High nitrous oxide isotopic variability during denitrification by Pseudomonas species bearing NirK and NirS

Nitrous oxide (N₂O) isotopocules provide key insights into microbial nitrogen cycling, but their interpretation requires well-constrained values for both oxygen isotope signatures (δ¹⁸O–N₂O) and intramolecular ¹⁵N site preference (SP) associated with N₂O production pathways. Site preference is widely used to distinguish N₂O formation pathways because bacterial denitrification is generally assumed to yield SP values near 0 ‰ through canonical NorB-mediated NO reduction. However, the extent to which SP remains stable across physiological states and changing NO reduction pathways remains poorly constrained. Likewise, interpretation of δ¹⁸O–N₂O associated with denitrification requires understanding the relative contributions of branching kinetic isotope effects and oxygen atom exchange between nitrite and water during N₂O formation.

Here, we investigated N₂O isotopic signatures during denitrification by Pseudomonas aureofaciens (NirK-bearing) and Pseudomonas chlororaphis (NirS-bearing) under active-growth and resuspension conditions using quantum cascade laser absorption spectroscopy (QCLAS) and isotope ratio mass spectrometry (IRMS). SP tracked canonical NorB-mediated NO reduction but transiently increased above +10 ‰ during early N₂O production, suggesting temporary activity of alternative NO reductases. These dynamics were only resolved through continuous QCLAS measurements, highlighting the importance of time-resolved isotopic observations. While SP remains a useful indicator of NO reduction mechanisms, these results show that even within denitrification, shifts between NO reduction pathways may lead to variable SP signatures.

In parallel, we quantified oxygen atom exchange between nitrite and water using incubations prepared in natural-abundance and ¹⁸O-enriched water. Contrary to expectations from denitrifier-method studies, P. aureofaciens exhibited substantial and highly variable oxygen-atom exchange (38 %–100 %), far exceeding previously reported values (<9 %). In contrast, P. chlororaphis showed consistently high but less variable exchange (∼ 66 %). Resuspension experiments reproduced the characteristic low- and high-exchange behavior reported for these strains under denitrifier-method conditions, demonstrating that these exchange values are specific to the methodological framework and not representative of actively growing systems. These results show that oxygen atom exchange is not governed solely by nitrite reductase identity (NirS vs. NirK) but is strongly modulated by physiological state and metabolic context, including active growth versus stationary-phase resuspension and differences in nitrite turnover. As a result, δ¹⁸O–N₂O cannot be interpreted as a fixed tracer of denitrification pathways outside the constrained conditions of the denitrifier method.

Together, these findings suggest that denitrifying bacteria may generate N₂O with a broader range of δ¹⁸O–N₂O and SP than previously assumed. This calls for a reassessment of N₂O isotopocule interpretations and emphasizes the need to integrate isotopic measurements with physiological and biochemical constraints.

1 Introduction

The intensification of agriculture and fossil fuel combustion over the past century has fundamentally altered the global nitrogen (N) cycle, leading to increased emissions of nitrous oxide (N₂O), a potent greenhouse gas and stratospheric ozone-depleting substance (IPCC, 2023; WMO, 2024). Microbial processes, particularly denitrification – the sequential reduction of nitrate (NO${}_{\mathrm{3}}^{-}$) to dinitrogen (N₂) via nitrite (NO${}_{\mathrm{2}}^{-}$), nitric oxide (NO), and N₂O – account for most anthropogenic N₂O emissions (Denman et al., 2007; Reay et al., 2012). However, apportioning N₂O sources among microbial and abiotic pathways remains challenging due to the diversity of processes involved (Yu et al., 2020).

Stable isotope analysis of N₂O provides an important tool to trace microbial processes and identify N₂O sources. Bulk δ¹⁵N and δ¹⁸O values integrate information on substrate origin and isotope fractionation during N₂O formation (Sutka et al., 2006; Toyoda et al., 2005; Denk et al., 2016). In multistep pathways such as denitrification, the apparent isotope effect reflects the combined influence of multiple enzymatic reactions (Ostrom and Ostrom, 2011). The intramolecular site preference (SP), defined as the difference in ¹⁵N abundance between the central (α) and terminal (β) positions in N₂O (Yoshida and Toyoda, 2000), is widely used to distinguish microbial formation pathways as it is considered to be largely substrate-independent. Bacterial denitrification typically yields SP values near 0 ‰, whereas fungal denitrification, hydroxylamine oxidation, and abiotic nitrite reactions, including chemodenitrification, can produce higher or more variable SP values (Toyoda et al., 2005; Frame and Casciotti, 2010; Ostrom and Ostrom, 2011; Jones et al., 2015; Toyoda et al., 2017; Wei et al., 2019; Yu et al., 2020). Recent work has further highlighted the importance of Fe(II)-mediated nitrite transformations and their potential contribution to abiotic N₂O formation under environmentally relevant conditions (Visser et al., 2020). These low SP values are generally attributed to NO reduction by the canonical nitric oxide reductase NorB. However, recent work has shown that alternative NO detoxification pathways, particularly via flavohemoglobins (Fhp), can produce elevated SP values under high-NO conditions (Wang et al., 2024). These reactions do not represent a separate environmental pathway, but rather an alternative enzymatic fate of NO within denitrifying organisms. Together, these findings demonstrate that while SP remains a powerful discriminator of broad N₂O formation mechanisms, its expression may be more sensitive to which enzymes are involved and to physiological state than is typically assumed.

In contrast, the oxygen isotopic composition of N₂O (δ¹⁸O–N₂O) reflects both NO reduction by NorB and the preceding transformations of nitrate and nitrite, and depends on the balance between nitrate-derived oxygen, nitrite–water exchange, and branching isotope effects. The extent of oxygen atom exchange between nitrite and water prior to NO reduction is a particular point of variation. Among denitrifiers, two structurally distinct nitrite reductases are found: the cytochrome cd₁-type NirS and the copper-containing NirK. Differences in oxygen isotope exchange between nitrogen oxide intermediates and ambient water have often been attributed to Nir identity, largely based on observations from the denitrifier method developed for nitrate ${}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}$ and ${}^{\mathrm{18}}\mathrm{O}{/}^{\mathrm{16}}\mathrm{O}$ isotope analysis (Casciotti et al., 2002). Under these stationary-phase, washed-cell conditions, Pseudomonas chlororaphis subsp. chlororaphis (NirS) incorporates a large fraction of oxygen from water into N₂O (39 %–76 %), whereas the closely related Pseudomonas chlororaphis subsp. aureofaciens (NirK) shows minimal exchange (∼ 6 %). This contrast has often been interpreted as evidence that NirS and NirK differ systematically in their influence on δ¹⁸O–N₂O expression (Kool et al., 2007; Gruber et al., 2022). However, this inference is based on a narrow experimental framework and has not been systematically tested under active growth conditions. Earlier microbiological studies (e.g., Ye et al., 1991) and more recent work in soils and pure cultures report substantial variability in oxygen atom exchange behavior that cannot be explained by a simple NirK–NirS dichotomy (Lewicka-Szczebak et al., 2016; Rohe et al., 2017; Yu et al., 2020). Whether observed δ¹⁸O–N₂O variability reflects intrinsic enzyme properties or instead arises from physiological state, substrate availability, and reaction dynamics therefore remains unresolved.

The denitrifier method not only provides well-established information on the behavior of NirS- and NirK-bearing denitrifiers but also serves as a calibration framework for isotopic analyses. Complete conversion of nitrate to N₂O allows direct determination of δ¹⁵N–NO${}_{\mathrm{3}}^{-}$ from δ¹⁵N–N₂O (Sigman et al., 2001). For oxygen isotopes, however only one of the six oxygen atoms originally present in the combined nitrate pool is retained in N₂O, while the others are abstracted and transferred to water during reduction. Under controlled conditions where oxygen atom exchange is low and invariant, the offset between δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ and δ¹⁸O–N₂O remains constant, enabling correction of δ¹⁸O–N₂O measurements (Casciotti et al., 2002). This approach implicitly assumes that oxygen atom exchange remains stable across experimental conditions. If exchange varies with physiological state or reaction dynamics, the δ¹⁸O–N₂O offset is no longer constant, and δ¹⁸O–N₂O cannot be interpreted as a fixed tracer of nitrite reductase identity. Understanding the controls on oxygen atom exchange during denitrification is therefore important both for interpreting δ¹⁸O–N₂O signatures and for evaluating the growth conditions under which the denitrifier method yields reliable results.

In this study, we investigate how nitrite reductase type, substrate availability, and growth phase influence N₂O isotopic signatures in two closely related denitrifier strains, P. aureofaciens and P. chlororaphis, both lacking NosZ and therefore accumulating N₂O. We combine (i) real-time measurements of δ¹⁵N, δ¹⁸O, and SP using quantum cascade laser absorption spectroscopy (QCLAS) with (ii) isotope ratio mass spectrometry (IRMS) analysis of the accumulated product in closed batch incubations to compare active growth and resuspension conditions. This experimental design allows us to separate the effects of physiological state during active growth from those associated with washed-cell resuspension conditions during N₂O production.

Together, this approach addresses a central question: to what extent do N₂O isotopic signatures reflect intrinsic enzyme properties versus differences associated with physiological state and experimental conditions? Resolving this distinction is critical for evaluating the validity and limitations of widely used interpretive frameworks, including the proposed relationship between nitrite reductase identity (NirK/NirS) and the degree of oxygen atom exchange with water and the broader applicability of the denitrifier method, and the interpretation of SP as a stable proxy for NorB-mediated NO reduction.

2 Material & Methods

2.1 General experimental framework

2.1.1 Bacterial strains

Pseudomonas chlororaphis subsp. aureofaciens (formerly P. aureofaciens, ATCC 13985) and Pseudomonas chlororaphis subsp. chlororaphis (formerly P. chlororaphis, ATCC 9446) were obtained from the University of Basel Aquatic and Isotope Biogeochemistry culture collection. Growth protocols were adapted from the denitrifier method (Sigman et al., 2001; Casciotti et al., 2002; Weigand et al., 2016).

2.1.2 Overview of the experiments

Two complementary incubation approaches were used to determine how species identity and physiological state influence N₂O isotopic signatures. All experiments were performed in either natural-abundance water (nat) or ¹⁸O-enriched water (en), and all media are described in Sect. 2.1.3.

Experiment codes follow the structure X_species_water, where X can be GF for gas flushed incubations or CB denotes closed-batch incubation, CB-R denotes a resuspension assay in which actively grown cultures were harvested by centrifugation and resuspended in a defined nitrate-containing medium, following an approach adapted from the denitrifier method used to analyse the N and O isotopic composition of nitrate (Sigman et al., 2001; Casciotti et al., 2002; Weigand et al., 2016), CB-RS indicates a resuspension assay using nitrate reference standards. Species can be aur or chlor, which denotes P. aureofaciens and P. chlororaphis, respectively, and water can be nat and en indicating natural-abundance or ¹⁸O-enriched water.

Table 1 Overview of experimental conditions for gas-flushed (GF) and closed-batch (CB) incubations. Experiments were conducted with P. aureofaciens (P. aur) and P. chlororaphis (P. chlor) using natural-abundance (nat) or ¹⁸O-enriched (en) water. Gas flushed incubations (GF_aur_nat, GF_aur_en, GF_chlor_nat) were performed during active growth under continuous N₂ stripping. Closed-batch incubations include: (i) active-growth experiments in natural-abundace or ¹⁸O-enriched water (CB_aur_nat, CB_chlor_nat, CB_aur_en, CB_chlor_en); (ii) stationary-phase resuspension experiments in natural-abundance or ¹⁸O-enriched water (CB-R_aur_nat, CB-R_chlor_nat, CB-R_aur_en, CB-R_chlor_en); and (iii) nitrate-standard resuspension assays (CB-RS_aur, CB-RS_chlor) using USGS32, USGS34, IAEA-N3, and ¹⁸O-enriched IAEA-N3 (IAEA-N3-spiked).

^* For ¹⁸O-enriched resuspension assays with IAEA-N3-spiked, incubation water was prepared by mixing natural water (δ¹⁸O = −9.5 ‰) with ¹⁸O-enriched water (δ¹⁸O ≈ +780 ‰), yielding a final δ¹⁸O–H₂O of +187.8 ‰ (see Sect. 2.1.4).

Gas-flushed (GF) incubations (GF_aur_nat, GF_aur_en, GF_chlor_nat) were conducted in a temperature-controlled bioreactor under continuous N₂ stripping, allowing real-time quantification of N₂O concentration and isotopic composition during active growth (Fig. 1).

Closed-batch (CB) incubations (CB_aur_nat, CB_chlor_nat, CB_aur_en, CB_chlor_en, CB-R_aur_nat, CB-R_chlor_nat, CB-RS_aur, CB-RS_chlor) were conducted in sealed vials and served three purposes. First, active-growth closed-batch incubations (CB_aur_nat, CB_chlor_nat, CB_aur_en, CB_chlor_en) were conducted in active-growth medium to generate cumulative N₂O for quantifying water–nitrite oxygen exchange during growth. Second, for stationary-phase resuspension incubations (CB-R_aur_nat, CB-R_chlor_nat), cultures were harvested by centrifugation (4700 rpm, 10 min) and resuspended in a defined nitrate medium prepared in natural-isotope-abundance water. Third, nitrate-standard resuspension assays (CB-RS_aur, CB-RS_chlor) replaced KNO₃ with USGS32, USGS34, IAEA-N3, or ¹⁸O-enriched IAEA-N3 (see Sect. 2.1.4).

2.1.3 Media composition and resuspension procedure

Two distinct media formulations were used depending on experimental objective: an active-growth medium for gas-flushed and closed-batch incubations, and a defined resuspension medium for stationary-phase assays and nitrate-standard experiments. Active growth was carried out in a denitrifier-method medium formulation (Weigand et al., 2016) containing final concentrations of 10 mM KNO₃, 15 mM NH${}_{\mathrm{4}}^{+}$ supplied as (NH₄)₂SO₄, 30 g L⁻¹ tryptic soy broth (TSB, Merck Germany), and 5 g L⁻¹ K₂HPO₄. Cultures grown in this medium reduced nitrate quantitatively and produced N₂O for isotopic analysis.

For stationary-phase resuspension incubations, actively grown cultures were harvested by centrifugation and resuspended in a simplified medium (Weigand et al., 2016) containing 7.5 mM NH${}_{\mathrm{4}}^{+}$ supplied as NH₄Cl, 30 g L⁻¹ TSB, and 5 g L⁻¹ K₂HPO₄ in the final solution. Cell pellets were resuspended in 3 mL of this medium in 20 mL crimp-sealed vials. Vials were purged with N₂ for ∼ 1 h to establish an anoxic headspace and to remove pre-existing gaseous products (including N₂O) prior to initiating the incubation. The resuspension protocol was adapted from the denitrifier method; after purging, 20 nmol KNO₃ was added, and cultures were incubated overnight to allow quantitative conversion to N₂O. Thereafter, N₂O was analyzed by GC-IRMS from the vial headspace.

For CB_RS_aur and CB_RS_chlor (closed-batch resuspension assays converting nitrate reference standards with P. aureofaciens and P. chlororaphis, respectively; experiment codes defined in Sect. 2.1.3 and Table 1), the same resuspension procedure was used, except that the nitrate substrate (20 nmol KNO₃) was replaced with 20 nmol of an international nitrate isotope reference standard (USGS32, USGS34, IAEA-N3, or ¹⁸O-enriched IAEA-N3-spike).

2.1.4 Characterization of ¹⁸O-labelled water

Oxygen exchange between reaction intermediates and water in both GF and CB experiments was assessed using replicate incubations in natural-abundance and ¹⁸O-enriched water. The natural water used for all baseline incubations had a δ¹⁸O–H₂O = −9.51 ± 0.22 ‰. Two batches of ¹⁸O-enriched water were prepared and used: one with δ¹⁸O–H₂O = +68.31 ± 0.17 ‰, and a second with δ¹⁸O–H₂O = +73.53 ± 0.29 ‰ (Table 1). For nitrate-standard experiments (CB-RS-aur and CB-RS-chlor, Table 1), an ¹⁸O-enriched IAEA-N3 spike was prepared by mixing 1 mL of ¹⁸O-enriched water (δ¹⁸O–H₂O ≈ +780 ‰) with 3 mL of natural water (δ¹⁸O–H₂O = −9.5 ‰), yielding a solution with δ¹⁸O–H₂O ≈ +187.8 ‰.

The δ¹⁸O isotopic composition of both natural and ¹⁸O-enriched waters was measured using a cavity ring-down spectroscopy (CRDS) analyzer (L2130-i, Picarro Inc., USA). Measurements were calibrated on the VSMOW–SLAP scale using three international reference waters: VSMOW2 (δ¹⁸O = 0.00 ± 0.02 ‰), SLAP2 (−55.50 ± 0.02 ‰), and IAEA-607 (+99.02 ± 0.13 ‰), which were measured together with the samples during each analytical run to establish a three-point isotope calibration.

2.1.5 Endpoint N₂O isotopic analysis (IRMS)

Accumulated N₂O produced during incubations was analyzed using gas chromatography coupled to isotope ratio mass spectrometry (GC-IRMS; Delta V Plus coupled to a GasBench system for N₂O purification, Thermo Fisher Scientific, Germany). Isotopic composition was referenced to AIR–N₂ (δ¹⁵N) and VSMOW (δ¹⁸O) using three laboratory N₂O reference gases (STD1–STD3; ∼ 90 ppm N₂O in N₂) measured alongside samples. Assigned delta values (in ‰) were: STD1: δ¹⁵N^α = −22.21 ± 0.39, δ¹⁵N^β = −49.28 ± 0.40, SP = 27.08 ± 0.56, δ¹⁵N^bulk = −35.74 ± 0.07, δ¹⁸O = 26.94 ± 0.23; STD2: δ¹⁵N^α = 1.71 ± 0.47, δ¹⁵N^β = 94.44 ± 0.70, SP = −92.73 ± 0.84, δ¹⁵N^bulk = 48.09 ± 0.23, δ¹⁸O = 36.01 ± 0.27; STD3: δ¹⁵N^α = 17.11 ± 0.12, δ¹⁵N^β = −3.43 ± 0.17, SP = 20.54 ± 0.21, δ¹⁵N^bulk = 6.85 ± 0.06, δ¹⁸O = 35.39 ± 0.17. Data processing, including scale normalization and correction for ion-source scrambling effects, was performed using the PyIsotopomer package (Kelly et al., 2023).

2.2 Gas-flushed (GF) incubations and online isotope monitoring

2.2.1 Experimental setup for gas-flushed incubations

For continuous N₂O isotope monitoring under cultivation conditions, strains were grown in the active-growth medium described in Sect. 2.1.2 (Fig. 1). Incubations were performed at 30 ± 1 °C for P. aureofaciens and 20 ± 1 °C for P. chlororaphis, reflecting optimal conditions for growth and N₂O production. Cultures were stirred using a magnetic stirrer to ensure homogeneous mixing, and maintained anaerobic by continuous N₂ flushing (100 mL min⁻¹). Dissolved oxygen, pH (Mettler-Toledo, Switzerland), and optical density (OD₅₅₀) were monitored throughout the experiments. Substrate consumption was monitored by daily nitrite measurements. Incubations were typically completed within 5–8 d. Isotopic measurements were stopped when N₂O concentrations dropped below 50 ppm, whereas concentration measurements by FTIR continued until N₂O levels dropped below detection limits (0.0075 ppm N₂O), confirming complete turnover of nitrogen substrates (Fig. 2). Gas exiting the bioreactor was conditioned prior to analysis; carbon dioxide and water vapor were removed using two consecutive washing bottles containing 1 M NaOH, followed by permeation drying (Perma Pure, USA) (Fig. 1). The CO₂-free, dehumidified sample gas was subsequently filtered through a sintered metal filter (2 µm pore size) and analyzed for trace gas concentrations (N₂O, NO) using an online FTIR analyzer (CX-4000 or CX-4015, Gasmet Technologies, Finland) (Wunderlin et al., 2012). Three-minute average N₂O concentration values were used to calculate dilution ratios and regulate the MFC settings to maintain an approximately constant N₂O concentration (∼ 50 ppm) in the diluted sample gas, which minimized concentration effects on isotope ratio measurements by QCLAS (Wunderlin et al., 2013). Choosing 50 ppm as target concentration for N₂O isotope analysis was a compromise between data coverage and response time of the experimental setup but does not represent a lower threshold of the analytics.

Figure 1 Schematic of the setup applied for bacterial incubations, continuous gas sampling, and real-time analysis of trace gases and N₂O isotopologues. N₂ is used to purge reaction products from the liquid phase via the headspace of the incubation vessel toward the analyzers. Trace gas concentrations (N₂O, NO, residual CO₂ and H₂O) are determined in the CO₂-free and dehumidified sample gas by FTIR spectroscopy. The N₂O concentration is used to set the MFC for N₂ dilution and stabilize the N₂O concentration for QCLAS analysis to 50 ppm. Downstream of the FTIR, the gas is directed to the QCLAS for isotopic analysis of N₂O. Calibration of the QCLAS is conducted via automated switching between sample gas and reference standards (valves 1–5). Calibration gas (Cal 1, Cal 2) flows are regulated with mass flow controllers (MFC). During calibration phases, the sample gas is vented to the atmosphere (valve 1); during measurement phases valves 1, 2 and 5 are switched in parallel, directing the sample gas toward the QCLAS. A pressure controller upstream of the QCLAS stabilizes the multipath cell pressure and ensures stable flow conditions.

Automated sample gas dilution and calibration of the QCLAS system were controlled via a LabVIEW interface (National Instruments Corp., USA) connected to mass flow controllers (Vögtlin Instruments Inc., Switzerland) and electromagnetic valves (Series 9, Parker Hannifin, USA).

2.2.2 Online analysis of N₂O isotopic composition (QCLAS)

Temporally-resolved (1 Hz) N₂O isotopic analysis in the diluted sample gas was performed using a compact quantum cascade laser absorption spectrometer (mini-TILDAS, pathlength 76 m, Aerodyne Research Inc., USA), operated in flow-through mode at a sample pressure of 26.6 hPa (20 Torr) (Ibraim et al., 2018). The instrument simultaneously quantified the concentrations of the four most abundant N₂O isotopologues in the ν₃ absorption band (2203 cm⁻¹): ¹⁴N¹⁴N¹⁶O, ¹⁴N¹⁵N¹⁶O (¹⁵N^α), ¹⁵N¹⁴N¹⁶O (¹⁵N^β), and ¹⁴N¹⁴N¹⁸O. Raw concentrations were logged in ASCII format. Time series for each isotopologue were averaged to 60 s intervals as the first step in the data-processing workflow, prior to any correction or calibration. Isotopologue ratios (¹⁴N¹⁵N¹⁶O${/}^{\mathrm{14}}$N¹⁴N¹⁶O, ¹⁵N¹⁴N¹⁶O${/}^{\mathrm{14}}$N¹⁴N¹⁶O, and ¹⁴N¹⁴N¹⁸O${/}^{\mathrm{14}}$N¹⁴N¹⁶O) were then calculated from these averaged concentrations using a customized R script. Allan deviations at a 60 s averaging time were used to propagate uncertainties in isotope delta values (see Appendix A).

Two N₂O isotope reference gases diluted in N₂ were used (Mohn et al., 2022); CG1 (RM1A, anchor gas, in ‰): δ¹⁵N^α = −0.22 ± 0.46, δ¹⁵N^β = 0.84 ± 0.46, δ¹⁸O = 39.22 ± 0.15; and CG2 (RM3A, span gas, in ‰): δ¹⁵N^α = 50.96 ± 0.47, δ¹⁵N^β = 53.06 ± 0.47, δ¹⁸O = 103.04 ± 0.16. CG1 was measured every 40 min for 10 min, to correct for instrumental drift, while the calibration span was determined twice daily analyzing CG1 and CG2. From the measured delta values, the following parameters were calculated: δ¹⁵N-bulk = (δ¹⁵N^α + δ¹⁵N^β)$/\mathrm{2}$ and SP = δ¹⁵N^α−δ¹⁵N^β, following the nomenclature of Yoshida and Toyoda (2000). Data processing steps are detailed in Appendix A.

For validation an independent N₂O isotope reference gas (RM3B) with assigned values of δ¹⁵N-bulk = 16.08 ± 0.0 5 ‰, δ¹⁸O = 55.17 ± 0.15 ‰, and SP = −0.68 ± 0.91 ‰, was diluted using a two-step diluter (METAS, Switzerland) to a target concentration of 50 ppm N₂O. Measurements were conducted during a short validation campaign in April–May 2024. RM3B was analyzed within the existing CG1/CG2 calibration framework, and the measured values agreed with assigned values within <0.5 ‰ across all isotope parameters.

2.2.3 Isotopic Fractionation Analysis (Rayleigh Model – QCLAS Time Series)

Isotope fractionation during denitrification was assessed using a Rayleigh-type cumulative product model, following the definitions of enrichment factors (ε) provided by Mariotti et al. (1981) and Sutka et al. (2006), which describe the isotopic discrimination between the substrate and the accumulated product over the course of the reaction.

Changes in the isotopic composition of N₂O were modeled as a function of nitrate reduction using the equation:

$$\begin{array}{}\text{(1)}& y=a+b\times \left[x\right]\end{array}$$

where y is the isotopic composition (δ value) of the N₂O product, a and b are fitted coefficients, and [x] represents the reaction progress. The variable [x] was calculated using the Rayleigh equation (Sutka et al., 2006):

$$\begin{array}{}\text{(2)}& x=-f\times {\displaystyle \frac{\ln \left(f\right)}{(\mathrm{1}-f)}}\end{array}$$

Here, f is the fraction of remaining nitrate, calculated as:

$$\begin{array}{}\text{(3)}& f=\mathrm{1}-\left(\mathrm{2}\times {\displaystyle \frac{n_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}}{n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}}}\right)\end{array}$$

where n denotes the molar quantities of accumulated N₂O and initial NO${}_{\mathrm{3}}^{-}$, respectively. The slope b corresponds to the apparent enrichment factor ε (in ‰), while the intercept a represents the initial isotopic composition of the product pool. This interpretation assumes Rayleigh-type fractionation behavior, i.e. a closed substrate pool with unidirectional consumption and negligible back-reaction. Microbial incubations featuring multistep processes may deviate from these conditions, particularly when O isotope exchange with water or partial recycling of intermediates occurs. Nevertheless, the Rayleigh model provides a useful first-order approximation for comparing fractionation patterns across experiments.

More complex Rayleigh formulations have been proposed to explicitly account for intramolecular isotope effects during N₂O formation, including site-specific treatments of δ¹⁵N^α and δ¹⁵N^β (e.g., Rivett et al., 2025). In the present study, Rayleigh modeling was applied only to δ¹⁵N-bulk, for which the standard cumulative product formulation is sufficient.

Fractionation calculations were performed using a custom R pipeline that included uncertainty propagation for N₂O gas concentration, sample gas flow, and the initial substrate amount (NO${}_{\mathrm{3}}^{-}$). Full computational details are provided in the Appendix A.

2.2.4 Monitoring of nitrate and nitrite during GF incubations and nitrate isotope characterization

During gas-flushed incubations, NO${}_{\mathrm{3}}^{-}$ and NO${}_{\mathrm{2}}^{-}$ concentrations were monitored daily to track substrate depletion and the progression of nitrate reduction. Nitrite was measured spectrophotometrically immediately after sampling using the Griess assay (Hansen and Koroleff, 1999). For nitrate concentration analysis, 1 mL samples were collected daily, filtered through 0.22 µm syringe filters, and stored in Eppendorf tubes at −18 °C prior to analysis. Nitrate concentrations were determined by quantitative reduction to nitric oxide (NO) using acidic vanadium(III), followed by chemiluminescence detection (Braman and Hendrix, 1989).

The isotopic composition of the nitrate substrates used to prepare incubation media was determined prior to the experiments. In addition, selected samples from GF incubations were analyzed to assess changes in the isotopic composition of the residual nitrate pool during denitrification. Nitrate isotope analyses were not performed for closed-batch incubations.

For nitrate isotopic analysis, aliquots containing 20 nmol N were converted to N₂O using the denitrifier method (Sigman et al., 2001; Casciotti et al., 2002). The nitrate stock solution used for all active-growth media had a δ¹⁵N–NO${}_{\mathrm{3}}^{-}$ = +5.7 ± 0.3 ‰ and a δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ = +12.4 ± 0.3 ‰ (n=3).

Calibration was performed against international nitrate reference materials USGS32 (KNO₃, δ¹⁵N = +180 ‰, δ¹⁸O = +25.4 ± 0.2 ‰), USGS34 (KNO₃, δ¹⁵N = −1.8 ± 0.1 ‰, δ¹⁸O = −27.78 ± 0.37 ‰), and IAEA-N3 (KNO₃, δ¹⁵N = +4.7 ± 0.2 ‰, δ¹⁸O = +25.6 ± 0.4 ‰). Additional reference materials included UBN-1 (δ¹⁵N = +14.15 ‰, δ¹⁸O = +25.7 ‰), Deep Pacific nitrate (δ¹⁵N ≈ +5.0 ‰, δ¹⁸O ≈ +2.0 ‰), and an IAEA-N3-spike standard (IAEA-N3 dissolved in water with δ¹⁸O–H₂O = +780 ‰, see Sect. 2.1.4).

2.3 Closed batch (CB) incubations

2.3.1 Active-growth incubations (natural-water and enriched-water)

Closed-batch incubations were used to generate cumulative N₂O under controlled growth conditions. All experiments were conducted in 500 mL Wheaton bottles containing 400 mL of active-growth medium (Sect. 2.1.2) and incubated at 23 °C for 7 d. Experiments performed in natural-abundance water (CB_aur_nat, CB_chlor_nat) and ¹⁸O-enriched-water (CB_aur_en, CB_chlor_en) differed only in the isotopic composition of the water used to prepare the medium. The enriched-water incubations produced δ¹⁸O–N₂O endpoint values that were regressed against δ¹⁸O–H₂O to quantify oxygen atom exchange between nitrite and water. After complete nitrate reduction, accumulated N₂O was analyzed by GC-IRMS (Sect. 2.1.5).

2.3.2 Resuspension incubations in defined nitrate medium (stationary phase)

To obtain stationary-phase δ¹⁸O–N₂O endpoint values, actively grown cultures were pelleted and resuspended in the defined nitrate medium described in Sect. 2.1.2. These resuspension assays (CB-R_aur_nat, CB-R_chlor_nat) were performed with stationary-phase cultures resuspended in fresh nitrate medium. The experiments were conducted only in natural-abundance water. After overnight nitrate reduction, the accumulated N₂O was analyzed by GC-IRMS (Sect. 2.1.5).

2.3.3 Resuspension incubations with nitrate isotope standards (quantification of oxygen isotope exchange)

Additional stationary-phase incubations were performed to quantify oxygen-atom exchange between nitrite and water using nitrate standards with contrasting δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ values (CB-RS_aur, CB-RS_chlor): USGS32, USGS34, IAEA-N3. These were accompanied by an ¹⁸O-enriched IAEA-N3-spike to match the typical approach for quantifying oxygen-atom exchange in the denitrifier method (Sect. 2.1.2). Following quantitative reduction of the added nitrate, δ¹⁸O–N₂O was measured by GC-IRMS (Sect. 2.1.5). The resulting δ¹⁸O–N₂O values were regressed against the known δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ values of the standards. The δ¹⁸O–N₂O versus δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ relationship was applied to derive stationary-phase oxygen-exchange fractions.

This nitrate-standard approach provides an independent estimate of oxygen exchange complementary to the enriched-water experiments (Sect. 2.3.1). Whereas regressions of δ¹⁸O–N₂O versus δ¹⁸O H₂O quantify exchange from the sensitivity of N₂O to water isotopic composition, regressions of δ¹⁸O–N₂O versus δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ quantify the O-atom exchange from the degree of scale compression relative to nitrate isotope standards. Under conditions of no oxygen exchange, δ¹⁸O–N₂O scales directly with δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ (slope ≈ 1), whereas increasing exchange reduces this dependence (slope < 1). The fraction of oxygen atoms in N₂O derived from water can therefore be estimated from the regression slope (Casciotti et al., 2002; Snider et al., 2009; Lewicka-Szczebak et al., 2016).

3 Results and Discussion

3.1 Denitrifying growth and near-quantitative N₂O production in gas-flushed and closed-batch incubations

Both P. chlororaphis (NirS-bearing) and P. aureofaciens (NirK-bearing) showed consistent denitrifying behavior under anoxic conditions, with N₂O production closely coupled to nitrate reduction. Biomass accumulation and substrate consumption followed the expected progression of anoxic denitrifying growth, indicating that the incubation conditions supported stable and active metabolism throughout.

Biomass increased during the phase of active N₂O production and stabilized as nitrate became limiting, while NO${}_{\mathrm{3}}^{-}$ concentrations decreased in parallel with N₂O formation (Fig. 2C, D). This tight coupling indicates efficient conversion of nitrate to N₂O, with only transient accumulation of nitrite (Fig. 2E). This tight coupling indicates efficient conversion of nitrate to N₂O with no substantial accumulation of intermediates. Accordingly, cumulative N₂O yields indicated efficient denitrification (Fig. 2A), although they varied between incubations, indicating that N₂O was not always the sole nitrogen oxide produced (Appendix B, Fig. B1).

Across gas-flushed incubations, N₂O yields ranged from 60 %–100 % for P. aureofaciens (n=6) and 50 %–100 % for P. chlororaphis (n=2). These results demonstrate that both incubation approaches supported efficient denitrification and provided well-constrained systems for isotopic interpretation. Dissolved O₂ concentrations remained below detection (<1 µM), and pH varied only slightly (6.5–7.5), confirming stable anoxic conditions throughout the experiments. Nitrite accumulated transiently during active nitrate reduction but did not persist, indicating rapid turnover within the denitrification pathway.

While such growth dynamics are well established for denitrifying systems (Zumft, 1997), the present gas-flushed setup enables direct observation of N₂O production dynamics under continuous stripping, providing a temporally resolved view that is not accessible in conventional closed systems.

In closed-batch incubations, near-complete nitrate reduction was similarly observed, as indicated by the absence of residual NO${}_{\mathrm{3}}^{-}$ and NO${}_{\mathrm{2}}^{-}$ and the cessation of N₂O production. These results demonstrate that both incubation approaches achieved near-quantitative conversion of nitrate to N₂O under the conditions applied, providing well-constrained systems for isotopic interpretation. N₂O isotopic compositions were determined from endpoint measurements and are discussed in Sect. 3.3 and 3.4.

Figure 2 Representative temporal dynamics of N₂O production over days, cumulative N₂O yield, and culture characteristics during incubation of P. aureofaciens (GF_aur). (A) Cumulative N₂O yield (% of initial nitrate converted to N₂O); (B) Instantaneous N₂O formation, measured in N₂ purge gas; (C) Optical density at 550 nm (OD₅₅₀, circles), as a proxy for biomass accumulation; (D) Residual nitrate concentration; (E) Nitrite concentration over the course of the experiment.

Figure 3 Temporal evolution of N₂O isotopic composition during gas-flushed incubations in natural-abundance water (GF_aur_nat, GF_chlor_nat). Panels show isotopic composition as a function of reaction progress for P. aureofaciens (n=6) (Nirk) and P. chlororaphis (n=2) (NirS). Reaction progress (f) was calculated from cumulative N₂O production and rescaled for each incubation such that the first sampled point corresponds to f=0 and the final point to f=1, allowing comparison across experiments with different final yields. Measurements were grouped into equally spaced bins of reaction progress, and isotopic values were averaged within each bin. Points therefore represent bin-averaged values, with vertical error bars indicating within-bin variability and horizontal error bars indicating the spread in reaction progress of contributing measurements. (A) δ¹⁵N–Bulk versus the Rayleigh coordinate $\mathrm{1}-\frac{-f\cdot \ln \left(f\right)}{\mathrm{1}-f}$, which linearizes Rayleigh-type isotope fractionation during substrate consumption. (B) Site preference (SP) versus reaction progress (1−f). (C) δ¹⁸O–N₂O versus reaction progress (1−f). Panels (B) and (C) use the simpler (1−f) coordinate to directly visualize temporal trends, whereas panel (A) uses the Rayleigh transformation to resolve fractionation behavior. In panel (C), horizontal lines indicate ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ (−9.5 ‰; solid grey) and ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{NO}}_{\mathrm{2}},\mathrm{eq}}$ (+4.5 ‰; dashed grey). The shaded red band (+14.5 to +19.5 ‰) represents the expected δ¹⁸O–N₂O range under full nitrite–water equilibration with branching fractionation.

3.2 Rayleigh-type ¹⁵N enrichment in the N₂O pool during nitrate reduction

The δ¹⁵N-bulk of accumulated N₂O increased linearly over the course of nitrate reduction in all incubations when expressed against the reaction coordinate $\mathrm{1}-(-f\cdot \ln (f)/(\mathrm{1}-f\left)\right)$ using the Rayleigh equation as presented in Mariotti et al. (1981) and Sutka et al. (2006) (Fig. 3A). The isotopic composition of the accumulated reaction product N₂O was calculated from the amount and isotopic composition of instantaneously formed and analysed N₂O. This pattern is consistent with Rayleigh-type enrichment expected during unidirectional substrate consumption under closed-system conditions. Enrichment factors (ε¹⁵N) were estimated for each incubation by linear regression of δ¹⁵N-bulk against the reaction coordinate using the specific reaction progress of each experiment (individual experiment regressions are shown in Appendix B Fig. B1). The rescaling and binning shown in Fig. 3A serve only to visualize common trajectories across incubations.

Enrichment factors (ε¹⁵N) derived from this linear Rayleigh approximation ranged from +16 to +55 ‰ (35.5 ± 12 ‰) for P. aureofaciens (n=6) and from +13 ‰ to +45 ‰ (25.4 ± 14 ‰) for P. chlororaphis (n=2). Variability across replicate incubations likely reflects differences in nitrate turnover rates and additional biological variability, although no systematic relationship between nitrate reduction rate and ε¹⁵N could be resolved with the present dataset.

The applicability of the linear Rayleigh model is supported by the consistent increase in δ¹⁵N-bulk over the reaction coordinate, which reflects the expected kinetic isotope enrichment pattern during progressive substrate consumption (Mariotti et al., 1981). Nevertheless, the linear Rayleigh approximation represents an idealized description when applied to multistep microbial pathways such as denitrification. In such systems, intrinsic isotope effects may be modulated by intermediate pool dynamics, diffusion limitation, or partial reversibility, potentially leading to deviations from a single kinetic fractionation factor. These complexities have been discussed in detail by Haslun et al. (2018) and are not explicitly resolved here. Rather, the Rayleigh analysis is used as a first-order framework to derive apparent ε¹⁵N values from the cumulative N₂O product pool, allowing comparison across strains.

To place the ε¹⁵N estimates obtained in this study in context, we compared them with a compilation of fractionation factors for N₂O production from a range of denitrifying organisms and environmental systems (Fig. 4). This dataset, largely derived from Denk et al. (2016), includes enrichment factors determined under diverse experimental conditions and using different formulations of the Rayleigh model applied to either the instantaneous or accumulated product, or to the substrate. Nonetheless these enrichment factors provide a context for comparing the magnitude of isotope fractionation observed in the present study. The ε¹⁵N values obtained here fall within the broader range reported in the literature and align particularly well with previous results for Pseudomonas spp. under nitrate-reducing conditions. Additionally, we include instantaneous isotope effects derived from non-linear Rayleigh formulations, reported as η¹⁵N values by Haslun et al. (2018). Although expressed using a different notation, these values are conceptually analogous to ε¹⁵N and allow comparison with the fractionation factors derived here. Taken together, these comparisons show that the magnitude of fractionation observed here falls well within the established range for denitrifying systems, indicating that the gas-flushed setup does not introduce atypical isotope effects.

Figure 4 Isotopic enrichment factors (ε¹⁵N) for N₂O production across denitrifying microbial communities reported in the literature and observed in this study. Most literature values are compiled from Table S1 of Denk et al. (2016), which integrates enrichment factors derived from different experimental systems and using different mathematical formulations (e.g., soils, aqueous environments, and pure-culture incubations). Instantaneous isotope effects reported as η¹⁵N by Haslun et al. (2018) for P. aureofaciens, and P. chlororaphis, as well as ε¹⁵N for P. fluorescens (Toyoda et al., 2005) are also included for comparison. For clarity and comparability, all values shown here are expressed using a common sign convention, where positive ε¹⁵N indicates normal isotope effects, i.e., preferential reaction of the light isotope.

3.3 Transient elevated SP suggests variable NO reduction pathways

SP values measured at the endpoint of closed-batch incubations clustered near 0 ‰ for both P. aureofaciens and P. chlororaphis (Fig. 5B), within the canonical range reported for bacterial denitrification (−8 ‰ to +10 ‰; Yu et al., 2020). This outcome is consistent with the common assumption that SP during bacterial denitrification is invariant and reflects NO reduction by the nitric oxide reductase NorB, which yields values near 0 ‰. This interpretation is supported by measurements from intact denitrifying cultures and by direct assays of purified NorB enzyme (Sutka et al., 2006; Yamazaki et al., 2014; Wang et al., 2024; Rivett et al., 2025; Fig. 5A). Because these measurements integrate N₂O produced over the full course of the reaction, they represent time-averaged isotopic signatures. When assessed using these conventional accumulated-product approaches, N₂O formation appears broadly consistent with NorB-mediated denitrification, although such temporal integration may obscure short-lived deviations from canonical SP behavior.

In contrast to such endpoint observations, our time-resolved dataset shows that elevated SP values (+8 ‰ to +20 ‰) arise transiently but reproducibly during the early stages of N₂O formation under gas-flushed conditions (Figs. 3B; 5B). Elevated SP values have occasionally been reported in denitrifying cultures. Toyoda et al. (2005), for example, observed SP values up to +22 ‰ in P. fluorescens, which they attributed to an abiotic pathway of unknown mechanism. Over the course of nitrate reduction, SP subsequently converged toward ∼ 0 ‰ as the reaction progressed (Fig. 3B). When averaged over the full reaction progress, gas-flushed incubations yielded SP values near 0 ‰, with a slightly elevated median and broader variability compared to closed-batch endpoint values (Fig. 5B), yet still within the canonical range reported for bacterial denitrification. This convergence toward canonical SP values, despite pronounced early-stage elevations (Fig. 3B), indicates that accumulated N₂O in closed-batch systems integrates over temporally variable production pathways and thereby masks transient deviations in SP. These transient SP elevations are most clearly expressed in P. aureofaciens (n=6). In P. chlororaphis (n=2) they are less apparent in the binned averages due to limited replication and experiment-to-experiment variability, but they are evident in individual incubation trajectories (Appendix B Fig. B1).

Figure 5 Site preference (SP) of N₂O produced by three classes of N₂O-forming systems. (A) Literature-derived SP values grouped by system type: left, intact denitrifiers with genetically verified N₂O-forming enzymes, where both strain identity and the active enzyme system (NorB, Hcp–Hcr, or Fhp) were confirmed (Xu et al., 2024; Wang et al., 2024); center, intact denitrifiers, strains are known but additional N₂O-forming pathways cannot be excluded (Toyoda et al., 2005; Yu et al., 2020); and right, isolated enzyme assays, in which purified NorB was studied directly, yielding enzyme-specific SP values (Yamazaki et al., 2014; Rivett et al., 2025). (B) SP values obtained in this study for intact denitrifiers with known strain background, shown separately for closed-batch and gas-flushed incubation modes. Boxplots show the distribution of SP values within each category; horizontal bars indicate mean ± standard deviation. Gas-flushed incubations represent time-resolved SP measurements, whereas closed-batch incubations reflect SP integrated over the accumulated N₂O pool.

Although still within the broader isotopic space reported for bacterial denitrification and related enzyme systems (Fig. 5; Toyoda et al., 2005; Yamazaki et al., 2014; Haslun et al., 2018; Wang et al., 2024; Xu et al., 2024), the consistent early-stage SP elevations suggest that NorB may not be the sole contributor to N₂O formation during the onset of denitrification. One plausible explanation is that rapid NO accumulation during early Nar/Nir activity initially exceeds the capacity of NorB, such that NO is partially reduced by alternative enzymes until NorB becomes transcriptionally or functionally dominant. Recent work by Wang et al. (2024) directly demonstrated that SP depends on NO reductase identity: NorB activity produced SP values near 0 ‰, whereas flavohemoglobin (Fhp) activity under high-NO conditions yielded elevated SP values of approximately +10 ‰ (Fig. 5A). Using Δfhp mutants and inducible norB expression systems, the authors further showed that the balance between these enzymes shifts with growth phase and NO availability. Although the experimental conditions in that study differ from ours, it is plausible that early nitrate respiration in actively growing cultures similarly produces transient NO accumulation combined with low NorB expression, allowing temporary Fhp activity to elevate SP at the onset of denitrification. Future transcriptomic or proteomic analyses would help confirm which NO reductases are expressed during this early phase.

Importantly, several of the transient SP values observed here (Fig. 5B) exceed not only the typical NorB range but also the Fhp-associated values reported by Wang et al. (2024), motivating consideration of additional NO-reducing pathways. Beyond Fhp, other NO detoxification systems may contribute to transient SP variability. Xu et al. (2024) reported N₂O production during dissimilatory nitrate reduction to ammonium (DNRA) and attributed it to the hybrid cluster protein–hybrid cluster reductase (Hcp–Hcr) system based on genomic and transcriptomic evidence (Fig. 5A). While this attribution remains less firmly established than for NorB or Fhp, it defines a distinct high-SP isotopic signature that broadens the reference space for interpreting transient SP behavior. Flavodiiron proteins, which reduce NO to N₂O via asymmetric diiron intermediates (Caranto et al., 2014a, b), are also encoded in many Pseudomonas genomes, although their SP signatures remain uncharacterized.

Future work integrating SP-resolved N₂O measurements with transcriptomics, proteomics, or targeted inhibitor assays will be essential to determine which NO reductases are active, when they operate, and how their expression depends on metabolic state and environmental conditions. Taken together, these observations indicate that SP expression during denitrification can be more dynamic than implied by static reference ranges derived from endpoint measurements.

3.4 δ¹⁸O systematics during denitrification across strains and incubation conditions

While site preference primarily reflects the identity of NO reductases operating during N₂O formation, the oxygen isotopic composition of N₂O integrates upstream processes, particularly the extent of oxygen atom exchange between nitrite and water prior to NO reduction. Because nitrite is the immediate precursor to NO, its isotopic composition reflects both oxygen inherited from nitrate reduction and any subsequent equilibration with ambient water. As a result, δ¹⁸O–N₂O does not represent a fixed enzymatic property, but rather a composite signal that depends on the relative contributions of nitrate-derived oxygen, nitrite–water exchange, and branching isotope effects. Consequently, its interpretation as a tracer of nitrite reductase identity requires that these processes remain constant – an assumption that has not been tested. Accordingly, δ¹⁸O–N₂O patterns are interpreted relative to reference scenarios spanning nitrate-dominated signatures, full nitrite–water equilibration, and intermediate exchange. In the following sections, we examine how δ¹⁸O–N₂O varies across strains and incubation conditions as an observational framework, before explicitly quantifying oxygen exchange in Sect. 3.4.2.

3.4.1 Strain-dependent δ¹⁸O–N₂O patterns during active growth

A wide range of δ¹⁸O–N₂O endpoint values was observed in natural-abundance water incubations under the two active-growth modes (gas-flushed and closed-batch), as summarized in Fig. 6A. In closed-batch incubations, P. aureofaciens produced relatively low δ¹⁸O–N₂O values (∼ 9 ‰), whereas P. chlororaphis yielded substantially higher values (∼ 47 ‰). Under gas-flushed conditions, δ¹⁸O–N₂O endpoint values shifted in a strain-specific manner: values for P. aureofaciens increased to an intermediate range (26 ‰–42 ‰), while P. chlororaphis produced consistently elevated values (57 ‰–67 ‰). These contrasts indicate a strong incubation-mode sensitivity in P. aureofaciens, whereas P. chlororaphis maintained consistently elevated δ¹⁸O–N₂O values with a less pronounced response to incubation configuration. Time-resolved δ¹⁸O–N₂O trajectories during gas-flushed incubations further highlights this strain-dependent behavior (Fig. 3C). In P. aureofaciens, δ¹⁸O–N₂O starts at high values (∼ 50 ‰–60 ‰) early in nitrate reduction and declines progressively toward ∼ 30 ‰ as the reaction proceeds. In contrast, P. chlororaphis maintains elevated δ¹⁸O–N₂O values throughout the reaction, varying within a narrow band around 60 ‰. Thus, under identical conditions, P. aureofaciens shows strong variability in δ¹⁸O–N₂O, whereas P. chlororaphis maintains consistently high values with comparatively little temporal change.

Figure 6 δ¹⁸O–N₂O signatures for Pseudomonas aureofaciens (NirK) and P. chlororaphis (NirS) incubations in natural-abundance water. (A) Active-growth incubations. Closed-batch experiments show δ¹⁸O–N₂O of the accumulated N₂O pool (n=2 per strain; mean ± SD). Gas-flushed experiments show final δ¹⁸O–N₂O values from time-resolved incubations (P. aureofaciens, n=6; P. chlororaphis, n= 2; mean ± SD). (B) Resuspension closed-batch incubations following transfer of actively grown cells into fresh nitrate medium (n=2 per strain; mean ± SD). Gas-flushed experiments show the final (endpoint) δ¹⁸O–N₂O values from the time-resolved incubations (P. aureofaciens, n=6; P. chlororaphis, n=2; mean ± SD), whereas closed-batch experiments show the δ¹⁸O–N₂O of the accumulated N₂O pool. Horizontal reference lines in both panels indicate ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ (−9.5 ‰; solid grey) and ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{NO}}_{\mathrm{2}},\mathrm{eq}}$ (+4.5 ‰; dashed grey). The shaded red band (+14.5 ‰ to +19.5 ‰) represents the expected δ¹⁸O–N₂O range assuming complete oxygen atom equilibration between nitrite and water and a branching isotope effect of approximately 10–15 ‰ (Casciotti et al., 2002; 2007).

To interpret the observed variability in δ¹⁸O–N₂O, three reference scenarios can be defined. Following the framework of Casciotti et al. (2002, 2007), nitrate reduction to nitrite is associated with an oxygen isotope fractionation of approximately 25 ‰–30 ‰, while NO${}_{\mathrm{2}}^{-}$ reduction to N₂O is associated with a branching isotope effect of approximately 10 ‰–15 ‰. In the absence of oxygen atom exchange between nitrite and water, δ¹⁸O–N₂O is therefore expected to be approximately 50 ‰, reflecting the nitrate-source signature (δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ = +12.4 ± 0.3 ‰) shifted by the combined isotope effects described above. If nitrite fully equilibrates with water prior to reduction, its isotopic composition approaches δ¹⁸O–NO${}_{\mathrm{2}}^{-}$eq = δ¹⁸O–H₂O + ε¹⁸eq (here +4.5 ‰), resulting in δ¹⁸O–N₂O values of +14.5 ‰ to +19.5 ‰ after addition of the branching isotope effect (Casciotti et al., 2002; 2007). The δ¹⁸O of water itself (−9.5 ‰) represents a conceptual lower limit approached only by direct incorporation of O atoms from water with no kinetic isotope effects or equilibrium exchange. Because oxygen exchange requires sufficient residence time of nitrite, the transient NO${}_{\mathrm{2}}^{-}$ accumulation observed during active growth (Fig. 2E) provides a mechanistic basis for such exchange.

Against this framework, the two strains exhibit contrasting behavior. P. aureofaciens, in closed-batch incubations, yields δ¹⁸O–N₂O values below the full exchange plus branching range, indicating extensive oxygen exchange, while gas-flushed conditions produce intermediate values (26 ‰–42 ‰), consistent with reduced but still substantial exchange. In contrast, P. chlororaphis yields consistently high δ¹⁸O–N₂O values under both incubation modes (≈47 ‰–67 ‰), clustering near the nitrate-dominated regime and indicating limited equilibration with water.

These patterns are consistent with previous observations under comparable active-growth conditions (Rohe et al., 2017; Haslun et al., 2018), but here can be interpreted explicitly in terms of oxygen exchange dynamics. Taken together, these results show that δ¹⁸O–N₂O reflects the combined influence of nitrate-derived oxygen, oxygen-atom exchange with water, and branching fractionation, which vary with strain and incubation mode. To quantify these contributions, we derived oxygen exchange rates using ¹⁸O-enriched water experiments (Sect. 3.4.2).

3.4.2 Quantifying oxygen exchange with water during active growth

To quantify oxygen exchange between nitrite and water during active growth under gas-flushed conditions, P. aureofaciens (NirK) was incubated in ¹⁸O-enriched water (GF_aur_en; Table 1). δ¹⁸O–N₂O values began near ∼ 40 ‰, well below the δ¹⁸O of the enriched water (+68 ‰; Fig. 7). As nitrate reduction progressed, δ¹⁸O–N₂O increased steadily, crossed the δ¹⁸O-H₂O level, and approached 80 ‰ toward the end of the incubation. Throughout the experiment, δ¹⁸O–N₂O remained below values, anticipated for δ¹⁸O-NO${}_{\mathrm{2}}^{-}$ under the nitrite–water equilibrium (δ¹⁸O-NO₂eq ≈ +82 ‰) and well below the expected range for δ¹⁸O-N₂O derived from fully equilibrated nitrite water combined with branching fractionation (δ¹⁸O-NO${}_{\mathrm{2}}^{-}$eq + ${\mathit{\epsilon }}_{\mathrm{B}}^{\mathrm{18}}$ ≈ +91 ‰ to +97 ‰; Fig. 7).

This trajectory – beginning below δ¹⁸O-H₂O, rising above it, and stabilizing below δ¹⁸O-NO₂eq – indicates that the N₂O product contains a mixture of nitrate-derived and water-exchanged O atoms, with incomplete approach to full nitrite–water equilibration. The initial δ¹⁸O–N₂O values reflect expression of the branching isotope effect under minimal water exchange, whereas the later ¹⁸O enrichment reflects the combined influence of branching fractionation and increasing nitrite–water exchange. This behavior is consistent with the elevated δ¹⁸O–N₂O endpoints observed for gas-flushed incubations in natural-abundance water (Figs. 3C; 6A).

Figure 7 δ¹⁸O–N₂O time series as a function of reaction progress (1−f) for incubation of P. aureofaciens (NirK) in ¹⁸O-enriched water. Horizontal reference lines indicate ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ (+68 ‰; solid grey) and ${{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}_{{\mathrm{NO}}_{\mathrm{2}},\mathrm{eq}}$ (+82 ‰; dashed grey). The shaded red band (+92 ‰ to +97 ‰) represents the expected δ¹⁸O–N₂O range under full nitrite–water equilibration with branching fractionation. These references provide a framework to distinguish nitrate-derived oxygen, oxygen-atom exchange between nitrite–water, and branching-related ¹⁸O enrichment.

To quantify these processes, δ¹⁸O–N₂O values from natural-water and ¹⁸O-enriched incubations were combined in δ¹⁸O–N₂O vs. δ¹⁸O–H₂O regressions (Fig. 8), following the framework of Casciotti et al. (2002). In this approach, the regression slope represents the fraction of oxygen atoms in N₂O derived from water during nitrite reduction, whereas the y-intercept at δ¹⁸O–H₂O = 0 ‰ isolates the component of the N₂O oxygen isotope signature independent of water isotopic composition. Under conditions of complete nitrite–water equilibration prior to reduction, the intercept approximates the sum of the nitrite–water equilibrium isotope effect and the branching isotope effect (i.e., b ≈ ε¹⁸eq + ε¹⁸B; Casciotti et al., 2002, 2007). Deviations from this expectation indicate incomplete equilibration and/or retention of nitrate-derived oxygen in the N₂O product.

Closed-batch incubations with P. chlororaphis (NirS) exhibited a slope of 0.67 ± 0.05, consistent with partial water exchange (Fig. 8). Its intercept (53.7 ± 4.1 ‰) is strongly elevated relative to ε¹⁸eq + ε¹⁸B (+24 ‰ to +30 ‰), reflecting combined contributions from nitrate-derived oxygen, incomplete exchange, and branching effects.

Figure 8 δ¹⁸O–N₂O as a function of δ¹⁸O–H₂O for both endpoint (closed batch) and gas-flushed incubations of P. aureofaciens (NirK) and P. chlororaphis (NirS). The regression slope from incubations in natural-abundance (δ¹⁸O–H₂O ≈ –9.5 ‰) and ¹⁸O-enriched water (δ¹⁸O–H₂O ≈ +68.3 ‰ or +73.5 ‰) reflects the extent of oxygen-atom exchange between nitrite and water during stepwise N₂O formation. The intercept represents the δ¹⁸O–N₂O value expected for incubation in water with δ¹⁸O–H₂O = 0 ‰, and thus reflects the combined effects of the nitrite–water equilibrium isotope effect and the branching isotope effect for the reaction of NO${}_{\mathrm{2}}^{-}$ → N₂O, plus any contribution from nitrate-derived oxygen that is not removed by nitite-water exchange. The slope for P. aureofaciens in gas-flushed incubation (0.38) indicates partial exchange (38 %), whereas endpoint incubations for P. aureofaciens and P. chlororaphis suggest near-complete (≈ 100 %) and partial exchange (≈ 66 %), respectively.

For P. aureofaciens, closed-batch incubations yielded a slope of 1.03 ± 0.06, indicating complete oxygen-atom exchange of nitrite with water during active growth. The corresponding intercept (18.7 ± 4.5 ‰) is at the lower end of values expected for ε¹⁸eq + ε¹⁸B. In contrast, gas-flushed incubation of P. aureofaciens yielded a slope of 0.38 ± 0.01, indicating only partial oxygen-atom exchange. The intercept (42.6 ± 1.4 ‰) is substantially higher than both the ε¹⁸eq + ε¹⁸B expectation and the fully exchanged closed-batch intercept, indicating strong retention of nitrate-derived oxygen and enhanced expression of branching fractionation under gas-flushed conditions.

These results demonstrate that oxygen isotope exchange in P. aureofaciens during active growth is highly sensitive to incubation conditions, spanning from complete to strongly limited exchange. In contrast, P. chlororaphis maintained consistently high oxygen-atom exchange across the experimental conditions investigated. These contrasts suggest that the canonical low-exchange behavior attributed to NirK is not an intrinsic property of the enzyme, but instead a condition-specific outcome of the denitrifier method.

3.4.3 Stationary-phase resuspension incubations recover canonical Nir-dependent oxygen exchange

To assess whether exchange patterns observed during active growth reflect intrinsic enzyme behavior or experimental conditions, we performed resuspension experiments in which actively grown cultures were pelleted and transferred into a defined nitrate medium. This setup places both strains into a stationary-phase reduction regime closely resembling the denitrifier method (Casciotti et al., 2002; Weigand et al., 2016).

Resuspension in natural-abundance water produced high and strain-specific δ¹⁸O–N₂O endpoints (Fig. 6B): 59.6 ± 2.5 ‰ for P. aureofaciens and 50.3 ± 0.04 ‰ for P. chlororaphis. These values lie well above the range expected under full nitrite–water equilibration (∼ 14.5 ‰–19.5 ‰), indicating limited oxygen exchange and strong retention of nitrate-derived oxygen, consistent with denitrifier-method observations.

Because endpoint values do not directly constrain exchange, nitrate standards spanning a range of δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ values can be applied to quantify exchange from δ¹⁸O–N₂O vs. δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ regressions. Across both nitrate-standard pairs (USGS32–USGS34 and IAEA-N3–¹⁸O-enriched IAEA-N3), the two strains reproduced the canonical low- versus high-exchange behavior reported previously (Casciotti et al., 2002; Appendix B Fig. B2). P. aureofaciens exhibited low oxygen exchange (1.5 %–4.3 %), whereas P. chlororaphis showed substantially higher exchange (64.7 %–76.6 %), in close agreement with published ranges. These results confirm that resuspension experiments recover the expected strain-specific exchange behavior under denitrifier-method conditions.

3.5 Physiological controls on N₂O isotopic signatures: implications for the denitrifier method and interpretation of N₂O isotopocules

The combined isotopic evidence presented here demonstrates that δ¹⁸O–N₂O is strongly controlled by physiological state and experimental conditions, rather than reflecting fixed enzyme-specific properties. Oxygen isotope signatures are modulated by the balance between nitrate-derived oxygen, nitrite–water equilibration, and branching processes, all of which vary with metabolic activity and reaction environment.

A direct comparison across incubation regimes (Fig. 9) reveals a clear contrast. During active growth, oxygen exchange is highly variable: P. aureofaciens spans from partial to near-complete exchange (∼ 38 % under gas-flushed conditions to ∼ 100 % in closed-batch incubations), whereas P. chlororaphis exhibits consistently higher but more stable exchange (≈ 66 %). In contrast, under stationary-phase resuspension conditions, both strains reproduce the characteristically low- versus high-exchange behavior reported for the denitrifier method, with P. aureofaciens showing low exchange (≈ 2 %–4 %) and P. chlororaphis high exchange (∼ 65 %–75 %).

This contrast demonstrates that the widely used δ¹⁸O–N₂O signatures commonly associated with NirK and NirS are not intrinsic enzyme properties, but arise under the constrained conditions of the denitrifier method. Outside this experimental framework, oxygen-atom exchange is dynamic and reflects physiological state rather than nitrite reductase identity alone.

Figure 9 Compilation of water exchange (%) for P. aureofaciens (NirK) and P. chlororaphis (NirS) under active growth and resuspension conditions. Exchange during active growth was derived from δ¹⁸O–N₂O versus δ¹⁸O–H₂O relationships using ¹⁸O-enriched water (Fig. 8). Under resuspension conditions, exchange was quantified from δ¹⁸O–N₂O versus δ¹⁸O–NO${}_{\mathrm{3}}^{-}$ regressions using nitrate standards spanning a range of δ¹⁸O values (USGS32/34, IAEA-N3 ± spike), based on the degree of scale compression. These two independent approaches provide consistent constraints on oxygen exchange. For active growth, P. aureofaciens showed 38.3 ± 1.4 % (gas-flushed) and 102.9 ± 5.9 % (end-point batch) exchange, whereas P. chlororaphis showed 66.6 ± 5.2 % (end-point batch). Closed triangles indicate reference values from Casciotti et al. (2002), plotted at the midpoint of reported ranges (2 %–9 % for P. aureofaciens, 61 %–78 % for P. chlororaphis).

A mechanistic explanation for this variability likely lies in the dynamics of the nitrite intermediate pool (Casciotti et al., 2007). Oxygen exchange between nitrite and water requires sufficient residence time of NO${}_{\mathrm{2}}^{-}$ to approach isotopic equilibration. During active growth, differences in nitrate reduction rates, nitrite accumulation, and consumption can alter both the size and lifetime of this intermediate pool, thereby modulating the extent of exchange. In addition, because actively growing cultures simultaneously undergo biomass synthesis and enzyme expression, nitrate reduction and downstream nitrite reduction may be less tightly coupled than in resuspension assays, allowing nitrite to persist longer before reduction. In contrast, under resuspension conditions, fully induced cells rapidly reduce the supplied nitrate, and tighter coupling between nitrate and nitrite reduction likely limits nitrite accumulation and, consequently, oxygen isotope exchange. Additional physiological factors, such as pH-dependent exchange kinetics (Buchwald and Casciotti, 2013) or changes in the cellular microenvironment, might also contribute but could not be resolved in the present study and therefore warrant future investigation. These observations indicate that oxygen exchange reflects system-level metabolic dynamics rather than fixed enzymatic behavior.

Consistent strain-specific differences in δ¹⁸O–N₂O under active-growth conditions have been reported previously (Rohe et al., 2017; Haslun et al., 2018; Sect. 3.4.1). Their agreement with the patterns observed here suggests that such behavior may be more general but has not been systematically evaluated within a process-based framework.

These findings have important implications for the interpretation of N₂O isotopocules. Application of fixed δ¹⁸O–N₂O endmember ranges assumes that oxygen exchange is stable and pathway-specific. The results presented here demonstrate instead that δ¹⁸O–N₂O is condition-dependent, and that variability in oxygen isotope signatures reflects changes in exchange dynamics rather than differences in nitrite reductase type. As a result, δ¹⁸O–N₂O does not provide a reliable tracer of nitrite reductase identity (NirK vs. NirS) outside the constrained conditions of the denitrifier method. Consequently, exchange characteristics derived from denitrifier-method experiments should not be extrapolated to microbial systems without accounting for physiological context. These findings do not imply that isotopic signatures currently used to identify N₂O produced by denitrification should be replaced by a single, much broader range of delta values. Rather, they demonstrate that physiological state of the microbial community should be considered explicitly when defining and applying isotopic signatures for environmental interpretation. . More generally, accurate interpretation of δ¹⁸O–N₂O requires frameworks that explicitly incorporate metabolic state, intermediate dynamics, and environmental conditions, rather than relying on static enzyme-based classifications.

4 Conclusion

The results presented here demonstrate that N₂O isotopic signatures are strongly controlled by physiological state and experimental conditions, rather than reflecting fixed enzyme-specific properties. In particular, δ¹⁸O–N₂O varies extensively with oxygen atom exchange between nitrite and water, which depends on metabolic activity and reaction context. Only under stationary-phase resuspension conditions do enriched-water and nitrate-standard approaches reproduce the characteristic exchange behavior reported in classical denitrifier-method studies. This shows that the widely used δ¹⁸O–N₂O exchange rates are specific to the denitrifier method and do not represent general physiological behavior, but instead reflect the constrained conditions under which the method operates. As a result, δ¹⁸O–N₂O cannot be interpreted as a reliable tracer of nitrite reductase identity outside these conditions.

Site preference (SP) measurements provide complementary, time-resolved insight into N₂O formation pathways during active growth. SP trajectories exhibit a reproducible pattern, with early high values (+10 ‰ to +20 ‰) followed by a transition toward values near 0 ‰. These dynamics suggest transient activity of alternative NO reductases, such as flavohemoglobins, during the onset of denitrification, before canonical NorB-mediated NO reduction dominates. Importantly, these shifts occur within the same denitrifying microorganisms and suggest that temporary engagement of NO detoxification pathways may contribute to N₂O formation during phases of elevated NO stress.

These findings have important implications for environmental interpretation of N₂O isotopocules. The application of fixed δ¹⁸O–N₂O or SP endmember ranges assumes that isotopic signatures are stable and pathway-specific constants. Our results demonstrate instead that isotopic expression is conditional. For example, SP values in the range of ∼ 5 ‰–15 ‰, are often interpreted as an evidence for mixed or non-denitrification sources when using fixed endmember frameworks (e.g., Opdyke et al., 2008). However, they could arise entirely from denitrification through shifts in NO reduction pathways. Similarly, variability in δ¹⁸O–N₂O may reflect changes in oxygen exchange dynamics rather than differences in nitrite reductase type, and denitrification may give rise to N₂O with a broader range in δ¹⁸O–N₂O than is typically assumed. Moreover, abiotic nitrite reactions, including chemodenitrification and reactions between nitrite and organic matter, have also been shown to produce a broad range of SP values overlapping those of biological pathways (Jones et al., 2015; Visser et al., 2020; Wei et al., 2019). Together, these findings further emphasize that N₂O isotopocules should be interpreted within their physiological and environmental context rather than as unique process-specific fingerprints.

Accurate interpretation of N₂O isotopocules therefore requires frameworks that explicitly account for physiological state, intermediate dynamics, and environmental context, rather than relying on static metabolism or enzyme-based classifications. Instead of defining and interpreting isotopic signatures as fixed constants, our results demonstrate that they should be interpreted in the context of the physiological and environmental conditions under which they were established. Constraining process signatures under more realistic environmental conditions (Strubbe et al., 2026) will be essential for improving the interpretation of N₂O isotopic signatures in natural systems. Integrating isotopocule measurements with approaches that resolve metabolic activity and enzyme expression may further help link isotopic signatures to specific microbial processes.

Appendix A

A1 Calibration of isotopic data provided by Quantum Cascade Laser Absorption Spectroscopy (QCLAS)

Isotopic composition (δ¹⁵N^α, δ¹⁵N^β, δ¹⁸O) of N₂O was derived from uncorrected QCLAS output values (TDL Wintel, Aerodyne Research, USA) using a dedicated R script (IsotopeRead 2.0, N. Chénier, Empa). The processing pipeline includes (i) temporal averaging, (ii) extraction of sample and calibration-gas intervals via external command language (ECL) indices, (iii) drift correction to reference gas CG1, (iv) calibration-factor determination from CG1–CG2 differences, and (v) uncertainty propagation based on Allan deviation and signal intensity.

A1.1 Data averaging and ratio calculation

QCLAS output data are reported using HITRAN-style shorthand (e.g., 446 equivalent to ¹⁴N¹⁴N¹⁶O) and averaged over 1 min time intervals. Isotopologue ratios (e.g. R448) are computed from the concentration of the minor isotopologue (e.g. i448) to the 446 isotopologue:

• R448 = i448/i446

• R456 = i456/i446

• R546 = i546/i446

Temperature stability of the laser and optical cell was verified through automated plotting.

A1.2 Identification of gas sample and calibration intervals

ECL indices assigned during acquisition were used to identify sample blocks and the two calibration gases (CG1 and CG2). Only intervals with the correct predefined length were retained to ensure consistent calibration.

A1.3 Calibration gases and normalization

Two N₂O isotope reference gases diluted in N₂ and calibrated to international isotope-ratio scales (Air–N₂ for ${}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}$, VSMOW for ${}^{\mathrm{18}}\mathrm{O}{/}^{\mathrm{16}}\mathrm{O}$) by several expert laboratories were used (Mohn et al., 2022):

• CG1 (RM1A; anchor gas): δ¹⁵N^α = −0.22 ± 0.46 ‰, δ¹⁵N^β = 0.84 ± 0.46 ‰, δ¹⁸O = 39.22 ± 0.15 ‰

• CG2 (RM3A; span gas): δ¹⁵N^α = 50.96 ± 0.47 ‰, δ¹⁵N^β = 53.06 ± 0.47 ‰, δ¹⁸O = 103.04 ± 0.16 ‰

For each sample block, isotopologue ratios were normalized by dividing the sample ratio by the mean CG1 ratio measured immediately before and after the sample:

$$R_x={\displaystyle \frac{R_{x,\mathrm{sample}}}{R_{x,\mathrm{CG}\mathrm{1}}}}$$

A1.4 Calibration-factor determination

Calibration factors (a_x) were calculated from the measured ratio differences between CG1 and CG2 and the known isotopic differences:

$$a_x={\displaystyle \frac{\mathrm{\Delta }{\mathit{\delta }}_x^{\left(\mathrm{true}\right)}}{\mathrm{\Delta }{R}_{x,\mathrm{measured}}}}$$

Uncertainty in a_x incorporates both the assigned uncertainty of CG1 and CG2 and the variance of their measured ratios.

Corrected delta values were computed as:

$$\mathit{\delta }X=\left({\displaystyle \frac{R_x}{R_{x.CG\mathrm{1}}}}-\mathrm{1}\right)\times \mathrm{1000}\times ax+\mathit{\delta }{X}_{CG\mathrm{1}}$$

A1.5 Uncertainty estimation

Instrumental precision was assessed using the Allan deviation at 60 s spectral averaging and was better than 0.1 ‰ for all δ values.

Uncertainty in δ¹⁵N^α, δ¹⁵N^β, and δ¹⁸O was assessed by propagating contributions from (i) Allan deviation of the relevant isotopologue ratios, (ii) signal-intensity variability (i446 and minor isotopologues), and (iii) variability in calibration-factors.

The uncertainty for derived quantities was calculated using standard error-propagation rules. For example, site preference (SP = δ¹⁵N^α − δ¹⁵N^β) uncertainty was calculated as:

$$\mathit{\sigma }\mathrm{SP}=\sqrt{{\mathit{\sigma }}_{\mathit{\alpha }}^{\mathrm{2}}+{\mathit{\sigma }}_{\mathit{\beta }}^{\mathrm{2}}}$$

Uncertainty in δ¹⁵N-bulk and δ¹⁸O was propagated analogously from their respective isotopologue components.

A1.6 Data output

Corrected delta values with propagated uncertainties were exported as .csv files. Diagnostic plots (SP, δ¹⁵N-bulk, δ¹⁸O) were automatically generated for quality assurance.

All processing was performed in RStudio (R Core Team, 2020). The full script (IsotopeRead 2.0) is available upon request.

A2 Calculation of N₂O yield and fractionation factors

N₂O yield and isotopic fractionation as well as their uncertainties were calculated using a customized R script.

The molar amounts of N₂O (n N₂O) produced during each time interval ΔT were calculated from FTIR-derived concentrations (C_gas in ppm; 10⁻⁶ L L⁻¹) and nitrogen gas flow rates (Q in mL min⁻¹), using a molar volume of 22.4 L mol⁻¹. NO was treated analogously (n_NO), considering concentrations which exceed the analytical detection limit. For intervals where NO remained below detection, n_NO was not calculated, and no NO yield was reported.

$$n{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{gas}}=\left({\displaystyle \frac{\left(\frac{Q\times \mathrm{\Delta }T}{\mathrm{22.4}}\right)\times \left(\frac{C_{\mathrm{gas}}}{{\mathrm{10}}^{\mathrm{6}}}\right)}{\mathrm{1000}}}\right)$$

Uncertainties in N₂O production were calculated by propagation through partial derivatives of the above expression, incorporating both flow and concentration uncertainties. The uncertainty of the measured N₂O and NO concentrations was attributed to either the instrumental detection limit (0.0075 ppm for N₂O and 0.133 ppm for NO), or a relative uncertainty of 10 % for both N₂O and NO, with the larger value used at each time point. Uncertainty in the nitrogen flow rate was assumed to be 0.3 % based on mass flow controller specifications (Vögtlin Instruments Inc., Switzerland).

The N₂O yield (in %) was calculated from the molar amount of N₂O produced over the experiment related to the molar amount of nitrogen substrate (KNO₃, molar mass 101.1 g mol⁻¹). Associated uncertainty was propagated from balance precision (±0.01 g) and purity (≥99 %, conservatively estimated at ±0.5 %).

To calculate Rayleigh-type enrichment factors (ε), the isotopic composition of the accumulated N₂O product gas (δ_cum) is required. This was calculated as a weighted average from temporal trends in delta values (δ_i) weighted by the molar amount of N₂O (n_iN2O) emitted in the respective time interval. Calculations were performed on synchronized data averaged over 15 min time intervals:

$$\mathit{\delta }\mathrm{cum}={\displaystyle \frac{\sum ({\mathit{\delta }}_i\times n_{i{\mathrm{N}}_{\mathrm{2}}\mathrm{O}})}{\sum n_{i{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}}}$$

Uncertainties in δ_cumwere computed from uncertainties in individual δ-values and the associated molar amount of N₂O. Uncertainties in δ_cum were propagated by summing the individual variances associated with δ-values and their corresponding N₂O fluxes. At each time step, the square root of the cumulative variance yielded the standard error used to construct time-resolved confidence intervals for δ¹⁵N-bulk, δ¹⁸O, and SP.

The fraction of remaining substrate (f) in the Rayleigh reaction progress variable $x=-f\cdot \ln \left(f\right)/(\mathrm{1}-f)$ was calculated as:

$$f=\mathrm{1}-{\displaystyle \frac{\mathrm{2}\times n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}}{n_{{\mathrm{N}}_{\mathrm{2}}\mathrm{O}}}}$$

Uncertainties in f and x were propagated from uncertainties in the molar amount of substrate (n_NO3−), calculated from the nitrate mass and its molecular mass, and the cumulative molar amount of N₂O.

Enrichment factors (ε) were obtained by Rayleigh-type regressions, plotting δ values of the accumulated N₂O product gas against the transformed progress variable.

Daily averages, cumulative profiles, and model fits were exported as CSV files. Summary statistics include regression intercept, slope, standard errors, and confidence intervals for each isotopic parameter.