Coupled nitrification and N2 gas production as a cryptic process in oxic riverbeds

The coupling between nitrification and N2 gas production to recycle ammonia back to the atmosphere is a key step in the nitrogen cycle that has been researched widely. An assumption for such research is that the products of nitrification (nitrite or nitrate) mix freely in the environment before reduction to N2 gas. Here we show, in oxic riverbeds, that the pattern of N2 gas production from ammonia deviates by ~3- to 16-fold from that predicted for denitrification or anammox involving nitrite or nitrate as free porewater intermediates. Rather, the patterns match that for a coupling through a cryptic pool, isolated from the porewater. A cryptic pool challenges our understanding of a key step in the nitrogen cycle and masks our ability to distinguish between sources of N2 gas that 20 years’ research has sought to identify. Our reasoning suggests a new pathway or a new type of coupling between known pathways in the nitrogen cycle.

Issue 1: ATU (allythiourea) may be an inhibitor of long standing, but it was originally tested before we knew about ammonia oxidizing archaea. The authors need to convince the reader that ATU inhibits the organisms that they say it does and not others. Basically, as the authors noted in the present paper, in these two oxygen minimum zone papers, the isotopic composition of labeled N2 cannot be explained by the binominal distribution when anammox is taken into account. In Change and De Brabandere, there is too much 29N2 for the amount of denitrification that should be present. Both papers explain this data by suggesting an internal nitrite pool for denitrifiers. Which is to say, that the nitrite used by denitrifiers is not mixing with the spiked surrounding water. Exactly as seen in the current paper in pore waters. Issue 3. The data in the current paper can be explained by particles. The current paper takes place in sediments. Sediments are composed of particles. We already know that the fact that sediments are composed of particles greatly affects N cycling there. Particles are the explanation why the natural fractionation of N2 production in sediments is close to zero. Nitrate is completely consumed in the particles. Implicit in this accepted argument is the idea that the inside of particles and the pore waters are not exchanging quickly. See For this to explain the current data, I believe that spiked ammonium would have to diffuse into particles but nitrite would not diffuse back out. It becomes part of an internal nitrite pool. This pool could be inside the particle or inside an organism. The experiments in the current paper were 8 hours long-pretty short. Probably a longer incubation would have more exchange. Ammonium is a precious item that organisms want. Particles also explain anaerobic processes under oxygen. This entire phenomenon is related to particles and particles need to be addressed in the paper. Issue 4. Given that the data in the paper can be explained by denitrification in sediment particles, which we already know happens, it seems like invoking a new player (or coupling) in the N cycle is unnecessary.
Detailed comments: Line 51: "Similarly,aerobic nitrification can fuel both anaerobic denitrification9 and anammox10 at the margins of the vast oceanic oxygen minimum zones" Here ref 9 is Ward et al 2009-that paper has absolutely nothing to do with aerobic nitrification fueling denitrification. I just reread to be sure. Reference 10 is Lam et al 2007, which is about aerobic nitrification fueling anammox (specifically) in the Black Sea. The Black Sea is fundamentally different from oceanic oxygen minimum zones in that it has a large flux of ammonium coming from its underlying sulfide zone. If you would like to see these fluxes quantified see Fuchsman et al 2008. On the other hand, in the giant oceanic oxygen minimum zone, ammonium is below detection (<10 nM) in the most of the oxygen minimum zone. See both Widner et al 2018s for ammonium data in the ETNP and ETSP. Bristow et al 2016 indicates that the Km for oxygen for aerobic ammonium oxidation is higher than the Km for nitrite oxidation. Rather than aerobic ammonium oxidation fueling denitrification/anammox in the oceanic oxygen minimum zones, nitrate reduction coupled to nitrite oxidation is a key process using the small concentrations of oxygen. Also note that, unlike the Black Sea, in OMZs nitrate concentrations are >20 uM from ambient seawater. aka oxidized N is not a limiting factor for denitrification. Please delete. Also this means that the authors have to reword that entire paragraph.
Line 96: This paper uses a lot of math. It might help the reader to follow if instead FA from fraction of ammonium, you used FNH3 and FNOx because FA could also be fraction anammox. It is a simple change that could make things easier to follow.
Perhaps Table 1 should include the oxygen concentrations for each experiment.
Line 188: Here we go again. The Black Sea is not like the margins of oxygen minimum zones due to the large flux of ammonium into the Black Sea suboxic zone. Both references 10 and 30 are about the Black Sea. The Kalvelage et al 2011 reference is more legitimate. However, Kalvelage assumes rather than shows that aerobic ammonium oxidation and anammox are linked. If you want to say this, you should really be citing Lam et al 2009 PNAS. That is where this idea is originally coming from. In that paper it comes from a calculation based on the balance of rates. However, back in the day of the Lam paper, the rubber stoppers were infecting denitrification rate measurements with oxygen and inhibiting them, so that calculation is very probably incorrect. If you look at models by Zakem et al 2020 ISME 14: 288-301-like Fig 3-you will see that aerobic ammonium oxidation to nitrite is not a key player in the OMZ system or its edge. You don't need to cite oxygen minimum zones for this process to be important. Sediments are quite important by themselves.
Reviewer #2 (Remarks to the Author): This paper uses isotope pairing methods on oxic riverine sediments in a lab to deduce that there is a cryptic intermediate pool of oxidized N that is not part of the measurable porewater pool. If true, this is a tremendously interesting finding. My criticisms of the paper have nearly nothing to do with the "if true" part. This is high-risk, high-reward science and as such I support it fully. Methods and modeling are as good as they can be to address this question in this paper. My criticisms are with manuscript presentation and explanation of how the authors link that data and mathematical framework to new understanding. Thus my comments below are meant to improve the manuscript and not to argue against its publication. I struggled to follow along with the paper from the methods the data and the mathematics. There are two reasons for this. 1. This work is inherently highly technical and never is going to be easy to understand. Despite 25 y of N isotope experience and a recent foray into isotope pairing in my lab, this paper took a lot of work to review. The authors may wish that I were smarter, and I would agree with them. But I am not, so 2. I think that there is a lot of room for clarifying the paper to enable readers to follow along with the reasoning. This clarification can include: mathematical notation, explanation of methods, figures. The storyline of the paper is very much falls along how the authors discovered it: data followed by modeling to see what is possible and then a conclusion. Would putting the modeling first followed by data that supports (or not) the models work better? I have a lot of comments below.
Consider some sort of diagram that outlines the methods and how they lead to a conclusion. A flowchart may work, but this is not to be prescriptive. But I think at any way to lead the reader from the methods to results to understanding would be a big help.
This paper lives and dies on it methods. The authors have done new techniques to putatively show new N pathways. But the methods section is written very tersely for few specialists who do these methods. I think that there should be more text linking what the authors want to know with how the method addresses this point. I admit to having trouble making these points myself despite having just starting using isotope pairing methods in my lab to attempt to measure denitrification in oxic aquifers. The Results section has a lot of this text and yes, it covers some of the methods there, great. But I would spell out these details in both places.
The arguments for what is actually happening to drive these patterns (starting on line 171) are critical parts of the paper. But I note with interest how the discovery of these pathways derive from data and not theory. That is fine, but differs from the way we came to know anammox, with a chemist staring at thermodynamic tables and positing that anammox was a possible reaction until it was later found. Here is the opposite-great. But are these possible reactions thermodynamically feasible? I have no idea, that is too far from what I know.
Despite that I am excited by the findings in this paper and their ramifications for understanding N cycling, this is but one study and thus too early to "conclude" or to "overturn". 145. This paragraph is the crux of the authors' argument, yet is very difficult to follow.
165. "Conclude" is too strong a word for a single lab study. "We suggest that the coupling…" 172. Consider a picture for this point.
185. Overturn is too strong a word. Let's wait for a few more observations of this phenomenon before we "overturn" our knowledge. This is a single study at a single time.
213. So a big headspace in these vials.
215. Why add ATU? Yes, I see it is in the results, but should be here too 216. That is super high NH4. I understand why, but given that this paper is sent to a general journal. I think the methods need to be described in a way to link clearly with the hypotheses and to state exactly what the methods are doing and why. E.g. high concentrations of 15NH4 enable…" 230-235. Split this epically long sentence. On line 232 after conditions state how this approach will achieve this further understanding.
259. That R was used is not that useful; this point can be buried at the end of the paragraph. Instead focus on how the statistical approach enables understanding and inference.
274. This method of providing data seems anachronistic in this age of cloud storage and open data.
And who decides what constitutes a reasonable request? Being extra polite? I urge the authors to post the data and code used to analyze them, after publication of course. Conclusions (e.g. line 165) will come only after scrutiny of these data and replication of this work. Code and data are needed for that.
296. "had no effect" is an incorrect interpretation of a null hypothesis significance test. There may very well be an effect, but it is not evident given the variability in the data. P=0.13 implies that there might be an effect; we cannot tell. But I cannot make this point strongly enough: P>0.05 does not mean the null hypothesis is true. A better way to make the point would be to calculate the parameter estimate and its uncertainty interval. If this interval is smaller than what the authors might say is an effect that matters, then that provides more information saying the false "no effect". I see from the results that the ratios are in fact not that different from one another, good.  In principle, this type a figure is a great way to make the point. In practice, I think this figure needs some work to make these difficult concepts more easy for the reader. First is that the points and fonts are tiny, nearly all focus is on the ribbon. Consider alternative ways of plotting, I am not sure what these would look like. A data visualization specialist might be able to help. One way might be to make a gif where the figure rotates and one can see the ribbon and the other points, but that would be for the supplement Supplementary equations. These equations need some work to be clear. First, define all variables here, even if already defined in the text (e.g. D). Give units (or specify if a fraction). What are the rates for D? I think of rates as 1/time. Use a horizontal line for division and not /. Variables should be in italics. I now follow the advice from Edwards and Augur Methe, Methods in Ecology and Evolution 2018 for writing equations. ra is confusing, it could be r times a, make it r with subscript a (r_a if using LaTeX). These quibbles aside, I really appreciate the details of this math laid out here in this form, and so will the readers.
Reviewer #3 (Remarks to the Author): In a convincing set of experiments and calculations, the authors show that the production of N2 from incubations of oxic riverbed slurries cannot be explained by pathways including free nitrite or nitrate pools that can be measured. Instead, it wsa coupled tightly to the ammonium pool.
While I agree with the authors of this well written manuscript in most points, I disagree in their final conclusion: I do not think that the results call for a novel pathway or novel coupling between pathways. We can explain the results with known pathways such as nitrifier denitrification or tight coupling, also known as nitrification-coupled denitrification.
Despite this disagreement, I still regard this manuscript as very important and very worth publishing in this journal, as most readers would not be aware that these pathways or such tight coupling could dominate N2 (or N2O) production. We mostly think in terms of denitrification or anammox when we think about N2. Thus, this would be one of the very, very few studies showing N2 production by other processes.

Reviewer #1 (Remarks to the Author):
In "Coupled nitrification and N2 gas production as a cryptic process in oxic riverbeds," Ouyang et al present nice experimental data indicating that when 15N-NH4+ spikes were used to calculate rates of N2 production, the intermediate, nitrite, did not mix in the sediment pore waters. Thus the basic assumption of the technique that is widely used to obtain N2 production rates was found to be untrue. While this paper does an excellent experimental job of proving the presence of this problem, the problem, or a very similar problem with 15N-NO2-, has already been noted and explained in previous papers (see below). I believe that the fact that sediments are composed of particles can explain the author's data and this should be addressed in the paper. Proposing the activity of a novel player in the N cycle is unnecessary. Overall, after editing, this paper will be a good addition to the literature that will highlight a fundamental problem with a widely used technique.
Additional data before the details of our reply. There is more to our case than we presented in our original manuscript. We omitted an additional set of treatments from the original manuscript in an effort to try and simplify what was clearly an already complex story. In a parallel set of the same oxic incubations, we added 15 N-tracer as 15 N-nitrite rather than 15 N-ammonia -all with and without ATU etc., (Treatments 5 & 6 in Table 1 below) and measured no significant production of 15 N-N 2 gas. See lines 132-134 and 183-197. We also measured no difference in 29 N 2 production from 15

N-ammonia with or without 14 N-nitrite. This is now our major reason for not supporting nitrifier-denitrification or canonical denitrification as sources of N 2 gas in oxic incubations with 15 N-ammonia. Reviewer 1 also raises lots of points in relation to anaerobic nitrate reduction supplying nitrite in oxygen minimum zones (OMZs) and having reviewed the data in support of a coupling between aerobic ammonia oxidation and N 2 gas production in OMZs we have decided to completely remove all mention of OMZs from our manuscript (see Detailed comment 1).
Issue 1: ATU (allythiourea) may be an inhibitor of long standing, but it was originally tested before we knew about ammonia oxidizing archaea. The authors need to convince the reader that ATU inhibits the organisms that they say it does and not others. I shouldn't have to figure it out for myself. and not the "standard", freshwater 80-100µM applied here; though they did confirm inhibition of both β-and γ-proteobacterial ammonia oxidising bacteria (AOB). We did know about the van de Graaf et al (1996) paper and the lack of effect of ATU on anammox and also the Jensen et al (2007) 3 paper demonstrating no effect on denitrification and anammox (now cited on line 86). The important point here though is that we added ATU to establish a link between aerobic ammonia oxidation and subsequent N 2 gas production and clearly from the data in Fig. 1   Basically, as the authors noted in the present paper, in these two oxygen minimum zone papers, the isotopic composition of labeled N2 cannot be explained by the binominal distribution when anammox is taken into account. In Change and De Brabandere, there is too much 29N2 for the amount of denitrification that should be present. Both papers explain this data by suggesting an internal nitrite pool for denitrifiers. Which is to say, that the nitrite used by denitrifiers is not mixing with the spiked surrounding water. Exactly as seen in the current paper in pore waters.  We are aware of the earlier studies implying internal nitrite pools. An important distinction, however, is that the experimental studies mentioned employ (near-)anoxic incubations and suggest an internal pool within a group of anaerobes (denitrifiers) already known to carry out the entire pathway in question (the stepwise reduction of nitrate to N 2 ), whereas explaining our observations with existing models requires two types of organisms with opposing oxygen requirements (aerobic ammonium oxidizers and anaerobic N 2producers). Thus, while the earlier observations can be explained by an intracellular nitrite pool with limited exchange to the outside, such an explanation is not possible in our case.
Furthermore, there is a lot here in relation to anaerobic nitrate reduction supplying nitrite in OMZ waters. We looked again at the evidence for a coupling between aerobic ammonia oxidation and N 2 gas production at the margins of OMZs  Yes particles have diffusive boundary layers and yes the data in Simon et al., show elevated concentrations for nitrate and ammonia on the inside of particles but, just to be clear, Wilson, who we contacted, said "However we did not see any increase in NO2-" i.e., they did not measure elevated nitrite in oxic particles. Besides, the take home message in the Ploug et al. (1997) is that anoxia (in highly organic i.e. 100%, lab-made aggregates) is an "ephemeral phenomenon" that they only found in 2 out of 8 aggregates and that "…would limit anoxic conditions to occurring only over a few hours, depending on the size of the aggregates." Further, they say "The volumetric oxygen respiration rate around an anoxic center in a 1.4 mm large aggregate (Fig. 2) The data in the current paper can be explained by particles. The current paper takes place in sediments. Sediments are composed of particles. We already know that the fact that sediments are composed of particles greatly affects N cycling there. Particles are the explanation why the natural fractionation of N2 production in sediments is close to zero. Nitrate is completely consumed in the particles. *Implicit in this accepted argument is the idea that the inside of particles and the pore waters are not exchanging quickly. **For this to explain the current data, I believe that spiked ammonium would have to diffuse into particles but nitrite would not diffuse back out. It becomes part of an internal nitrite pool. This pool could be inside the particle or inside an organism. The experiments in the current paper were 8 hours long-pretty short. Probably a longer incubation would have more exchange. Ammonium is a precious item that organisms want. Particles also explain anaerobic processes under oxygen. This entire phenomenon is related to particles and particles need to be addressed in the paper.  Table 2) that should both -from the accepted point of viewinfluence the ratio of 29 N 2 and 30 N 2 produced (Fig. 2a) but they do not (Fig. 3b,c and Fig. 4). We of course agree that a cryptic intermediate pool and/or process could be inside a particle and/or an organism (that is the point of our paper) but we do not agree that it is as simple as an internal nitrite pool for the very reason that we see 15 NO 2 from 15 NH 4 + "on the outside" in the porewater.
As a point of detail, the incubations were 12 hours long, not 8, with steady production of 15 N 2 over the first 9-10 hours (Fig. 1). We don't see why this is "pretty short" from a diffusion perspective? We were working with samples of gravel and sand dominated sediments with particles in the incubations of up to 2mm -though these would be largely inorganic with thinner organic biofilms (as above). If we take 2mm as the upper size limit and porosity of either 0.45 or 0.9, then nitrate (Li & Gregory, 1974) Ammonia is of course a rare commodity in the ocean but it accumulates in sediments and in these riverbeds can range in situ from 10s to 1000s of µM -hence, spiking the porewater to ~390 µM 15

Issue 4.
Given that the data in the paper can be explained by denitrification in sediment particles, which we already know happens, it seems like invoking a new player (or coupling) in the N cycle is unnecessary.
Quite simply, if 15 NO 2 and 15 NO 3 can diffuse "out" (Fig. 1b) from where ever 15 NH 4 + is being oxidised, then ~24µM 15  added to the porewater can diffuse "in", and if the "aggregates" can go anoxic as the reviewer suggests -bearing in mind that would require far higher respiration than we measured, then we would expect production of 15   See above, reply to detailed comment 1.
3, Bristow et al 2016 indicates that the Km for oxygen for aerobic ammonium oxidation is higher than the Km for nitrite oxidation. Rather than aerobic ammonium oxidation fueling denitrification/anammox in the oceanic oxygen minimum zones, nitrate reduction coupled to nitrite oxidation is a key process using the small concentrations of oxygen. Also note that, unlike the Black Sea, in OMZs nitrate concentrations are >20 uM from ambient seawater. aka oxidized N is not a limiting factor for denitrification.
See above, reply to detailed comment 1. 4, Please delete. Also this means that the authors have to reword that entire paragraph.
See above, reply to detailed comment 1 and the rewrite of lines 52-64. 5, Line 96: This paper uses a lot of math. It might help the reader to follow if instead FA from fraction of ammonium, you used FNH3 and FNOx because FA could also be fraction anammox. It is a simple change that could make things easier to follow.

Reviewer 2 also asked us to revise the mathematical notation, symbols and equations. We have revised all the equations in both the text and SI. We use 'x' to denote multiplication and have revised F N and F A with subscripts throughout. See line 95-113, 302-305 and the Supplement.
For convention, we propose to retain "ra" for the relative contribution from anammox to the overall production of N 2 , as proposed by Risgaard-Petersen et al. (2003), as it is now part of this field's literature and, to avoid any possible confusion with "r x a", we have retained x to indicate multiplication in all the equations. Table 1 should include the oxygen concentrations for each experiment.

6, Perhaps
We did not measure oxygen concentrations in parallel incubations for all 12 rivers as that would have been quite simply impossible. However, we do know from our former work in many of the riverbeds revisited again here 2 and our extensive studies across the southern UK 6 their respiration rates and that oxygen will not run out. We now state in the methods, lines 236-244, that "Oxic slurries were prepared by adding approximately 3 g sediment (~0.75 ml of porewater) and 2.7 ml air-saturated synthetic river water into 12 ml gas-tight vials (Exetainer, Labco), leaving an approximate 6 ml headspace of air which is equivalent to ~58 µmol O 2 per prepared vial. We know from previous incubations with similar sediments from 28 rivers 6 respiration rates to be ~187 nmol O 2 g -1 h -1 , on average (± 64.3, 95%, C.I.), that would consume ~12% of the total oxygen during a 12h incubation. In addition, we also checked oxygen over time using a microelectrode (50µm, Unisense) in parallel sets of scaled-up slurries (120 mL and same ratio of sediment to water to headspace) for two rivers and found comparatively little consumption as before 2 (Supplementary Figure 2)." 7, Line 188: Here we go again. The Black Sea is not like the margins of oxygen minimum zones due to the large flux of ammonium into the Black Sea suboxic zone. Both references 10 and 30 are about the Black Sea. The Kalvelage et al 2011 reference is more legitimate. However, Kalvelage assumes rather than shows that aerobic ammonium oxidation and anammox are linked. If you want to say this, you should really be citing Lam et al 2009 PNAS. That is where this idea is originally coming from. In that paper it comes from a calculation based on the balance of rates. However, back in the day of the Lam paper, the rubber stoppers were infecting denitrification rate measurements with oxygen and inhibiting them, so that calculation is very probably incorrect.
See above, reply to detailed comment 1. All reference to OMZs removed. Fig 3-you will see that aerobic ammonium oxidation to nitrite is not a key player in the OMZ system or its edge. You don't need to cite oxygen minimum zones for this process to be important. Sediments are quite important by themselves.

8, If you look at models by Zakem et al 2020 ISME 14: 288-301-like
See above, reply to detailed comment 1. All reference to OMZs removed.

Reviewer #2 (Remarks to the Author):
This paper uses isotope pairing methods on oxic riverine sediments in a lab to deduce that there is a cryptic intermediate pool of oxidized N that is not part of the measurable porewater pool. If true, this is a tremendously interesting finding. My criticisms of the paper have nearly nothing to do with the "if true" part. This is high-risk, high-reward science and as such I support it fully. Methods and modeling are as good as they can be to address this question in this paper. My criticisms are with manuscript presentation and explanation of how the authors link that data and mathematical framework to new understanding. Thus my comments below are meant to improve the manuscript and not to argue against its publication.
1, I struggled to follow along with the paper from the methods the data and the mathematics. There are two reasons for this. 1. This work is inherently highly technical and never is going to be easy to understand. Despite 25 y of N isotope experience and a recent foray into isotope pairing in my lab, this paper took a lot of work to review. The authors may wish that I were smarter, and I would agree with them. But I am not, so 2. I think that there is a lot of room for clarifying the paper to enable readers to follow along with the reasoning. This clarification can include: mathematical notation, explanation of methods, figures. The storyline of the paper is very much falls along how the authors discovered it: data followed by modeling to see what is possible and then a conclusion. Would putting the modeling first followed by data that supports (or not) the models work better? I have a lot of comments below.

See combined reply to points 1 & 2 below.
2, Consider some sort of diagram that outlines the methods and how they lead to a conclusion. A flowchart may work, but this is not to be prescriptive. But I think at any way to lead the reader from the methods to results to understanding would be a big help.
In reply to points 1 and 2. We have completely overhauled the paper, rewriting to simplify large sections of the text, methods and revising the mathematical notation. We have also increased the number of figures from 2 to 4 in order to breakdown and simplify the presentation of the data which we hope helps to map the data onto the narrative and methods. We now also include a schematic diagram (Fig. 2) to illustrate the accepted (2a) framework for how substrate pools and reactions interact to generate N 2 gas and our proposed alternative (2b). We now also include Broda's 1977 thermodynamic predictions for the complete aerobic oxidation of ammonia to N 2 (equation/reaction 5, line 51) which provides a theoretical framework for our data and -as we now more explicitly argue at the end of our paper, lines 198-206, -actually offers the simplest explanation for our data (more details below).
3, This paper lives and dies on it methods. The authors have done new techniques to putatively show new N pathways. But the methods section is written very tersely for few specialists who do these methods. I think that there should be more text linking what the authors want to know with how the method addresses this point. I admit to having trouble making these points myself despite having just starting using isotope pairing methods in my lab to attempt to measure denitrification in oxic aquifers. The Results section has a lot of this text and yes, it covers some of the methods there, great. But I would spell out these details in both places.

This is a perfectly valid criticism of the methods section from a non-specialist's perspective and we have now revised them extensively. Including: a detailed explanation of the availability of oxygen throughout the 12h incubations (in reply to reviewer 1) on lines 236-244; an explanation of what is being traced with 15 N-ammonia; why we enriched the ammonia pool by ~ 400µM; and clearer phrasing of the use of allylthiourea on lines 251-255.
We now also include data for two additional treatments (5&6, Table 1) that were omitted from the original manuscript in an effort to simplify the story. Here the incubations were exactly as described for 15 N-ammonia but instead we added 15 N-nitrite and state which reactions they were screening for -see detailed reply to reviewer 1 and lines 284 to 290. We now also describe explicitly why and how we manipulated the fraction of 15

4,
The arguments for what is actually happening to drive these patterns (starting on line 171) are critical parts of the paper. But I note with interest how the discovery of these pathways derive from data and not theory. That is fine, but differs from the way we came to know anammox, with a chemist staring at thermodynamic tables and positing that anammox was a possible reaction until it was later found. Here is the opposite-great. But are these possible reactions thermodynamically feasible? I have no idea, that is too far from what I know.
The reviewer raises an interesting point that prompted us to revisit Broda's 1977 7 thermodynamic ponderings that, along with Richards observations (1965) 8 , drove the original quest for anammox (anaerobic ammonium oxidation). Not only did Broda propose the potential for anammox through either reaction 1 or 2 (below) in nature, where 2 was later proven to be the anammox reaction 9 , he also postulated the complete oxidation of ammonia with oxygen to N 2 gas through reaction 3. This aerobic oxidation of ammonia to N 2 has rough thermodynamic equivalence to anammox (2) and complete aerobic nitrification to NO 3 -, reaction 4. We have now included this in our introduction and discussion. So yes, the reaction is thermodynamically feasible and it actually offers the simplest explanation for our data. See lines 48-52 of the introduction and lines 198-206  Despite that I am excited by the findings in this paper and their ramifications for understanding N cycling, this is but one study and thus too early to "conclude" or to "overturn".
We appreciate the reviewer's excitement for our work. Whereas this may only be one study but so were the original studies on anammox, comammox and many, many others and few, if any, presented findings for 12 genuinely independent field sites, with many basing their conclusions on pseudoreplication. We have, however, toned down "overturn" to "challenges" and "conclude" to "propose": "We propose that the coupling between ammonia oxidation and N 2 gas production in oxic, permeable riverbed sediments involves a cryptic intermediate pool…". It is certainly cryptic from the perspective of the currently accepted mathematical framework e.g. that of Song 10 but also many others too. See lines 174-178.

Specific comments
18. How does it violate? Results needed. The abstract nicely states the context of the study, but it is hard to tell what the authors actually did.
We have revised the abstract throughout and now include a key "simple" fact identified through the revisions to points 1 and 2 above. We do however want to keep any technical jargon to a minimum for the more general audience we are targeting.

32.
Might be worth mentioning that nitrifiers are chemoautotrophs in this general introduction.

Most research…
yes, more concise. Done, see line 65.

Independent of concentrations of nitrate?
No, it is not the concentration per se, it is simply the fact that the pattern of 15 Nlabelling in the porewater NO x pool had no discernible influence on the 15 N-labelling of the N 2 gas produced -that you would expect according to the accepted mathematical framework common to this type of 15 N-work in sediments. Concentration may affect the rate of reaction but that would apply equally to both 14 N and 15 N so wouldn't affect the "patterns".

This is the first sentence of the results. Further from what?
It was meant to be further to our former work published in 2016 (cited 2 and described in the section above) on the coupling between aerobic nitrification and putatively anaerobic N 2 gas production in oxic riverbeds. We have rephrased to make it more explicit. See line 79-81.
96. Clarity needed. What if the "degree of 15 labeling"? The fraction of the pool that is 15N? Something else? Also, FN could be interpreted as F*N; subscript the N.
We have rewritten this entire section as suggested, added equations to the methods (10 & 11)

See 296
For 111 and point 296 below. We have completely revised both the way we present and analyse the data for the ratios of 29 N 2 to 30 N 2 i.e. R. We have now calculated averages and confidence intervals for both our measured R values and the predicted R values (equations 6 and 7, respectively) for both denitrification and anammox. See lines 109-139 and Table 2. In the new Fig. 3 we use boxplots to show the overall spread in the data, plotting the measured and predicted values next to each other to show the discrepancy between the two. In the text, the statement "diluting F N had no discernible effect on the values for R…" is then followed by the averages with their 95% CI and reference to Table 2. The figure caption that contained text to the same effect i.e., "see 296" has been completely revised -along with the figure -to form the new figure 4. 117. Delete clearly.

Done.
132. Equation could be clearer. Use horizontal line for division. Use single letters for variables (with subscripts). In that case the \times symbol can be deleted.
We have revised equations 6 and 7 (now 8 and 9) in the main text (see lines 146-153) and equations 1 to 14 in the supplement. For convention, we propose to retain "ra" for the relative contribution from anammox to the overall production of N 2 , as proposed by Risgaard-Petersen et al. (2003), as it is now part of this field's literature and, to avoid any possible confusion with "r x a", we have retained 'x' to indicate multiplication in all equations. 142. 'rather counterintuitively". This paper is difficult enough to follow. Spell out exactly what you expect, what you found, and why it is counterintuitive.
We really do not want our paper to be difficult to follow at all. We have removed "rather counterintuitively" and extensively revised the text both leading to and following on from this section and hope that helps. Lines 154-156 and the revisions either side for context.

145.
This paragraph is the crux of the authors' argument, yet is very difficult to follow.
Addressing point 111 above led to us revising all of the figures which, in turn, enables us to first introduce the reader to a clearer, simpler presentation of the discrepancies in our data i.e., the simple comparison of our measured R values and those predicted by the accepted mathematical framework. This then enabled us to simplify the crux of our argument that revolves around the now fully revised 3D figure (see point below, now Fig. 4). We hope that these simplifications make our argument easier to follow. Lines 157-172, revised Fig. 4 and new Fig. 2. 165. "Conclude" is too strong a word for a single lab study. "We suggest that the coupling…" As above "We propose". Line 174 onwards.

Consider a picture for this point.
We now include the schematic Fig. 2 showing both the accepted scenarios and our proposed cryptic scenario which we refer to throughout the text to help guide the reader.

185.
Overturn is too strong a word. Let's wait for a few more observations of this phenomenon before we "overturn" our knowledge. This is a single study at a single time.
As above, replaced "overturn" with "challenge" on line 207 but also see the extensive revisions either side for context.

So a big headspace in these vials.
We have completely revised the methods section as described above for reviewer 1 and now describe what the 6 mL headspace is equivalent to as an amount of oxygen and how that compares to our measured rates of respiration for these gravel/sand sediments. Line 236-244.

215.
Why add ATU? Yes, I see it is in the results, but should be here too.

216.
That is super high NH4. I understand why, but given that this paper is sent to a general journal. I think the methods need to be described in a way to link clearly with the hypotheses and to state exactly what the methods are doing and why. E.g. high concentrations of 15NH4 enable…"

As above and see lines 248-250 for an explanation in relation to what it is we were measuring. It is not actually that high and we only labelled about 50% of the ammonia pool.
230-235. Split this epically long sentence. On line 232 after conditions state how this approach will achieve this further understanding.
The whole methods section has been completely rewritten in light of this and the previous comments. See lines 245-290.

259.
That R was used is not that useful; this point can be buried at the end of the paragraph. Instead focus on how the statistical approach enables understanding and inference.

We have moved R and other package details to the end of this section but are not sure what else the reviewer wants us to include in what is just a fairly routine description of our statistics? Further details are provided in both the main text and supplemental tables. See lines 318-336.
274. This method of providing data seems anachronistic in this age of cloud storage and open data. And who decides what constitutes a reasonable request? Being extra polite? I urge the authors to post the data and code used to analyze them, after publication of course. Conclusions (e.g. line 165) will come only after scrutiny of these data and replication of this work. Code and data are needed for that. This is just standard text from the Nature guide to authors. We can provide the data presented in the figures if we get published.
296. "had no effect" is an incorrect interpretation of a null hypothesis significance test. There may very well be an effect, but it is not evident given the variability in the data. P=0.13 implies that there might be an effect; we cannot tell. But I cannot make this point strongly enough: P>0.05 does not mean the null hypothesis is true. A better way to make the point would be to calculate the parameter estimate and its uncertainty interval. If this interval is smaller than what the authors might say is an effect that matters, then that provides more information saying the false "no effect". I see from the results that the ratios are in fact not that different from one another, good.   In principle, this type a figure is a great way to make the point. In practice, I think this figure needs some work to make these difficult concepts more easy for the reader. First is that the points and fonts are tiny, nearly all focus is on the ribbon. Consider alternative ways of plotting, I am not sure what these would look like. A data visualization specialist might be able to help. One way might be to make a gif where the figure rotates and one can see the ribbon and the other points, but that would be for the supplement.
We have completely revised all of the figures. Specifically in relation to the 3D "ribbon", which is now Fig. 4, we have: reduced the number of data points to just the overall average estimates for R; removed the too busy legend; increased the size of the symbols and axes labels; truncated the ribbon by reducing R from -2 to -1 i.e. the x-axis; and also provided two zoomed-in views from different angles. The senior author, Trimmer, does not have access to any data visualisation specialists at Queen Mary -or anywhere else as all spending at QM has been frozen -and this is the best that can be done with the resources available. I think it is quite clear that our measured values fall near to each other and the gap where there are no solutions, while those predicted simply for denitrification do not.
Supplementary equations. These equations need some work to be clear. First, define all variables here, even if already defined in the text (e.g. D). Give units (or specify if a fraction). What are the rates for D? I think of rates as 1/time. Use a horizontal line for division and not /. Variables should be in italics. I now follow the advice from Edwards and Augur Methe, Methods in Ecology and Evolution 2018 for writing equations. ra is confusing, it could be r times a, make it r with subscript a (r_a if using LaTeX). These quibbles aside, I really appreciate the details of this math laid out here in this form, and so will the readers.
As we say above, we have completely revised the equations in both the main text and supplement. We have added rate units (nmol N g -1 dry sediment h -1 ) for both denitrification and anammox (though any unit would do here) and also defined both F N and F A as the fraction of either porewater pool labelled with 15 N and now show how each is calculated in the methods, lines 302-305. For convention, we propose to retain "ra" for the relative contribution from anammox to the overall production of N 2 , as proposed by Risgaard-Petersen et al. (2003), as it is now part of this field's literature and, to avoid any possible confusion with "r x a", we have retained x to indicate multiplication in all the equations.

Reviewer #3 (Remarks to the Author):
In a convincing set of experiments and calculations, the authors show that the production of N2 from incubations of oxic riverbed slurries cannot be explained by pathways including free nitrite or nitrate pools that can be measured. Instead, it wsa coupled tightly to the ammonium pool.
While I agree with the authors of this well written manuscript in most points, I disagree in their final conclusion: I do not think that the results call for a novel pathway or novel coupling between pathways. We can explain the results with known pathways such as nitrifier denitrification or tight coupling, also known as nitrification-coupled denitrification.
Despite this disagreement, I still regard this manuscript as very important and very worth publishing in this journal, as most readers would not be aware that these pathways or such tight coupling could dominate N2 (or N2O) production. We mostly think in terms of denitrification or anammox when we think about N2. Thus, this would be one of the very, very few studies showing N2 production by other processes.
Both reviewers 1 and 3 say there is no need to call for a novel pathway. We would like to start by reiterating that we only ever posed it as a possibility and left it open i.e., "Whether it transpires that our cryptic coupling is mediated by a novel organism or, an as of yet, masked combination of known players in the nitrogen cycle remains to be resolved." We also included complete nitrifier-denitrification as a possibility, describing the need for nitrosocyanin as a plausible substitute to canonical N 2 O-reductase to enable complete nitrifier-denitrification to N 2 gas 11 .
However, there is more to our case than we presented in our original manuscript. We omitted an additional set of treatments from the original manuscript in an effort to try and simplify what was clearly an already complex story. In a parallel set of the same oxic incubations, we added 15 N-tracer as 15 Table 2). This is now our major reason for not supporting nitrifier-denitrification or canonical denitrification as sources of N 2 gas from 15 N-ammonia. As we do not wish to get into an argument over complete nitrifier-denitrification to N 2 we emailed the reviewer (as they had signed their review) for clarification on this point. The reviewer's claim below (point for line 62) that "we also know that nitrifiers… reduce nitrite to N 2 O and also N 2 in nitrifier denitrification" is not actually known for N 2 . Instead, and as we stated, complete nitrifier-denitrification to N 2 would require nitrifiers to have nitrosocyanin as a plausible substitute to canonical N 2 O-reductase to enable them to completely reduce nitrite to N 2 gas 11 . As for reviewer 2, we do now formally introduce the complete aerobic oxidation of ammonia to N 2 as a further possibility, as proposed by Broda (equation 5) and just as Broda originally proposed for anammox. See lines 48-51, 183-197. In the revised final section "Internal NO x cycling or a novel pathway or organism" we now discuss more fully these two scenarios along with the known potential coupling between nitrifiers and anammox bacteria as in CANON reactors. This section now comes to the open conclusion "Regardless of the actual pathway that produces the N 2 gas (Fig. 2b), an isolated cryptic intermediate pool has to have the same 15 N-labelling of the ammonia pool (F Ncry = F A ). As a consequence of this equality, we can no longer distinguish between sources of N 2 gas, be it complete nitrifier-denitrification, canonical denitrification, anammox or complete aerobic ammonia oxidation, as they would all produce 29 N 2 and 30 N 2 at the same ratio (Fig.  2b where R is equal for each process).
Our observations challenge the current understanding of a key coupling in the nitrogen cycle in permeable, oxic riverbed sediments that may also apply to other biomes where the oxidation of ammonia is tightly coupled to the production of N 2 gas, such as continental shelf-sediments 12,13 and groundwater aquifers 14 . Whether it transpires that our cryptic coupling is mediated by a novel organism or, an as of yet, masked combination of known players in the nitrogen cycle remains to be resolved." See lines 201-212.
Hence to simply state "We can explain the results with known pathways such as nitrifier denitrification or tight coupling, also known as nitrification-coupled denitrification" is not quite true for nitrifier-denitrification nor is it simple to reconcile our results with canonical denitrification coupled to nitrification for the reasons described above.
I have few other comments, provided in an annotated copy.

Reviewer 3's comments from their annotated copy.
Abstract, line 23. Neither the pathway nor the type of coupling have to be new. Maybe just less present in the minds of most researchers.

As detailed above.
The abstract provides very little concrete information at the moment and is therefore difficult to understand for readers who have not read the whole text.
As for reviewer 2, we have revised the abstract throughout and now include a key "simple" fact identified through this revision. We do however want to keep any technical jargon to a minimum for a more general audience.
Line 38. Although bacterial denitrification is mostly anaerobic, aerobic denitrification has also been discussed in the literature.
There is a lot of potential confusion in the literature when comes to the terminology used to describe oxygen. We prefer to stick to the convention of using oxic and anoxic to describe the presence or absence of measurable oxygen in an environment and aerobic and anaerobic when stating the mode of respiration on either oxygen or alternative electron acceptors e.g. NO  Line 62. This may be true in aquatic systems. In soils, 'free mixing' is inherently difficult, although it might be easier for nitrite and nitrate than e.g. for ammonia. Anyway, we also know that nitrifiers, for example, can reduce nitrite further to N2O and also N2 in nitrifier denitrification. Although they can take up nitrite from the surrounding, they will also produce nitrite and directly reduce it further.
With regard to free mixing. We have added "sediments" to indicate that we are focusing on aquatic systems, as a full description of the problems with mixing ammonia in non-saturated soils, or soils in general, is beyond the scope of our manuscript even though they are a major global source of N 2 131-134 and 183-197. This is now our major reason for not supporting nitrifier-denitrification or canonical denitrification as our source of N 2 gas from 15 N-ammonia. We do not wish to get into an argument over complete nitrifier-denitrification to N 2 which is why we emailed the reviewer (as they had signed their review) for clarification on this point. The reviewer's claim above that "we also know that nitrifiers… reduce nitrite to N 2 O and also N 2 in nitrifier denitrification" is not actually known for sure for N 2 . Instead and as we state, complete nitrifier-denitrification to N 2 would require nitrifiers to have nitrosocyanin as a plausible substitute to canonical N 2 O-reductase to enable complete reduction of nitrite to N 2 gas 11 .
Line 70. This is not a complete sentence, please rephrase.
This whole section has been revised, see lines 67-70.
The original isotope pairing technique developed by Nielsen in 1992 15 was designed to do just that in whole, intact sediment cores and he coined the terms D w and D n . Where D w is denitrification of "fertiliser" nitrate originating from the overlying water in the sediment core and D n , denitrification of nitrate borne from nitrification in the upper oxic sediment layers i.e. coupled nitrification-denitrification. Even with the advent of anammox in 2002 this distinction could still be made i.e. Trimmer et al., 2006 16 . However, for the technique to work properly, the added 15 NO 3 must be allowed to mix by diffusion with 14 NO 3 already in the system, which can be checked by plotting the ratio of 29 N 2 to 30 N 2 production over time 13 . Even though we can distinguish between these two sources of nitrate, there is still only one poolfed from the two sources -at the point of "denitrification". For example, if we imagine a system with no 14  in the overlying water but a strong nitrification, 14 NO 3 producing potential in the oxic sediments below -the North Sea in May is analogous. We add 15  to the overlying water which diffuses in and mixes with 14  borne in the sediment. Denitrification will then produce 30 N 2 for D w and 29 N 2 for D n but there is only one mixed pool (F N ) of 14 NO 3 and 15  integrated in the production of 29 N 2 and 30 N 2 . What we are reporting now for oxic, permeable sediments is distinct. Here we added 15 NH 4 + that we know was oxidised to produce 15 NO 3 and 15  in the porewater ( 15 NO x -, new Fig. 1b), however, that 15 NO x appears isolated from the pool of 15 N (whatever it may be) being used to make 15 N 2 gas i.e. there is more than one pool; one measurable in the porewater and one cryptic at the point of "denitrification" (or whatever the process is that produces N 2 gas).
Line 142. Why do you think this is counterintuitively? Ammonia is not directly the substrate for N2 production. Any effect ammonia oxidation has, will be mirrored in the enrichment of nitrite or nitrate. In natural abundance studies, this might be different, as fractionation plays a larger role and any nitrite measured will only be the 'left-over' and not the real pool seen by the microbes. If the coupling is very tight or N2 is produced in nitrifier denitrification, the correlation between the measured nitrite pool and the enrichment of N2 produced will also be minor.
If we add 15 NO 3 to a sediment with a DNRA potential that reduces 15 NO 3 to 15  Line 228. Also same ratio of air to slurry? They were shaken, correct?
Yes, the same ratios were used throughout all of the incubations described and yes they were all mixed by gentle rotation. See lines 236 and 244.
Line 239. As far as I understand, you measured in the normal background of 80% N2 in the overhead. How did this work?
Do you mean how do we detect 15 N atom % enrichment in N 2 above natural abundance? The mass-spec that we use for this work has a sensitivity of about 0.1‰ N which, in the dimensions described here, translates to ~0.08 nmol 29 N 2 g -1 dry sed. In Fig. 1, total 15 N-N 2 had already accumulated to about 2 (± 0.3) nmol N g -1 dry sed after 1 hour which is easily in excess of the detection limit and we have done it similarly since Trimmer first started reporting anammox in estuarine sediments back in 2003 of 1-10 nmol N g -1 wet sediment h -1 (back then). Admittedly, the mass spec is less sensitive to 30 N 2 , so to calculate the ratios we only use the data >1<10h when 30 N 2 is typically above 0.1 nmol N g -1 dry sed. There are those who advocate degassing water with He first to lower the background for more sensitive work in OMZ waters but that is not the case here -but even that is tricky because you need to make sure you lower the N 2 to same concentration in each vial.
Line 292. Looks like it is up to maybe 11 h.
Thanks for pointing this out. The last time point with data before the plateau is actually 9h, so we have recalculated the ratios for the data >0<10. The simple overall average rates of production in Fig. 1a and Table 1 are for the overall 12 hours.