Quantifying Oxygen Management and Temperature and Light Dependencies of Nitrogen Fixation by Crocosphaera watsonii.

Crocosphaera is a major dinitrogen (N2)-fixing microorganism, providing bioavailable nitrogen (N) to marine ecosystems. The N2-fixing enzyme nitrogenase is deactivated by oxygen (O2), which is abundant in marine environments. Using a cellular scale model of Crocosphaera sp. and laboratory data, we quantify the role of three O2 management strategies by Crocosphaera sp.: size adjustment, reduced O2 diffusivity, and respiratory protection. Our model predicts that Crocosphaera cells increase their size under high O2 Using transmission electron microscopy, we show that starch granules and thylakoid membranes are located near the cytoplasmic membranes, forming a barrier for O2 The model indicates a critical role for respiration in protecting the rate of N2 fixation. Moreover, the rise in respiration rates and the decline in ambient O2 with temperature strengthen this mechanism in warmer water, providing a physiological rationale for the observed niche of Crocosphaera at temperatures exceeding 20°C. Our new measurements of the sensitivity to light intensity show that the rate of N2 fixation reaches saturation at a lower light intensity (∼100 μmol m-2 s-1) than photosynthesis and that both are similarly inhibited by light intensities of >500 μmol m-2 s-1 This suggests an explanation for the maximum population of Crocosphaera occurring slightly below the ocean surface.IMPORTANCE Crocosphaera is one of the major N2-fixing microorganisms in the open ocean. On a global scale, the process of N2 fixation is important in balancing the N budget, but the factors governing the rate of N2 fixation remain poorly resolved. Here, we combine a mechanistic model and both previous and present laboratory studies of Crocosphaera to quantify how chemical factors such as C, N, Fe, and O2 and physical factors such as temperature and light affect N2 fixation. Our study shows that Crocosphaera combines multiple mechanisms to reduce intracellular O2 to protect the O2-sensitive N2-fixing enzyme. Our model, however, indicates that these protections are insufficient at low temperature due to reduced respiration and the rate of N2 fixation becomes severely limited. This provides a physiological explanation for why the geographic distribution of Crocosphaera is confined to the warm low-latitude ocean.

INTRODUCTION

Nitrogen (N) availability is recognized as a growth-limiting factor for primary producers in the ocean (1–4), controlling the flow of carbon (C) through the ecosystem (5–7). Dinitrogen fixation (N2 fixation) represents an important source of N that is estimated to account for nearly 50% of the fixed N input in the ocean (7). The microorganisms that fix N2 are termed “diazotrophs” and are physiologically diverse, including unicellular, filamentous, and heterocystous cyanobacteria with life strategies that include symbiotic, free-living, and colonial forms (8). Crocosphaera watsonii is a major phototrophic diazotroph and makes a significant contribution to the pool of fixed N in oligotrophic environments of the subtropical and tropical Atlantic and Pacific oceans (9–12). Observations show that the niche of Crocosphaera is limited to the region above 20°C (12, 13). Similarly, laboratory culturing experiments show that Crocosphaera grow only above 20°C (14, 15).

The enzyme responsible for N2 fixation, termed “nitrogenase,” is highly sensitive to oxygen (O2) (16, 17), thus necessitating careful O2 management by diazotrophs (18). In particular, Crocosphaera is a cyanobacterium with oxygen-producing photosynthesis, and fixing both C and N2 simultaneously would be a challenge. To circumvent the potential problem caused by O2 production, Crocosphaera fix N2 predominantly during the dark period in both laboratory (19–21) and natural (22) populations, thereby temporally segregating N2 fixation from O2-producing photosynthesis. However, O2 in the ocean is mostly saturated (∼200 μM in low latitudes) (23), and diurnal fluctuation of O2 is relatively small (∼10 μM) (24). Thus, even during the dark period, cells are likely to be exposed to a considerable influx of O2. Even at 5% O2 (∼50 μM), nitrogenase activity decreases to less than 30% within 20 min (17). Thus, questions remain about how Crocosphaera protects nitrogenase against O2.

O2 management by Crocosphaera must be considered within the context of their distinct daily physiological cycle. One metabolic strategy to constrain O2 is to sustain high rates of respiration in excess of the energetic demand during the night by using C stored from photosynthesis during the day (25). This distinct physiological cycle is paralleled by management of intracellular iron (Fe). Crocosphaera shuttles intracellular Fe between photosystems and nitrogenase during the daytime and the dark period to support photosynthesis and N2 fixation, respectively. The nitrogenase complex in particular is completely degraded and resynthesized each day (21). Despite the significance of the intracellular Fe cycling, the quantitative models have not mechanistically included the cycling nor have they linked it with other metabolisms, i.e., those affecting C, N, and O2. Developing a model which explicitly links Fe cycling to cellular metabolisms allows us to test how O2 can be managed within the context of the distinct daily cycle of Fe, C, N, and O2.

Physiological model of Crocosphaera.

First, we describe a new model of the C, N, Fe, and O2 budgets of Crocosphaera, and we then use it as a tool to explore the role of different O2 protection mechanisms. A more detailed description of the model is found in Materials and Methods and in Text S1 in the supplemental material.

Supplemental methods. Download Text S1, PDF file, 0.3 MB.

Simulating the daily cycle of metabolism based on Fe translocation.

We quantify the daily metabolic cycle for Crocosphaera by developing a coarse-grained model of Crocosphaera (cell flux model of Crocosphaera [CFM-Croco]), as depicted in Fig. 1 (see Materials and Methods and Text S1 for details). A previous dynamic model of Crocosphaera was developed to examine the daily cycle of C and N in Crocosphaera driven by a cellular clock and time-dependent functions (26). In our model, we explicitly link Fe cycles to C, N, and O2 metabolisms. As a starting point, we assume the total Fe constant within the cell and simulate the temporal variation of the fraction of Fe in different pools. During the light period, a predominant amount of Fe exists in photosystems contributing to photosynthesis. After sunset, Fe moves to nitrogenase, increasing the rate of N2 fixation. Before sunrise, Fe moves back to photosystems, preparing for daytime photosynthesis. We linearly link the amount of Fe in photosystems with the rate of photosynthesis and that in nitrogenase with the rate of N2 fixation leading to diurnal fluctuation of these metabolic rates. During the daytime, with photosynthesis, C storage (starch) is accumulated and fuels nitrogen fixation during the night. Nighttime metabolism also includes respiratory depletion of intracellular O2, which depends on the amount of C storage and the temperature-dependent metabolic capacity.

FIG 1

Schematics of modeled C, N, O2, and Fe fluxes. (A and B) C, N, and O2 fluxes for light and dark periods, respectively. Black solid arrows represent material fluxes, red dashed arrows represent energy fluxes, and a black dotted arrow represents photon flux. C-based molecules are in yellow, N-based molecules are in pink, O2 is in red, and H2O is in blue. CS and NS, C and N storage, respectively; Chl, chlorophyll. (C and D) Fe fluxes (black solid arrows) for light and dark periods, respectively. The large circular frame indicates the cellular boundary.

Quantifying the rate of N2 fixation.

N2 fixation is modeled as explicitly dependent on the intracellular concentration of nitrogenase, the size of the intracellular carbohydrate and fixed-N stores, the intracellular O2 concentration, and the temperature. During the dark period at a fixed temperature, the rate of N2 fixation (N2fix; mol N cell−1 h−1) is assumed to be affected by the fluctuation of Fe, the respiratory depletion of intracellular O2, and the storage of N and C as depicted in Fig. 2 where AN2fix is a rate constant (mol N mol Fe−1 h−1), FeN is the mass of Fe in nitrogenase (mol Fe cell−1), and fN(CS, NS, ) scales the rate of N fixation between zero and its maximum value per nitrogenase (AN2fix), based on the available C storage (CS; mol C cell−1) and N storage (NS; mol N cell−1) and the presence of intracellular O2 (; mol O2 cell−1). Increasing nitrogenase concentrations (as proxied by FeN) increase the encounter rate of N2 gas, with nitrogenase proportionally/linearly increasing N2fix (Fig. 2A). CS positively influences N2fix, since it provides energy for N2 fixation. We have assigned a saturating dependence (Michaelis-Menten type curve) to CS (Fig. 2B), the C substrate. On the other hand, we assume that NS negatively influences N2 fixation (Fig. 2C), as reactive N is often observed to inhibit N2 fixation (27–29). Intracellular O2 () also negatively influences N2 fixation, since the proteins in the nitrogenase complex are sensitive to O2 (16, 17) (Fig. 2D). We assign a critical O2 concentration () above which N2 fixation does not occur, below which we assumed that N2fix increases linearly with decreasing . This assumption is to represent an in vitro experiment of nitrogenase activities, where there are rather gradual negative correlations between O2 and activities of nitrogenase subunits (17).

FIG 2

Schematics of how each factor influences N2fix in the model. (A) FeN; (B) CS; (C) NS; (D) . is the maximum N storage capacity, and is the critical O2 concentration.

Simulating O2 management.

To simulate the intracellular O2 concentration, we assume a balance between diffusive flux into the cell and the respiratory O2 consumption within it, which can be expressed as follows (18): where (mol O2 m−3) represents the intracellular concentration of O2, [O2] (mol O2 m−3) is the environmental concentration of O2, r is the cell radius (m), γnet is the net respiration rate (respiration rate − photosynthesis) per cell volume (mol O2 m−3 s−1), and κO2 is the effective O2 diffusion coefficient (m2 s−1) which accounts for the diffusivity in both the molecular boundary layer surrounding the cell and a semipermeable cell membrane layers. In order to minimize , cells may live in low [O2] environments, increase cell size (increasing r), increase respiration (increasing γnet), or decrease O2 diffusivity through the cell membrane layers (decreasing κO2).

Temperature dependence of metabolic processes.

To study why Crocosphaera’s niche exists mostly above 20°C, we use a commonly used temperature factor [f(T)] based on the Arrhenius equation (30, 31): where T is temperature (K), Tref is a reference temperature (K), and A is a constant factor (K−1). This factor independently modulates three key metabolic functions, namely, N2 fixation, photosynthesis, and respiration, and simulates the daily integrated rates of metabolisms. We explore the significance of the temperature dependence of each metabolic component.

Quantifying light dependence of metabolisms with laboratory measurements.

We model the dependence of photosynthesis on light using the commonly employed saturating functional form (32, 33) with photoinhibition:where I is light intensity (μmol m−2 s−1), A is a light absorption/processing factor (μmol−1 m2 s), and Ω(I) is a photoinhibition term (dimensionless). We have also conducted laboratory measurements of N2 fixation rates and photosynthetic electron transfer rates by Crocosphaera watsonii WH8501 for various light intensities (see Materials and Methods) and compared them with the model.

RESULTS AND DISCUSSION

Analysis of daily metabolic cycles.

We have simulated time-dependent laboratory cultures of Crocosphaera (25) and the linked Fe allocation within the cell (21). The model accurately predicted rates of photosynthesis and respiration both qualitatively and quantitatively for different O2 concentrations in the culture (Fig. 3A): 20% (186 μM, the normal atmospheric composition and surface ocean concentration in tropics) and 5% (46 μM, one-quarter of the normal composition), as used in the previous laboratory experiment (25). The rate of photosynthesis was maximal during the middle of the day for both 20% and 5% O2 values.

FIG 3

Simulated diurnal cycle of Crocosphaera for different O2 concentrations (curves) and laboratory data (circles). (A) O2 fluxes based on photosynthesis (gray and pink) and respiration (red and black). Here, O2 production is positive for photosynthesis, and O2 consumption is positive for respiration. (B) O2 concentrations in the cell. (C) N2 fixation rates. (D) C per cell. (E) N per cell. (F) Fe allocation. In panels A to E, error bars are the standard deviations of laboratory data (25). Here, we used a theoretical factor of 3 for C2H4:N2 (59). Red (or pink in panel A) is at 20% O2, and black (or gray in panel A) is at 5% O2. In panel F, Fe used by metabolism is based on quantitative protein data (21) for Fe in photosystems (FeP; orange) and nitrogenase (FeN; brown). In the model, the rest of the Fe exists in the buffer (an intracellular Fe storage). The key shown in panel C applies to panels A to E (pink and gray apply only to the photosynthesis (Pho) in panel A). In all panels, gray shading indicates dark periods. Temperature and light intensity are 28°C and 150 μmol m−2 s−1, respectively (21, 25).

The rate of photosynthesis was correlated with Fe cycles, since the rate is proportional to Fe in photosystems (FeP) (Fig. 3F); as the sun rises, Fe moves from the buffer (an intracellular Fe storage, e.g., ferritin and bacterioferritin [21]) to the photosystems, but in the afternoon, it starts moving back to the buffer, which was predicted by relating Fe to CS. As CS increases and approaches maximum storage levels, there is no benefit to further photosynthesis. Therefore, the amount of photosystems was downgraded, and Fe was moved back to the buffer. We predicted a limited difference in photosynthesis between 5% and 20% O2, consistent with laboratory data.

We also reproduced the observed daily cycle of respiration and showed that higher respiration rates occurred at 20% O2 during the dark period due to respiratory protection (25). Because of this respiratory protection, intracellular O2 concentrations decreased to almost zero during the middle of the night (Fig. 3B), leading to peak N2 fixation during this period (Fig. 3C).

The data showed that N2 fixation increased more quickly at 5% O2 than at 20% O2 during the early dark period and can be explained by the concentration of intracellular O2. Based on the model, cellular O2 was eliminated more quickly at 5% (Fig. 3B), reaching zero before 14 h, while such elimination occurs after 15 h for 20% O2, thereby delaying N2 fixation. This delay in N2 fixation under normal O2 conditions is widely observed both in the laboratory (19, 34) and in natural populations (22). This delay may reflect the extra time required for O2 elimination, given that Crocosphaera’s nifH gene is transcribed following the initiation of the dark period (19, 21, 22), and both the model and laboratory data showed a much smaller delay in N2 fixation in a low-O2 environment. We capture this trend with the O2 dependence of N2 fixation (equation 1) (Fig. 2D); at 5% O2, the intracellular O2 is depleted quickly (Fig. 3B) and thus the rate of N2 fixation increases earlier (Fig. 3C).

During the dark period, as the nitrogenase enzyme is synthesized, Fe moves from the buffer to nitrogenase, initiating N2 fixation. As the dark period approaches dawn, Fe begins moving back to the buffer, preparing for daytime photosynthesis through degradation of the nitrogenase protein complex (19, 21), accompanied by decreased respiration (Fig. 3A), leading to the drop in the rate of N2 fixation (Fig. 3C) and increased intracellular O2 (Fig. 3B). We can use the model to consider how Crocosphaera’s diel cycle might be regulated. If the C storage reservoir were to be the trigger for Fe transfer, we would expect C storage to be significantly reduced during the dark period. However, even at the end of the dark period, we predict a significant amount of C storage remaining in the cell. If N storage is the trigger, Fe should start moving earlier in the case of 5% O2 than in the case of 20% O2, as the cell fixes N2 faster under low O2. The data show, however, that the rate of N2 fixation drops at almost the same time for the two O2 cases. Also, the peak of N2 fixation appears during similar time ranges among different studies (19, 21, 34). Finally, since Crocosphaera maintains the daily cycle even under continuous light (35, 36), it seems that the Fe transfer within Crocosphaera is largely controlled by a circadian clock that regulates key cellular functions. To further examine what controls Fe transfer, higher-resolution measurement of N2 fixation (34) under various O2 concentrations would also be useful.

Based on the metabolic rates (respiration, photosynthesis, cellular growth, and N2 fixation), we computed the cellular C and N quotas (Fig. 3D and E). During the light period, the cells accumulate C, while during the dark period, C storage decreases due to respiration and N2 fixation. During the light period, the data show that C accumulation is slightly greater for 20% O2 than for 5% O2; the model predicts this trend, with increased cell size for higher O2 (thus, larger cell size for 20% O2). During the dark period, however, it gets lower for 20% O2 than for 5% O2 , due to higher respiration for O2 management. Due to the larger cell size (discussed in “Sensitivity studies”), cells under 20% O2 have higher N. However, at the end of the dark period, cellular N levels under these different O2 concentrations get closer since the rate of N2 fixation is higher for 5% O2. The slight decrease in N during the early light period is due to cell division.

Sensitivity studies.

In the following three sections, we describe sensitivity studies performed with the model to probe the significance of different O2 protection strategies. To examine the effect of each strategy, we specifically turned off each O2 management mechanism (size change, respiratory protection, and diffusion management) and the model results (cellular C, N, O2 fluxes, and N2 fixation rates) were compared with the default run with all the mechanisms present.

Relationship between cell size and O2.

An increase in cell size is a potential physiological strategy for Crocosphaera, since it decreases the surface-to-volume ratio, thereby decreasing passive O2 uptake per volume (equation 2) (18). Adjusting the cell size based on O2 concentrations facilitates replication of the laboratory data (Fig. 4).

FIG 4

Simulated daily cycle of Crocosphaera with no size change based on O2 concentration. (A) C per cell. (B) N per cell. Curves represent simulations, and points with error bars (standard deviations) represent laboratory data (25). Here, we used a theoretical factor of 3 for C2H4:N2 (59). Dashed curves represent the run with no size change (NSC), and solid curves represent the default run (DR) (as in Fig. 3). Red indicates 20% O2, and black indicates 5% O2. NSC and DR show the same results for 5% O2 since the same size value is used. The key in panel B applies to both panels. Gray shading on the x axis indicates the dark period. Temperature and light intensity are 28°C and 150 μmol m−2 s−1, respectively (25).

During the light period, if the cell size is independent from O2 concentration, the model shows identical values for C and N per cell for different O2 concentrations, while the data show generally higher values for 20% O2; as a result, more predictions are outside the error bars of the data, especially for C per cell (Fig. 4A). During the dark period, the data show a reverse effect in relation to C: the C per cell in 20% O2 starts at a higher value but ends up at a lower value. This trend was reproduced only by including the size variation (Fig. 4A). N per cell is almost the same value at the end of the dark period, but the model with a fixed cell size shows much lower values in 20% O2 outside the error bar (Fig. 4B). These results indicate that the cells acclimate to higher O2 environments by adjusting their size. Recent studies have shown that there are two size classes of Crocosphaera (14, 22, 37). The model indicates that the larger cells have a significant advantage in O2 management and might be a result of adapting to the high O2 environments widespread in oceanic surface waters.

Respiratory protection against O2.

In order to examine whether respiratory protection is essential, we ran the model without respiratory protection (Fig. 5; see Fig. S1 in the supplemental material). In this case, respiration serves only to provide energy for N2 fixation. At 5% O2, the N2 fixation rate is almost the same as that for the simulation with respiratory protection (Fig. 5B). Once the dark period initiates and photosynthesis stops, the cellular O2 concentration drops low enough for N2 fixation. As N2 fixation initiates, respiration increases to provide energy, further decreasing intracellular O2 to zero, until N2 fixation peaks. On the other hand, at 20% O2, even after the initiation of the dark period, the cellular O2 concentration was still high (Fig. S1A), preventing N2 fixation (Fig. 5B). The respiration rate was much lower than the laboratory values (Fig. 5A), especially at 20% O2. Since there is no flux that consumes C at 20%, the model overestimated intracellular C (Fig. S1B). Together these results imply that respiratory protection is occurring in Crocosphaera and is essential for N2 fixation at normal O2 concentrations in the environment.

FIG 5

Simulated daily cycle of Crocosphaera with no respiratory protection. (A) Respiration. (B) N2 fixation. Curves represent simulations, and points with error bars (standard deviation) represent laboratory data (25). Here, we used a theoretical factor of 3 for C2H4:N2 (59). Dashed curves represent the run with no respiratory protection (NRP), and solid curves represent the default run (DR) (as in Fig. 3). Red indicates 20% O2, and black indicates 5% O2. The key in panel B applies to both panels. Gray shading on the x axis indicates the dark period. Temperature and light intensity are 28°C and 150 μmol m−2 s−1, respectively (25).

Simulated daily cycle of Crocosphaera with no respiratory protection. (A) O2 concentration in the cell; (B) C per cell. Curves represent simulations, and points with error bars (standard deviations) represent laboratory data (25). Here, we used a theoretical factor of 3 for C2H4:N2 (59). Dashed curves represent the run with no respiratory protection (NRP), and solid curves represent the default run (DR) (as in Fig. 3). Red represents 20% O2, and black represents 5% O2. The key in panel A applies to both panels. Gray shading on the x axis indicates the dark period. Temperature and light intensity are 28°C and 150 μmol m−2 s−1, respectively (25). Download FIG S1, TIF file, 0.4 MB.

Diffusion management.

A model-data comparison indicates that the diffusivity of the cell membrane layers must be extremely low relative to both the diffusivity in the molecular boundary layer and to the diffusivity of the cell membrane layers inferred from other N2-fixing organisms. To achieve the results illustrated in Fig. 3, the effective diffusivity of O2 across the cell membrane layers must be set to 1/(6.45 × 104) of the diffusivity of O2 in water. Previous studies of the heterotrophic and photoautotrophic diazotrophs Azotobacter vinelandii and Trichodesmium also inferred low cell wall permeability [1/(1.27 × 103) (18, 38) and 1/(1.60 × 103) (39) of the diffusivity of O2 in water, respectively], but the above predicted value for Crocosphaera is even lower. In contrast, the permeability of non-N2-fixing bacterial cells is much higher [1/(5.30 × 102)] (40). Applying the value inferred for Azotobacter results in poor simulations of the laboratory data (Fig. S2), significantly overestimating the respiration at 5% O2 (Fig. S2A) and suppressing N2 fixation (Fig. S2B) because the O2 influx could not be matched. We conclude that Crocosphaera and other N2-fixing microbes necessarily control the cell wall permeability for O2; otherwise, N2 fixation would be impossible. However, the required protection varies between species, and the details of this adjustment need to be further investigated.

Simulation of daily cycle of Crocosphaera with higher (rather normal) diffusivity of cell membrane layers. (A) Respiration; (B) N2 fixation; (C) O2 concentration in the cell; (D) C per cell. Curves represent simulations, and points with error bars (standard deviations) represent laboratory data (25). Here, we used a theoretical factor of 3 for C2H4:N2 (59). Dashed curves represent the runs with higher (rather normal) diffusivity (HD) of the cell membrane layers, and solid curves represent the default run (DR) (as in Fig. 3). Red represents 20% O2, and black represents 5% O2. The key in panel B applies to all the panels. Gray shading on the x axis indicates the dark period. Temperature and light intensity are 28°C and 150 μmol m−2 s−1, respectively (25). Download FIG S2, TIF file, 0.7 MB.

One possibility is that carbohydrate storage may act as an O2 barrier. As shown previously (41), during cell division, starch granules are accumulated near the cell membranes rather than spread evenly in the cytoplasm. Our original electron microscopy images of Crocosphaera ultrathin sections revealed that the location of the granules close to the membranes is well preserved in both the light and dark periods (Fig. 6). Since the starch granules are relatively rigid and have dense hydrophilic structures, it is likely that they act as a barrier against O2 during the night. The images also show thylakoid membranes surrounding the granules (Fig. 6) (see also reference 41). Since respiration occurs on the thylakoid membranes as well as cellular membranes (42), such localization may make it possible for the cells to consume O2 before it reaches the inner cytoplasm, as well as further physically decreasing the diffusivity of O2.

FIG 6

Transmission electron micrographs of Crocosphaera cells harvested at the 6-h time point during the light period (A to C) and at the 6-h time point during the dark (D to F). Starch granules (SG) and thylakoid membranes (THY) are observed mostly on the edge of the cytosol. More-detailed images (C and F) show that SG are observed mostly between THY.

Another possible barrier against O2 diffusion is the production of extracellular polymeric substances (EPS), which may create a thick hydrophilic layer, where the diffusion of O2 molecules is reduced. It has been hypothesized that Azotobacter vinelandii excrete alginate (one kind of EPS) to decrease the passive O2 uptake and thus protect nitrogenase (43). Its effect on N2 fixation has been further studied using quantitative modeling (18) and laboratory studies (44), supporting the hypothesis. In a batch culture, Crocosphaera produce EPS roughly proportional to their growth (37) and the production of EPS increases during the dark period (41). Given these findings, we hypothesize that the EPS produced by Crocosphaera plays an important role in reducing O2 diffusion. Recent observations suggest that hopanoid lipids may also play a role in diffusion management, as they have biochemical properties that potentially decrease the permeability to extracellular O2 and hopanoid synthesis genes are specifically observed in non-heterocyst-forming cyanobacterial diazotrophs (45).

Temperature dependence of N2 fixation.

As we illustrate below, the model suggests that the temperature dependence of N2 fixation, and thus the fitness of Crocosphaera, is largely explained by the temperature dependence of respiration. N2 fixation by Crocosphaera is observed to have a strong dependence on temperature. Cell-specific rates of N2 fixation are maximal at approximately 30°C and decrease to almost zero at 22°C (15). These laboratory-derived physiological observations are supported by field observations of Crocosphaera being most prevalent in warm oceanic regions above 20°C (12, 13).

In the model, N2 fixation, photosynthesis, and respiration are each modeled with independent, Arrhenius equation-like temperature dependence (equation 3). By employing these in combination, the model replicates the observed temperature dependence of N2 fixation (Fig. 7A). We tested which temperature dependence has the strongest effect by applying equation 3 to only one of the metabolisms (Fig. 7B). The results show that the temperature dependence on respiration has the strongest effect, closely representing the predicted results with all the temperature dependences. This indicates that the negative effect of temperature on N2 fixation is largely due to decreased rates of respiration being insufficient to draw down intracellular O2, and therefore nitrogenase is unable to fix N2. A decrease in the rate of respiration will also decrease the supply of energy for nitrogenase. Decreased temperature will also have effects on other related metabolic processes, such as a direct effect on the rate of enzymatic activity of nitrogenase and a decrease in photosynthesis and therefore less C storage for respiration (Fig. 7B). All of these impacts, however, turned out to be smaller than the decrease in respiratory protection against O2.

FIG 7

Simulated temperature dependence on N2 fixation, photosynthesis, and respiration. (A) Simulated temperature dependence on these metabolic fluxes when the temperature function is assigned to all of these fluxes. N2fix, N2 fixation; Resp, respiration; Photo, photosynthesis. (B) Impact of each temperature dependence on N2 fixation rate. The solid curve represents when all three fluxes are temperature dependent. The other curves represent when only one of these fluxes is temperature dependent (see the key in the figure; i.e., N2fix, Photo, and Resp indicate that the temperature function is assigned only to N2 fixation, photosynthesis, and respiration, respectively). A light intensity of 150 μmol m−2 s−1 is used (25). Also, a saturating O2 concentration is used based on the specified temperature and a salinity of 35 (60). The temperature dependence of diffusivity is given based on Walden’s rule (61) and the temperature-dependent viscosity of water (62). The diffusivity of the cell membrane layers is assumed to be proportional to that of water (18).

The rate of N2 fixation maximized at moderate light intensity.

To examine light dependence on N2 fixation for Crocosphaera, we have simulated the rate of N2 fixation at various light intensities. In the model, the light intensity influences the rate of photosynthesis based on the equation of light saturation and photoinhibition (equation 4). The model shows that the rate of N2 fixation increases at low light intensity due to increased photosynthesis and, thus, increased C storage (Fig. 8A). However, despite photosynthesis rates increasing with light intensities up to ∼700 μmol m−2 s−1 (Fig. 8B), N2 fixation saturates at a relatively low light intensity (∼100 μmol m−2 s−1) (Fig. 8A), since it becomes limited by the availability of nitrogenase (here proxied by FeN). This prediction is confirmed by our original measurements of the rates of acetylene reduction (proxy for N2 fixation) and ETR (photosynthetic electron transfer rate) for various light intensities from this study. Above 140 μmol m−2 s−1, the rate of N2 fixation becomes stable despite the significant increase in ETR.

FIG 8

Experimental data and model simulation of the light dependence of daily integrated rates of N2 fixation and photosynthesis of Crocosphaera. (A) Simulated light dependence of the N2 fixation rate of Crocosphaera at 20% O2 (left axis) compared with the acetylene reduction data obtained in this study (right axis). (B) Simulated light dependence of the photosynthesis rate (left axis) compared with the average daytime ETR (electron transfer rate) measured in this study (right axis). Error bars represent the standard deviations of the samples. A temperature of 28°C was used.

Our measurements also show that above certain light intensities, both of the rates (N2 fixation and photosynthesis) start dropping (Fig. 8), likely due to photoinhibition. These results may explain why the maximum population of Crocosphaera is often observed below the surface but above a depth of 50 m (12, 13), where they can receive moderate light intensities (100 to 400 μmol m−2 s−1), enough for N2 fixation without photoinhibition. The model resolves photoinhibition, capturing the trend in ETR (Fig. 8B). However, it does not predict the observed decrease in N2 fixation under strong light, despite the drop in photosynthesis above 700 μmol m− 2 s−1, meaning that the rate of photosynthesis or the level of C storage cannot explain the decreasing trend in N2 fixation (Fig. 8A). This indicates that high light intensity rather directly inhibits nitrogen fixation, potentially by damaging machinery for nitrogenase synthesis or subunits of nitrogenase before its assembly.

Conclusions.

We have developed a coarse-grained model of Crocosphaera (CFM-Croco) and simulated a daily cycle of Crocosphaera metabolism with distinct C, N, O2, and Fe fluxes. The model mechanistically links the diurnal cycle of Fe with that of C, N, and O2, reproducing published observations (21, 25). This indicates that including the Fe cycle is essential for simulating the diurnal cycle of Crocosphaera metabolism and nutrient fluxes. The model results suggest that Crocosphaera employs multiple mechanisms to manage intracellular O2: size change, respiratory protection, and decreased diffusivity. Since respiratory O2 management is crucial for N2 fixation, the temperature dependence of respiration has a significant impact on N2 fixation, which provides a hypothesis for the strong temperature constraint on their growth and niche in the environment. The light dependence of photosynthesis does not give an advantage to N2 fixation under extremely high light due to photoinhibition and limitations on nitrogenase concentration, the latter of which may be constrained by the intracellular space. This indicates that the optimum depth is likely not at the very surface, despite the potentially highest availability of Fe dust.

MATERIALS AND METHODS

Cell flux model of Crocosphaera.

Here, we describe the algorithms employed to implement the model. The model schematic is depicted in Fig. 1. Time-dependent equations are given to describe the rates of change in each of the macromolecular pools (Table 1). The fluxes between macromolecular pools are quantified at each time step. The time-dependent equations (Tables 1 and 2) are advanced in finite time steps, updating the status of the cells. Parameter values and nomenclature with units are available in Tables S1 and S2 in the supplemental material, respectively.

TABLE 1

Fundamental relations of C-, N-, and O2-based molecules

Equationa	Equation no.
dCSdt=PIChl−λ(1+E)−PCO2N2fix−PCO2RP−Exc	5
dXdt=XλQC	6
dN_Sdt=N_2fix−λYbio-allN:C	7
dO2dt=PO2−RO2+VO2	8

CS, C storage; t, time; P, photosynthesis rate per chlorophyll; Chl, chlorophyll; λ, biomass production rate; E, conversion factor of biomass production to biosynthetic CO2 production; N2fix, N2 fixation rate; , CO2 production due to electron donation to and respiratory energy production for N2 fixation; , CO2 production due to respiratory protection; Exc, C excretion rate; X, population density of cells; QC, cellular C quota; NS, N storage per cell;, N:C of biomass including storage; O2, O2 per cell; PO2, O2 production rate; RO2, respiration rate; VO2; O2 exchange by diffusion.

TABLE 2

Fundamental relationships of Fe-related molecules

Equationa	Equation no.
dFePdt=FBP−FPB	9
dFeBdt=−FBP+FPB−FBN+FNB	10
dFeNdt=FBN−FNB	11
dChldt=(FBP−FPB)YphotoChl:Fe	12

FeP, Fe in the photosystems; and , translocation of Fe from the buffer to the photosystem and vice versa; FeB, Fe in the buffer; and , translocation of Fe from the buffer to nitrogenase and vice versa; FeN, Fe in nitrogenase;, Chl:Fe in the photosystems.

Values used for tunable parameters. Download Table S1, PDF file, 0.2 MB.

Parameters, definitions, and units used in both the main text and the supplemental material; the parameters are listed roughly in order of appearance from the main text to Text S1 (supplemental methods). Download Table S2, PDF file, 0.2 MB.

C, N, and O2 metabolism.

In order to compute the time variation of intracellular C, N, and O2 pools and the cell density, we consider the chemical fluxes that impact them. Specifically, we include time variation of CS, cell population density (X) based on biomass production, NS, and O2 (equations given in Table 1 and schematics given in Fig. 1A and B). The balance in C storage pool CS (equation 5) is based on the balance among photosynthesis (P Chl), biomass production (λ), biosynthetic CO2 production (Eλ), CO2 production for N2 fixation (), CO2 production due to respiratory protection (), and C excretion (Exc). Cellular C and N are the sum of the baseline biomass and the C and N storages, respectively.

We assume that biomass production is used for the production of new cells, which drives the time change in population density (equation 6). Biomass production is supported not only by C but also by N. Thus, we consider the effect of biomass production on N5 () (equation 7), which is balanced by N2 fixation (N2fix). Finally, the O2 budget is based on photosynthesis (O2 production rate [PO2]), the respiration rate (RO2), and the diffusive exchange of O2 (VO2) (equation 8).

Since the metabolism differs between the light and dark periods, we employed different parameterizations of the fluxes in Table 1 at different times of day. Specifically, P, λ, Exc, and PO2 are unique to the light period, and N2fix, , and are specific to the dark period.

In order to solve the model equations, we have applied a finite-difference method to equations 5 to 7. Since the time scale of O2 concentration is small relative to that of other metabolites (C, N, Fe), we have assumed a pseudo-steady state; thus, O2 uptake and O2 production are always balanced by respiration. For the calculation of fluxes that influence the time variation of each pool, we consider the size of the elemental pools and O2 concentrations (the details of the flux calculations are described in Text S1 in the supplemental material).

Fe metabolism.

The rates of C and N2 fixation both depend on the Fe allocation to the enzymes which mediate those processes. Here, we model the time-dependent allocation to those Fe pools. The time-dependent equations for the Fe system are given in Table 2. We assume that the exchange of Fe between photosystems and nitrogenase is mediated by an Fe buffer, such as bacterioferritin protein (Fig. 1C and D) (21). Thus, the time variation of Fe in the photosystems is based on its exchange with the buffer Fe pool (equation 9). The buffer Fe pool is influenced not only by the Fe from the photosystems but also by the exchange of Fe with nitrogenase (equation 10). The Fe allocation to nitrogenase results from the balance between the loss to and gain from the buffer (equation 11).

Connecting Fe fluxes to C, N, and O2 fluxes.

The amount of Fe in photosystems (FeP) proportionally influences photosynthesis, thus impacting C and O2 fluxes. We have assumed that the ratio of chlorophyll to Fe in a photosynthetic apparatus (mol C mol Fe−1) is constant (); thus, the balance in chlorophyll is proportional to the balance in photosystem Fe (equation 12). The amount of chlorophyll in turn influences the rate of photosynthesis (equation 5). The rate of N2 fixation (N2fix) is assumed to be proportional to the amount of nitrogenase proxied by Fe in nitrogenase (FeN). Thus, through the rate of N2 fixation, FeN influences C and N fluxes, and through the associated respiration providing energy for N2 fixation, it can influence O2 fluxes.

In order to calculate the amount of Fe pools and chlorophyll, we applied a finite-difference method to equations 9 to 12. For the computation of Fe fluxes, we considered various factors, such as the size of the Fe pool of the origin and the destination, time, O2 concentration, and carbohydrate storage. Fe fluxes are parameterized based on these factors to reproduce the laboratory observations (21) (Fig. 3F) (see Text S1 in the supplemental material).

Differentiating light and dark periods.

To reflect a distinct diurnal cycle of Crocosphaera, we resolve differences in metabolic configuration during the day and night; some fluxes in Tables 1 and 2 are specific to a certain time of day. The schematics of which flux applies to each time period are illustrated in Fig. 1. The following section broadly describes the day-night differentiation. The detailed fluxes are described in Text S1.

Light period.

During the light period, cells can harvest light and fix C, accumulating C storage and producing biomass (Fig. 1A). However, N2 fixation is small and accordingly respiratory protection is also small. For the N source for biomass production, the cell relies on N storage. To reflect this, all the terms in equations 5 to 8 (Table 1) are used except N2fix, , and (∼0). Also, we assume that the translocation of Fe from the buffer to nitrogenase () is ∼0, since no FeN was observed during the light period (21); this assumption depletes FeN (Fig. 1C).

Dark period.

During the dark period, photosynthesis does not occur, but the cell uses stored C for respiration and N2 fixation (Fig. 1B). Also, we assume that biomass production and excretion do not occur. Thus, in equation 5, P = λ = Exc = 0. This assumption allows accumulating N storage with N2 fixation, as observed previously (25). According to the observed targeted proteomics (21), there is limited net Fe flux to the photosystems, and we assume that the translocation of Fe from the buffer to the photosystem () is zero. This assumption creates the flow of Fe from photosystems to nitrogenase (Fig. 1D), increasing the rate of N2 fixation during the early dark period. During the later dark period, we assume that is ∼0, and the model forces the movement of Fe from nitrogenase to buffer as predicted (21).

Simulating temperature and light dependences on metabolisms.

The temperature dependence is simulated based on applying a temperature factor f(T) (equation 3) to N2 fixation, photosynthesis, and respiration. To test the effect of temperature dependence on each metabolism, we applied f(T) to only one of these metabolisms and plotted the rate of N2 fixation (Fig. 7B). To represent the light dependence of photosynthesis, we have applied a light factor, f(I), (equation 4) to the maximum rate of photosynthesis.

Preparing Crocosphaera watsonii WH8501.

Stock cultures of Crocosphaera watsonii WH8501 were obtained from the Culture Collection Yerseke (The Royal Netherlands Institute for Sea Research, Yerseke, The Netherlands; strain number CCY 0601). The cells were maintained in N-free YBC-II medium (46) at 28°C in glass flasks under constant white light of 150 μmol μm−2 s−1 using a 12-h:12-h light-dark (12L:12D) cycle. At the beginning of each experiment, the cultures were transferred into flat-panel photobioreactors (FMT150; Photon System Instruments, Brno, Czech Republic) (47) with a sinusoidal 12L:12D growth irradiance peaking at 400 μmol m−2 s−1 with aeration. Cultures were acclimated to these conditions and maintained in exponential growth for at least 5 generations (about 15 days).

Transmission electron microscopy.

Crocosphaera cells (∼108 cells ml−1) were harvested by centrifugation (5 min at 5,000 × g). The cells were resuspended in 1 volume of the growth medium mixed 1:1 with 5% (vol/vol) glutaraldehyde fixative in 0.2 M cacodylate buffer, pH 7.2. After 15 min of rotary shaking at room temperature, cells were transferred to 0.1 M cacodylate buffer containing 2.5% (vol/vol) glutaraldehyde and fixed overnight at 4°C. Pelleted cells were washed with cacodylate buffer and postfixed with 1% (wt/vol) osmium tetroxide for 2 h. After washing steps with the same buffer, cells were dehydrated through a graded series of acetone, embedded in low-viscosity Spurr resin (EMS), and polymerized at 60°C for 48 h. Ultrathin sections of 60 nm were cut using an ultramicrotome (UCT, Leica). Sections were collected on Formvar-coated copper grids and stained with 1% (wt/vol) aqueous uranyl acetate for 10 min and with Sato’s lead citrate for 3 min (48). Prepared sections were examined in a JEOL 1010 transmission electron microscope (JEOL) equipped with a Mega View III camera (SIS). Acquired pictures were analyzed by ImageJ software (49).

N2 fixation measurements.

To determine the rates of N2 fixation by acetylene reduction assays (50), 5 ml of cell suspensions grown under different light intensities were dispensed into HCl-rinsed glass vials. After each vial was sealed with a septum, 10 ml of acetylene gas (99.7% [vol/vol]; Linde Gas) was injected by replacing the same volume of headspace. The samples were incubated at 28°C in the dark for 12 h. Subsamples of the headspace were taken immediately after acetylene addition and then at the end of the incubation to measure their ethylene content with a flame ionization gas chromatograph (HRGC 5300; Carlo Erba Instruments). Ethylene production during the incubation was analyzed, and produced ethylene was calculated according to Breitbarth et al. (51).

Variable-fluorescence light response curves.

The diel changes in the dependence of photosynthesis on light intensity was assessed with photosynthesis versus irradiance (P versus E) curves using the electron transfer rate (ETR) through photosystem II as a photosynthesis proxy. Cells were harvested in 2-h intervals throughout the diel cycle (52). Samples were acclimated to the dark for 10 min and placed inside a FL3500 fast repetition rate (FRR) fluorometer (Photon Systems Instruments, Czech Republic) maintained at the same temperature as the stock cultures. A series of 100 simultaneous blue (463 nm) and amber (617 nm) flashes of 1-μs duration was applied to induce a single turnover of the reaction centers of photosystem 2 (RCII) at 10 different light intensities ranging from 0 to 1,600 μmol quanta m−2 s−1 (0 to 840 μmol quanta m−2 s−1 of blue light combined with 0 to 600 μmol quanta m−2 s−1 of amber light). The resulting fluorescence light curves were fitted to the model of Kolber et al. (53) to derive the maximum (F′), operational (F′), and minimum (F′) fluorescence values at given actinic light, the effective PSII absorption cross-section (σPSII), and the connectivity between photosystems (p). These parameters were then used to calculate the ETR (54):where E is the intensity of the actinic light, ΦRCII is the quantum yield of photochemistry within RCII [taking constant values of 1 mol e− (mol photons−1)], F′ is variable fluorescence in the light (F′ − F′), F′ is the maximal variable fluorescence in the light (F′ = F′ − F′), and nPSII is the ratio of functional reaction centers of PSII to total chlorophyll a (55, 56).

The ETR values were then plotted versus irradiance and modeled after the reports of Eilers and Peeters (57) and Silsbe and Kromkamp (58) to derive the maximum ETR (ETRmax), the initial slope of the P versus E curve, and the light saturation point of the ETR (E).

Data availability.

The model developed in this paper as well as the plotted data have been uploaded in Zenodo/GitHub and is freely available from https://zenodo.org/record/3265448.