Author Correction: Heterogeneous nitrogen fixation rates confer energetic advantage and expanded ecological niche of unicellular diazotroph populations

Nitrogen fixing plankton provide nitrogen to fuel marine ecosystems and biogeochemical cycles but the factors that constrain their growth and habitat remain poorly understood. Here we investigate the importance of metabolic specialization in unicellular diazotroph populations, using laboratory experiments and model simulations. In clonal cultures of Crocosphaera watsonii and Cyanothece sp. spiked with 15N2, cellular 15N enrichment developed a bimodal distribution within colonies, indicating that N2 fixation was confined to a subpopulation. In a model of population metabolism, heterogeneous nitrogen (N2) fixation rates substantially reduce the respiration rate required to protect nitrogenase from O2. The energy savings from metabolic specialization is highest at slow growth rates, allowing populations to survive in deeper waters where light is low but nutrients are high. Our results suggest that heterogeneous N2 fixation in colonies of unicellular diazotrophs confers an energetic advantage that expands the ecological niche and may have facilitated the evolution of multicellular diazotrophs. Takako Masuda et al. show that individual cells in clonal populations of Crocosphaera watsonii and Cyanothece sp exhibit varied nitrogen fixation rates. This heterogeneity within the population decreases the energetic cost of respiration and expands the viable habitats for these unicellular diazotrophs.

N itrogen (N 2 ) fixing microorganisms (diazotrophs) are critical suppliers of bioavailable nitrogen (N) in the world's oceans. The N 2 fixed by these organisms supports cell growth, but also enters the food web through grazing by zooplankton and excretion of ammonium (NH þ 4 ) or other dissolved nitrogenous compounds [1][2][3][4][5] . All diazotrophs have a N 2 fixing enzyme complex, nitrogenase. Since most nitrogenase enzymes are irreversibly damaged by molecular oxygen 6,7 , diazotrophs separate photosynthesis and N 2 fixation spatially or temporally 8,9 . Diazotrophs are taxonomically diverse and occupy distinct large-scale habitats [9][10][11][12] , suggesting there are multiple strategies for managing the energetic demands of photosynthesis, growth, and N 2 fixation under a wide range of ocean conditions. However, the links between diverse physiological strategies and the resulting ecological niches and spatial distributions remain poorly understood 10,[13][14][15] .
Crocosphaera watsonii (hereafter Crocosphaera), a marine unicellular diazotroph, is abundant and widespread in tropical and subtropical oceans 10,11,16,17 , and its areal N 2 fixation rate (µmol N m −2 d −1 ) can be equal to or greater than that of Trichodesmium, a filamentous diazotroph abundant in tropical oceans 16,18,19 . Due to its strong diel alternation between C and N metabolisms, Crocosphaera is a promising model for investigating cellular C and N physiology 17,[20][21][22][23] . Cyanothece is another well studied unicellular diazotroph. It is closely related to the sequence-defined genus, UCYN-C 24,25 , which has been observed to supply N to other phytoplankton and contribute to vertical POC (particulate organic carbon) transport 26 . Intensive studies on Cyanothece physiology make it a model organism to study the physiology of unicellular diazotrophic cyanobacteria 27,28 .
When exposed to a light:dark cycle, the peak of N 2 fixation activity of most unicellular photosynthetic diazotrophs is restricted to the dark period. A similar diel cycle is observed in Crocosphaera [20][21][22]29 and Cyanothece 27 , however, both taxa can be forced to fix N 2 , if maintained under constant illumination for an extended period 23,30,31 . This observation led to speculation that its metabolism is heterogeneously distributed among cells in a population 14 as observed in Trichodesmium 8 .
Recent technological advances in the visualization of enriched stable isotopes in individual cells using NanoSIMS enable cell level analyses of N 2 fixation activity [32][33][34][35][36][37][38] . With this technology, high variations in C and N 2 fixation activity from in situ "Crocosphaera-like" cell colonies were shown, suggesting heterogeneity of metabolisms 17 . During the same period of time, similar physiological heterogeneity was observed among the clonal population of Crocosphaera (WH8501) 23 . These observations lead us to question how widely this heterogeneity applies and how it impacts the cellular energetics and resulting ecological niches.
Here, we investigated physiological heterogeneity among clonal populations of multiple genera of cyanobacteria, Crocosphaera (PS0609A) and Cyanothece (ATCC51142), by quantifying the pattern in N 2 fixation and C uptake at the sub-cellular level. Using clonal populations prevents interference from other N fixing organisms, a potential problem noted in the in situ study 17 and using different genera and strains of cyanobacteria allows us to evaluate the generality of the pattern. We have also applied multiple statistical methods to quantify the heterogeneity in C and N 2 fixation. To analyze the energetics and C consumption of the observed cell-level heterogeneity, we present a model of diazotroph population to simulate the advantage of maintaining both nitrogen fixing and non-N 2 fixing cells. We used oceanographic data to predict the implications of metabolically differentiated populations for the ecological niche of unicellular diazotrophs through the photic zone.

Results
Heterogeneity in N enrichment among cells. 15 N enrichment was variable within a single strain of continuous culture grown Crocosphaera cells (Figs. 1 and 2) and batch culture grown Cyanothece (Fig. 2). Initially, ratios of 13 C: 12 C (= 13 C/ 12 C) and 15 N: 14 N (= 15 N/ 14 N) were 8.8 ± 0.5‰ and 3.5 ± 0.1‰, respectively in Crocosphaera harvested at steady state under continuous culture and were 11.0 ± 0.4‰ and 3.6 ± 0.2‰, respectively in Cyanothece harvested at exponential phase under batch culture ( Fig. 3 and Supplementary Table 1). After 11 h in the dark, two cells ( Fig. 1; white arrows in panel 11D 15 N: 14 N) were more strongly enriched in 15 N compared to the other four cells, of which one cell showed the least enrichment ( Fig. 1: blue arrow). However, the least 15 N enriched cells were actively 13 C enriched in the light period (e.g., cells with blue arrow in panel 3L 13 C: 12 C) showing that these cells were alive and metabolically active. The variable 15 N enrichment was observed not only under continuous culture but also under exponentially growing batch culture and suggests that heterogeneous 15 N 2 fixation happens with or without nutrient stress.
The 15 N 2 fixation in the dark was observed based on the temporal changes in cellular 15 N: 14 N ratios in both Crocosphaera and Cyanothece (Fig. 3a, d and Supplementary Table 1). Calculated per-cell 15 N enrichment rates, ρ, followed similar trends as the 15 N: 14 N ratio, and increased significantly (p = 0.014 by one-way ANOVA 39 ) in Crocosphaera from 0 fmol N cell −1 h −1 at the start of the dark period to a mean of 17.3 fmol N cell −1 h −1 at 7D, but with a range of 0 fmol N cell −1 h −1 to 37.7 fmol N cell −1 h −1 (Supplementary Table 1b). These values are comparable to those reported in earlier studies (Supplementary Table 2). Cyanothece also showed a similar trend within population heterogeneity; ρ varied from 0 fmol N cell −1 h −1 to 12.7 fmol N cell −1 h −1 across 84 cells at the time of highest mean 15 Table 1b). The 15 N: 14 N ratios measured by NanoSIMS were in good agreement with the ratios measured by mass spectrometer (Supplementary Fig. 1).
The proportion of Crocosphaera cells that incorporated detectable 15 N (i.e., cells with 15 N: 14 N exceeding 2 SD above the mean at time 0: 3.8‰ for Crocosphaera, 4.0‰ for Cyanothece) increased from 40 to 75% in the dark, suggesting that at least~25% of cells did not detectably fix N 2 (Fig. 3b, e). Higher variability of 15 N enriched cells in Crocosphaera compared to Cyanothece may be the result of low number of observed cells (between 7 to 33 cells at each time point) (Fig. 3b, d). Hotspots of 15 N: 14 N were observed in the dark period. The 15 N hotspots started to appear after 5D, and continued to form until the beginning of the light period (2 L), with the peak of 62% at 10D ( Fig. 1 and 3c) in Crocosphaera. Similar temporal changes were observed for the proportion of cells with 15 N hotspot among total cells in Cyanothece, from 2D to 6 L with a peak at 6D. Therefore, the lack of 15 N hotspot in at least~40% of cells again shows that a large fraction of cells did not detectably fix N 2 . N 2 fixation earlier in the diel cycle in Cyanothece compared to Crocosphaera (Fig. 3) supports previous reports of a peak around 4D in Cyanothece and 9D in Crocosphaera under 12 L:12D cycle 21,40 .
To quantify the differentiation of rates within each population, we examined the statistical distribution of C and N isotope enrichments among all cells. Intercellular metabolic heterogeneity was defined as the coefficient of variation (CV; ref. 41 ) in each isotope ratio. The variations in 15  For example, in the 13 C: 12 C ratio of 3 L in Fig. 1, all 14 cells are enriched similarly, with 13 C: 12 C ratios between 7.9‰ and 9.4‰ (8.7‰ ± 0.5‰, CV = 6.2%) in Crocosphaera (Fig. 2). The CV for 15 N: 14 N (23.6 to 31.4% during 6D to 12D, 25.4 to 48.0% during 6 L to 12 L) were greater than those estimated for 13 C: 12 C during 6 L to 12 L (4.8 to 10.6%), suggesting higher heterogeneity in 15 N 2 fixation compared to 13 15 N and 13 C enrichment. c Schematic view of scatter plot. Blue, data obtained during 0D6D; Green, data obtained during 7D-12D; Orange; data obtained 1L-6L; Pink, data obtained 7L-12L. Higher 13 C uptake in Crocospharea compared to Cyanothece is likely to reflect higher initial 13 C enrichment in the culture for Crocosphaera: 9.7 atm% for Crocosphaera and 1.7 atm% for Cyanothece (see Methods).   14 N for Crocosphaera and Cyanothece (6 L to 12 L) and c, d 13 C: 12 C for Crocosphaera and Cyanothece (6 L to 12 L), respectively. Red dashed curve is the normal distribution for the initial condition (t = t 0 ) with the special y-axis on the right (that on the left is for other plotted values). Green dashed curve is the normal distribution based on the mean value and standard deviation of the probability density. S, bimodal separation; Dev, deviation from the normal distribution; n, number of samples. Both for Crocosphaera and Cyanothece, S and Dev are larger for 15 N: 14 N, suggesting stronger heterogeneity for N uptake.
The distribution of isotope ratios among cells reveals qualitatively different enrichment trends for C compared to N, for both Crocosphaera and Cyanothece (Fig. 4). The distribution of 15 N: 14 N reveals two distinct peaks after 12 h, one that remains near the initial ratio and a second that develops at enriched levels of 15 N, for both Crocosphaera and Cyanothece (Fig. 4a, b). In contrast, few cells remain at the initial ratio 13 C: 12 C (Fig. 4c, d), and only a single broad peak is evident. To evaluate this bimodality, we calculated the "bimodal separation" (S; ref. 42 ), a distance between the means of two Gaussian distributions fit to the data (see Methods). The separations of peaks in 15 N: 14 N was consistently larger than for 13 C: 12 C, both for Crocosphaera (S = 1.45 for N, vs. S = 0.42 for C) and for Cyanothece (S = 0.79 for N, vs. S = 0.004 for C). We have also applied the bimodal curve fitted with 15 N: 14 N to 13 C: 12 C with the curve shape maintained (relative relation between two normal distributions and S are maintained); even after the curve is fitted to 13 C: 12 C, the difference between the data and the curve is statistically significant for both diazotrophs (p < 0.001), indicating a significant difference between 15 N: 14 N and 13 C: 12 C.
To confirm that the distribution of N isotopes develops a bimodal structure indicative of distinct rates among subpopulations, we compared the observed frequency distributions to a single Gaussian distribution with the same mean value and standard deviation (Fig. 4). For 15 N: 14 N, the peak of the normal distribution appears near the local minima between the two peaks of the data (Fig. 4a, b), again indicating strong bimodal separation. In contrast, the normal distribution largely overlaps with the data for 13 C: 12 C (Fig. 4c, d). We computed the deviation (Dev) from the normal distribution by adapting a commonly used form of Chi square (χ 2 ) normalized by the sample number (n) (see Methods). The deviations from a single Gaussian distribution are stronger for 15 N: 14 N than for 13 C: 12 C for both diazotrophs (Dev = 1.97 vs. 0.42 for Crocosphaera and 0.81 vs. 0.33 for Cyanothece). These results qualitatively and quantitatively support stronger heterogeneity in N uptake than for C uptake, indicating a clear separation between N 2 fixing cells and non-N 2 fixing cells, without a comparable separation of C fixation.
Although Crocosphaera and Cyanothece are generally referred to as free-living unicellular cyanobacteria, they have been reported in colonies of more than two cells 17,23 (Fig. 1). In the Crocosphaera culture, 55% of total cells were observed as colonies of 3 to 5 cells in this measurement ( Supplementary Fig. 2). Colonial Crocosphaera cells were shown in earlier culture studies 23 , and an in situ study found that 45 to 85% of Crocosphaera-like cells were observed as colonies of 3 to 242 cells 17 . Colonial formation of cells might increase the efficiency of excreted NH þ 4 transfer among cells.
Simulating population heterogeneity of N 2 fixation. The strong concentration of newly fixed N in a sub-population of colonial unicellular diazotrophs suggests that localizing the costly process of N 2 fixation may confer an advantage to the population as a whole. A large part of the energetic cost of N 2 fixation is incurred in the protection of nitrogenase from O 2 , which is achieved through excess respiration of C (refs. 43,44 ). We therefore hypothesize that having only a limited proportion of cells to pay the oxygen management cost could reduce community C requirements, potentially leading to overall higher growth.
To evaluate the potential benefits of confining N 2 fixation to a sub-population, we used a Cell Flux Model of a N 2 fixer 44 . The model uses a coarse-grained metabolic flux network including core metabolisms of respiration, biosynthesis and N 2 fixation, which are constrained by mass, electron and energy balance (Fig. 5) (see Methods for details). We simulate a steady state environment where cells grow at a rate of μ (d −1 ). To maintain the prescribed rate of growth, energy must be provided by respiration, with distinct rates allocated to N 2 fixation and biomass production 44,45 . In turn, the total respiration rate predicts the intracellular O 2 concentrations, for a given diffusivity of O 2 across the cell membrane. Additional respiration is added as needed to maintain anoxia inside the cell, thus protecting the nitrogenase enzyme and enabling N 2 fixation 44 . The total carbon consumption rate per cell is computed to satisfy the sum of all 3 demands: biomass growth, N 2 fixation, and respiratory protection against O 2 .
Here we adapted this cellular model 44 to represent a heterogeneous colony of cells (the model version named CFM-Colony, with a fraction f N that fix N 2 , and a remaining fraction 1 − f N , that do not. The two sub-populations share a common medium, allowing N 2 -fixing cells to transfer fixed nitrogen NH þ 4 À Á to non-N 2 -fixing cells. The transfer of newly fixed N is prescribed by an efficiency parameter, E N , with the remaining fraction (1 − E N ) of excreted NH þ 4 being lost from the entire colony.
To quantify the impact of heterogeneous rates of N 2 fixation, we compare its population-scale rate of C consumption (denoted C S ), to the rate that would apply to a homogeneous population of the same size (denoted C 0 S ). When C S =C 0 S < 1, the colony has lower C consumption with heterogeneous N 2 fixation than homogeneous N 2 fixation. The rate of N 2 fixation by a heterogeneous community, N S , relative to a population with uniform rates, N 0 S (when f N = 1) can be expressed as follows: The ratio of C consumption associated with N 2 fixation and respiratory protection follows the ratio of N fixation rates by heterogeneous versus homogeneous populations (Eq. 1).
Modeled colonies with N 2 fixation confined to a subpopulation benefit from a substantial drop in overall C consumption, due to lower community level requirements for respiratory protection of nitrogenase (Fig. 6). For typical Crocosphaera growth rates (μ = 0.2) and a low efficiency of NH þ 4 transfer (E N = 0.2) C savings amount to~8 fmol C cell −1 h −1 , which is >30% of the C budget of a population with homogeneous rates (Fig. 6a, b). Total C consumption reaches a minimum value at an intermediate value of f N , due to two opposing factors; as f N initially decreases below 1, respiratory protection is reduced. However, as f N decreases, a larger portion of cells must also rely on transferred NH þ 4 , which allows more NH þ 4 to be dissipated into the environment, requiring higher C consumption to replace it. This effect is represented by (Eq. 1) where increasing f N leads to increasing N S . At an intermediate value of f N , these two factors minimize Cs, and respiratory protection is covered by energetically balanced productive flows of respiration.
The value of f N that maximizes C savings tends to increase with decreasing E N due to increased costs for N 2 fixation [Eq. 1] (Fig. 7b). When E N = 0.1, C S (thus C S =C 0 S ) reaches a minimum at f N~0 .56 ( Supplementary Fig. 3), a level of heterogeneity similar to that seen in the culture experiments, in which about a half of cells fix N 2 . This optimum f N also increases with the growth rate µ due to increased energy costs for biomass production and N 2 fixation (Fig. 7d). The 2D plot of C S and C S =C 0 S for various f N and E N shows that up to 55% of C can be saved at high E N and low f N (Fig. 7a, b). On the other hand, even at E N < 0.1, heterogeneity can still save carbon (Fig. 7b), due to the small cost of N 2 fixation relative to respiratory protection 44 . Considering the fact that C is one of the limiting factors for the growth for diazotrophs 28,46,47 ,  heterogeneity of N 2 fixation might be an important strategy to increase their growth rates.
Because unicellular diazotrophs can use NH þ 4 , growth efficiency should be maximized when cells can meet their N demand from NH þ 4 in the environment, thus saving the considerable cost of N 2 fixation (Fig. 6a, c). If cells rely solely on the N 2 fixation for their N source, higher growth rate would render respiratory protection negligible, yielding higher growth efficiency. For example, the cell flux model (Fig. 6) predicts that as growth rate increases beyond~0.28 (d −1 ), respiratory protection is no longer needed and the growth efficiency reaches its highest level. This occurs at a specific f N where respiratory protection is minimized with minimum loss of N to the environment (C S and C S =C 0 S at f N~0 .38 in Fig. 6a, b respectively and cyan dashed curve in Fig. 7b).
The amount of C saved by heterogeneous N 2 fixation depends only slightly on the poorly known value of E N . This insensitivity is based on the relatively small cost for N 2 fixation 44 . While N 2 fixation requires 16 ATP per N 2 , when E N = 1, the cost is predicted to be low relative to the whole cell energy requirement for biosynthesis since N 2 fixation is just one reaction and there are many other pathways where ATP is consumed in the process of biosynthesis. In addition, cost for O 2 management is overwhelming. As E N decreases, the cost for N 2 fixation increases inversely proportional to E N , but due to the relatively low costs of N 2 fixation, the whole cell C costs (thus C S and C S =C 0 S ) are relatively insensitive to E N .
The energetic advantage of heterogeneous N 2 fixation rates increases as growth rates decline (Figs. 6c, d and 7c, d). Slower growth rates reduce the costs of biomass synthesis and N 2 fixation, thus making respiratory protection a dominant energetic and C cost (Fig. 6c). Since heterogeneous populations can lower this cost by focusing N 2 fixation in a fraction of cells, more C can be saved at lower μ. Over 90% of C can be saved at low μ and low f N (Fig. 7d). On the other hand, when μ > 0.35 (d −1 ), C S =C 0 S can go above 1 (Figs. 6d and 7d) due to high costs for growth and N 2 fixation, and N loss to the environment. The growth rates of Crocosphaera compiled from laboratory studies have a mean value of μ < 0.3 (d −1 ) (ref. 48 ). In the ocean, nutrients such as iron and phosphorus are generally more limited compared to culture conditions leading to even lower μ. Thus, with a typical growth rate in the ocean, it is likely that population heterogeneity in N 2 fixation can save a considerable fraction of population C costs.
Implications for vertical habitat range. Fixed C is required for N 2 fixation, respiration and cellular growth, providing energy, electrons and reduced C. In the open subtropical ocean, chlorophyll concentrations typically reach a maximum at the bottom of the photic zone, and the top of the nutricline,~100 m depth, where both light and nutrients are adequate for growth, albeit at low rates. Below these depths, available light becomes so low that it prevents cells from fixing enough C to be viable (here we define maximum viable depth, MVD). Since heterogeneous N 2 fixation reduces the overall C requirement of such populations, it could act to extend their MVD deeper into the nutricline.
We simulated the depth variation of the growth rate for Crocosphaera populations with homogeneous versus heterogeneous N 2 fixation rates (see Methods). The model result shows that MVD of the heterogeneous population is~25 m deeper than that of the homogeneous population (Fig. 8a). This expanded MVD may be important because the available nutrient typically increase with depth and expanding MVD allows Crocosphaera to utilize the higher concentration of the growth-essential nutrient. For example, at the Hawaii Ocean Time-series (HOT) site at 22°4 5'N, 158°00'W (ref. 49 ), the concentration of phosphate (PO 3À 4 : one of the potentially limiting nutrients) increases below~80 m depth and heterogeneous populations would be able to utilizẽ 40% higher concentration than homogeneous populations (Fig. 8b). A similar depth profile of PO 3À 4 is observed in the South Pacific Gyre at 25°S, 170°W, where the highest nifH gene concentration of Crocosphaera have also been observed 50 . Under those conditions, the model predicts heterogeneous population would utilize up to~90% higher concentration of PO 3À 4 ( Supplementary Fig. 4a).
In these observations, NO À 3 concentrations also increase with depth, which may lead to a partial suppression of N 2 fixation ( Fig. 8c and Supplementary Fig. 4b). However, the NO À 3 concentrations in the expanded vertical niche remain well below what would cause full suppression [51][52][53] . For example, the concentration of NO À 3 at MVD is below 2 µM whereas even 5 µM does not fully suppress N 2 fixation of Crocosphaera 51-53 . Since respiratory protection is required regardless of the level of N 2 fixation (thus required even when N 2 fixation is partially suppressed) 54 , heterogeneous population would still save C even at depths near the MVD.

Discussion
The results of our laboratory observations demonstrate that unicellular diazotrophic cyanobacteria form colonies in which the key metabolic function of N 2 fixation is confined to a distinct subpopulation. Guided by these observations, metabolic modeling shows that this functional specialization may provide an energetic advantage, especially in oligotrophic regions where nutrient availability increases as light diminishes. These findings have important implications for role of metabolic specialization in the evolution of multi-cellularity, and the biogeography of unicellular diazotrophs and their role in biogeochemical cycles. Evaluating these broader implications will require a more complete understanding of the mechanisms and economics of material transfers within colonies, and the environmental factors that influence and sustain them.
Our results suggest that the exchange of newly fixed N within colonies is key to reducing population carbon costs, potentially explaining why the cells are often observed in aggregations (Fig. 1). However, the mechanisms of NH þ 4 transfer between cells and its overall efficiency (E N ) within each colony remain poorly constrained. It is likely that the surface:volume ratio of the cell and the size of aggregated colonies can both influence E N . The diffusivity between the cellular spaces, might be affected by the production of extracellular polymeric substances. Also, the uptake properties of the cells (i.e. the maximum uptake rate and the half saturation constants of NH þ 4 ) influence how effectively they obtain NH þ 4 . For example, if the N is transported with intercellular transporters, E N would decrease considerably. To understand what regulates population heterogeneity of N 2 fixation, it may be useful to examine the heterogeneity of N 2 fixation under varying growth conditions, including different ambient NH þ 4 and O 2 concentrations. Also, it is possible that N 2 fixation is tied to specific phase of the cell cycle, which requires further experiments. Recent ocean ecological and biogeochemical models simulate various functional groups of diazotrophs including unicellular types 55,56 , but diazotrophs within the same functional groups are generally represented as a uniform metabolic population. Given the observed bimodality of N 2 fixation and its impact on C cost, our study suggests that resolving such heterogeneity and its underlying causes may be essential to simulating the ocean ecosystems and predicting the niche of unicellular diazotrophs. In particular, the dependence of C savings on cellular growth rate would help to test the model predictions for expanded vertical habitat. On the other hand, our model shows that population C savings are relatively insensitive to uncertainties in E N , especially at low growth rate, where the rate of N assimilation becomes small and costs of respiratory protection dominate ( Fig. 7c and Supplementary Fig. 5). Thus, while the expansion of vertical niche depends on the growth rate dependence of C savings, it appears robust to uncertainty in N transfer efficiency, E N .
Given the ubiquity of phenotypic heterogeneity 57 and intercellular cooperation 58 , metabolic heterogeneity may be a general strategy for maximizing fitness among diazotrophic cyanobacteria. It remains an open question whether filamentous diazotroph Trichodesmium separates N 2 fixing cells (diazocytes) and cells responsible for photosynthesis 8,59-61 or not 35,62 . If Trichodesmium separates N 2 fixation and photosynthesis on cellular level, the observation of heterogeneity of N 2 fixation in both Crocosphaera and Cyanothece together with the heterogeneity in N 2 fixation in Trichodesmium 35 suggest an evolutionary relationship between unicellular and filamentous diazotrophs. However, it remains an open question whether there is connection between heterogeneity in N 2 fixation in unicellular diazotrophs and multicellular diazotrophs, as well as whether unicellular or multicellular diazotrophs evolved first in the cyanobacterial lineage [63][64][65] . The finding that heterogeneity in N 2 fixation occurs in both unicellular and multicellular diazotrophs may support the hypothesis that the division of labor is a key factor driving multi cellular cooperation in evolutionary transitions 66,67 .

Methods
Phytoplankton cultures. A Crocosphaera strain isolated from the surface of the western subtropical Pacific 68 was grown in a continuous 1.2 L culture in N-free medium. To closely represent their habitat (the euphotic zones of subtropical gyres), the culture was maintained in a chemostat with a dilution rate 0.20 d −1 (40% of the maximum growth rate), at a temperature of 26°C, an irradiance of 200 µmol photons m −2 s −1 , and a dark:light cycle of 12:12 h (1D to 12D, 1 L to 12 L). The beginning of the dark period was considered time 0 (0D). The N-free medium was prepared from seawater collected from the surface of the western North Pacific Ocean (34°20'N, 138°40'E), enriched with 20 µM of NaH 2 PO 4 , f/2 vitamins, and f/2 trace metals 69,70 . Cyanothece sp. ATCC51142 was grown in a 1.0 L culture in Nfree ASP2 medium 71 which contains 28.7 µM of K 2 HPO 4 , a temperature 26°C, an irradiance of 400 µmol photons m −2 s −1 , and a dark:light cycle of 12:12 h (1D to 12D, 1 L to 12 L) at growth rate (μ) of 0.30 d −1 .
15 N and 13 C uptake. N 2 fixation was measured following the method described by Mohr et al. 23 . Briefly, N-free medium was degassed and rapidly transferred to 125 mL glass bottles with minimal agitation until the maximum volume of the bottles was reached. These were septum-capped and enriched by injecting 1 mL of 15 N 2 gas (99.8 atom% 15 N, lot #11059; SI Science Co., Ltd., Tokyo, Japan) into the 24 vials. Previous study confirmed no contamination of 15 NO À 3 and 15 NH þ 4 in the 15 N 2 gas 72 . To observe 15 N and 13 C uptake, 0.5 mL of the 15 N 2 -enriched medium was then added to 9.0 mL of Crocosphaera cultures (4.1 × 10 5 cells mL −1 ) harvested from the continuous culture in 10 mL serum vials, to a final N 2 enrichment of 5.5 atom% and 0.5 mL NaH 13 CO 3 was injected simultaneously to a final enrichment of 9.7 atom%. These vials (n = 24) were sealed with crimp-seal butyl tube closures to eliminate headspace and air bubbles, preventing dilution of 15 N 2 with atmospheric 14 N 2 . The vials were incubated under the same conditions as previously described and harvested one vial every hour beginning at the start of the dark period (6 PM), and split into three aliquots for NanoSIMS, PON and mass spectrometry, and flow cytometry. Samples prior to isotope injection were also collected and analyzed as time 0. Samples at 4 L were lost. Cells observed under NanoSIMS analysis were from 7 to 37 cells at each time point.
In Cyanothece, 15 N and 13 C uptake were analyzed as described for Crocosphaera, except for small differences in the source of 15 N 2 gas (98 atom% 15  NanoSIMS imaging. Cells (1 mL) were fixed in 2.0% w/v glutaraldehyde, and collected using 0.2-µm Isopore TM GTTP Millipore Membrane filters (Merck Millipore, Billerica, Massachusetts, USA), which were then washed with Milli-Q ultrapure water and stored at −20°C until further processing. For analysis, samples were sputtered with gold and secondary ions were imaged in 5 or 10 serial images (layers) on a NanoSIMS 50 (Cameca, Gennevilliers, France) to quantify 12 C, 13 C, 12 C 14 N, and 12 C 15 N in 7 to 220 cells per time point, following earlier studies 34,73 . Secondary ions were generated by pre-sputtering with a 300 or 500 pA Cs + beam before scanning a raster of 256 × 256 pixels (10-15 µm 2 total raster size) with a 1.7-1.8 pA Cs + primary beam. Ratios of 15 N: 14 C (inferred from the 12 C 15 N/ 12 C 14 N) and 13 C: 12 Table 1). The system was tuned for~9,000 mass resolving power to overcome isobaric interference, and confirmed against isotopic ratios obtained in organic particulates determined by Flash EA elemental analyzer (Thermo Electron Corporation, Waltham, Massachusetts, USA) coupled to a DELTA plus XP mass spectrometer (Thermo Electron Corporation, Waltham, Massachusetts, USA) ( Supplementary Fig. 1).
Elemental analysis and mass spectrometry. Cells (8 mL) were collected on Whatman GF/F filters (GE Healthcare UK Ltd., Little Chalfont, Buckinghamshire, United Kingdom) pre-combusted at 450°C for 6 h, and frozen at −20°C until further processing. For analysis, filters were dried at 50°C overnight, exposed to HCl fumes for 2 h, and then dried again. The concentration and isotopic composition of total particulate organic C and N were measured on a Flash EA elemental analyzer (Thermo Electron Corporation, Waltham, Massachusetts, USA) coupled to a DELTA plus XP mass spectrometer (Thermo Electron Corporation, Waltham, Massachusetts, USA). The abundance of 13 Table 3).
Calculation of carbon and nitrogen uptake rates. Images obtained by NanoSIMS were processed in ImageJ 74 following methods described by Popa et al. 34 . Briefly, the mean isotopic compositions in each cell, delineated by the 12 C 14 N images, were integrated over 5 or 10 serial images, corrected against reference standards, and converted to percentage uptake with a measurement precision of 0.8-1.5%. Cells with a 12 C 15 N: 12 C 14 N ( 15 N: 14 N) ratio exceeding 2 standard deviations above the average at time 0 (at which 15 N: 14 N was 3.8 ‰ for Crocosphaera, 4.0 ‰ for Cyanothece) were considered 15 N-enriched. Similarly, cells with a 13 C: 12 C ratio exceeding 2 standard deviations above the mean at time 0 (at which 13 C: 12 C was 9.8 ‰ for Crocosphaera, 11.8 ‰ for Cyanothece) were considered 13 C-enriched.
The rate of N 2 fixation was defined as the change in % 15 N h −1 relative to the initial measurement. Per-cell net N uptake rates (ρ; fmol N cell −1 h −1 ) were calculated using a method adapted from Popa et al. 34 , described in [Eq. 2].
where Fx net is the ratio between 15 N in a cell afterΔt and the initial 15 N content, and CellQ is the cellular N quota calculated as the sum of particulate organic 15 N and 14 N normalized to the cell density. As N 2 fixation in Crocosphaera occurs only at night 21,29 , 15 N enrichment in the dark (0-12 h) and during light (13-24 h) were treated as N 2 fixation and re-uptake of excreted dissolved 15 N, respectively.
Statistics and reproducibility. 15 N: 14 N ratios were compared by one-way ANOVA 39 with 25 time points as factor levels, and individual cells in a sample as independent replicates. Differences were considered significant if p < 0.05. Heterogeneity was defined by the coefficient of variation (CV; ref. 41 ): where x is the mean and σ is the standard deviation among the cells. Normality assumptions were confirmed after logarithmic transformation (p > 0.05 by K-S test, n = 7-37 for Crocosphaera, n = 87-220 for Cyanothece) and residuals had a mean of zero. Dunnett's T-3 multiple comparisons 75 were used to compare background ratios.
To compute the bimodal separation, we first fit the sum of two Gaussian distributions to the histogram 42 : where F B (x) is frequency of x, A i is amplitude, x i is mean and σ i is standard deviation (i = 1 or 2 and x 2 > x 1 ). We obtain A i , x i and σ i with Metropolis Algorithm 76,77 , that minimizes the sum of square error between [Eq. 4] and the histogram. Based on values of x i and σ i , obtained, we calculate the bimodal separation: To examine the statistical significance of the difference between N and C uptake, we use the curve fitted to 15 N: 14 N, and re-fitted to 13 C: 12 C, by maintaining the original relative relationship between A 1 and A 2 , x 1 and x 2 , and σ 1 and σ 2 and value of S obtained based on 15 N: 14 N of the same diazotroph. The p value is obtained based on the difference between the data of 13 C: 12 C and the fitted curve as a null hypothesis.
To compute the deviation from the normal distribution, we applied the following procedure. If variation in the rate of C or N uptake is randomly distributed among cells of a population with a constant mean rate, we expect the probability density of C and N uptake follows the normal distribution 78 : where E(x) is the expected probability density for value x based on the normal distribution, A is the total area of the histogram, σ is the observed standard deviation, and x is the observed mean value. If the C or N uptake of the population is heterogeneous, we expect stronger deviation from [Eq. 6]; we calculate the deviation from the Chi squared (χ 2 ) statistic 79 , normalized by the sample number: where O(x) is observed probability density for the value x. The normalization by n makes results with different sample numbers comparable (here Crocosphaera and Cyanothece). Reproducibility was confirmed by analyzing 7 to 37 independent Crocosphaera cells, and 87 to 220 independent Cyanothece cells (Supplementary Table 1).
Numerical model of heterogeneous metabolisms. To represent heterogeneous metabolisms within a single clonal population of unicellular diazotrophs, we have modified the Cell Flux Model of diazotrophs 44 by simulating two types of cells; N 2fixing and non-N 2 fixing (Fig. 5). The model resolves a coarse-grained metabolic flux network based on mass, electron and energy (ATP) balance. These balances quantify stored C use for 3 cellular functions: biosynthesis, electron donation for N 2 fixation, and respiration. Respiration can be further classified into three uses; respiration for biosynthesis, for N 2 fixation and for respiratory protection (Fig. 5). The model was parameterized for Crocosphaera based on a respiration budget 43 by reducing the diffusivity of cell membranes 44 . We use cellular N of 30 fmol N cell −1 and a diameter of 3μm and temperature of 28°C to better represent Crocosphaera (strain WH8501) in Großkopf and Laroche 43 , which gives the diffusivity coefficient of the membrane of 1.51 × 10 −5 , slightly higher than previously estimated (1.38 × 10 −5 ). To represent Crocosphaera in this study (strain PS0609A) we used a cell diameter of 5 µm (based on Fig. 1 and Sohm et al. 80 for a larger size class), a cellular N of 60 fmol cell −1 , and the maximum N 2 fixation rate of 6.1 fmol cell −1 h −1 . To represent the laboratory condition, we applied temperature T = 26°C and assume saturated O 2 concentration [O 2 ] = 208 µM (ref. 81 ), and μ = 0.20 d −1 (when µ is constant). We have used a uniform growth rate among cells following previous studies [82][83][84][85][86] .
Application of the model to one dimensional water column. To simulate the light attenuation in the one-dimensional water column, we used Beer's law: where I(z) is the light intensity (µmol m −2 s −1 ) at the depth of z (m), I 0 is the light intensity at the surface (µmol m −2 s −1 ), and k is the extinction coefficient (m −1 ).
To simulate the photosynthesis rate by Crocosphaera, we adapt a commonly used equation with saturating light based on Target theory 85,87 : where P(I) is the rate of photosynthesis (fmol C cell −1 h −1 ) at the light intensity of I, P max is the maximum photosynthesis rate (fmol C cell −1 h −1 ), I P 0 is the reference light intensity at which P becomes (e − 1)/e. Then, with the Cell Flux Model, we find the growth rate µ (d −1 ) where C S (µ) = P(I), where we use E N = 0.2 and f N = 0.5 for the population with heterogeneous N 2 fixation and f N = 1 for the population with homogeneous N 2 fixation. The loss of C to the environment is assumed equal for both of these populations. We consider a simple 12:12 (h) light:dark cycle, at which photosynthesis occurs only during the light period and N 2 fixation and respiratory protection occur only during the dark periods. We apply I 0 = 1000 and z 0 = 30 to resemble observed depth profile of light in the subtropical gyres 50,88 , and P max = 7 and I P 0 ¼ 100 where the simulated maximum growth rate becomes close to the highest side of the observed range 48 and MVD of the population of heterogeneous N 2 fixation becomes close to 125 (m), below which the nifH copies of Crocosphaera is observed to drop considerably.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
The data used to generate the graphs presented in the main figures can be found as Supplementary Data 1. All other data that support the findings of this study are available on request from the corresponding author (TM).