strains) from the others, suggesting more subtle differences exist between the Prochlorococcus strains in the organic matter they produce or in their response to N starvation (e.g. [67, 68]).

Our results identify patterns in the interactions between clades of abundant marine phototrophs and heterotrophs, under conditions where nutrients are scarce, and their availability likely depends on recycling between phototrophs and heterotrophs. Whether or not such mechanisms may be physiologically relevant in the oligotrophic ocean, much of which is N-stressed [40], remains to be tested. For example, in the oceans, rapid turnover of Prochlorococcus cells due to grazing and viral lysis likely means that cells are, on average, younger than those in laboratory cultures, which may affect their mortality rates [69]. Furthermore, stressors such as phage infection and grazing are missing in laboratory cultures. It is, however, noteworthy that the high heterotroph/phototroph biomass ratio observed during long-term N starvation here and in other studies [18] is similar to that of much of the open oligotrophic ocean (e.g. [70] and references therein). Additionally, Alteromonas may allow Prochlorococcus to adapt to light starvation [43] and to the presence of ROS (e.g. [71]), as well as other stressors that can be encountered in the open ocean. The supportive role of Alteromonas cannot be taken for granted, as it also depends on culture conditions, for example CO2 concentrations [27].

The co-cultures did not reach a steady state, and did not represent a closed system. Thus, processes not represented in these simplified laboratory co-cultures, are necessary to explain the long-term stability over decades of Prochlorococcus in the oceans [72]. Such processes could include multi-organism interactions, as natural communities are much more complex than the laboratory co-cultures, as well as oceanographic processes such as nutrient injection through deep mixing. More generally, cell mortality is intimately linked with the amount and type of recycled organic matter, yet the rate of mortality in natural communities is highly unconstrained [73]. Hence, better representation of mortality in mathematical models (e.g. the use of appropriate mortality formulations) is likely important for understanding biogeochemical cycles [73]. This may entail using one of the “off the shelf” models presented here, with their limitations (e.g. the Weibull model requires an estimate of the time of decline, whereas quadratic expressions for mortality are already used in such models [74,75,76]), or the development of new models that better link cell physiology, ecology, perhaps genome structure, and mortality.

Materials and methods

Strains and experiment set up

Axenic Prochlorococcus strains MED4 (HLI), MIT9312 (HLII), MIT0604 (HLII), NATL2A (LLI), and MIT9313 (LLIV) were maintained under constant cold while light (27 μmole photons m−2 s−1) at 22 °C [12, 77]. We used Pro99 media (natural seawater-based) that was modified by reducing the concentration of NH4 from 800 μM to 100 μM (Pro99-LowN), resulting in Prochlorococcus entering stationary stage due to the depletion of available inorganic N [78]. Alteromonas strains HOT1A3, Black sea 11, ATCC27126, AltDE1, and AltDE were maintained in ProMM [42]. Prior to the experiment, the axenicity of the Prochlorococcus cultures was tested by inoculating 1 ml culture into 15 ml ProMM [77], and no heterotrophic contaminants were observed by flow cytometry in axenic cultures after 60, 100, and 140 days. At the start of each co-culture experiment, Alteromonas cells from stationary-stage cultures (24–72 hour old) were centrifuged (10 minutes, room temperature, 10,000 g), the growth media decanted, and the cells re-suspended in the experimental media (Pro99-LowN). The Prochlorococcus cultures (growing exponentially) and the re-suspended Alteromonas cells were then counted using BD FACSCanto II Flow Cytometry Analyzer Systems (BD Biosciences). The initial cell concentrations in both co-cultures and axenic controls were 1 × 106 Prochlorococcus cells ml−1 and/or 1 × 107 Alteromonas cells ml−1. Axenic Alteromonas cultures were grown without any added C source besides DOC from the seawater-based media. The experiment was performed using triplicate 20 ml cultures in borosilicate test tubes (2.5 cm diameter, 15 cm length).

Fluorescence and Flow cytometry

Bulk chlorophyll fluorescence (FL) (ex440; em680) was measured almost daily using a Fluorescence Spectrophotometer (Cary Eclipse, Varian). Samples for flow cytometry were taken after 60, 100, and 140 days of experiment E1, fixed with glutaraldehyde (0.125% final concentration), incubated in the dark for 10 min and stored in −80 °C until analysis. Fluorescent beads (2 μm diameter, Polysciences, Warminster, PA, USA) were added as an internal standard. Data was acquired and processed with FlowJo software. Flow cytometry was performed unstained to count Prochlorococcus cells followed by staining with SYBR Green I (Molecular Probes/ ThermoFisher) to count Alteromonas cells.

Growth rate

Growth was computed––by solving the equation:

$$N_t = N_0e^{\mu (t - L)}$$

Where Nt represents the number of cells at time t, N0 is the initial number of cells, µ is the growth rate, and L is the growth lag. The LAN transformed equation was used to compute growth rate:

$$\ln \left( {N_t} \right) = \ln \left( {N_0} \right) + \mu (t - L)$$

Linear regression was run on the growth phase, predicting ln(Nt) based on time t with R2 > 0.9. The growth rate µ is the regression coefficient.

Carrying capacity

The carrying capacity of the cultures was defined as the amount of nitrogen retained in cell biomass (rather than as dissolved organic N) at various stages of long-term co-culture. Cell numbers from flow cytometry were converted into nitrogen using 7 fg N cell−1 for the high-light strains MED4, MIT9312, and MIT0605, 10.5 fg N cell−1 for strain NATL2A and 14 fg N cell−1 for strain MIT9313 [79, 80]. For Alteromonas we used a value of 13 fg N cell−1 [50, 81]. We note that the values we used are at the lower end of measured cell values, which reach up to 20 fg N cell−1 for low-light Prochlorococcus and 25 fg N cell−1 for Alteromonas, since using the higher N cell quota leads to biomass that is higher than the total nitrogen available in the system (Supplementary Text S4). This assumption is supported by studies showing that cells contain less nitrogen under long-term N stress compared to exponential growth [33, 82, 83].

The cell numbers were converted to μmol/L by the formula:

$$\begin{array}{l}{{{{{{{\mathrm{biomass}}}}}}}}\left[ {\mu {{{{{{{\mathrm{mol}}}}}}}}/{{{{{{{\mathrm{L}}}}}}}}} \right] = {{{{{{{\mathrm{X}}}}}}}}\left[ {{{{{{{{\mathrm{cell}}}}}}}}/{{{{{{{\mathrm{ml}}}}}}}}} \right] \ast {{{{{{{\mathrm{Q}}}}}}}}_{{{{{{{\mathrm{N}}}}}}}}^{{{{{{{{\mathrm{PRO}}}}}}}}}\left[ {{{{{{{{\mathrm{fg}}}}}}}}/{{{{{{{\mathrm{cell}}}}}}}}} \right] \ast 1{{{{{{{\mathrm{e}}}}}}}} - 9\\ \left[ {{{{{{{{\mathrm{converting\; femtomol}}}}}}}} - {{{{{{{\mathrm{ > \; micromol}}}}}}}}} \right]/1{{{{{{{\mathrm{e}}}}}}}} - 3\left[ {{{{{{{{\mathrm{ml}}}}}}}} - > \; {{{{{{{\mathrm{L}}}}}}}}} \right]/{{{{{{{\mathrm{MW}}}}}}}}_{{{{{{{\mathrm{N}}}}}}}}\left[ {{{{{{{{\mathrm{g}}}}}}}}/{{{{{{{\mathrm{mol}}}}}}}}} \right]\end{array}$$

Where X is the number of cells per ml, QN is the cell N quota, and MWN is the molecular weight of nitrogen. See Supplementary Text S4 for the detailed calculations and caveats.

Fit to decline models

The following functions were used to fit against the measured fluorescence:

$${{{{{{{\mathrm{Exponential}}}}}}}}:FL_t = FL_{max}e^{ - a\left( {t - t_{max}} \right)}$$
$${{{{{{{\mathrm{Bi}}}}}}}} - {{{{{{{\mathrm{exponential}}}}}}}}:FL_t = FL_{{{{{{{{\mathrm{max}}}}}}}}}\left( {f\;e^{ - a_{1\left( {t - t_{max}} \right)}} + \left( {1 - f} \right)\;e^{ - a_2\left( {t - t_{max}} \right)}} \right)$$
$${{{{{{{\mathrm{Harmonic}}}}}}}}:FL_t = FL_{{{{{{{{\mathrm{max}}}}}}}}}\frac{1}{{1 + a\;t}}.$$
$${{{{{{{\mathrm{Weibull}}}}}}}}:FL_t = FL_{{{{{{{{\mathrm{max}}}}}}}}}e^{ - a\;t^n}$$

Where FLt is the Fluorescence measured at time t, FLmax is the maximum fluorescence measured, tmax is the time when the fluorescence was highest, and a, a1, a2, n, f are the model parameters estimated by the fitting function.

The decline function was fit against each growth curve via curve_fit() function from scipy package (1.3.0), using the parameters: method=‘dogbox’, loss=‘soft_l1’, f_scale = 0.1. Each model was fit using random initial parameter values and the initial values of 0.5 per parameter, and the fit with the lowest RSME selected. Goodness of fit was measures using root mean square error (RMSE).

In the Weibull model the time needed to reduce the population by d factors of 10 (td2) was estimated as in [59], using the formula:

$$t_d = a\left( { - ln\left( {10^{ - d}} \right)^{\frac{1}{n}}} \right)$$

Random forest classification

To detect difference in the curve pattern and not timing specific differences, the curves were aligned such that max growth point are at time zero, and time points from 10 days prior to max growth to 80 days after were selected. Since the specific measurement time points were different in different experiments and samples, rolling average was used to get mean fluorescence per day, and interpolation used to fill in missing measurements. The Fluorescence measurements were standardized via standard scalar by subtracting the mean and scaling to unit variance of each feature. Random forest model was run in 10x cross validation [84] to classify the curves by Prochlorococcus and by Alteromonas strains. To find the most significant days in Prochlorococcus classification, the model was built 30 times and the mean importance of all features (i.e., measurement days) calculated. Data preprocessing was done by pandas (0.25.0). Scaling and model fitting using sklearn (0.21.2).

PCA ordination

PCA ordination was run on the growth curves. The fluorescence measurements were standardized via standard scalar by subtracting the mean and scaling to unit variance of each feature. Ordination was computed via principal component analysis (PCA). Data preprocessing was done by pandas (0.25.0). Scaling and PCA was done using sklearn (0.21.2).

Statistics

Statistics were computed using the statsmodels package in python. Multi test correction was done by t_test_pairwise() using Bonferroni correction. Permanova analysis by adonis2 from R vegan package (R 3.61, vegan 2.5-7).