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Conceived and designed the experiments: WM DWRW JL. Performed the experiments: WM. Analyzed the data: WM TG DWRW JL. Wrote the paper: WM. Contributed to figure preparation/schematic diagrams: TG.
The two commonly applied methods to assess dinitrogen (N2) fixation rates are the 15N2-tracer addition and the acetylene reduction assay (ARA). Discrepancies between the two methods as well as inconsistencies between N2 fixation rates and biomass/growth rates in culture experiments have been attributed to variable excretion of recently fixed N2. Here we demonstrate that the 15N2-tracer addition method underestimates N2 fixation rates significantly when the 15N2 tracer is introduced as a gas bubble. The injected 15N2 gas bubble does not attain equilibrium with the surrounding water leading to a 15N2 concentration lower than assumed by the method used to calculate 15N2-fixation rates. The resulting magnitude of underestimation varies with the incubation time, to a lesser extent on the amount of injected gas and is sensitive to the timing of the bubble injection relative to diel N2 fixation patterns. Here, we propose and test a modified 15N2 tracer method based on the addition of 15N2-enriched seawater that provides an instantaneous, constant enrichment and allows more accurate calculation of N2 fixation rates for both field and laboratory studies. We hypothesise that application of N2 fixation measurements using this modified method will significantly reduce the apparent imbalances in the oceanic fixed-nitrogen budget.
Biological dinitrogen (N2) fixation is the major source of fixed nitrogen (N) in the oceanic N budget . Current estimates of global oceanic N2 fixation are ~100–200 Tg N a−1 . N2 fixation rates can be assessed through geochemical estimates, modelling of diazotroph abundances and growth rates  and direct measurements of N2 fixation. Geochemical estimates rely on the measurement of, e.g., nutrient stoichiometry and estimates or models of ocean circulation ,  or the distribution of stable isotope abundances (e.g., ). Direct measurements of N2 fixation are obtained either using the 15N2-tracer addition method ,  or the acetylene reduction assay (ARA) , . However, direct measurements of N2 fixation rates account for ≤50% of the geochemically-derived estimates . Furthermore, the sink terms in the oceanic fixed N budget significantly exceed the current estimates of N2 fixation and other source terms for fixed N , . This gap between sources and sinks of fixed N implies an oceanic nitrogen imbalance, which may reflect a non-steady-state of the oceanic fixed-N inventory, or result from over-estimation of loss processes and/or under-estimation of fixed nitrogen inputs , . However, isotopic signatures in sediments suggest that the fixed N budget is in a steady-state .
The comparison of N2 fixation rates measured simultaneously using the 15N2-tracer addition and the ARA shows that the 15N2-tracer addition generally yields lower rates (for a summary see ). In addition, mass balance analyses of 15N2-based N2 fixation rates measured in experiments with cultured diazotrophs, indicate that the 15N2-tracer addition method yields rates that are too low for sustaining the observed growth rates and biomass , . The discrepancies between the two methods and the lack of mass balance in culture experiments have often been attributed to the excretion of recently fixed nitrogen as ammonium (NH4+) or dissolved organic nitrogen (DON). The discrepancies have led to the operational definition of gross and net N2 fixation ,  as measured by the ARA and the 15N2-tracer addition approaches, respectively. However, the measured release of NH4+ or DON is rarely sufficient to balance the observed growth in culture, and even invoking recycling of the dissolved fixed N rarely accounts for the observed discrepancies between N2 fixation rate and growth rate/biomass .
The apparent oceanic N imbalance, differences between geochemical estimates and measured rates of N2 fixation, and the difficulties in reconciling discrepancies between ARA and 15N2-based estimates of N2 fixation in the field and in culture experiments, led us to re-assess the 15N2-tracer addition method. This method is based on the direct injection of a 15N2 gas bubble into a seawater sample  sufficient to yield a final enrichment of 2–5 atom percent (atom%) and incubation for 2–36 hours . N2 fixation rates are then retrieved from the incorporation of 15N2 into the particulate organic nitrogen (PON). The method assumes implicitly that the injected gas fully and rapidly equilibrates with the surrounding water, and this assumption is the basis for calculation of the initial 15N enrichment of the dissolved N2 pool. Knowledge of this enrichment is pivotal to the calculation of N2 fixation rates with this method as seen in equation 1 (equations combined from ):
where A=atom% 15N in the particulate organic nitrogen (PN) at the end (final) or beginning (t=0) of the incubation or in the dissolved N2 pool (N2).
In applications of the method, all parameters of the equation are measured except for the atom% 15N in the dissolved N2 pool (AN2). Equation 1 shows that calculation of N2 fixation rates depends strongly on this value which is calculated from the predicted equilibrium dissolved N2 concentration , , its natural 15N abundance, and the amount of 15N2 tracer added with the bubble. The calculation assumes that there is complete isotopic equilibration between the injected bubble of 15N2 and the surrounding water at the start of the incubation.
Here we report results of experiments that were designed to assess the rate of equilibration of an introduced 15N2 gas bubble with the surrounding water. Based on results of these experiments, we developed a modified approach involving addition of 15N2-enriched seawater which assured a well-defined and constant 15N enrichment of the dissolved N2 gas at the beginning of the incubations. We propose the application of the modified approach for future assessments of N2 fixation rates in natural microbial communities and in laboratory cultures.
A first set of experiments (isotopic equilibration experiments) was carried out to assess the time required to attain isotopic equilibrium in the dissolved pool of N2 gas after injection of a known amount of 15N2 gas as a bubble into sterile filtered seawater. A gas bubble of pure 15N2 was injected directly into incubation bottles which were manually inverted fifty-times (~3 min agitation) and left standing for up to 24 h. Concentration of dissolved 15N2 was followed over the 24 h period to assess the degree of equilibration of the 15N2 gas bubble with the surrounding water as a function of time. Dissolved 15N2 concentrations in the seawater increased steadily with the incubation time (Fig. 1A). After eight hours, dissolved 15N2 concentrations reached about 50% of the concentration calculated assuming complete isotopic equilibration of the injected bubble with the ambient dissolved N2 gas in the seawater sample. At the end of the 24 h incubation, the dissolved 15N2 concentration had increased to about 75% of the calculated concentration.
Similar results were obtained in the incubation experiments with pure culture of Crocosphaera watsonii (culture experiments), which confirmed the incomplete and time-dependent equilibration of the injected bubble of 15N2 gas with the surrounding water (Fig. 1B). These experiments also demonstrated the associated underestimation of N2 fixation rates. Culture experiments were conducted after 15N2 addition as a gas bubble and also after 15N2 addition in the form of 15N2-enriched seawater (our modified method, see Methods section). The incubation of C. watsonii after injection of a bubble of 15N2 gas and without prior incubation of this bubble in algal-free media, gave a N2 fixation rate which was only 40% of the maximum rate measured in the incubations to which 15N2-enriched seawater had been added. In other words, for the 12-h incubation period under the described experimental conditions, the N2 fixation rate was underestimated by 60% when the 15N2 was introduced as a gas bubble. In contrast, in both the isotopic equilibration and the culture experiments, the concentration of dissolved 15N2 remained stable at the predicted value throughout the 24 h in incubations to which 15N2-enriched water was added.
Continuous, vigorous shaking (50 rpm) greatly increased the concentration of 15N2 in the media (Fig. 2) reaching ~67% of the calculated concentration after 30 minutes whereas the initial, manual agitation, i.e. inverting bottles 50 times (~3 min), resulted in only ~13% of the calculated concentration. Information on agitation is generally not provided in the published literature, but this is clearly a variable factor in incubations, especially if performed at sea. Continuous, vigorous shaking, as tested here (50 rpm; Fig. 2), is difficult to achieve in field experiments and may, in addition, be detrimental to some diazotrophs (e.g. Trichodesmium colonies).
Increasing the size of the incubation bottles, increasing the amount of gas injected per liter of seawater and the addition of dissolved organic matter (DOM) led in all cases except one to slower equilibration of the 15N2 gas bubble with the surrounding water (Fig. 3 and and4A),4A), even when bottles were shaken continuously for one hour (Fig. 4B). Only with the injection of 8 ml of 15N2 gas per liter of water and one hour of continuous, vigorous shaking, was near-complete equilibration achieved (97% of calculated concentration).
Both the isotopic equilibration and the culture experiments demonstrated clearly that the equilibration of 15N2 gas injected as a bubble into N2-saturated seawater is time-dependent and incomplete, even after 24 hours. The lack of complete equilibration causes the resulting calculated N2 fixation rates to be variably and significantly underestimated (see Equation 1). The equilibration, i.e. the isotopic exchange between the 15N2 gas in the bubble and the surrounding water is controlled primarily by diffusive processes. The major variables that influence the rate of isotopic exchange include the surface area to volume ratio of the bubble, the characteristics of the organic coating on the bubble surface , temperature and the rate of renewal of the water-bubble interface . The renewal of the water-bubble interface appears to have the greatest effect on the isotopic exchange, as continuous vigorous shaking of the incubation bottles generated the highest enrichment of 15N2 in the water phase. However, the calculated (equilibrium) enrichment in 15N2 was not attained fully even after one-hour of continuous shaking at 50 rpm on a rotary shaker. Incubations carried out on board a research vessel will provide some agitation of the bubble but this will not approach the high and constant agitation tested in our experiments. The implication is that variable sea-state conditions encountered during sea-going incubations, and the details of individual experiments, will lead to variable 15N2 enrichments and hence variable underestimation of N2 fixation rates. Further, N2 fixation studies in the oligotrophic regions of the ocean usually require the use of large incubation volumes (e.g., 2–4 L), so that continuous shaking for one hour or more is not practical, and in addition would likely be detrimental to the natural microbial communities.
The experiments with variable bottle sizes and DOM additions (Fig. 3 and and4)4) demonstrated that there are factors in addition to the bubble incubation time that affect the equilibration. On the other hand, the addition of 15N2-enriched seawater to the incubations led to a stable enrichment over the 24 h incubation time which was instantaneous and independent of the agitation of the bottles.
This study was motivated partly by the mismatches between the ARA and 15N2-based measurements of N2 fixation as well as imbalances between 15N2-fixation rates and biomass-specific rates (~growth rate) or CN fixation ratios (Table 1). Such mismatches have been observed in environmental studies and in culture studies, mainly with Trichodesmium. Although it has been shown that Trichodesmium can excrete recently fixed N2 as NH4+ or DON , , the excretion of 15NH4+ or DO15N rarely accounts for the observed discrepancies , . The operational definition of gross and net N2 fixation as obtained through ARA and 15N2 incubations, respectively, has been mainly based on the mismatch between the rates measured by the two methods. Our results demonstrate that N2 fixation rates, as measured with the 15N2 method  are underestimated. Therefore, the magnitude of the exudation of recently fixed nitrogen and the conditions promoting this process should be re-evaluated, taking into account the results presented here.
We reviewed published studies that have used the direct injection of a 15N2 gas bubble to assess N2 fixation rates in order to evaluate the magnitude of under-estimation. However, first attempts to assess the degree of underestimation of field and culture N2 fixation rates were obscured by a wide range of experimental conditions among the studies. Bottle sizes ranged from 14 ml to 10 L, the amount of 15N2 injected varied from 0.2 to 40.8 ml 15N2 per L seawater and incubation times ranged from 0.25 to 48 hours, with the majority of the field studies using 2–4 L bottles and 24 h incubations. In addition, information on agitation was, in general, not available. There were no obvious trends of reported N2 fixation rates with either bottle size, incubation time or the amount of injected 15N2 gas probably because of the large variability of geographic locations and environmental conditions prevailing in the individual studies, which would have a dominant effect on the local diazotrophic communities and their N2 fixation rates. An evaluation of the degree of possible underestimation of 15N2 fixation rates in environmental studies is further confounded by diel periodicity of N2 fixation –. The lack of knowledge on the exact timing and magnitude of the individual N2 fixation activity of the different diazotrophs relative to the timing of 15N2 gas injection hinders back-calculation of published N2 fixation data. This can be illustrated, for example, with a hypothetical diazotroph community that is dominated by unicellular cyanobacteria which fix nitrogen during the night period only (Fig. 5A). In this microbial community, measurements of N2 fixation using the direct injection of a 15N2 gas bubble during a 24 hour incubation will lead to a variable underestimation of the true N2 fixation rate, depending on the timing of the incubation start relative to the peak in the nitrogenase activity (Fig. 5C, solid lines). The underestimation will be more pronounced if the start of the incubation is coincident with the onset of the active N2 fixation period. In contrast, incubations with enriched 15N2 seawater, will not lead to an underestimate, regardless of the incubation start relative to the diel cycle (Fig. 5C, dashed lines).
The discrepancies and mismatches/imbalances observed in field and laboratory studies could, in part, be explained by the variable underestimation of the true N2 fixation rate due to the methodological uncertainty reported here. We propose the addition of 15N2-enriched seawater to incubations to assess N2 fixation rates in laboratory and field studies. We suggest that measurements using this approach are likely to increase measurements and estimates of N2 fixation at species, regional and global level and lead to a reduction in the apparent oceanic nitrogen imbalance.
The diazotrophic cyanobacterium Crocosphaera watsonii WH8501 was grown in batch cultures in N-free YBCII media  at 28°C in a temperature-controlled growth chamber. C. watsonii was subjected to 1212 h darklight cycles.
We first examined the rate of equilibration between an injected bubble of 15N2 gas and seawater. Two series of incubations were started by injecting 140 µl of 15N2 into 133 ml of an artificial seawater media (YBCII) contained in headspace-free, septum-capped glass bottles. In the first series (isotopic equilibration experiments), all bottles were inverted fifty times (~3 min) after injection of the 15N2 gas bubble and left at room temperature in the laboratory. One bottle was sampled immediately after the agitation in order to determine how much 15N2 gas had dissolved initially. The other bottles were opened and sampled after standing for periods from 1 to 24 h. Upon opening of the bottles, samples to measure the dissolved 15N2 were taken and stored in gas-tight glass vials (Exetainer®) until analysis.
In the second series (culture experiments), the YBCII media was pre-heated to 28°C in a temperature-controlled chamber before being used to fill septum-capped glass bottles. As with the first series, samples were agitated and left standing for varying periods of time after the injection of a 15N2 gas bubble. Instead of taking subsamples for 15N2 analysis, 13 ml of media were replaced by C. watsonii WH8501 culture upon opening of the bottles. This series of experiments was timed so that the introduction of culture into the media took place at the start of a dark phase of the 1212h darklight-adapted C. watsonii culture. The samples with the culture were then incubated for 12 h at culture growth conditions (28°C, dark phase, i.e. N2-fixing) and filtered onto pre-combusted GF/F (Whatman; 450°C for 4 h) filters at the end of the incubation. Filters were dried immediately after (50°C, 6 h) and stored at room temperature until analysis. To obtain a measure of underestimation using the direct injection of a 15N2 gas bubble, one bottle containing 13 ml of C. watsonii culture was incubated for 12 h after the injection of 140 µl 15N2 gas at the start of the dark phase and without release of the bubble, essentially resembling a laboratory or field incubation.
An alternative, modified 15N2 tracer addition method was developed, which involved addition of an aliquot of 15N2-enriched water to incubations. This alternative method was based on earlier approaches used to study oxygen cycling using 18O2  and the release of DON using 15N2 . The preparation of the 15N2-enriched water was started by degassing 0.2 µm-filtered artificial seawater (YBCII media). Degassing was carried out by applying vacuum (≤200 mbar absolute pressure) to continuously stirred (stir bar) media for about 30 min. The degassed water was transferred rapidly but gently into septum-capped glass bottles until overflow, and 1 ml of 15N2 gas (98 at%; Campro Scientific) was injected per 100 ml of media. The bottles were shaken vigorously until the bubble disappeared. Aliquots of this 15N2-enriched water were then added to the incubation bottles, with the enriched water constituting no more than 10% of the total sample volume. This alternative enrichment method was applied to the two series of experiments described above.
We assessed possible effects of varying bottle size, amounts of injected gas and different amounts of agitation on their contribution to the equilibration between a bubble of 15N2 gas and the surrounding seawater. For the bottle size comparison, incubations were performed in 0.13 L bottles and in 1.15 L bottles. The amount of injected gas varied between 1 ml 15N2 per 1 L seawater up to 8 ml 15N2 per 1 L seawater. The incubations were agitated either by inverting fifty times manually (~3 min) or by continuous agitation on a rotating bench-top shaker (Biometra WT 17) at 50 rpm (rotations per minute). We also added marine broth (Difco 2216; 0.2 µm filter-sterilized; 230 mg DOM L−1 media) to some bottles to examine the effect of dissolved organic matter (DOM).
Subsamples taken during the equilibration experiments were analysed for 15N2 concentration with a membrane-inlet mass spectrometer (MIMS; GAM200, IPI) within one week of subsampling. Dried GF/F filters were pelletized in tin cups, and PON as well as isotope ratios were measured by means of flash combustion in an elemental analyser (Carlo Erba EA 1108) coupled to a mass spectrometer (Thermo Finnigan Delta S).
The expected concentration of 15N2 following bubble injections was calculated assuming rapid and complete isotopic equilibration between bubble and surrounding seawater and considering atmospheric equilibrium concentrations of dissolved N2 . When 15N2-enriched aliquots were added, the amount of 15N2 originally dissolved in the degassed seawater and the volume of the aliquot added were taken into account. The calculations of N2 fixation rates in the culture incubations were made according to Equation 1 and are presented as a percentage of the highest rate measured. For the comparison between methods, the measured 15N2 concentrations are presented as a percentage of the expected concentration calculated as follows
for the direct injection of a 15N2 gas bubble where is the volume of the 15N2 gas bubble, MV is the molar volume and VTOTAL is the total (water) volume of the incubation. The expected concentration was corrected for the amount of 15N2 gas which remains in the bubble at isotopic equilibrium with the surrounding water. For the addition of 15N2-enriched water the expected concentration is
where VDG is the volume of degassed water, VEW is the volume of 15N2-enriched water added to the incubation and VTOTAL is the total (water) volume of the incubation.
We thank Marcel Kuypers and Hannah Marchant (Max Planck Institute for Marine Microbiology Bremen) for providing access to and advice on the membrane-inlet mass spectrometry. The assistance and suggestions of Gert Petrick and Karen Stange (IFM-GEOMAR) concerning the early analyses of 15N2 is also gratefully acknowledged.
Competing Interests: The authors have declared that no competing interests exist.
Funding: This work is a contribution of the Collaborative Research Centre 754 “Climate - Biogeochemistry Interactions in the Tropical Ocean” (www.sfb754.de), which is supported by the German Research Association. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.