Mechanistic Model for the Coexistence of Nitrogen Fixation and Photosynthesis in Marine Trichodesmium

Trichodesmium is a major nitrogen-fixing cyanobacterium and exerts a significant influence on the oceanic nitrogen cycle. It is also a widely used model organism in laboratory studies. Since the nitrogen-fixing enzyme nitrogenase is extremely sensitive to oxygen, how these surface-dwelling plankton manage the two conflicting processes of nitrogen fixation and photosynthesis has been a long-standing question. In this study, we developed a simple model of metabolic fluxes of Trichodesmium capturing observed daily cycles of photosynthesis, nitrogen fixation, and boundary layer oxygen concentrations. The model suggests that forming a chain of cells for spatially segregating nitrogen fixation and photosynthesis is essential but not sufficient. It also requires a barrier against oxygen diffusion and high rates of oxygen scavenging by respiration. Finally, the model indicates that the life span of intracellular oxygen is extremely short, thus enabling cells to instantly create a low-oxygen environment upon deactivation of photosynthesis.

nase requires large amounts of energy and electrons (2)(3)(4). Furthermore, the nitrogenase enzyme contains metal cofactors that are irreversibly disabled in the presence of even trace levels of oxygen (O 2 ) (5, 6). The mechanisms by which cells of a few micrometers in size maintain an active nitrogenase enzyme in an O 2 -rich environment are diverse and not fully understood (7). Some nitrogen fixers form a thick glycolipid layer of specialized cells (heterocysts) that prevent O 2 diffusion into the N 2 -fixing cells (8). Other nitrogen fixers maintain high respiration rates to counteract the passive O 2 diffusion (9)(10)(11)(12). The metabolic strategies that enable N 2 fixation to function in an oxygenated environment occur at the expense of other physiological activities, including growth. The growth rate handicap of diazotrophs is considered a key ecological trade-off (13)(14)(15)(16)(17) with important implications for the global N cycle (18,19).
In the marine environment, a major contributor to N 2 fixation is the photosynthetic diazotroph Trichodesmium, mainly observed in oligotrophic tropical and subtropical oceans (20)(21)(22)(23). Although this species forms trichomes, they do not contain heterocysts to protect from O 2 invasion (24,25). Moreover, they are observed to fix N 2 during the day, when photosynthetic production of O 2 is also occurring (26,27). Some studies show Trichodesmium respiration rates exceeding those of non-N 2 -fixing cyanobacteria (10,26), despite a positive net O 2 evolution rate during the daytime (25). Despite over a century of research on Trichodesmium, there is no unequivocal explanation for how N 2 fixation occurs when the cells are photosynthetically active and O 2 should be at its highest levels.
In response to this physiological enigma, it has been hypothesized that N 2 fixation and photosynthesis are temporally and/or spatially segregated (28,29). Spatial segregation is a highly debated strategy, as some previous work revealed the presence of nitrogenase in almost all cells (29,30), while other reports showed nitrogenase occurred in about 10% to 20% of the cells (24,31,32). In support of temporal segregation, it has been shown that the rates of N 2 fixation and respiration increase, while the rate of photosynthesis decreases, during the middle of the light period (26). Whether this temporal segregation is sufficient for photosynthesis and N 2 fixation to occur simultaneously remains unclear (25). A recent approach to the Trichodesmium paradox has been to track 13 C and 15 N uptake at the cellular level using high-resolution secondary ion mass spectrometry (33,34). However, even with near-hourly resolution measurements, it was not possible to determine spatial segregation along the trichome because the redistribution of newly fixed N occurs on a time scale of minutes (33).
Compiling previous studies reveals a common general feature of diurnal cycles in Trichodesmium physiology (Fig. 1). Rates of photosynthesis increase at sunrise and peak in early morning (Fig. 1A). The rate decreases during midday, increases slightly again toward evening, and decreases to nearly zero at night. The rate of N 2 fixation, on the other hand, reaches its maximum value during the midday and its minimum (approximately zero) during the night (Fig. 1B). Similarly to N 2 fixation, respiration rates peak during the midday, yielding a dip in near-cell O 2 within a colony. Whereas some studies show reduced O 2 within a colony of Trichodesmium (28), recent work shows that photosynthesis causes the boundary layer to have O 2 levels that are 20% to 30% higher than those seen in the ambient water, where O 2 is nearly saturated (34). Therefore, Trichodesmium needs to manage O 2 fluxes not only directly from the photosynthetic cells (P cells) but also from the boundary layer environment within a colony. The question remains as to how these observed trends relate to the temporal coexistence of photosynthesis and N 2 fixation.
In this study, we take a fresh approach to investigation of the Trichodesmium paradox by modeling the physiology of Trichodesmium (cell flux model of Trichodesmium [CFM-Tricho]) over a diurnal cycle to evaluate the hypothesized spatial and temporal strategies of the cyanobacteria for maintaining N 2 fixation and photosynthesis. It has been suggested that colony formation by Trichodesmium plays an important role in creating a low-O 2 environment to facilitate N 2 fixation (28,35), though some evidence contradicts assertions of such a role (34,36). Recent studies show that the majority of Trichodesmium exists as filaments (37), which have higher rates of N 2 fixation per cell than colony-maintained Trichodesmium cells (38). We focused the model on a single trichome due to its simple morphology. However, the considerations are equally valid for colonies, as the model resolves the near-cell environment (referred to here as the "boundary layer") where O 2 concentrations are influenced by cellular metabolism. The model simulates cellular resource allocation by combining a model of the cellular reserves of C and N (39) with a representation of O 2 management critical to nitrogenase activity (12). The primary mechanisms of O 2 protection include high respiration rates (respiratory protection [including dark respiration and light-dependent respiration]), segregation of N 2 -fixing cells from photosynthetic cells (trichome formation), and low diffusivity between cells (diffusion barriers). The diurnal variation of metabolism can be explained by fluctuations in the relative abundances of photosynthetic cells and nonphotosynthetic cells. The quantitative model requirements are evaluated against our current knowledge of Trichodesmium and other diazotrophs.

RESULTS
Simulating cellular differentiation. The model resolves two types of cells: photosynthetic cells (P cells) and nonphotosynthetic cells (N cells) (Fig. 2). The fractions of P and N cells are represented by f P and f N , respectively. The P cells fix carbon and make it available for growth, storage, and respiration. The N cells use stored C obtained from P cells for O 2 consumption and N 2 fixation. The proportion of cells carrying out each metabolic function determines the rates within and fluxes from the trichome as a whole. We are interested in the rates of N 2 fixation (F Nfix ; here, "F" indicates fluxes), which we assume depend on O 2 and the standing stocks of stored N and C, as represented in equation 1: Here, F Nfix max is the maximum possible rate of N 2 fixation for the average cell in the colony, which depends on the fraction of cells with active nitrogenase: F Nfix max ϭ F Nfix full f N f NITROGE (see Materials and Methods). The remaining terms, which scale that rate between 0 and 1, represent the inhibition by O 2 in N cells, limitation by C storage in those cells, and inhibition by an excess of stored N in the entire trichome. Complete inhibition occurs for O 2 in P cells above a critical concentration, ͓O 2 ͔ crit , but declines linearly as O 2 levels fall below that level. Similarly, N 2 fixation rates rise as N storage is depleted below a specific value (N Sto max ). Finally, rates of N 2 fixation increase but saturate with available C storage in the nonphotosynthetic cells (C Sto N ϭ C Sto ⁄f N ).
To resolve the variation in O 2 concentrations outside the cells due to photosynthesis and respiration, the O 2 balance in the boundary layer environment is included. The model normalizes fluxes and molecules to the volume of the entire trichome. Therefore, the model can represent any number of cells with a certain proportion of N 2 -fixing cells. The model assumes that the supply of CO 2 and N 2 does not limit the rate of photosynthesis and N 2 fixation, a common assumption of most diazotroph models. Instead, photosynthesis is a function of light and stored C, and N 2 fixation is limited by stored C and N (equation 1). Further details are provided in Materials and Methods and Text S1 in the supplemental material. We run the model under a 12-h/12-h light/dark cycle, with f P prescribed as a step function in time (Fig. 3A). These transitions occur smoothly in nature and in experimental observations (26,33,34). Because our goal is to elucidate mechanisms, rather than to simulate precise details of particular experiments, we choose abrupt transitions that can be clearly discerned in the model output. As a check on the broad applicability of our diurnal forcing, we compared the trend of averaged Fv/Fm (photosynthetic quantum yield of photosystem II) to previous observations (26) (Fig. 3B). Fv/Fm is an indication on the efficiency of light use, which tends to be lower when cells are actively fixing nitrogen (26,40). Also, it indicates the activity of photosystem II and thus the  production of O 2 (26,41). The general trend in observations is captured by Fv/Fm ϭ 0.5 and 0.1 for P cells and N cells, respectively. Similar values were observed during photosynthetic and nonphotosynthetic periods in Crocosphaera (40).
Mechanisms of O 2 management. The maintenance of low intracellular O 2 levels to permit N 2 fixation can be achieved through several potential mechanisms, including the following: (i) trichome formation, (ii) respiratory protection, and (iii) diffusion barriers. All of these factors need to be included in order to reproduce the observed diurnal variation in metabolic rates (Fig. 1). Here we describe model results that evaluate the importance of each mechanism.
Trichome formation. Due to the production of O 2 , N 2 fixation cannot occur in the photosynthetic cells. Thus, trichome formation with differently functioning cells is a key factor for temporal coexistence of N 2 fixation and photosynthesis. We reproduce the observed daily cycle of photosynthesis and N 2 fixation (Fig. 4) by simulating the daily cycle of the fractions of P cells and N cells (Fig. 3A).
The observed cycle of photosynthesis with midmorning and midafternoon peaks (26, 33) ( Fig. 1) is reproduced by the model. This is achieved by an increase in levels of N 2 -fixing cells (decreased f P ) during the middle of the day (from h 3 to h 9). In the early morning, photosynthesis increases rapidly because of increased light levels, followed by a sharp decrease during the middle of the light period ( Fig. 4A) due to decreasing levels of photosynthetic cells. After the colony shifts toward greater numbers of photosynthetic cells in the evening (h 9), the photosynthesis rate increases again but at lower rates than in early morning, a difference that is consistent with observations ( Fig. 4A). In the model, this difference is due to C storage reaching the maximum capacity of finite cell volumes at the end of the light period. The levels of N cells increase at the expense of P cells, and the rate of N 2 fixation rises. This temporal physiological shift has been experimentally observed when a decrease in the rate of photosynthesis coincided with an increase in the rate of N 2 fixation (Fig. 4B) (26,33). The model captures this trend with increased f N levels (and thus decreased f P levels), but does not do so if f N and f P levels are held constant (see Fig. S1 in the supplemental material), suggesting that diurnal shifts in metabolic function of cells are important.
The rate of N 2 fixation peaks during the middle of the day due to increased levels of nonphotosynthetic cells and accumulated C. During the period from ϳh 0 to ϳh 3, C stores accumulates due to high rates of photosynthesis, leading to a gradual increase in the rate of N 2 fixation (Fig. 4B). When the trichomes shift toward greater numbers of N 2 -fixing cells (f P levels having decreased from 0.8 to 0.55) later in the morning (h 3), the rate of N 2 fixation almost doubles. A smaller subsequent decrease is due to loss of C storage and simultaneously N storage getting closer to its maximum, both of which act to reduce F Nfix rates (equation 1). In the evening (h 9), the rate is decreased by almost half due to the decreased presence of nonphotosynthetic cells before finally dropping to zero at the onset of the dark period.
Respiratory protection. Light harvesting is essential for providing the organic C and electrons needed to maintain low O 2 concentrations via respiratory activity. Over 80% of C is used for respiratory protection during the light period, except for storage accumulation (Fig. 5). In comparison, the consumption of C to supply energy and electrons for N 2 fixation was less than 10%. The fraction of C corresponding to respiratory protection was above 70% during the dark period (Fig. 5). This large quantity of C used for respiratory protection explains the previously observed differences between apparent levels of C fixation and O 2 evolution. Under optimal conditions, the mean O 2 production can reach rates of 26 mg O 2 (mg Chl-a) Ϫ1 h Ϫ1 , while the net C fixation rate is 4.5 mg C (mg Chl-a) Ϫ1 h Ϫ1 (10). The difference in respiration between day and night corresponds to light-dependent respiration levels; the predicted ratio of light-dependent respiration to dark respiration (Fig. 5) is close to what has been previously observed (42). The model also explains the unusually high basal rates of dark respiration observed in Trichodesmium: 0.18 mol O 2 (g Chl-a) Ϫ1 h Ϫ1 (10,42). Estimated rates of basal dark respiration for Skeletonema costatum and Pavlova lutheri are ϳ5% to ϳ6% of those for Trichodesmium (43,44). This high respiration rate indicates that Trichodesmium maintains low intracellular O 2 levels even during the dark period, possibly to maintain and/or synthesize nitrogenase.
The use of C/electron for respiratory protection comes at the expense of cellular growth and therefore may also explain the low growth rate of Trichodesmium. While non-nitrogen fixers have nutrient replete growth rate ( max ) of over 1 day Ϫ1 (45), that for Trichodesmium is about 0.1 to 0.5 day Ϫ1 (10,45). Under conditions of nutrient repletion, the max rate for the cell can be described as follows: where F Cfix Q c is the C fixation rate per cellular C quota (Q C ) and Y Bio:Cfix is the biomass yield of production for a given amount of C fixation. Because ϳ80% of C is used for respiratory protection (Fig. 5), max is reduced to ϳ20% of its potential value, which is close to the observed difference in the max values between Trichodesmium and other non-nitrogen-fixing phytoplankton (45). Thus, the energetic demands of maintaining the intracellular O 2 at a level low enough for N 2 fixation appears to explain the reduced growth rates of this species in relation to other phytoplankton. This growth rate handicap is a critical factor in plankton ecology (13,14,17) and in the dynamics of the F Csto , C storage production; F RP , respiratory protection; F ResN2 , respiration for providing energy for N 2 fixation; F Nfix , carbon consumption for providing electrons for N 2 fixation; F ResBio (ϭF Res P ), respiration for providing energy for biomass production; F Bio , biomass production. Light period, 0 to 12 h; dark period, 12 to 24 h (indicated by gray shading). During the light period, the origin of C is photosynthesis, while during the dark period, it is C storage. F ResN2 is computed based on energetic balance (12,45), and F RP represents the remaining respiration (see Text S1). (B) C fluxes in fraction.
global N cycle (19,46). Without such a handicap, it is possible that Trichodesmium could outcompete non-nitrogen fixers even where N is not limited.  (Fig. 6A, red circles) (34), with maxima in the early morning and evening, echoing variations in photosynthesis rate. Although O 2 is consistently supersaturated in the boundary layer during the day, its levels become slightly lower during the night. These observations provide a key constraint on the model representation of O 2 diffusion and the importance of the Trichodesmium strategy to protect N 2 fixation by minimizing diffusive O 2 fluxes (Fig. 6).
The observed trends in levels of O 2 in the boundary layer can be captured when we apply low diffusivity for cell membrane layers (lower than 10 Ϫ3 of that in water) (here referred to as "model diffusivity") ( Fig. 6A and B). First, we predict consistently higher levels of O 2 in the boundary layer than in the environment, as observed (34) (Fig. 6A). Despite the respiratory protection, net O 2 production rates are still positive, increasing the levels of boundary layer O 2 . Second, [O 2 ] B reached two peaks: each peak during the early and later parts of the day. This high O 2 concentration is due to high rates of photosynthesis (Fig. 4A). The peak value during early light period is slightly higher (ϳ400 M) than that in the evening, consistent with the observations (34 (Fig. 6B), supporting the importance of strong diffusion barriers. Decreasing diffusivity would increase the passive uptake of O 2 by N cells, requiring a higher amount of C. For diffusivity levels exceeding twice that of our default model diffusivity, intracellular O 2 cannot be maintained at the minimum level. Also, when the diffusivity is higher than three times the default value, the boundary layer O 2 concentration becomes similar to that in the environment, failing to reproduce higher concentrations in the boundary layer environment. If we assume diffusivity of water for the cellular membrane (47), all the boxes have similar averaged O 2 levels (Fig. 6B), and N 2 fixation cannot be maintained. The predicted low diffusivity is qualitatively consistent with the results of a recent study (38).

DISCUSSION
Potential explanations for low diffusivity. One explanation for the low level of model diffusivity is the low diffusivity of the bacterial membranes. Trichodesmium is a Gram-negative bacterium whose cell envelope has multiple layers (48), with inner and outer lipid membranes separated by a periplasm containing peptidoglycan. The outer lipid membrane is connected to lipopolysaccharide (LPS), creating a capsule. Possibly due to the presence of these layers, the O 2 diffusivity of bacterial membranes is predicted to be ϳ2 to ϳ3 orders of magnitude lower than that of water (12,49,50). The diffusivity of cells with simple lipid bilayers is generally within the same order of magnitude as that of water (50). Thus, it is likely that the layers of LPS or peptidoglycan provide strong barriers against O 2 in Trichodesmium.
Although the Gram-negative membrane might be sufficient, another potential mechanism for the diffusion barrier may be production of extracellular polymeric substances (EPS). Recent studies suggest involvement of EPS in protecting heterotrophic nitrogen fixers of the species Azotobacter vinelandii (12,51,52). This has been supported by a laboratory study where respiration decreases with EPS production (53). Trichodesmium produces EPS especially under nutrient-limited conditions (54)(55)(56). Here, given the low model diffusivity, another purpose of EPS might be the management of O 2 from the environment, which accounts for over 80% of O 2 input in model simulations (see Fig. S2 in the supplemental material). The remaining ϳ10% to ϳ20% of O 2 input is directly transported from neighboring photosynthetic cells, and this intercellular flux must also be minimized.
To reproduce the observed fluctuations of O 2 concentration in the boundary layer, the model required 45% of nonphotosynthetic cells during the middle of the light period; fractions below 45% result in insufficient diel fluctuations of O 2 . This value sits between two observational results; some studies show almost all the cells having nitrogenase (30,57), whereas other laboratory studies show that only ϳ10% to ϳ20% of cells actually contain nitrogenase (24,31,32). In the latter case, nitrogenase may be confined to a subset of nonphotosynthetic cells.
Given the predicted low diffusivity, certain cells may play a role in reducing O 2 diffusion from photosynthetic cells to N 2 -fixing cells. On the basis of this hypothesized function, we refer to them as "buffer cells." Because cell membranes have significantly slower diffusion and higher viscosity than water, having more membranes between P cells and N cells containing nitrogenase would decrease O 2 transport between them. Because EPS can prevent O 2 diffusion from the environment only, such buffer cells may represent an alternative to the glycolipid layers seen in heterocysts and thus may be essential for the coexistence of photosynthesis and N 2 fixation (Fig. 7).
The double layer of Gram-negative membranes between two adjacent cells could effectively reduce O 2 transport. However, such cells and membranes could also slow the transport of carbon or other reduced molecules. To circumvent such problems, we hypothesize that cells may selectively transfer molecules. Such a mechanism seems to exist in heterocystous cyanobacteria, which rapidly transfer sucrose through cell junctions (58). It is also possible that sites for N 2 fixation occur where C storage is sufficiently accumulated. This would explain why the lowest fractions of N 2 -fixing cells are observed just before dawn, when cellular C storage is most depleted (24,31).
The residence time of O 2 is significantly shorter than time scales of metabolic switching. Fluorescence kinetics data show various states of photosynthetic activity throughout a trichome (41). However, until now, it has not been resolved whether cellular O 2 management strategies can keep up with changes in photosynthetic activity, which occur over time scales of minutes (25). Since our model focuses on the averaged state of a trichome based on the fraction of different metabolisms (photosynthetic or nitrogen fixing), it does not resolve such dynamic locational shifts of photosynthetic activity. It does show, however, that the residence time of O 2 is extremely short, on the order of 1 s. The predicted daytime rate of respiration is ϳ2 mol O 2 mol C Ϫ1 day Ϫ1 , equivalent to 0.424 mol O 2 m Ϫ3 s Ϫ1 with a cellular C concentration of 1.83 ϫ 10 4 mol m Ϫ3 (59). For a typical concentration of O 2 in tropical surface water (ϳ0.2 mol m Ϫ3 ), the time scale of O 2 turnover is ϳ0.5 s. Even if we apply our predicted O 2 concentration in photosynthetic cells (ϳ0.6 mol m Ϫ3 ), the time scale is only ϳ1.4 s. This simple calculation indicates the potential for photosynthetic cells to quickly switch to nitrogen-fixing cells as long as nitrogenase can be preserved within the photosynthetic cells. The capability of preserving nitrogenase may be supported by evidence indicating that nitrogenase is found in most of the cells (30,57). However, how nitrogenase is preserved during photosynthesis needs to be further investigated. Potential mechanisms include "conformational protection," in which the activity of nitrogenase is rapidly and reversibly switched off in response to high O 2 concentrations (2, 60, 61), thereby limiting the time-consuming processes of resynthesizing or repairing nitrogenases.
Broader context: how can photosynthesis and N 2 fixation occur simultaneously in general? Nitrogenase is highly sensitive to O 2 (5,6,9); therefore, photosynthetic O 2 production is detrimental to N 2 fixation. However, some major nitrogen fixers and their symbioses enable these conflicting processes to occur simultaneously; e.g., Trichodesmium, diatom diazotroph association (DDA) (62,63), and UCYN-A and phytoplankton symbiosis (64). Here, on the basis of a simple model of Trichodesmium, we discuss how these processes can coexist over short distances.
First, N 2 fixation and photosynthesis should not occur in the same cell simultaneously. Nitrogenase exists in the cytoplasm, while photosynthesis occurs on the intracytoplasmic membranes. Thus, photosynthesis would likely release O 2 into cytoplasm, damaging nitrogenase. Also, we predict that rates of respiration exceeding that of photosynthesis would be required for consuming this O 2 . This would not be sustainable in cells that lack metabolic specialization. On the other hand, if these processes occur in different cells, the amount of O 2 that needs to be managed decreases significantly. Thus, it would make sense that such functional separation has been selected through evolution.
Second, diffusivity control of O 2 and high respiration rates must occur together, unless diffusivity is perfectly controlled. The model uses low diffusivity through membranes, but it still requires high respiration rates. High respiration has been reported not only in Trichodesmium, but also Crocosphaera, unicellular photoautotrophic nitrogen fixers (11). Organisms with heterocysts may not require such high levels of respiration with sophisticated O 2 barriers. It is likely that decreasing the diffusion can affect the uptake/transfer of other important nutrients/metabolites. Thus, for such strong barriers, selective transfer of organic C substrates to fuel respiration must be involved.
Conclusions. With a mechanistic model of Trichodesmium, we investigate how these photosynthetic cyanobacteria manage to fix nitrogen while also fixing carbon. The model reproduces observed patterns of diel cycling in Trichodesmium physiology and indicates that these conflicting processes must occur in different cells and also need to be separated by a barrier to O 2 diffusion. These results support the hypothesis that a Gram-negative membrane could represent an essential diffusion barrier against O 2 . EPS and buffer cells might additionally decrease O 2 diffusion. The remaining O 2 must be consumed through respiratory protection for N 2 fixation to occur, and such respiration may explain the observed low growth rate of Trichodesmium. The model indicates that the residence time of O 2 within trichomes is a few seconds, significantly shorter than the time scale of switching on and off photosynthesis. Our model and the results provide a theoretical basis for investigating how these two conflicting processes occur in one of the major sources of new N to the oligotrophic surface ocean.

MATERIALS AND METHODS
Model equations. In this section, we explain the assumptions and equations used in the model. This model resolves C, N, and O 2 budgets (Fig. 2) within cells, as well as the O 2 budget in the immediate vicinity (boundary layer) of those cells. The budgets consist of biochemical rates within each type of cell and exchange between cells of each type and between cells and the environment. At any given time, these rates depend on the fraction of the trichome that is assigned to each metabolic function. We denote f P and f N as the fractions of photosynthetic and nonphotosynthetic cells, respectively. Of the nonphotosynthetic cells (f N ), a constant fraction (f NITROGE ) is assumed to contain nitrogenase and thus to be able to fix N 2 . The detailed nomenclature (with units) is provided in Table S1 in the supplemental material. To determine the rate of N 2 fixation (equation 1), we need to specify N and C storage and cellular O 2 in the N 2 -fixing cells. Since these quantities are themselves governed by an allocation of resources that varies with environmental conditions, we model these variables with a set of differential equations. The difference between C production (photosynthesis) and consumption (respiration, N 2 fixation, and biomass production) leads to the change in C storage (C Sto ). Similarly, the change in N storage (N Sto ) is governed by the balance of N 2 fixation and biomass production as represented in the following equations: where C Sto represents C storage, t represents time, F Cfix represents C fixation rate, F Bio represents biomass production rate, F Nfix represents N 2 fixation rate, Y Nfix C:N represents a C:N conversion term for N 2 fixation, F Res represents respiration rate, N Sto represents N storage, and Y Bio N:C represents N:C of biomass.
C Sto and N Sto are governed by 2 common rates (F Nfix and F Bio ), whereas C Sto has additional input from C fixation and respiration that need to be modeled. The C Sto and N Sto values are computed with a finite-difference method and therefore cause temporal variations in C:N values.
We assume that the rate of biomass production (F Bio ) is a minimum function of available storage resources (C Sto and N Sto ), calculated as follows: The rate of C fixation (F Cfix ) is proportional to the level of chlorophyll available for photosynthesis: Here C fixation saturates with light and slows as C storage approaches its maximum capacity. We assume that the level of chlorophyll per P cell is constant and proportional to the fraction of P cells f P (ϭ 1 -f N ) since the model runs at constant light during the light period as follows: Chl P ϭ f P Chl full (8) where Chl full is chlorophyll content when all the cells are carbon fixing; thus Chl C ϭ Chl full when f P ϭ 1. The total respiration rate (F Res ) is the sum of the rates in P cells (F Res P ) and in N cells (F Res N ) and is calculated as follows: Inomura et al.
We assume that biosynthesis occurs mostly in P cells, and the respiration for supporting the biosynthesis assumed to be proportional with a constant ratio of Y Res:Bio , leading to the following equation: To compute F Res N , we use the O 2 balances as follows: Here, V i represents the volume of box i (i ϭ P, N, or B, representing boxes for photosynthetic cells, nonphotosynthetic cells, or boundary layer, respectively); V ϭ V P ϩV N , ͓O 2 ͔ i represents the O 2 concentration of box i (i ϭ P, N,  and Y O 2 :C represents C-to-O 2 conversion in respiration and C fixation. Since the time scale of O 2 equilibration is much smaller than that of N and C, we assume a pseudo-steady state of O 2 . This assumption largely applies since the cellular concentrations of C and N are on the order of 10 4 and 10 3 (mol m Ϫ3 ), respectively, while that of O 2 is generally below 1 (mol m Ϫ3 ) despite the fact that the magnitudes of the fluxes are similar. The pseudo-steady-state assumption gives a single solution for F Res N as well as for the O 2 concentration in each box. Since  (Table S2). These include elemental stoichiometry of biomass and boundary conditions such as light intensities and O 2 concentrations in the environment. The remaining parameters are selected to reproduce the observed metabolic rates of Trichodesmium as compiled from multiple published studies (10,27,29,42,(65)(66)(67) (Table S3). In general, the key metabolic processes follow a well-defined order, with N 2 fixation being the slowest (ϳ0.006 to ϳ0.146 mol N mol biomass C Ϫ1 day Ϫ1 ), O 2 production being the fastest (ϳ1.10 to ϳ288 mol O 2 mol biomass C Ϫ1 day Ϫ1 ), and net C fixation being intermediate between the other two (ϳ0.16 to ϳ2.57 mol C mol biomass C Ϫ1 day Ϫ1 ). The remaining parameters have been tuned to bring averaged model output values within these ranges.
Model availability. The model in this study was written in Python 3 and is freely available at https://zenodo.org/record/1245128.