Isotopic overprinting of nitrification on denitrification as a ubiquitous and unifying feature of environmental nitrogen cycling

Significance

Stable isotopes of nitrate have long provided a tool for tracking environmental sources and biological transformations. However, divergent interpretations of fundamental nitrate isotope systematics exist among disciplinary divisions. In an effort to transcend disciplinary boundaries of terrestrial and marine biogeochemistry, we use a quantitative model for coupled nitrogen and oxygen isotopes of nitrate founded on benchmarks established from microbial cultures, to reconcile decades of nitrate isotopic measurements in freshwater and seawater and move toward a unified understanding of cycling processes and isotope systematics. Our findings indicate that denitrification operates within the pervasive context of nitrite reoxidation mechanisms, specifically highlighting the relative importance of nitrification in marine denitrifying systems and anammox in groundwater aquifers.

Abstract

Natural abundance nitrogen and oxygen isotopes of nitrate (δ¹⁵N_NO3 and δ¹⁸O_NO3) provide an important tool for evaluating sources and transformations of natural and contaminant nitrate (NO₃⁻) in the environment. Nevertheless, conventional interpretations of NO₃⁻ isotope distributions appear at odds with patterns emerging from studies of nitrifying and denitrifying bacterial cultures. To resolve this conundrum, we present results from a numerical model of NO₃⁻ isotope dynamics, demonstrating that deviations in δ¹⁸O_NO3 vs. δ¹⁵N_NO3 from a trajectory of 1 expected for denitrification are explained by isotopic over-printing from coincident NO₃⁻ production by nitrification and/or anammox. The analysis highlights two driving parameters: (i) the δ¹⁸O of ambient water and (ii) the relative flux of NO₃⁻ production under net denitrifying conditions, whether catalyzed aerobically or anaerobically. In agreement with existing analyses, dual isotopic trajectories >1, characteristic of marine denitrifying systems, arise predominantly under elevated rates of NO₂⁻ reoxidation relative to NO₃⁻ reduction (>50%) and in association with the elevated δ¹⁸O of seawater. This result specifically implicates aerobic nitrification as the dominant NO₃⁻ producing term in marine denitrifying systems, as stoichiometric constraints indicate anammox-based NO₃⁻ production cannot account for trajectories >1. In contrast, trajectories <1 comprise the majority of model solutions, with those representative of aquifer conditions requiring lower NO₂⁻ reoxidation fluxes (<15%) and the influence of the lower δ¹⁸O of freshwater. Accordingly, we suggest that widely observed δ¹⁸O_NO3 vs. δ¹⁵N_NO3 trends in freshwater systems (<1) must result from concurrent NO₃⁻ production by anammox in anoxic aquifers, a process that has been largely overlooked.

The advent of the Haber–Bosch process late in the 19th century initiated an unprecedented increase in anthropogenic loading of reactive nitrogen (N) to the biosphere, setting into motion cascades of environmental impacts, including eutrophication and hypoxia, ecosystem acidification, and loss of biodiversity (1). This intensification of environmental N release from agricultural and industrial activities, power generation, municipal and septic wastewater, and domestic fertilizer has tremendously altered the global N cycle, effectively doubling annual global N turnover (1). In groundwater, the most common nitrogenous contaminant is nitrate (NO₃⁻), with recognized and long-term effects on both human and ecological health. Thus, control and elimination of NO₃⁻ contamination are priorities of environmental and health agencies worldwide. Despite its significance to global health and ecosystem function, identifying sources of NO₃⁻, tracing its dispersal and attenuation, and gauging its ecological impact remain challenging.

Mitigation of NO₃⁻ pollution has necessitated identification of its sources and hydrologic flow paths to monitor the fate and natural attenuation processes occurring in pollutant plumes. To this end, the natural abundance stable isotope ratios of nitrogen (¹⁵N/¹⁴N) and oxygen (¹⁸O/¹⁶O) in NO₃⁻ have provided an invaluable tool to differentiate sources, track their distribution, and determine the biogeochemical transformations acting on NO₃⁻. By convention, isotope ratios are reported using δ notation, where δ¹⁵N = ([¹⁵N/¹⁴N]_sample/[¹⁵N/¹⁴N]_air − 1) × 1,000 and δ¹⁸O = ([¹⁸O/¹⁶O]_sample/[¹⁸O/¹⁶O]_VSMOW − 1) × 1,000, in units of per mille (‰). Given two isotopic tracers for a single compound, this approach can be powerful, as each isotope system provides complementary information on sources and biogeochemical transformations (2). Accurate interpretation of isotope distributions, however, strongly hinges on knowledge of the isotope composition of source terms and on a rigorous understanding of isotopic discrimination associated with biological transformations of N pools. The isotopic discrimination associated with specific N transformations is quantified by the isotope effect, ε, where ε (‰) = [(^lightk/^heavyk) − 1] × 1,000, and k refers to the respective specific reaction rate constants of light and heavy isotopologues (3). Although many of the important source terms and isotope effects of the N cycle are constrained, some remain equivocal. In particular, recent observations emerging from bacterial and archaeal cultures and from incubations of environmental samples have uncovered isotopic discrimination trends for NO₃⁻ isotopes that appear at odds with trends typically ascribed to analogous biological transformations in soils and aquifers (4–14). This development has led to conflicting environmental interpretations, reflecting a lack of consensus on fundamental isotope systematics of the processes driving the N cycle. Importantly, the discrepancies between isotopic trends in environmental systems and those from culture-based observations raise the possibility that biogeochemical N dynamics inferred from environmental NO₃⁻ isotopic measurements reflect more complexity than previously realized.

Conventional interpretation schemes for NO₃⁻ isotopes differ from culture observations with regard to the isotope systematic of denitrification, the stepwise reduction of NO₃⁻ to NO₂⁻ (nitrite), nitric oxide, nitrous oxide, and finally N₂ by heterotrophic bacteria, which is the dominant loss term of reactive N from the biosphere. Early studies of NO₃⁻ isotope dynamics in groundwater documented parallel enrichment of δ¹⁵N and δ¹⁸O of NO₃⁻ in association with NO₃⁻ attenuation from denitrification, approximating a linear trajectory with a slope 0.5–0.8 (15–17). Indeed, this salient trend has long been considered a unique diagnostic signal of denitrification (2). However, following the advent of the denitrifier method (18, 19), measurements in cultures of both freshwater and marine denitrifying bacteria revealed dual isotope enrichments associated with assimilatory and dissimilatory NO₃⁻ consumption systematically following linear trajectories of ∼1 (9, 10, 12, 19, 20), contrasting with the lower values widely observed in freshwater systems. This invariant coupling of N and O isotopic enrichments has been shown to originate from fractionation during enzymatic bond-breakage (8, 21, 22), confirmed directly from in vitro enzyme studies of eukaryotic assimilatory and prokaryotic dissimilatory NO₃⁻ reductases (11, 23).

Interpretation schemes conventionally ascribed to nitrification are also at odds with isotope systematics uncovered in culture observations. Nitrification refers to the sequential oxidation of ammonia (NH₃) to NO₂⁻ then NO₃⁻ by chemoautotrophic bacteria and archaea, coupled to aerobic respiration. Oxidation of NO₂⁻ to NO₃⁻ also occurs during the anaerobic oxidation of NH₃ to N₂ by anammox bacteria (24). Nitrification constitutes the sole biological production term for NO₃⁻. The NO₃⁻ δ¹⁸O values reportedly produced by nitrification in freshwater lakes and aquifers span a contended range of 30‰, from −15‰ to 15‰ (2, 25), attributed to the origin of the oxygen atoms appended to NH₃ during the two-step process of nitrification: the biological oxidation of NH₃ to NO₂⁻ incorporates one oxygen atom from molecular O₂ and one from water (7, 26, 27); the subsequent oxidation of NO₂⁻ to NO₃⁻ incorporates an O atom derived from water (28). Recent work, however, has revealed kinetic isotope effects associated with enzymatic incorporation of each of the three O atoms into the product NO₃⁻ (5, 6), as well an inverse kinetic isotope effect on the reactant NO₂⁻ during oxidation to NO₃⁻ (4) and the isotopic equilibration of O atoms between NO₂⁻ and water (29, 30). These isotope effects have traditionally not been considered in interpreting NO₃⁻ isotope distributions, yet play a fundamental role in defining the isotopic composition of nitrified NO₃⁻ in tandem with compositional differences of the O atom sources (7, 13, 31). Thus, moving beyond early studies in which the δ¹⁸O_NO3 from nitrification was interpreted as a three-part mixture of O atom sources, it is clear that consideration of several isotope fractionation processes is required for accurate interpretation of sources and cycling mechanisms.

To date, observations in marine systems have revealed linear trajectories of ∼1 and trajectories distinctly above the nominal value of 1 associated with water–column denitrification (32–37). Positive deviations from 1 are generally interpreted as reflecting the isotopic imprints of biological NO₂⁻ reoxidation superimposed on the trajectory of biological NO₃⁻ consumption (34, 38). In freshwater studies, however, this discrepancy between cultures and environment has been scantly acknowledged. Notably, some workers have put forth a number of postulates to explain this conundrum, detailed in S1. Postulates to Explain Deviations from 1 in ∆δ¹⁸O:∆δ¹⁵N Trajectories in Freshwater. Among these, the biological production of NO₃⁻ by nitrifiers occurring in tandem with denitrification has been proposed to account for the apparent differences in δ¹⁸O vs. δ¹⁵N trajectories between cultures and freshwater environments (39, 40), although this tenet has not been examined specifically. The potential for analogous biogeochemical dynamics to affect isotope distributions in freshwater and marine systems clearly merits exploring.

To arrive at a shared understanding of environmental NO₃⁻ isotope systematics, we present the results of a multiprocess numerical model of dual NO₃⁻ isotope dynamics parameterized on the basis of fundamental features revealed from culture studies. From this improved understanding of isotopic fractionation during redox cycling of N, we explore implications for NO₃⁻ production – by NO₂⁻ oxidizing bacteria and by anammox—occurring concurrently with denitrification, specifically focusing on resulting NO₃⁻ N and O isotope trajectories. We use this framework to evaluate the potential extent of processes other than unidirectional NO₃⁻ consumption by denitrification, which may harbor the key for resolving the discrepancy between decades of groundwater NO₃⁻ observations and our physiological understanding of the isotope systematics of microbial N cycling. The scenarios explored herein call attention to the potential influence of N cycling dynamics that have been largely overlooked in aquatic environments and provide a unified framework for future investigations of N isotope biogeochemistry.

2. A Multiprocess Model of NO₃⁻ Dual Isotopes: Rationale and Assumptions

To evaluate the impact of nitrite reoxidation on coupled NO₃⁻ N and O isotope trajectories, termed ∆δ¹⁸O:∆δ¹⁵N henceforth, we devised a time-dependent one-box model simulating the evolution of N and O isotopologue pools of NO₃⁻ and NO₂⁻ in a closed system during denitrification coincident with aerobic and anaerobic NO₂⁻ oxidation by nitrifiers or by anammox bacteria, respectively (Fig. 1; terms defined in Table 1). The isotopologue-specific formulation of the model is described in S2. Equations Used in Time-Dependent NO₃⁻ Isotope 1 Box Model.

Fig. 1.

Box model architecture showing N transformations and associated isotope effects influencing (A) δ¹⁵N_NO3 and (B) δ¹⁸O_NO3. See text and Table 1 for details and references.

Table 1.

Ranges of parameter values explored in the finite-differencing model exercise, including values prescribed in “standard” model parameterizations

Initial conditions	Description	Range	Standard	Comment	Reference
[NO3−]initial	Initial [NO3−]	100 µmol/L	100 µmol/L
[NO3−]initial	Initial [NO2−]	0 µmol/L	0 µmol/L
δ15NNO3,initial	Initial δ15NNO3	−10‰ to +15‰	+5‰
δ18ONO3,initial	Initial δ18ONO3	−10‰ to +15‰	+5‰
δ15NNH4,initial	Initial δ15NNH4	−20‰ to +15‰	+5‰
δ18OH2O	δ18O of ambient H2O	−20‰ to 0‰
15εnar	N isotope effect for NO3− reduction	+5‰ to +25‰	+15‰	Coupled to 18εnar	(9)
18εnar	O isotope effect for NO3− reduction	+5‰ to +25‰	+15‰	Coupled to 15εnar	(9)
18εnarBR	Branching O isotope effect for NO3− reduction	25‰	25‰		(19)
15εnir	N isotope effect for NO2− reduction	0‰ to +20‰	+5‰	Coupled to 18εnir	(19, 64)
18εnir	O isotope effect for NO2− reduction	0‰ to +20‰	5‰	Coupled to 15εnir
15εnxr	N isotope effect for NO2− oxidation by nitrifiers	−35 to 0‰	−15‰		(4)
18εnxrNO2	O isotope effect for NO2− oxidation by nitrifiers or anammox	−7‰ to −3‰	−4‰		(5)
15εnxrAMX	N isotope effect for NO2− oxidation by anammox	−35‰			(43)
15εnxrAMX’	NXR-enabled equilibrium isotope effect between NO2− and NO3−	−61‰			(43)
18εnxrH2O	O isotope effect to H2O incorporation by nitrifiers and anammox	+12‰ to +18‰	+14‰		(5)
18εeq	Equilibrium isotope effect between NO2− and H2O	13.5‰	13.5‰		(30)
15εamo	N isotope effect for NH3 oxidation by aerobic ammonia oxidation	+26‰*	26‰*		(41)
18εamoH2O	O isotope effect for H2O incorporation by aerobic ammonia oxidation	+18‰ to +38‰†	14‰		(6)
18εamoO2	O isotope effect for O2 incorporation by aerobic ammonia oxidation	+18‰ to +38‰†	14‰		(6)
NXR/NAR	Ratio of NO2− oxidation by nitrifiers to NO3− reduction by denitrifiers	0–0.9	0.5
AMO/NAR	Ratio of NO2− production by aerobic ammonia oxidation vs. by NO3− reduction	0–0.9	0

^*Not expressed given prescription of complete consumption of the ammonium pool.

^†The isotope effects of O atom incorporation from O₂ and H₂O during NH₃ oxidation to NO₂⁻ have only been determined as a ‘combined’ isotope effect ranging between +18‰ and +38‰ at this time (7). A value of 28‰ was chosen and equally partitioned (+14‰) between the H₂O and O₂ pools.

In brief, the simulated NO₃⁻ pool is influenced by the dissimilative reduction of NO₃⁻ to NO₂⁻ (NAR) and the concurrent production of NO₃⁻ by NO₂⁻ oxidation (NXR; Fig. 1). The NO₂⁻ pool, in turn, reflects the balance of production by NAR and NH₄⁺ oxidation (AMO), as well as oxidation by NXR and reduction to nitric oxide (NIR). Both reductive processes, NAR and NIR, impart normal N isotope effects, ¹⁵ε_nar and ¹⁵ε_nir, which are equivalent to their corresponding O isotope effects, ¹⁸ε_nar and ¹⁸ε_nir (9, 34). During NAR, a branching isotope effect from O atom abstraction, ¹⁸ε_narBR (19, 29), also contributes to the δ¹⁸O of the NO₂⁻ product. In turn, NXR is characterized by inverse kinetic isotope effects for NO₂⁻ consumption, ¹⁵ε_nxr and ¹⁸ε_nxr (4, 5), and a normal isotope effect for O atom incorporation from water, ¹⁸ε_nxr,H2O (5). AMO also has normal isotope effects for N, ¹⁵ε_amo (3, 41), and for O atom incorporation from H₂O and molecular O₂, ¹⁸ε_amo,H2O and ¹⁸ε_amo,O2, respectively (6). However, we assume no accumulation of ammonium (NH₄⁺) from the remineralization of organic material, such that there is no expression of the N isotope fractionation associated with AMO (¹⁵ε_amo), and the NO₂⁻ produced by AMO adopts the δ¹⁵N of ammonium (δ¹⁵N_NH4). Finally, NO₂⁻ is subject to O isotope equilibration with water having an associated isotope effect, ¹⁸ε_eq (29, 30).

We further consider the potential role of anaerobic NH₃ oxidation (anammox), which stoichiometrically produces ∼0.26 moles of NO₃⁻ per mole of NH₃ oxidized (or per 1.3 moles of NO₂⁻ reduced) as a metabolic product from the NO₂⁻ pool (24, 42). The model functions as described, except that anammox operates (Fig. 1, blue line) in lieu of aerobic nitrification (Fig. 1, red lines). Notably, unlike in AMO, the δ¹⁵N of the NH₄⁺ pool does not enter into the NO₃⁻ mass balance during anammox. Similarly, the δ¹⁸O of NO₃⁻ is not indirectly influenced by NO₂⁻ production from NH₃, which only occurs aerobically. NO₂⁻ oxidation by anammox is prescribed an inverse N isotope effect, ¹⁵ε_nxrAMX (Table 1) (43). Given no constraint from culture work the corresponding O isotope effect, ¹⁸ε_nxrNO2AMX, it is assumed to be of similar magnitude to that for NO₂⁻ oxidizers (Table 1). Model parameter ranges are listed in Table 1 and justified in Section 6. For brevity, we also established “standard” model conditions having generally midrange values for isotope effects (Table 1).

3. Model Results

We discuss the contribution of distinct aspects of the reaction network, highlighting those features exerting the most influence on the isotope composition of the evolving NO₃⁻ pool, namely, the isotope composition of ambient water and the NO₂⁻ oxidation flux. We further explore features that exert moderate influence on coupled NO₃⁻ N and O isotope trajectories, including isotope effect values, the isotope composition of initial pools, and NO₂⁻ production via biological ammonia oxidation. We then consider scenarios specific to NO₃⁻ production by anammox and finally examine the isotope composition of NO₂⁻ that emerges among model scenarios. Model results are compared with environmental observations in Section 4.

3.1. Influence of δ¹⁸O_H2O.

Initial tests were parameterized using standard conditions (Table 1) to explore the sensitivity of the ∆δ¹⁸O:∆δ¹⁵N trajectory to the δ¹⁸O of ambient water (from −20‰ to 0‰), for a range of relative fluxes of NO₂⁻ oxidation (NXR/NAR from 0 to 0.9) and contrasting scenarios of NO₂⁻ equilibration with water. For simplicity, we predominantly consider the case of full equilibration of NO₂⁻ oxygen isotopes with water, which likely characterizes most freshwater systems, where equilibration is probably rapid relative to biological cycling given the generally low pH (13, 14, 29, 30, 44). In marine denitrifying regions, δ¹⁸O_NO2 measurements also suggest full isotopic equilibration with water (34, 35), despite the higher pH of seawater (≤8.2). Results for simulations without NO₂⁻ isotope equilibration are otherwise presented in the supplements (S3. Simulation Without Isotope Equilibration of NO₂⁻ with Water and Fig. S1).

Fig. S1.

Predicted evolution of NO₃⁻ ∆δ¹⁸O_NO3 (δ¹⁸O_NO3 – δ¹⁸O_NO3,initial) plotted on the corresponding ∆δ¹⁵N_NO3 (δ¹⁵N_NO3 – δ¹⁵N_NO3,initial) associated with net denitrification coincident with NO₃⁻ production by nitrification. Simulations derive from standard model conditions (Table 1) for incremental prescriptions of NXR/NAR (A–C) and of δ¹⁸O_H2O (colors), without oxygen isotopic equilibration of NO₂⁻ with water.

Foremost, results reveal that the evolution of the ∆δ¹⁸O:∆δ¹⁵N trajectory during net denitrification can be substantially deflected from a value of 1 by a co-occurring contribution of newly nitrified NO₃⁻ (Fig. 2). Resulting ∆δ¹⁸O:∆δ¹⁵N trajectories correspond to a broad range of solutions, from 0.1 to 3.2 (in terms of linear fits relating the dual isotopic composition of initial NO₃⁻ to that of any evolved modeled composition), of which a larger share yields slopes below the canonical value of 1.

Fig. 2.

Predicted evolution of NO₃⁻ ∆δ¹⁸O_NO3 (δ¹⁸O_NO3 – δ¹⁸O_NO3,initial) plotted on the corresponding ∆δ¹⁵N_NO3 (δ¹⁵N_NO3 – δ¹⁵N_NO3,initial) associated with net denitrification coincident with NO₃⁻ production by nitrification. Simulations derive from standard model conditions (Table 1) for incremental prescriptions of NXR/NAR (A–C) and of δ¹⁸O_H2O (colors), for full oxygen isotopic equilibration of NO₂⁻ with water.

In all cases, the water δ¹⁸O emerges as a strong determinant of the ∆δ¹⁸O:∆δ¹⁵N trajectory: the lowest trajectories are associated with the lowest δ¹⁸O_H2O and the highest trajectories with the highest δ¹⁸O_H2O (Fig. 2). Mechanistically, the δ¹⁸O of nitrified NO₃⁻ is directly related to the water δ¹⁸O_H2O through both O isotope equilibration of intermediate NO₂⁻ and the incorporation of an O atom from water during NO₂⁻ oxidation. Under conditions of full isotopic equilibration of NO₂⁻, ∆δ¹⁸O:∆δ¹⁵N trajectories are thereby insensitive to incorporation of O atoms from water or O₂ during any oxidation of NH₃ to NO₂⁻. The ∆δ¹⁸O:∆δ¹⁵N trajectories below 1 are associated with relatively lower δ¹⁸O_H2O values that contribute to lower δ¹⁸O values for nitrified NO₃⁻ (Fig. S2). By comparison, the few model solutions in which ∆δ¹⁸O:∆δ¹⁵N trajectories are above 1 at standard conditions are associated with higher δ¹⁸O_H2O values, characteristic of marine systems. Conversely, lower δ¹⁸O_H2O values, characteristic of freshwater systems, are largely associated with ∆δ¹⁸O:∆δ¹⁵N trajectories below 1.

Fig. S2.

Predicted evolution of the δ¹⁸O vs. the δ¹⁵N of nitrified NO₃⁻ produced from the oxidation of NO₂⁻ concurrently with denitrification (Fig. 2). Simulations from standard model conditions (Table 1) for incremental prescriptions of NXR/NAR (right to left) and of δ¹⁸O_H2O (colors), and for full vs. negligible oxygen isotopic equilibration of NO₂⁻ with water (dotted vs. full color lines). The black line delineates the ∆δ¹⁸O:∆δ¹⁵N trajectory for denitrification given no addition of NO₃⁻ from nitrification (and/or anammox).

3.2. Importance of the NO₂⁻ Oxidation Flux.

Given its importance in linking the composition of water with that of the evolving NO₃⁻ pool, the extent to which NO₃⁻ is produced relative to that reduced (expressed as NXR/NAR) is also clearly an influential driver of ∆δ¹⁸O:∆δ¹⁵N trajectory. However, this flux is central not only because it governs the extent to which nitrified NO₃⁻ is added back to the NO₃⁻ pool, but also because it modulates the δ¹⁵N_NO3 returned to the NO₃⁻ pool. The influence of NXR/NAR on the ∆δ¹⁸O:∆δ¹⁵N trajectory can be summarized as follows (Fig. 2): when NO₂⁻ oxidation is nearly equal to NO₃⁻ reduction (NXR/NAR ≥ 0.8), the δ¹⁵N_NO3 produced by nitrification converges on that removed by denitrification (notwithstanding the contribution to the NO₂⁻ pool from AMO; S4. Impact of NO₃⁻ Production by AMO), thus nearly “restoring” the δ¹⁵N of the NO₃⁻ pool to its original value. In turn, the δ¹⁸O of nitrified NO₃⁻ is insensitive to NXR/NAR, deriving primarily from the δ¹⁸O_H2O when NO₂⁻ is fully equilibrated, such that it can be either higher or lower than the δ¹⁸O_NO3 removed by denitrification depending on the δ¹⁸O_H2O. Thus, the largest excursions in ∆δ¹⁸O:∆δ¹⁵N trajectories, both above and below 1, occur at the higher values of NXR/NAR. In this respect, trajectories above 1, characteristic of marine denitrifying systems, congruently arise at elevated δ¹⁸O_H2O.

When NXR/NAR ratios are low (Fig. 2A), the transient NO₂⁻ pool is mostly reduced to NO rather than oxidized to NO₃⁻, rendering the δ¹⁵N of the NO₂⁻ pool relatively more ¹⁵N-enriched due to isotopic discrimination by ¹⁵ε_nir. The NO₃⁻ produced from the oxidation of NO₂⁻ is further ¹⁵N-enriched by the inverse effects of ¹⁵ε_nxr. Therefore, the δ¹⁵N of nitrified NO₃⁻ will be greater than that removed by denitrification, driving the ∆δ¹⁸O:∆δ¹⁵N trajectories to values below 1. The corresponding δ¹⁸O of nitrified NO₃⁻ (again insensitive to the prescribed NXR/NAR ratio due to full isotopic equilibration of NO₂⁻; Fig. S2) either counters or otherwise augments the negative offset in ∆δ¹⁸O:∆δ¹⁵N from 1 imposed by the δ¹⁵N_NO3 of nitrified NO₃⁻ depending on the δ¹⁸O of this nitrified NO₃⁻ (and thus, the δ¹⁸O of water). Regardless, all ∆δ¹⁸O:∆δ¹⁵N trajectories remain below 1 at low NXR/NAR ratios (Fig. S3), even for δ¹⁸O_H2O values characteristic of seawater.

Fig. S3.

Predicted NO₃⁻ ∆δ¹⁸O_NO3 (δ¹⁸O_NO3 – δ¹⁸O_NO3,initial) plotted on the corresponding ∆δ¹⁵N_NO3 (δ¹⁵N_NO3 – δ¹⁵N_NO3,initial) associated with net denitrification and concurrent NO₃⁻ production by nitrification in relation to (A) ¹⁵ε_nar (all solutions), (B) ¹⁵ε_nar, (C) NXR/NAR, (D) ¹⁵ε_nir, (E) ¹⁵ε_nxr, and (F) δ¹⁵N_NO2-NO3. Gray points indicate invalid ¹⁵ε_dnf solutions that exceed 30‰, where ¹⁵ε_dnf is derived from the change in δ¹⁵N_NO3 vs. the fraction of NO₃⁻ remaining. Discrete simulations derive from randomized sets of boundary conditions encompassing the parameter ranges in Table 1 where δ¹⁸O_H2O = −10‰ and NO₂⁻ is fully equilibrated with water.

3.3. Influence of N and O Isotope Effects.

To investigate the leverage of specific isotope effects on the evolving ∆δ¹⁸O:∆δ¹⁵N trajectories, we examine the response of NO₃⁻ trajectories while holding all other parameters constant (standard conditions; Table 1), plotting them against δ¹⁸O_H2O as a master variable (Fig. 3), given its central role in the composition of nitrified NO₃⁻ as described above.

Fig. 3.

Predicted NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trajectories (represented as the apparent linear slope calculated with respect to the initial NO₃⁻ isotope composition; color scale) associated with net denitrification and coincident NO₃⁻ production for a range of δ¹⁸O_H2O given full oxygen isotopic equilibration of NO₂⁻, plotted over (A) ¹⁵ε_nar, (B) ¹⁵ε_nir, (C) ¹⁵ε_nxr, and (D) δ¹⁵N_NO3,initial. Trajectories plotted over ¹⁵ε_nar for NO₃⁻ production by anammox only for (E) 30% of total N₂ production by anammox and for (F) 50% N₂ production by anammox, with ¹⁵ε_nirAMX = 20‰, and ¹⁵ε_nxrAMX = −35‰. Parameter values are otherwise anchored at standard conditions (Table 1).

Results indicate that the ∆δ¹⁸O:∆δ¹⁵N trajectory increases progressively with increasing ¹⁵ε_nar, the N isotope effect of nitrate reduction (Fig. 3A). This dynamic is best understood by considering the influence of ¹⁵ε_nar on the composition of the transient NO₂⁻ pool subject to reoxidation to NO₃⁻. The δ¹⁵N_NO2 returned to the NO₃⁻ pool by nitrification is more ¹⁵N-depleted at higher ¹⁵ε_nar values, tending to more elevated ∆δ¹⁸O:∆δ¹⁵N trajectories. However, although trajectories above 1 emerge more readily at higher prescribed ¹⁵ε_nar, the majority of these solutions are not viable, resulting in observed (or apparent) isotope effects for denitrification (¹⁵ε_dnf, derived from the change in δ¹⁵N_NO3 relative to the fraction of NO₃⁻ removed) substantially higher than the empirical maximum of ∼30‰ observed in the environment (Fig. S3). This dynamic arises because the N isotope effects for NO₂⁻ reduction (¹⁵ε_nir), NO₂⁻ oxidation (¹⁵ε_nxr), and the NXR/NAR flux ratio amplify the ¹⁵N-enrichment of the NO₃⁻ pool relative to its consumption beyond that imparted specifically by ¹⁵ε_nar, thus increasing apparent values of ¹⁵ε_dnf. Thus, viable solutions (i.e., ¹⁵ε_dnf ≤ 30‰) for ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 emerge predominantly at ¹⁵ε_nar amplitudes of ≤15‰. Conversely, viable solutions stemming from more elevated ¹⁵ε_nar amplitudes are only produced at relatively low NO₃⁻ production (NXR/NAR), corresponding to ∆δ¹⁸O:∆δ¹⁵N trajectories close to 1. Therefore, ∆δ¹⁸O:∆δ¹⁵N trajectories above 1, characteristic of marine denitrifying systems, and of ∼0.6 for freshwater systems, do not result at high ¹⁵ε_nar values, suggesting that the organism-level isotope effect for denitrification (¹⁵ε_nar) in environmental settings is generally not as high as the ¹⁵ε_nar of ∼25‰ often observed in culture conditions (10) (Section 4).

The amplitude of ¹⁵ε_nir for the reduction of NO₂⁻ also modulates the isotopic evolution of the NO₃⁻, with higher ¹⁵ε_nir (coupled here to ¹⁸ε_nir) corresponding to lower ∆δ¹⁸O:∆δ¹⁵N trajectories (Fig. 3B). Stronger ¹⁵N discrimination during NO₂⁻ reduction to NO acts to increase the δ¹⁵N of the NO₂⁻ pool, thereby increasing the δ¹⁵N of NO₃⁻ produced from any oxidation of NO₂⁻ and lowering the ∆δ¹⁸O:∆δ¹⁵N trajectory (Fig. S3).

The amplitude of the inverse isotope effect prescribed to ¹⁵ε_nxr also has an important influence on the δ¹⁵N_NO3 of newly nitrified NO₃⁻. Lower ¹⁵ε_nxr values (i.e., more negative) give rise to lower δ¹⁵N_NO2, countered by production of correspondingly higher δ¹⁵N_NO3, thereby acting to lower the ∆δ¹⁸O:∆δ¹⁵N trajectory (Fig. 3C). Conversely, less negative ¹⁵ε_nxr amplitudes produce NO₃⁻ having a relatively lower δ¹⁵N, leading to higher ∆δ¹⁸O:∆δ¹⁵N trajectories.

In the model, ¹⁸ε_nar is, by design, equivalent to the corresponding ¹⁵ε_nar. As such, its influence on ∆δ¹⁸O:∆δ¹⁵N trajectories appears identical to ¹⁵ε_nar (Fig. S4A). This congruence, however, is only incidental because the δ¹⁸O_NO2 produced from NO₃⁻ reduction is entirely erased given full isotopic equilibration of NO₂⁻ with water. Therefore, ¹⁸ε_nar actually has no bearing on the δ¹⁸O of newly nitrified NO₃⁻. Similarly, the oxygen isotope effect for NO₂⁻ reduction, ¹⁸ε_nir, also has an apparent influence on the NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trajectory related to its coupling with the corresponding ¹⁵ε_nir (Fig. S4C). Here again, however, any increase in the δ¹⁸O_NO2 imposed by its reduction to NO is ultimately erased due to isotopic equilibration of the NO₂⁻ with water, such that the value of ¹⁸ε_nir is inconsequential to the ∆δ¹⁸O:∆δ¹⁵N trajectory.

Fig. S4.

Predicted NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trajectories (color scale) associated with net denitrification and coincident NO₃⁻ production for a range of δ¹⁸O_H2O plotted over (A and B) ¹⁸ε_nar, (C and D) ¹⁸ε_nir, and (E and F) ¹⁸ε_nxrNO2. Simulations include full oxygen isotopic equilibration of NO₂⁻ with water (Left) or no oxygen isotopic equilibration of NO₂⁻ (Right) at standard conditions (Table 1).

In contrast, the amplitude of ¹⁸ε_nxrNO2 does affect the ∆δ¹⁸O:∆δ¹⁵N trajectory because the influence of ¹⁸ε_nxrNO2 occurs downstream of NO₂⁻ equilibration. Given this inverse isotope effect, lower (more negative) values of ¹⁸ε_nxrNO2 are associated with an increase in the δ¹⁸O of newly nitrified NO₃⁻, and consequently, a relative increase in corresponding ∆δ¹⁸O:∆δ¹⁵N trajectories (Fig. S4E). However, the influence of ¹⁸ε_nxrNO2 on ∆δ¹⁸O:∆δ¹⁵N trajectories is generally muted because ¹⁸ε_nxrNO2 only affects two-thirds of the O atoms in the newly nitrified NO₃⁻ and because the corresponding ¹⁵ε_nxr has a greater amplitude than ¹⁸ε_nxrNO2 (Table 1) but opposing influence on ∆δ¹⁸O:∆δ¹⁵N trajectories.

Finally, the isotope effect associated with the incorporation of an O atom from water during NO₂⁻ oxidation, ¹⁸ε_nxrH2O, also plays a role in determining the δ¹⁸O of nitrified NO₃⁻. As prescribed, the δ¹⁸O of the O atom incorporated from water during NO₂⁻ oxidation is ∼14‰ lower than that of ambient water, thus contributing a lower δ¹⁸O than that from the two oxygen atoms in NO₂⁻. Because the amplitude of ¹⁸ε_nxrH2O has so far proven to be relatively invariant among cultures and experimental strains (5, 7), we do not consider variations of this value on ∆δ¹⁸O:∆δ¹⁵N trajectories.

3.4. Initial Isotope Composition of the NO₃⁻ Pool.

The initial isotopic composition of NO₃⁻ is also linked to the evolution of its dual isotopic trajectory during net consumption coupled with contemporaneous production. Under conditions of a fully equilibrated NO₂⁻ pool, this dependence stems chiefly from the difference between the δ¹⁸O_NO3 and the δ¹⁸O_H2O. Mechanistically, the difference in δ¹⁸O values between NO₃⁻ and water imposes a corresponding difference between the δ¹⁸O_NO3 removed by NO₃⁻ reduction and the δ¹⁸O_NO3 returned to the NO₃⁻ pool by NO₂⁻ oxidation, in relation to the δ¹⁵N_NO3 concurrently being removed and returned.

For nearly all combinations of model conditions, the δ¹⁵N_NO3 added by nitrification is greater than that removed concurrently by denitrification, owing to the compounding influences of isotope effects associated with NO₂⁻ reduction (normal) and oxidation (inverse), ¹⁵ε_nir and ¹⁵ε_nxr. On its own, the higher δ¹⁵N of nitrified NO₃⁻ thus tends to lower the ∆δ¹⁸O:∆δ¹⁵N trajectory from a value of 1 for most model conditions.

The δ¹⁸O_NO3 produced by nitrification either counters or otherwise amplifies the negative deviations from a ∆δ¹⁸O:∆δ¹⁵N trajectory of 1 imposed by the corresponding δ¹⁵N_NO3. When the initial δ¹⁸O_NO3 is nearer to the δ¹⁸O_H2O, the δ¹⁸O_NO3 produced during nitrification is higher than that removed by denitrification, such that the ∆δ¹⁸O:∆δ¹⁵N trajectory increases (Fig. 3D). Conversely, when the initial δ¹⁸O_NO3 is elevated relative to the δ¹⁸O_H2O, denitrification removes a δ¹⁸O_NO3 that is similar to, or greater than, that added by nitrification, contributing further to a decrease in ∆δ¹⁸O:∆δ¹⁵N trajectory from a value of 1 imposed by corresponding δ¹⁵N_NO3 dynamics.

The difference in δ¹⁸O between water and NO₃⁻ thus provides a first order rule of thumb to explain the magnitude of the ∆δ¹⁸O:∆δ¹⁵N trajectory. For instance, in marine systems, the difference between the δ¹⁸O of subsurface NO₃⁻ (≥2‰) and seawater (∼0‰) is small. At any value of ¹⁸ε_nar, the δ¹⁸O of nitrified NO₃⁻ is greater than the δ¹⁸O_NO3 removed by denitrification, thus generating ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 for numerous model conditions (Fig. 3D and Fig. S5). In contrast, in freshwater systems, the difference between the δ¹⁸O of NO₃⁻ and water can be large (e.g., δ¹⁸O_NO3 of +20‰ and δ¹⁸O_H2O of −10‰ would not be unusual), such that the δ¹⁸O of nitrified NO₃⁻ tends to be similar to, or can be lower than, the δ¹⁸O_NO3 removed by denitrification, promoting ∆δ¹⁸O:∆δ¹⁵N trajectories below 1 under most conditions (Fig. 3D and Fig. S5). In this light, ∆δ¹⁸O:∆δ¹⁵N trajectories above a nominal value of 1 have an intrinsically greater likelihood of emerging in marine systems, whereas trajectories below 1 are more likely for freshwater systems.

Fig. S5.

Predicted NO₃⁻ ∆δ¹⁸O_NO3 (δ¹⁸O_NO3 – δ¹⁸O_NO3,initial) plotted on the corresponding ∆δ¹⁵N_NO3 (δ¹⁵N_NO3 – δ¹⁵N_NO3,initial) for δ¹⁸O_H2O = 0‰ vs. -10‰. Discrete simulations derive from randomized sets of boundary conditions for parameter ranges in Table 1, with full oxygen isotopic exchange of NO₂⁻, AMO/NXR = 0, δ¹⁵N_NO3,_initial = 5‰, and δ¹⁸O_NO3,_intial = 0‰, where ¹⁵ε_dnf ≤ 30‰ (¹⁵ε_dnf is derived from the change in δ¹⁵N_NO3 vs. the fraction of NO₃⁻ remaining).

3.5. Influence of NH₃ Oxidation to NO₂⁻.

As parameterized, the production of NO₂⁻ by AMO yields invalid ¹⁵ε_dnf values (>30‰) at elevated NO₂⁻ oxidation fluxes (NXR/NAR ratios ≥ 0.5) while exerting little influence on ∆δ¹⁸O:∆δ¹⁵N trajectories with lower NO₂⁻ oxidation (Fig. S6). For these reasons, we relegate detailed discussion of the impact of AMO to S4. Impact of NO₃⁻ Production by AMO.

Fig. S6.

(A) Predicted apparent isotope effect for denitrification, ¹⁵ε_dnf (color scale), as a function of the NO₂⁻ production by AMO (AMO/NAR) vs. NO₃⁻ production by NXR (NXR/NAR; Fig. 1). (B) Predicted NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trajectories (color scale) as a function of AMO/NAR vs. NXR/NAR. Parameter values are anchored at standard conditions (Table 1) and δ¹⁸O_H2O = 0‰. White region represents conditions under which predicted values of ¹⁵ε_dnf exceed an empirical maximum of 30‰.

3.6. NO₃⁻ Production by Anammox.

To assess whether NO₃⁻ production by anammox is potentially sufficient to induce departures of ∆δ¹⁸O:∆δ¹⁵N trajectories from a value of 1, we consider two scenarios, the first in which anammox rates are bounded by the organic matter remineralization stoichiometry of denitrification, and the second in which anammox rates contribute an equal proportion of the N₂ flux relative to denitrification (45). In the first scenario, anammox rates are controlled by NH₄⁺ supplied only from the decomposition of organic material coupled with NO₃⁻ respiration, wherein the release of 1 mol of NH₄⁺ from organic matter requires respiration of 5.9 mol of NO₃⁻ to N₂ (46). Each mole of NH₄⁺ then reacts with 1 mol NO₂⁻ (produced transiently by denitrification) to form N₂ (24, 42). Concurrently, an additional 0.3 mol NO₂⁻ is returned to the NO₃⁻ pool (42). Of the total N₂ produced, 30% originates from anammox and the rest from canonical denitrification. The oxidation of NO₂⁻ by anammox therein corresponds to a relatively small NXR/NAR flux ratio of 0.05.

The ∆δ¹⁸O:∆δ¹⁵N trajectories generated from these model conditions are consistently below 1, regardless of δ¹⁸O_H2O (Fig. 3E). In this respect, trajectories as low as 0.6, characteristic of freshwater system, are only attained with prescriptions of relatively low ¹⁵ε_nar of ≤5‰. Thus, within this scenario, anammox can only explain excursions in freshwater ∆δ¹⁸O:∆δ¹⁵N trajectories assuming specifically low values of ¹⁵ε_nar.

When the anammox rate is parameterized to account for 50% of N₂ production, the corresponding NXR/NAR flux ratio increases to ∼0.1 and ∆δ¹⁸O:∆δ¹⁵N trajectories are on the order of ∼0.6 for a relatively broader ranges of ¹⁵ε_nar amplitudes (Fig. 3F). Therefore, if anammox rates in freshwater systems are not strictly bounded by ammonification coupled to NO₃⁻ respiration—namely, if NH₄⁺ is also released via de-sorption from clays (47, 48) or from organic matter degradation pathways fueled by fermentation or other oxidants [e.g., Fe(III), Mn(III/IV)]—the production of NO₃⁻ by anammox could easily account for ∆δ¹⁸O:∆δ¹⁵N trajectories of 0.6 commonly observed in freshwater systems.

The amplitude of ¹⁵ε_nxrAMX is subject to some uncertainty. A recent study showed that enrichment cultures of anammox produced NO₃⁻ with a δ¹⁵N_NO3 ∼61‰ greater than corresponding δ¹⁵N_NO2 following initial resuspension of cells (interpreted as an “enzyme-catalyzed equilibrium isotope effect” between NO₃⁻ and NO₂⁻), after which NO₃⁻ production was associated with a ¹⁵ε_nxrAMX amplitude of −35‰ (43). Accordingly, if NO₃⁻ produced by anammox had a δ¹⁵N ∼61‰ greater than that of corresponding NO₂⁻, then an even smaller contribution of NO₃⁻ from anammox would be required to influence ∆δ¹⁸O:∆δ¹⁵N trajectories (Fig. S7). From any perspective, anammox clearly emerges as a compelling candidate to explain negative deviations from ∆δ¹⁸O:∆δ¹⁵N trajectories of 1 observed in freshwater systems.

Fig. S7.

Predicted evolution of NO₃⁻ ∆δ¹⁸O_NO3 (δ¹⁸O_NO3 – δ¹⁸O_NO3,initial) plotted on the corresponding ∆δ¹⁵N_NO3 (δ¹⁵N_NO3 – δ¹⁵N_NO3,initial) associated with net denitrification and coincident NO₃⁻ production by anammox. Simulations derive from standard model conditions (Table 1) for discrete contributions of anammox to total N₂ production (left vs. right panels), and incremental prescriptions of ¹⁵ε_nxrAMX (top to bottom panels) and δ¹⁸O_H2O (colors).

Notably, ∆δ¹⁸O:∆δ¹⁵N trajectories remain below 1 regardless of anammox rate or ¹⁵ε_nxrAMX values, owing to the relatively small NO₂⁻ oxidation flux permitted by anammox stoichiometry. By itself, anammox thus fails to reproduce ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 observed in marine systems. In our model, even if anammox accounts for 100% of N₂ production, the corresponding NXR/NAR ratio amounts to a mere 0.23, a value insufficient to generate ∆δ¹⁸O:∆δ¹⁵N trajectories akin to those observed in oxygen deficient zones, regardless of prescribed ¹⁵ε_nxrAMX amplitudes (Fig. S8). Thus a significant input of NO₃⁻ from aerobic NO₂⁻ oxidation (or NO₂⁻ oxidation coupled to other electron acceptors) is required to explain ∆δ¹⁸O:∆δ¹⁵N trajectories >1 in oceanic oxygen deficient zones (Section 4.1).

Fig. S8.

Predicted NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trajectories associated with net denitrification and coincident NO₃⁻ production by anammox plotted over % of total N₂ production by anammox for (A) δ¹⁸O_H2O = 0‰ and (B) δ¹⁸O_H2O = -10‰, in relation to ¹⁵ε_nar (colors). Discrete simulations derive from randomized sets of boundary conditions encompassing the parameter ranges in Table 1, with full oxygen isotopic exchange of NO₂⁻, ¹⁵ε_nirAMX = 20‰, and ¹⁵ε_nxrAMX = −35‰.

3.7. NO₂⁻ Isotope Dynamics.

Recent methodological advances enable the direct quantitation of NO₂⁻ δ¹⁵N and δ¹⁸O at environmental concentrations (49, 50), providing a complementary tracer from which to diagnose environmental N cycling. Under conditions examined here, the predicted δ¹⁵N of the NO₂⁻ pool ranges from 30‰ lower than the corresponding δ¹⁵N_NO3 (∆δ¹⁵N_NO2-NO3 = δ¹⁵N_NO2 − δ¹⁵N_NO3 = −30‰), to 10‰ greater than the corresponding δ¹⁵N_NO3 (Fig. 4). In the context of observed ∆δ¹⁸O:∆δ¹⁵N trajectories, δ¹⁵N_NO2 emerges as sensitive to the prescribed NXR/NAR flux ratio (Fig. 4 and Fig. S3). Relatively large negative ∆δ¹⁵N_NO2-NO3 offsets correspond to elevated ∆δ¹⁸O:∆δ¹⁵N trajectories and elevated NXR/NAR amplitudes. Conversely, more modest ∆δ¹⁵N_NO2-NO3 values are more prevalent at lower NXR/NAR amplitudes (≤0.2) and ∆δ¹⁸O:∆δ¹⁵N trajectories below 1. The δ¹⁸O_NO2, in turn, can provide affirmation that NO₂⁻ is equilibrated with water, which we anticipate in freshwater systems, and which has been observed in most denitrifying marine systems (34, 35). Therefore, if measured concurrently with those of NO₃⁻ (and ambient water), the δ¹⁵N and δ¹⁸O of NO₂⁻ offer added quantitative constraints on the relative flux of NO₂⁻ returned to NO₃⁻ pool under denitrifying conditions (29, 30, 33, 34).

Fig. 4.

Predicted difference between δ¹⁵N_NO2 and δ¹⁵N_NO3 (∆δ¹⁵N_NO2-NO3) associated with net denitrification and coincident NO₃⁻ production plotted against the NXR/NAR ratio, in relation to ¹⁵ε_dnf (color scale). Discrete simulations derive from randomized parameter ranges (Table 1), with full oxygen isotopic exchange of NO₂⁻, AMO/NAR = 0, δ¹⁸O_H2O = -10‰, δ¹⁵N_NO3,_initial = 5‰, and δ¹⁸O_NO3,_intial = 0‰. Open symbols correspond to model solutions where ¹⁵ε_dnf > 30‰.

4. Links to Environmental Studies

4.1. Marine Systems.

Discrete lines of evidence suggest that a substantial fraction of the NO₂⁻ produced by denitrification in low oxygen zones of the ocean is returned to the NO₃⁻ pool by aerobic NO₂⁻ oxidation (34, 51, 52). Mechanistically, the redox potential of waters bounding oxygen-deficient zones may be dynamic, responding to periodic advection of oxygenated waters near redox boundaries (51, 53). Evidence that NO₂⁻ reoxidation occurs concurrently with denitrification originates in part from observations of ∆δ¹⁸O:∆δ¹⁵N trajectories exceeding an expected value of 1. Measurements of the δ¹⁵N and δ¹⁸O of NO₃⁻ and NO₂⁻ from the Eastern Tropical Pacific and the Peru Upwelling region suggest that NO₂⁻ reoxidation is the more likely cause of such patterns (32–34). Specifically, the δ¹⁵N of NO₂⁻ at the subsurface is 30–40‰ lower than the coincident NO₃⁻ δ¹⁵N, reaching δ¹⁵N values as much as 60‰ lower than the coexisting NO₃⁻ (∆δ¹⁵N_NO2-NO3 = −30 to −60‰). Best fit solutions to an inverse finite-difference model tracking the evolution of NO₃⁻ and NO₂⁻ isotopes along isopycnals indicated substantial NO₂⁻ reoxidation flux, with NXR/NAR ≥ 0.50 (34). Model fits further diagnosed moderate ¹⁵ε_nar values of ∼13‰, ¹⁵ε_nxr values on the order of −30‰, no fractionation during NO₂⁻ reduction (¹⁵ε_nir of 0‰), complete oxygen isotope equilibration of NO₂⁻ with seawater, and no significant input of NO₂⁻ from AMO.

The interpretations of recent observations in marine denitrifying waters generally corroborate the predictions from the model presented here. For illustration, we adapted the model architecture outlined above to use an inverse approach to numerically optimize NO₃⁻ isotope measurements along a subsurface isopycnal at the Costa Rica Dome (35) (Fig. 5). The measurements evidenced a progressive NO₃⁻ decrease along the isopycnal surface with a concurrent increase in δ¹⁵N and δ¹⁸O, corresponding to a ∆δ¹⁸O:∆δ¹⁵N trajectory >1 and an apparent isotope effect, ¹⁵ε_dnf, of 28‰. Values of ¹⁵ε_nar, ¹⁵ε_nir, ¹⁵ε_nxr, and NXR/NAR were numerically optimized, iteratively finding the least squares fit to measured NO₃⁻ concentration, δ¹⁵N and δ¹⁸O, assuming negligible NO₂⁻ production by AMO and full equilibration of NO₂⁻ with water (S5. Model Inversion). Accordingly, the apparent ∆δ¹⁸O:∆δ¹⁵N trajectory corresponds to an elevated NXR/NAR flux ratio of 0.64 ± 0.07, and diagnoses of moderate values for ¹⁵ε_nar, ¹⁵ε_nxr, and ¹⁵ε_nir of 14.1 ± 2.3‰, 10.9 ± 4.4‰, and −16.0 ± 4.5‰, respectively (Fig. 5).

Fig. 5.

(A) Best inverse fit ∆δ¹⁸O:∆δ¹⁵N trajectory describing NO₃⁻ δ¹⁵N and δ¹⁸O in an oceanic oxygen deficient zone in the Eastern Tropical North Pacific (35). Initial NO₃⁻ concentrations were interpolated based on the “initial” profiles outside the oxygen deficient zone (35), δ¹⁸O_H2O = 0‰, and the AMO flux is assumed to be negligible. Best-fit estimates of ¹⁵ε_nar, ¹⁵ε_nir, and ¹⁵ε_nxr are +14.1 ± 2.3‰, +10.9 ± 4.4‰, and −16.0 ± 4.5‰, respectively, with a diagnosed NXR/NAR of 0.64 ± 0.07. Model-predicted Δδ¹⁵N_NO2-NO3 values are between −20‰ and −22‰ and the apparent isotope effect, ¹⁵ε_dnf, is 28‰. (B) Best inverse fit ∆δ¹⁸O:∆δ¹⁵N trajectory for NO₃⁻ δ¹⁵N and δ¹⁸O in a contaminated aquifer in Cape Cod, MA (54). Best-fit estimates of ¹⁵ε_nar, ¹⁵ε_nir, and ¹⁵ε_nxr for the ETNP are +10.2 ± 1.3‰, +9.6 ± 4.2‰, and −24.0 ± 7.7‰, respectively, with a diagnosed NXR/NAR of 0.31 ± 0.08, model-predicted Δδ¹⁵N_NO2-NO3 values between −6‰ and −7‰, and an apparent isotope effect, ¹⁵ε_dnf, of 16‰.

Interestingly, the curvature in ∆δ¹⁸O:∆δ¹⁵N trajectories apparent in our model results (Fig. 2) is substantiated by analogous curvature in dual NO₃⁻ isotope trajectories documented in denitrifying ocean waters (34–37) (Fig. 5). The increase of NO₃⁻ N and O isotope ratios associated with net denitrification along isopycnals in the subsurface follows apparent ∆δ¹⁸O:∆δ¹⁵N trajectories distinctly above a nominal slope of 1 that show clear curvature at higher extents of net NO₃⁻ consumption. In our model, the degree of curvature increases in proportion to the NO₂⁻ oxidation flux (Fig. 2), because the δ¹⁵N of nitrified NO₃⁻ increases progressively as a function of net NO₃⁻ consumption, whereas the corresponding δ¹⁸O of nitrified NO₃⁻ remains directly dependent on the δ¹⁸O of water (Fig. S2). The curvature in ∆δ¹⁸O:∆δ¹⁵N trajectory in our model simulations thus appear validated by analogous patterns in NO₃⁻ isotope distributions in marine denitrifying environments.

Anammox has been detected in oxygen minimum zones of the ocean, where its potential contribution to the total N₂ flux has generated considerable debate (54–57), with estimates ranging from 30% to 100% of the total N₂ flux. The model exercise here suggests that NO₃⁻ production by anammox cannot, by itself, explain ∆δ¹⁸O:∆δ¹⁵N trajectories exceeding 1, given diagnoses of NO₂⁻ reoxidation to the NO₃⁻ pool that far exceed stoichiometric constraints of anammox. Even if anammox is assumed to account for 100% of N₂ production, the corresponding NO₂⁻ flux remains insufficient to generate ∆δ¹⁸O:∆δ¹⁵N trajectories above 1. Accordingly, analyses of NO₃⁻ and NO₂⁻ isotope ratios in other denitrifying regions of the Pacific and Indian Oceans have converged on similar interpretations, ultimately diagnosing a substantial return flux of NO₂⁻ to the NO₃⁻ pool catalyzed largely by aerobic nitrification (34–37).

Despite general agreements between model and observations, some aspects remain puzzling. For one, the δ¹⁵N_NO2 in denitrifying marine waters can be substantially lower than predicted by the current exercise, with ∆δ¹⁵N_NO2-NO3 values ranging between −30‰ and −60‰ in situ (34, 35), compared with −20% and −30‰ in our model (Fig. 4). Indeed, the best-fit parameters to the Costa Rica Dome data predict corresponding ∆δ¹⁵N_NO3-NO2 values on the order of −20% to −22‰ (Fig. 5) compared with measured ∆δ¹⁵N_NO3-NO2 values between −20‰ and −50‰ (35). Lower ∆δ¹⁵N_NO3-NO2 values can only be generated in the current model framework by assuming an elevated reoxidation to reduction flux (NXR/NAR), as well as large amplitude isotope effects for ¹⁵ε_nar and ¹⁵ε_nxr on the order of 30‰ and −30‰, respectively. However, while realizing ∆δ¹⁵N_NO2-NO3 values as low as −60‰ and ∆δ¹⁸O:∆δ¹⁵N trajectories above 1, such simulations result in apparent values of ¹⁵ε_dnf that far exceed the empirical limit of 30‰ (Fig. 4). Otherwise, ¹⁵ε_nxr may be effectively subsumed into an equilibrium isotope effect of −61‰, the purported enzyme-catalyzed equilibrium isotope effect between NO₂⁻ and NO₃⁻ (43), such that the net production of NO₃⁻ by the NO₂⁻ oxidoreductase enzyme can generate ∆¹⁵N_NO2-NO3 values of ∼−60‰, albeit at elevated NXR/NAR flux ratios. This scenario, however, still results in apparent ¹⁵ε_dnf values that far exceed 30‰, thus inconsistent with observations. Arguably, isotopically catalyzed enzymatic isotope equilibration by NO₂⁻ oxidoreductase need not be associated with a net oxidative flux. Such a scenario is analogous to simulations here where NXR is nearly equal to NAR (with NAR representing NO₃⁻ reduction by NO₂⁻ oxidoreductase in lieu of NO₃⁻ reductase). The equilibrium isotope effect of −61‰ is then implicitly the sum of the oxidative and reductive isotope effects with respect to NO₂⁻, −31‰ for NO₂⁻ oxidation vs. −30‰ for NO₂⁻ production from NO₃⁻, wherein the resulting ∆¹⁵N_NO2-NO3 of the NO₂⁻ pool is ∼−60‰. Again, apparent values of ¹⁵ε_dnf emerging from such simulations are unrealistic (on the order of 60‰). Thus, within the current model framework, the putative enzyme-catalyzed equilibrium isotope effect between NO₂⁻ and NO₃⁻ does not appear to readily explain the very low ∆δ¹⁵N_NO2-NO3 observed in marine denitrifying systems.

The discrepancy between our modeled ∆δ¹⁵N_NO2-NO3 and observations may otherwise derive in part from the constant N transformation rates in our simulations, as more negative δ¹⁵N_NO2 values could be generated within representative model conditions given time/space-variable rates of NO₂⁻ accumulation and depletion and/or isotope effects. Nevertheless, inverse fits allowing for time-variable rates of N transformations still implicate ¹⁵ε_nxr values on the order of −30‰ (34, 35), distinctly lower than values observed in nitrifier cultures of –15‰ (5, 7). Additionally, the inverse-model fits are contingent on the diminished expression of ¹⁵ε_nir (5, 7), a diagnosis that is also echoed in our model (Fig. S3). Such low ¹⁵ε_nir amplitudes appear contradictory to expectations from cultures and enzymatic studies (19, 43, 58, 59) and are also inconsistent with some recent field observations (36), where an increase in δ¹⁵N_NO2 along isopycnal surfaces in a denitrifying eddy at the Peru margin (in which no NO₃⁻ remained) was associated with an apparent ¹⁵ε_nir of 12‰. The very low δ¹⁵N_NO2 observed in marine denitrifying zones thus remains perplexing and merits further inquiry.

4.2. Freshwater Systems.

As demonstrated here, the empirical ∆δ¹⁸O:∆δ¹⁵N trajectories between 0.5 and 0.8 recurrently observed in freshwater systems can be explained by superimposing the isotopic systematics of denitrification with those of oxidative NO₃⁻ production. This dynamic could arise on the premise that redox conditions in aquifers may be dynamic, owing to intercalated microzonation within sediments (60) and/or periodic downward percolation of oxygenated waters. However, nitrifying organisms and their biogeochemical activity are rarely detected at the heart of denitrifying aquifers (61, 62). Thus, in the absence of any O₂-requiring transformations, it is likely that any return of NO₂⁻ to the NO₃⁻ pool in anaerobic aquifers is associated with anammox, the anaerobic oxidation of NH₃ coupled to reduction of NO₂⁻, which yields NO₃⁻ (as well as N₂) as a metabolic product (24, 42). Indeed, recent studies suggest that a substantial fraction of N₂ production in aquifers originates from anammox (63–65), rivaling N₂ production by canonical denitrification in some instances (45).

We turn to a well-studied site of groundwater contamination on Cape Cod, MA (47), to estimate isotope effects and relative NO₂⁻ oxidation rates that could explain NO₃⁻ isotope distributions therein. Within the contaminant plume, ∼180 μM NO₃⁻ decreased to ∼35 μM along an anoxic groundwater flow path. Concomitant with this decrease in NO₃⁻ concentration, pronounced changes in δ¹⁵N_NO3 and δ¹⁸O_NO3 were also observed, increasing from ∼+15‰ to +45‰ and from −1‰ to +18‰, respectively, yielding a corresponding ∆δ¹⁸O:∆δ¹⁵N trajectory of ∼0.73 and an apparent N isotope effect for the observed denitrification, ¹⁵ε_dnf, of ∼16‰ (47). We use the inverse approach outlined above to numerically optimize values of ¹⁵ε_nar, ¹⁵ε_nir, ¹⁵ε_nxr, and NXR/NAR, iteratively finding the least squares fit to measured NO₃⁻ concentration, δ¹⁵N and δ¹⁸O (S5. Model Inversion). We also make a simplifying assumption that AMO is negligible in the anoxic portion of the aquifer. Given the pH and δ¹⁸O of groundwater at this site (∼6.5 and −6.5‰, respectively) (47), we also assume that any NO₂⁻ will be fully equilibrated with water.

As expected, deviation of the dual isotopic composition from a ∆δ¹⁸O:∆δ¹⁵N trajectory of 1–0.73 can be accommodated by concomitant production of NO₃⁻ along this flow path (Fig. S8). Best-fit solutions yield estimates of ¹⁵ε_nar, ¹⁵ε_nir, and ¹⁵ε_nxr of 10.6 ± 0.2‰, 10.2 ± 3.9‰, and −31.3 ± 7.7‰, respectively. Consistent with expectations, lower actual values of ¹⁵ε_nar are diagnosed (i.e., below the observed ¹⁵ε_dnf of ∼16‰), as the increase in δ¹⁵N_NO3 is also influenced by NO₃⁻ production with a relatively high δ¹⁵N via NXR. Under these conditions, the required amount of NO₃⁻ production relative to its removal is on the order of 13 ± 0.3% (i.e., NXR/NAR = 0.13), much lower than that predicted by recent dual isotope models of ocean denitrifying zones in which the diagnosed NXR/NAR can be as high as 0.9 (34). Although not measured in the original aquifer study, these best-fit parameters also allow us to predict the δ¹⁵N of coexisting NO₂^−—for which we arrive at ∆δ¹⁵N_NO2-NO3 values between −6.1‰ and −4.4‰. This prediction of a relatively small δ¹⁵N difference between coexisting pools of NO₃⁻ and NO₂⁻ under aquifer conditions provides a target for future studies and a means for refining our estimates of N cycling in groundwater and other environments.

Notably, the estimated value for ¹⁵ε_nxr of ∼−31‰ for the aquifer is higher than that observed in cultures of NO₂⁻ oxidizing bacteria (7), yet largely consistent with that for anammox (43), potentially implicating anammox as an important N removal process in this aquifer. The diagnosis of NXR/NAR ratio of 0.13 corresponds to ∼65% of total N₂ production in the aquifer fueled by anammox, a value also consistent with recent independent estimates made in the same aquifer (45). Indeed, given the stoichiometric constraints of NO₃⁻ production by anammox, we suggest these model results may prove diagnostic of the role of anammox in ground waters globally.

5. Summary and Conclusions

Foremost, our results demonstrate that deviations from the canonical ∆δ¹⁸O:∆δ¹⁵N trajectory of 1 for denitrification must emerge due to concurrent NO₃⁻ production catalyzed by nitrification and/or anammox, not only in marine systems, but also in freshwater systems, where this tenet has been given limited consideration. Assuming that full O isotopic equilibration of NO₂⁻ is pertinent to both freshwater and marine denitrifying systems, our results emphasize the sensitivity of the δ¹⁸O of newly produced NO₃⁻ to the δ¹⁸O of ambient water and the isotope effects for O atom equilibration and incorporation. Trajectories above 1 emerge specifically where the NXR/NAR flux ratio is high (≥0.5) and predominantly where the difference between the δ¹⁸O of NO₃⁻ and that of water is small. The diagnosis of high NO₃⁻ production in the generation of ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 disputes the notion that anammox could be the sole NO₃⁻-producing reaction in marine denitrifying systems, given stoichiometric and biochemical limitations on the amount of NO₂⁻ that anammox can return to the NO₃⁻ pool, and thus implicates a significant contribution by aerobic NO₂⁻ oxidation.

Importantly, the majority of solutions to randomized combinations of model conditions yield ∆δ¹⁸O:∆δ¹⁵N trajectories <1 for simulations using a fully equilibrated NO₂⁻ pool. In this respect, our analysis of NO₃⁻ isotopes from a representative aquifer (47) suggests that the characteristic ∆δ¹⁸O:∆δ¹⁵N trajectory therein (∼0.73) arises from relatively low NXR/NAR flux ratios (∼0.13), which is well aligned with the stoichiometric and biochemical constraints of anammox. Thus, in addition to the leverage of distinctive δ¹⁸O_H2O between freshwater and marine systems, characteristic NO₃⁻ isotope trends between denitrifying groundwater and marine systems also appear to reflect fundamental differences in key N transformation pathways operative in these systems.

Within this model framework, the δ¹⁵N of NO₂⁻ provides an additional diagnostic to estimate the relative contribution of nitrification (and/or anammox) to the NO₃⁻ pool. In particular, very deplete δ¹⁵N_NO2 values relative to the NO₃⁻ pool may be characteristic of elevated NXR/NAR flux ratios: a dynamic that appears corroborated by analogously low δ¹⁵N_NO2 values in marine denitrifying zones, albeit lower than those predicted by our model simulations.

Some uncertainties also remain that require resolution to ensure accuracy of interpretations. For one, O isotope effects associated with NO₃⁻ production by anammox remain undocumented; whereas dynamics may be similar to those for NO₂⁻ oxidizing bacteria, this should be confirmed. Second, the nature and environmental extent of the purported “enzyme-catalyzed equilibrium N isotope effect” between NO₃⁻ and NO₂⁻ during anammox should also be further explored. Diagnostic estimates of NXR/NAR flux ratios are sensitive to the broad potential range of N isotope effects during NO₂⁻ oxidation to NO₃⁻. Third, the apparent discrepancy between model and measured δ¹⁵N_NO2 in marine systems merits examination to assess the involvement of NO₂⁻ in potential abiotic/inorganic reactions. Finally, the premise that NO₂⁻ oxygen isotopes in marine and freshwater denitrifying systems are fully equilibrated with water should be further interrogated, as even partial O isotope disequilibrium could influence diagnostics of N fluxes and associated isotope effects (S3. Simulation Without Isotope Equilibration of NO₂⁻ with Water). Continued inquiry into isotope systematics of N cycling will lead to an increasingly robust framework from which to examine N cycle dynamics across ecosystems.

6. Materials and Methods

Given the number of variables involved in calculating the model solutions, we made a number of decisions for model parameterizations to maintain clarity. First, we chose a range of isotope effects based on published studies using pure cultures of representative organisms and/or purified enzymes when possible (Table 1). As studies of organism-level isotope effects have demonstrated broad variability, whether by bacterial strain or growth conditions, for brevity and simplicity, we also established “standard” model conditions having generally midrange values for isotope effects (Table 1). Second, a study published this year demonstrates that the N and O isotope effects for NIR are coupled differently depending on the type NO₂⁻ reductase involved (59). Our simulations, however, are based on parameterization of ¹⁵ε_nir and ¹⁸ε_nir coupled in a ratio of 1:1, assumed before this insight. Regardless, this inaccuracy does not ultimately impact the conclusions reached herein (Section 3.3 and S3.2. Influence of ¹⁸ε_nar and ¹⁸ε_nir). Third, the N and O isotope effects for NXR in the model parameterization remain uncoupled because studies of NO₂⁻-oxidizing organisms have evidenced no connection in their magnitudes (5). Finally, we allow the initial N and O isotopic composition of NO₃⁻ to vary across a representative range (−10‰ to +15‰ for both δ¹⁵N and δ¹⁸O) while using values of +5‰ for both as standard conditions.

To date, no information exists on O isotope systematics of anammox, such that we assume O isotope effects similar to that of NO₂⁻ oxidizing bacteria, as enzymatic pathways are analogous (66). However, the organism-level inverse N isotope effect reported for anammox cultures for NO₃⁻ production driven by NXR exhibits higher values (−35‰) (43) than those observed in cultures of bacterial NO₂⁻ oxidizing bacteria (−13‰) (4) and may also include a very large enzymatically driven isotope equilibrium between NO₃⁻ and NO₂⁻ of −61‰ (43).

S1. Postulates to Explain Deviations from 1 in ∆δ¹⁸O:∆δ¹⁵N Trajectories in Freshwater

The discrepancy between field observations and culture estimates of could stem from a methodological artifact and the lack of established δ¹⁸O_NO3 reference materials (67). Early δ¹⁸O_NO3 measurements were made by off-line sealed-tube pyrolysis, which may suffer from exchange of O-atoms with the glass and/or contamination by O-bearing contaminants (68). Such δ¹⁸O scale contraction is now corrected by use of calibrated NO₃⁻ reference materials (67). Importantly, the establishment of international NO₃⁻ isotopic reference materials has not eliminated the persistence of ∆δ¹⁸O:∆δ¹⁵N ∼0.6 found in freshwater systems (69). The activity of an auxiliary Nap NO₃⁻ reductase has been evoked to explain ∆δ¹⁸O:∆δ¹⁵N trends in freshwater environments (70), on the basis that NO₃⁻ reduction mediated by Nap has been shown to exhibit lower ∆δ¹⁸O:∆δ¹⁵N trajectories (9, 23, 70). However, evidence for this nonrespiratory pathway as a major environmental sink for NO₃⁻ is lacking and largely inconsistent with the enzymatic basis of heterotrophic respiratory NO₃⁻ consumption, which specifically implicates the Nar NO₃⁻ reductase. Plasticity in ∆δ¹⁸O:∆δ¹⁵N trajectories for Nar-mediated denitrification could also explain the apparent discrepancy between cultures and the environment and was reported among denitrifying cultures in one study (71). The δ¹⁸O_NO3 trends therein, however, were indirectly inferred from NO₂⁻ δ¹⁸O and may have been affected by NO₂⁻-water oxygen isotopic exchange (29, 30). Given lower δ¹⁸O_H2O values in freshwater systems relative to seawater, oxygen isotopic equilibration between NO₃⁻ and water could hypothetically lead to lower δ¹⁸O_NO3 values in freshwater systems and to a consequent decrease in ∆δ¹⁸O:∆δ¹⁵N trajectories. The timescale of this abiotic exchange process (>10⁹ y), however, precludes its overall relevance for modern biosphere processes (72). Nevertheless, the potential ingrowth of water oxygen atoms into NO₃⁻ could result from reverse activity of the Nar enzyme. Such enzymatic reversibility has been demonstrated to influence the evolving δ¹⁸O of sulfate during sulfate reduction (73). Although a similar dynamic has been suggested for NO₃⁻ (73), there is no evidence for enzymatic reversibility of Nar in the literature. Importantly, denitrifier cultures amended with incremental concentrations of ¹⁸O-enriched water showed no differences in ∆δ¹⁸O:∆δ¹⁵N trajectories among treatments, indicating that Nar activity is not reversed in vivo (12). In addition, the biological production of NO₃⁻ occurring in tandem with denitrification has been postulated to account for the apparent differences in ∆δ¹⁸O:∆δ¹⁵N trajectories between cultures and freshwater environments (39). Wunderlich et al. (40) showed that some NO₂⁻-oxidizing bacteria (e.g., Nitrobacter vulgaris) under suboxic conditions use NO₂⁻ oxidoreductase (Nxr) reversibly to reduce NO₃⁻, modifying apparent ∆δ¹⁸O_NO3:∆δ¹⁵N_NO3 trajectories during denitrification. Although intriguing, the environmental ubiquity of this specific process is difficult to assess. Nevertheless, this scenario raises a key premise that the biological oxidation of NO₂⁻ invariably results in the incorporation of water-derived O atoms into the NO₃⁻ pool.

S2. Equations Used in Time-Dependent NO₃⁻ Isotope 1 Box Model

$$\text{NAR}\left(\left[\text{N}\right]/\text{time}\right)=\text{rate}\hspace{0.17em}\text{of}\hspace{0.17em}{\text{NO}}_3^{-}\hspace{0.17em}\text{reduction}\hspace{0.17em}\text{to}\hspace{0.17em}{\text{NO}}_2^{-}$$

$$\text{NXR}\left(\left[\text{N}\right]/\text{time}\right)=\text{rate}\hspace{0.17em}\text{of}\hspace{0.17em}{\text{NO}}_2^{-}\hspace{0.17em}\text{oxidation}\hspace{0.17em}\text{to}\hspace{0.17em}{\text{NO}}_3^{-}$$

$$\text{NIR}\left(\left[\text{N}\right]/\text{time}\right)=\text{rate}\hspace{0.17em}\text{of}\hspace{0.17em}{\text{NO}}_2^{-}\hspace{0.17em}\text{reduction}\hspace{0.17em}\text{to}\hspace{0.17em}\text{NO}$$

$$\text{AMO}\left(\left[\text{N}\right]/\text{time}\right)=\text{rate}\hspace{0.17em}\text{of}\hspace{0.17em}{\text{NH}}_4^{\mathrm{+}}\hspace{0.17em}\text{oxidation}\hspace{0.17em}\text{to}\hspace{0.17em}{\text{NO}}_2^{-}$$

$$\mathrm{\alpha }={}^{\text{light}}k/{}^{\text{heavy}}k=\left(\mathrm{\epsilon }/1\text{,}000\right)+1$$

$${}^{14}\text{F}={}^{14}\text{N}/\left({}^{15}\text{N}+{}^{14}\text{N}\right)$$

$${}^{15}\text{F}={}^{15}\text{N}/\left({}^{15}\text{N}+{}^{14}\text{N}\right)$$

$${}^{16}\text{F}={}^{16}\text{O}/\left({}^{18}\text{O}+{}^{16}\text{O}\right)$$

$${}^{18}\text{F}={}^{18}\text{O}/\left({}^{18}\text{O}+{}^{16}\text{O}\right)$$

$${}^{18}f_{\text{eq}}=\text{fraction}\hspace{0.17em}\text{of}\hspace{0.17em}{\text{NO}}_2^{-}\hspace{0.17em}\text{pool}\hspace{0.17em}\text{in}\hspace{0.17em}\text{equilibrium}\hspace{0.17em}\text{with}\hspace{0.17em}{\text{H}}_2\text{O}$$

$$\text{NAR}=\text{NXR}+\text{NIR}$$

$${\left[{}^{14}\text{N}_{\text{NO}3}\right]}_{\left(\text{t}+1\right)}={\left[{}^{14}\text{N}_{\text{NO}3}\right]}_{\left(\text{t}\right)}+\left[\text{NXR}\ast {}^{14}\text{F}_{\text{NO}2\left(\text{t}\right)}-\text{NAR}\ast {}^{14}\text{F}_{\text{NO}3\left(\text{t}\right)}\right]\ast \text{dt}$$

$${\left[{}^{15}\text{N}_{\text{NO}3}\right]}_{\left(\text{t}+1\right)}={\left[{}^{15}\text{N}_{\text{NO}3}\right]}_{\left(\text{t}\right)}+\left[\text{NXR}/{}^{15}\mathrm{\alpha }_{\text{nxr}}*{}^{15}\text{F}_{\text{NO}2\left(\text{t}\right)}-\text{NAR}/{}^{15}\mathrm{\alpha }_{\text{nar}}\ast {}^{15}\text{F}_{\text{NO}3\left(\text{t}\right)}\right]\ast \text{dt}$$

$${\left[{}^{16}\text{O}_{\text{NO}3}\right]}_{\left(\text{t}+1\right)}={\left[{}^{16}\text{O}_{\text{NO}3}\right]}_{\left(\text{t}\right)}+\left[\text{NXR}\ast \left(2/3\ast {}^{16}\text{F}_{\text{NO}2\left(\text{t}\right)}+1/3\ast {}^{16}\text{F}_{\text{H}2\text{O}}\right)-\text{NAR}\ast {}^{16}\text{F}_{\text{NO}3\left(\text{t}\right)}\right]\ast \text{dt}$$

$${\left[{}^{18}\text{O}_{\text{NO}3}\right]}_{\left(\text{t}+1\right)}={\left[{}^{18}\text{O}_{\text{NO}3}\right]}_{\left(\text{t}\right)}+\left[\text{NXR}\ast (2/3\ast {}^{18}\text{F}_{\text{NO}2\left(\text{t}\right)}/{}^{18}\mathrm{\alpha }_{\text{nxrNO}2}+1/3\ast {}^{18}\text{F}_{\text{H}2\text{O}}/{}^{18}\mathrm{\alpha }_{\text{nxrH}2\text{O}})-\text{NAR}/{}^{18}\mathrm{\alpha }_{\text{nar}}\ast {}^{18}\text{F}_{\text{NO}3\left(\text{t}\right)}\right]\ast \text{dt}$$

$${\left[{}^{14}\text{N}_{\text{NO}2}\right]}_{\left(\text{t}+1\right)}={\left[{}^{14}\text{N}_{\text{NO}2}\right]}_{\left(\text{t}\right)}+\left[\text{NAR}\ast {}^{14}\text{F}_{\text{NO}3\left(\text{t}\right)}-\left(\text{NXR}+\text{NIR}\right)\ast {}^{14}\text{F}_{\text{NO}2}+\text{AMO}\ast {}^{14}\text{F}_{\text{NH}4}\right]\ast \text{dt}$$

$${\left[{}^{15}\text{N}_{\text{NO}2}\right]}_{\left(\text{t}+1\right)}={\left[{}^{15}\text{N}_{\text{NO}2}\right]}_{\left(\text{t}\right)}+[\text{NAR}/{}^{15}\mathrm{\alpha }_{\text{nar}}\ast {}^{15}\text{F}_{\text{NO}3\left(\text{t}\right)}-\left(\text{NXR}/{}^{15}\mathrm{\alpha }_{\text{nar}}+\text{NIR}/{}^{15}\mathrm{\alpha }_{\text{nir}}\right)\ast {}^{15}\text{F}_{\text{NO}2}+\text{AMO}/{}^{15}\mathrm{\alpha }_{\text{amo}}\ast {}^{15}\text{F}_{\text{NH}4}]\ast \text{dt}$$

$${\left[{}^{16}\text{O}_{\text{NO}2}\right]}_{\left(\text{t}+1\right)}={\left[{}^{16}\text{O}_{\text{NO}2}\right]}_{\left(\text{t}\right)}+[\left(1-{}^{18}f_{\text{eq}}\right)\ast ((\text{NAR}\ast {}^{16}\text{F}_{\text{NO}3\left(\text{t}\right)}-\left(\text{NXR}+\text{NIR}\right)\ast {}^{16}\text{F}_{\text{NO}2}+\text{AMO}\ast 1/2\ast \left({}^{16}\text{F}_{\text{O}2}+{}^{16}\text{F}_{\text{H}2\text{O}}\right))+{}^{18}f_{\text{eq}}\ast {}^{16}\text{F}_{\text{H}20}]\ast \text{dt}$$

$${\left[{}^{18}\text{O}_{\text{NO}2}\right]}_{\left(\text{t}+1\right)}={\left[{}^{18}\text{O}_{\text{NO}2}\right]}_{\left(\text{t}\right)}+[\left(1-{}^{18}f_{\text{eq}}\right)\ast (\left(\text{NAR}/{}^{18}\mathrm{\alpha }_{\text{nar}}\ast {}^{18}\text{F}_{\text{NO}3\left(\text{t}\right)}\right)/{}^{18}\mathrm{\alpha }_{\text{narBR}}-(\text{NXR}/{}^{18}\mathrm{\alpha }_{\text{nxrNO}2}+\text{NIR}/{}^{18}\mathrm{\alpha }_{\text{nir}})\ast {}^{18}\text{F}_{\text{NO}2\left(\text{t}\right)}\ast \text{AMO}\ast \left(1/2\ast {}^{18}\text{F}_{\text{O}2}/{}^{18}\mathrm{\alpha }_{\text{amoO}2}+1/2\ast {}^{18}\text{F}_{\text{O}2}/{}^{18}\mathrm{\alpha }_{\text{amoH}2\text{O}}\right))+{}^{18}f_{\text{eq}}\ast {}^{18}\text{F}_{\text{H}20}\ast {}^{18}\mathrm{\alpha }_{\text{eq}}]\ast \text{dt}.$$

S3. Simulation Without Isotope Equilibration of NO₂⁻ with Water

S3.1. Influence of δ¹⁸O_H2O.

Model simulations in which NO₂⁻ does not equilibrate with water yield ∆δ¹⁸O:∆δ¹⁵N trajectories that are predominantly above 1 (Fig. S1). The relative amplitudes of positive deviations correlate with the amplitude of the NXR/NAR flux ratio, with theoretical ∆δ¹⁸O:∆δ¹⁵N values upward of 7.0 at NXR/NAR ratios of 0.9. The δ¹⁸O_H2O in these parameterizations accounts for only modest differences among ∆δ¹⁸O:∆δ¹⁵N trajectories for any given NXR/NAR ratio, unlike corresponding parameterizations with completely equilibrated NO₂⁻, due to a lack of NO₂⁻–water equilibration. The reduced influence of the δ¹⁸O_H2O on ∆δ¹⁸O:∆δ¹⁵N trajectories arises because only a single O atom is incorporated during oxidation of NO₂⁻ to NO₃⁻ (Fig. 1 and Fig. S2). The δ¹⁸O of nitrified NO₃⁻ is otherwise determined largely by the δ¹⁸O of the NO₂⁻ pool, which is comparatively elevated due to the branching O isotope effect associated with NO₃⁻ reduction, ¹⁸ε_narBR, producing NO₂⁻ having a δ¹⁸O 25‰ greater than the NO₃⁻ δ¹⁸O concurrently abstracted (19, 33). Consequently, the δ¹⁸O of nitrified NO₃⁻ in simulations without O isotope exchange is considerably more elevated than the δ¹⁸O_NO3 removed concurrently by denitrification, resulting in net increases in δ¹⁸O relative to δ¹⁵N and, therefore, positive deviations in ∆δ¹⁸O:∆δ¹⁵N trajectories from a nominal value of 1.

In parameterizations without oxygen isotope equilibration of NO₂⁻, curvature in the ∆δ¹⁸O:∆δ¹⁵N trajectory is also apparent (Fig. 2) because the δ¹⁸O of nitrified NO₃⁻ does not increase in step with the δ¹⁸O increase of the NO₃⁻ pool, whereas the δ¹⁵N of nitrified NO₃⁻ still increases in constant proportion to the δ¹⁵N increase of the NO₃⁻ pool (Fig. S2). In this case, however, two of the oxygen atoms in nitrified NO₃⁻ deriving from NO₂⁻ do increase in proportion to the δ¹⁸O of the NO₃⁻ pool, whereas the δ¹⁸O of the single oxygen atom deriving from water remains constant. Curvature of the ∆δ¹⁸O:∆δ¹⁵N trajectory thus arises because of a lower degree of increase of the δ¹⁸O of nitrified NO₃⁻ relative to the corresponding rate of increase of the δ¹⁸O of the NO₃⁻ pool. Accounting for more representative ¹⁸ε_nir to ¹⁵ε_nir ratios (65) than those prescribed here would result in differences in ∆δ¹⁸O:∆δ¹⁵N amplitude and curvature, but would nevertheless yield largely analogous patterns.

S3.2. Influence of ¹⁸ε_nar and ¹⁸ε_nir.

In the case of no oxygen isotope equilibration of NO₂⁻ with water, the ∆δ¹⁸O:∆δ¹⁵N trajectory is, in fact, sensitive to variations in amplitude of ¹⁸ε_nar, in conjunction with that of the enzymatic branching isotope effect of NO₃⁻ reductase, ¹⁸ε_narBR, leading to ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 (Fig. S4B). The δ¹⁸O removed from the NO₃⁻ pool is a function of ¹⁸ε_nar, whereas the NO₂⁻ produced concurrently has a δ¹⁸O_NO2 that is ∼25‰ greater than the δ¹⁸O abstracted from the NO₃⁻ pool, due to the branching isotope effect (19, 29). The δ¹⁸O of NO₃⁻ produced by subsequent NO₂⁻ oxidation is thus consistently elevated compared with that removed by denitrification, consistently leading to ∆δ¹⁸O:∆δ¹⁵N trajectories above 1 (Fig. S1).

Without full equilibration, ¹⁸ε_nir has leverage on the ∆δ¹⁸O:∆δ¹⁵N trajectory that is counter to that of the corresponding ¹⁵ε_nir, but quantitatively less important than that of ¹⁵ε_nir because the ¹⁸O-enrichment of NO₂⁻ due to ¹⁸ε_nir is effectively diluted by the subsequent incorporation of an additional oxygen atom from water into NO₃⁻ during NO₂⁻ oxidation (Fig. 1 and Fig. S4D). More representative parameterizations of ¹⁸ε_nir relative to ¹⁵ε_nir would yield quantitatively different yet qualitatively analogous ∆δ¹⁸O:∆δ¹⁵N trajectories.

S3.3. Influence of Initial δ¹⁸O_NO3.

In simulations without oxygen isotope equilibration, the difference between δ¹⁸O_NO3 and δ¹⁸O_H2O has a comparatively diminished influence on the ∆δ¹⁸O:∆δ¹⁵N trajectory, because the δ¹⁸O of nitrified NO₃⁻ is no longer influenced by oxygen isotope equilibration with water, but only sensitive to oxygen atom incorporation from water during NO₂⁻ oxidation (Fig. 1 and Fig. S2). We note that the δ¹⁸O of nitrified NO₃⁻ is also rendered sensitive to oxygen atom incorporation from water during ammonium oxidation to NO₂⁻; however, an AMO flux is not prescribed under our standard model conditions (Table 1 and S4. Impact of NO₃⁻ Production by AMO). The δ¹⁸O_NO3 produced by nitrification when NO₂⁻ is not equilibrated is then comparatively ¹⁸O-enriched due to the branching isotope effect of NO₃⁻ reduction, ¹⁸ε_narBR, resulting in positive deviations in ∆δ¹⁸O:∆δ¹⁵N from a nominal trajectory of 1 (Figs. S1 and S2).

In simulations without isotopic equilibration of NO₂⁻, in which nearly all ∆δ¹⁸O:∆δ¹⁵N solutions are above 1, the amplitude of the positive offset from 1 is proportional to the NXR/NAR ratio for a given δ¹⁸O_H2O (Fig. S1), reflecting the relative amount of ¹⁸O-enriched NO₃⁻ returned to the NO₃⁻ pool by NO₂⁻ oxidation.

S4. Impact of NO₃⁻ Production by AMO

The presence of AMO in the model architecture, parameterized as the ratio of AMO/NAR, constitutes a net input of N to the system whose magnitude is not constrained numerically by that of other fluxes (S2. Equations Used in Time-Dependent NO₃⁻ Isotope 1 Box Model). AMO thus contributes directly to the NO₂⁻ pool (Fig. 1), where it is subject to reduction (NIR) and/or oxidation (NXR). The AMO flux is then compensated by increases NIR and/or NXR. We consider here only conditions resulting in the net removal of NO₃⁻, where the increased contribution of AMO is not allowed to result in the net production of NO₃⁻ (NAR ≥ NXR). Regardless, most model solutions at relatively elevated NXR/NAR ratios (NXR/NAR ≥ 0.5 and standard conditions) produce nonviable solutions in which apparent ¹⁵ε_dnf values exceed the empirical limit of 30‰ (Figs. S1 and S3A). The prescription of any AMO flux exacerbates this dynamic, increasing the NO₂⁻ δ¹⁵N, consequently producing relatively ¹⁵N-enriched NO₃⁻ that amplifies ¹⁵ε_dnf. Thus, where NXR/NAR ratios are ≥0.5, viable solutions persist only at very low prescriptions of AMO/NAR (≤0.05; Fig. S6). This general dynamic extends to the entire parameterized range of δ¹⁵N_NH4 values (−20‰ to 15‰; Table 1), which result in the production of ¹⁵N-enriched NO₂⁻ by AMO and a consequent increase in the δ¹⁵N_NO3 produced by NXR, under nearly all combinations of boundary conditions. Among the few viable solutions that remain at elevated NXR/NAR ratios, slight increases in the AMO/NAR ratio result in a marked reduction in the corresponding ∆δ¹⁸O:∆δ¹⁵N trajectory (Fig. S6B), due to an increase in ¹⁵ε_dnf that is not matched by a corresponding increase in ¹⁸ε_dnf. Together, the tendency for increasing AMO to lower ∆δ¹⁸O:∆δ¹⁵N trajectories while increasing the likelihood of generating invalid ¹⁵ε_dnf solutions appears to exclude any substantial flux of AMO in marine denitrifying systems. Trajectories therein reach upward of 1.3, values that are produced exclusively at elevated NXR/NAR ratios and thus minimal AMO (34, 35).

At lower NXR/NAR flux ratios, increasing the AMO flux leads to comparatively modest increases in ¹⁵ε_dnf and correspondingly modest reductions of ∆δ¹⁸O:∆δ¹⁵N trajectories (Fig. S6). The limited sensitivity of NO₃⁻ isotopes to any NO₂⁻ production from AMO thus renders the potential importance this flux difficult to detect from NO₃⁻ isotopes distributions alone. Nevertheless, we consider that any NO₃⁻ production in anaerobic aquifers (where NXR/NAR flux ratios may be relatively low; Section 3.5.2) is likely associated with anammox rather than aerobic nitrification, potentially discounting the involvement of ammonium δ¹⁵N in modulating NO₃⁻ ∆δ¹⁸O:∆δ¹⁵N trends altogether (Section 3.5.2). If correct, this inference would facilitate a more quantitative interpretation of relative N cycle fluxes in soils and aquifers from natural abundance NO₃⁻ (and NO₂⁻) isotope distributions, a topic addressed in Section 3.5.2.

S5. Model Inversion

Adapting the model architecture outlined above, we use an inverse approach to numerically optimize values of ¹⁵ε_nar, ¹⁵ε_nir, ¹⁵ε_nxr, and NXR/NAR. As the model system of equations is underdetermined, we use a genetic solving algorithm method in Solver (mutation rate = 0.75, convergence = 0.0000001, population size = 100; Frontline Systems; Microsoft Excel) and a least-squares criterion to iteratively find the best fit to the published values for NO₃⁻ concentrations (estimating the fraction of consumption or f_NO3) along with δ¹⁵N_NO3 and δ¹⁸O_NO3. Uncertainty in parameter estimates (1 SD) is expressed as the SE of successive model-runs (n > 25).