Anaerobic oxidation of methane does not attenuate methane emissions from thermokarst lakes

The ongoing global temperature rise enhances permafrost thaw in the Arctic, allowing Pleistocene‐aged frozen soil organic matter to become available for microbial degradation and production of greenhouse gases, particularly methane. Here, we examined the extent and mechanism of anaerobic oxidation of methane (AOM) in the sediments of four interior Alaska thermokarst lakes, which formed and continue to expand as a result of ice‐rich permafrost thaw. In cores of surface (~ 1 m) lake sediments we quantified methane production (methanogenesis) and AOM rates using anaerobic incubation experiments in low (4°C) and high (16°C) temperatures. Methanogenesis rates were measured by the accumulation of methane over ~ 90 d, whereas AOM rates were measured by adding labeled‐13CH4 and measuring the produced dissolved inorganic 13C. Our results demonstrate that while methanogenesis was vigorous in these anoxic sediments, AOM was lower by two orders of magnitude. In almost all sediment depths and temperatures, AOM rates remained less than 2% of the methanogenesis rates. Experimental evidence indicates that the AOM is strongly related to methanogens, as the addition of a methanogens' inhibitor prevented AOM. Variety of electron acceptor additions did not stimulate AOM, and methanotrophs were scarcely detected. These observations suggest that the AOM signals in the incubation experiments might be a result of enzymatic reversibility (“back‐flux”) during CH4 production, rather than thermodynamically favorable AOM. Regardless of the mechanism, the quantitative results show that near surface (< 1‐m) thermokarst sediments in interior Alaska have little to no buffer mechanisms capable of attenuating methane production in a warming climate.

Thawing permafrost in the Arctic is causing organic matter that has been frozen for millennia to become available for microbial degradation. This degradation results in production of greenhouse gases that can reinforce a climate warming feedback (Zimov et al. 1997(Zimov et al. , 2006. Thermokarst lakes, and the underlying thaw bulb (talik), are the result of abrupt ground ice melt, and become point sources of greenhouse gas emissions throughout discontinuous and continuous permafrost landscapes (Walter . These emissions include a large amount of methane (CH 4 ), produced by the fermentation of organic matter in the thawed talik, and contribute significantly to the Arctic CH 4 budgets (Schuur et al. 2015;Turetsky et al. 2020). Yet, before the CH 4 can be emitted to the atmosphere, this potent greenhouse gas can be microbially oxidized to carbon dioxide, which has a lower greenhouse effect (Bastviken et al. 2002;Segarra et al. 2015). However, the extent of CH 4 oxidation and its capacity to buffer the increasing CH 4 emissions in a warming climate is not well constrained.
In the water column of the thermokarst lakes, CH 4 is partially oxidized by aerobic methanotrophy Elder et al. 2018), which reduces the net CH 4 emissions. Anaerobic oxidation of methane (AOM) can also oxidize part of the CH 4 , occurring in the lake sediments parallel to CH 4 production (Martinez-Cruz et al. 2017Winkel et al. 2019). AOM may therefore attenuate CH 4 emissions to the atmosphere. However, the extent of the buffering capacity of AOM is poorly constrained.
In marine sediments, sulfate-AOM plays a major role in mitigating CH 4 emissions to the water column and the atmosphere by consuming up to 90% of the CH 4 produced by the microbial degradation of organic matter (Valentine 2002;Reeburgh 2007). Sulfate-AOM can also attenuate CH 4 emissions of freshwater systems (Schubert et al. 2011;Segarra et al. 2015;Su et al. 2020), but this will typically occur to a smaller extent due to lower sulfate availability. It is not easy to evaluate the role of AOM in freshwater sediments in a global manner, due to the large variations in water chemistry (particularly in sulfate concentrations) among different freshwater systems. In sulfate depleted systems, AOM can be coupled to the reduction of alternative electron acceptors, such as NO À 3 , NO À 2 , Fe 3+ , Mn 4+ , or humic substances (Raghoebarsing et al. 2006;Beal et al. 2009;Bar-Or et al. 2017;Cai et al. 2018;Valenzuela et al. 2019;Vigderovich et al. 2022). Although these AOM mechanisms have been proven in controlled lab experiments, and their potential was shown with geochemical evidence (Sivan et al. 2011;Crowe et al. 2011;Norði et al. 2013), their role in the natural environment is still under investigation.
Most freshwater thermokarst lakes are not geochemically suited to promote the conventional AOM since they are sulfate-depleted, and are also low in NO À 3 and NO À 2 (Martinez-Cruz et al. 2018;Winkel et al. 2019;Pellerin et al. 2022). Therefore, AOM in the anaerobic sediments underlying thermokarst lakes is likely powered by alternative electron acceptors such as Fe 3+ , Mn 4+ , or humic substances. Previous investigations of thermokarst lakes suggest that aerobic methanotrophs may perform CH 4 oxidation under anoxic conditions, in the water column beneath the oxicline (Cabrol et al. 2020) and also in the topmost (< 25 cm) sediments (Martinez-Cruz et al. 2017). However, in the absence of oxygen, the electron acceptor of CH 4 oxidation in thermokarst anoxic sediments remains unclear.
In young thermokarst lakes, AOM may also be limited at the metabolic level because of the long time required to establish a community capable of AOM (Thurber et al. 2020). This is due to the extremely low energetic yields of the reactions, resulting in very slow growth rates of the microbes responsible for AOM (Nauhaus et al. 2007).
Recently, it was suggested that the CH 4 emissions from thermokarst lakes are in the same magnitude as the integrated methanogenesis rates, with a relatively minor discrepancy (Pellerin et al. 2022). This may reflect that CH 4 oxidation occurs in a lower degree than previously estimated (Martinez-Cruz et al. 2018;Winkel et al. 2019). Therefore, it is critical to produce confident constraints on the rates of AOM. Since in thermokarst sediments, CH 4 concentrations can be above saturation (Pellerin et al. 2022), in situ AOM rates in these cases cannot be derived from modeling porewater profiles and should be evaluated experimentally. In this study, the AOM rates were quantified via stable isotope enrichments and calculated in two independent methods. This technique was performed in sediments from four different thermokarst lakes spanning gradients of lake age and thermokarst activity.

Study sites
The four studied lakes are located near Fairbanks (< 40 km distance), interior Alaska. This area hosts a diversity of stable and actively expanding thermokarst lakes. Three of the Lakes (Doughnut L., Oxbow L., and Big Trail L.) are located within Goldstream valley. Yedoma-type permafrost sediments from the Goldstream formation are one of the most widespread in central Alaska. In Goldstream Valley, these frozen soils consist of retransported bedded ice-rich silt with abundant vegetation that accumulated in valley bottoms (Péwé 1975). At Goldstream Creek, the Goldstream formation consists of transported loess of Pleistocene age (> 10,000 yr BP and > 39,000 yr BP) with evident syngenetic ice wedges, minute carbonized organic fragments, some peat lenses, sticks, and twigs (Péwé 1975). Sediments from the Goldstream formation froze soon after deposition (Péwé 1975). The fourth lake, Vault, is located north of the Goldstream Valley, near Vault Creek, also in silt-and ice-rich yedoma-type permafrost soils (Heslop et al. 2015).
Vault Lake (65.0293 N, 147.6988 W) is a young thermokarst lake which formed 100-400 yr BP (Heslop et al. 2020), in discontinuous permafrost. This 3200 m 2 water body is located in a valley setting of the boreal region of interior Alaska, approximately 40 km north of Fairbanks. This lake is well studied and the age of its sediment, CH 4 production, emissions, and lithology are described previously (Heslop et al. 2015(Heslop et al. , 2017(Heslop et al. , 2020Winkel et al. 2019).
Doughnut Lake (64.8988 N,147.9080 W) is a 34,000 m 2 thermokarst lake. The lake is thought to have formed about 1000 yr ago and has not expanded into yedoma permafrost in the last 60 yr .
Oxbow Lake (64.9086 N, 147.9414 W) is a U-shaped lake near Fairbanks, Alaska. Its origin is unknown and may have originated as a former creek channel. The lake is surrounded by ice-rich permafrost and appears to have thermokarst along some of its margins. This lake is distinct from the others that were studied because of its exceptionally high dissolved iron concentration in the water column (Supporting Information  Table S1) and low concentration of CH 4 in the ebullition bubbles. The formation of this lake is yet to be dated.
Big Trail Lake (64.9188 N, 147.8234 W), formed less than 60 years ago, is situated just north of Fairbanks, Alaska in the Goldstream valley at the junction between Goldstream Creek and Big Eldorado Creek, 6 km to the west of Goldstream Mine. Big Trail Lake is an actively expanding thermokarst lake that currently has a surface of about 40,000 m 2 and a maximum depth of about 4.1 m. The lake has a record of thermokarst activity that includes an exceptionally large number of vigorous CH 4 seeps (Walter Anthony et al. 2021). Degrading ice wedges beneath the lake are driving ground subsidence and expansion of the lake.

Sampling
Sediment cores were collected during two sampling campaigns, in November 2018 and in March 2020 (parallel data from the March 2020 sampling campaign is published at Pellerin et al. 2022). For the sampling procedure, coring equipment was installed on the frozen lake surface for all sampling sites. A hole was made in the ice with a chainsaw and a percussion corer was used to insert a polycarbonate core (6.6 cm diameter) into the sediment and to retrieve it back to the frozen surface of the lake. The sampled sediment sections ranged from the sediment water interface up to 70-174 cm depth (Table 1). We measured the dissolved O 2 concentration in the water column using a Hydrolab multiparameter probe. Sediment for incubation experiments was transferred anaerobically into serum bottles, sealed with rubber butyl stoppers, and flushed with N 2 at University of Alaska Fairbanks, and shipped for further treatment at Ben Gurion University. Porewater samples were extracted from the cores at University of Alaska Fairbanks, sealed anaerobically and/or fixed with relevant reagents and shipped to Ben Gurion University (detailed in Pellerin et al. 2022). To investigate the rates of AOM, sediment incubation experiments were conducted from specific sections of methanic sediments with relatively high porewater Fe 2+ concentrations (Supporting Information Table S2), possibly as a result of iron reduction during iron-dependent AOM (during the 2018 sampling campaign; Table 1). In Big Trail Lake, the AOM rates were determined in two different sites of the lake, by incubation experiments sampled from six arbitrary sediment horizons along a 1-m sediment profile (during the 2020 sampling campaign; Table 1).
In Vault Lake, a sediment core was collected near the western shoreline and two different sediment sections (50-60 and 80-90 cm) were devoted to long-term incubation experiments. Each section was separately homogenized (in sealed anaerobic bags) and divided to smaller portions according to the experimental settings. In Doughnut Lake, a sediment core was sampled near a large methane-rich ebullition seep the northeastern shoreline and one sediment section (65-75 cm) was homogenized and devoted to long term incubation experiments. The core sampling in Oxbow Lake took place within the south-east area of its narrow U-shape, and one sediment section (50-60 cm) was devoted to incubations.
The sampling campaign in Big Trail Lake was more extensive; cores were collected from two different sites, one in the shallow part of the lake (site S), with a water depth of 0.6 ms and the other near the deepest point (site D), with a water depth of 2.5 m. In both sites, sediments for long-term incubations were sampled from six different depths along a $ 1-m sediment profile. The lithology, sediment age, as well as CH 4 production rates of parallel $ 1-m Big Trail Lake cores have been measured previously for both sites (Pellerin et al. 2022). At Big Trail Lake, the two sampling sites reflected similar lithological trends, which are associated with the formation steps of thermokarst lakes (Rampton 1988). All four cores sampled from Big Trail Lake consisted four parallel lithological units (bottom to top): Unit 1, lower silt, Unit 2, peat, Unit 3, upper silt and Unit 4, dark silt. The full lithologic description is available in Pellerin et al. 2022.

Long-term incubation experiments
Evaluation of AOM rates in the deep (50-90 cm) sediments Each sediment section was homogenized and diluted with anoxic autoclaved deionized water in a 1:3 sediment water weight ratio. Slurry portions of 40 mL were transferred directly to 60 mL serum bottles, sealed and flushed with pure N 2 gas for three intervals of 5 min, and vigorously shaken between the intervals. Duplicate bottles were conducted from each sediment section. Then, 2 mL of 99% 13 C-CH 4 was injected to production rates the headspace, and the initial CH 4 concentrations were determined by the volume injected (by the ideal gas law). Incubations were stored at 4 C in the dark. The incubations were sampled to monitor variations in dissolved inorganic carbon (DIC) concentrations and δ 13 C-DIC over the course of 250 or 375 d. AOM rates were calculated in two different methods by a static and dynamic calculation.
Evaluation of AOM and methanogenesis rates along sediment profiles Samples from several depths ( Table 1) along 1-m sediment cores retrieved from two different sites (S and D) in Big Trail Lake were collected for long-term incubations (90 d). The samples were harvested 1 d after sampling, upon slicing the core horizontally. We attempted to avoid using areas that were exposed to oxygen during slicing ($ 5 cm from the sliced area), as oxygen could have altered the microbial community and the original electron acceptor availability. Aliquots of $ 5 mL of sediment were immediately inserted into 25-mL serum bottles sealed with chlorobutyl rubber stoppers and crimped with aluminum caps. The bottles were sealed and flushed with pure N 2 gas as described above. Sediment direct exposure to room air was about 1-2 min. Samples were then weighed and stored at 4 C at the dark and brought to Ben Gurion University of the Negev. Then, four replicates from six depths were dedicated to measure the AOM rates percentage of the net CH 4 production rates. The sediment was diluted with anoxic autoclaved deionized water in a 1:1 weight ratio, and flushed again with N 2 for three intervals of 5 min. Then, 0.5 mL of 99% 13 C-CH 4 was inserted into the headspace of the bottles, and the initial CH 4 concentrations, DIC concentrations, and δ 13 C-DIC were measured. Two replicates from each depth were stored at 4 C while the two others in 16 C, for 3 months of incubation at dark. The final CH 4 concentrations, DIC concentrations, and δ 13 C-DIC were measured by the end of this period. AOM rates were calculated as a function of the CH 4 concentration, the δ 13 C-CH 4 , CH 4 production rates, DIC concentration and the δ 13 C-DIC, in two different methods (see "Calculation of AOM rates" section). Only results of the static calculation are presented in Fig. 2, since the different calculations yielded similar results. The parallel results of the dynamic calculation (a forward model that separately simulated each bottle) are presented in Supporting Information Fig. S1.

Incubations amended with electron acceptors or inhibitors
To investigate the mechanism of AOM, slurry incubations (prepared as described previously) were amended with electron acceptors and inhibitors (Supporting Information Table S3). The sediments were retrieved from specific depth sections of the four different lakes. Details among the different additions and their concentrations are presented in Supporting Information Table S3. From each sediment section, duplicate bottles per treatment were set, in addition to duplicate controls without additions and duplicate autoclaved controls. To evaluate the extent of AOM, 2 mL of 99% 13 C-CH 4 was injected, and the incubations were sampled to monitor variations in the δ 13 C-DIC over a period of 250 or 375 d of incubation at the dark. In this experimental setup, all bottles were kept at 16 C.

Analytical methods
Concentrations of CH 4 were measured from the headspace of the serum bottles (after vortexing) by GC-FID (Thermo) with a Packed ShinCarbon column (a precision of AE 2 μM). Porewater CH 4 concentrations were back calculated to the weight of sediment in each serum bottle. The concentration and isotopic ratios of the dissolved inorganic carbon were measured in a Gas Source-IRMS (Thermo) in the Department of Earth and Environmental Sciences at Ben Gurion University. Concentrations were calculated from the peaks of the isotopic measurement with precision of AE 0.2 mM and the isotopic ratios were measured relative to Vienna Pee Dee Belemnite with a precision of AE 0.1‰. Dissolved Fe(II) was measured using the ferrozine method (Stookey 1970), by a spectrometer (Spectroquant Pharo 100) at a wavelength of 562 nm (a precision of AE 0.3 μmol kg À1 , a detection limit of 1 μmol kg À1 ). SO 2À 4 concentrations were measured by ion chromatography on a Compact IC Flex, Metrohm, with a detection limit of 6 μM. Nitrite (NO À 2 ) was measured using a colorimetric method (Grasshoff et al. 2009), using a Flow Injection Autoanalyzer (Lachat Instruments Model QuickChem 8500). Nitrate (NO À 3 ) was reduced to NO À 2 by a copperized cadmium column, and then measured calorimetrically (a detection limit of 0.05 μM).

Calculations of AOM rates
In order to calculate the rate of anaerobic oxidation of CH 4 , the results were interpreted in two distinct ways. First, the incubations were interpreted in a "static" mode that did not take into account the changing pools of DIC and CH 4 . This is the conventional approach used with tracer incubations to calculate AOM rates. In a second approach, the incubations were interpreted in a "dynamic" mode that takes into account the changing sizes of the DIC and CH 4 pool and the resulting tracer dilutions. The second approach results in slightly higher AOM rates, as expected.

Static calculation of AOM rates
A simple mass balance equation describes mixing between a 99% 13 C-DIC reservoir (the product of the oxidation of labeled 13 C-CH 4 ) and the initial DIC reservoir as described by (Eq. 1) where F 13 C DIC (t f ) is the fraction of 13 C/( 13 C + 12 C) in the final DIC pool, x is the mixing fraction between the oxidized CH 4 and the initial DIC pool, F 13 CH 4 is the fraction of 13 C/( 13 C + 12 C) of the injected CH 4 (0.99, labeled), and F 13 C DIC (t 0 ) is the fraction of 13 C/( 13 C + 12 C) in the initial DIC.
The amount of CH 4 oxidized throughout the experiment is described as (Eq. 2) where CH 4 (ox) is the concentration of CH 4 oxidized during the entire incubation course and DIC(t f ) is the final DIC concentration. To obtain the AOM rates, CH 4 (ox) is divided by incubation time to determine daily rates.
Dynamic calculation of AOM rates During AOM, the 13 C-CH 4 is transformed into 13 C-CO 2 and integrated into the DIC pool. However, in thermokarst lakes, vigorous methanogenesis influences the pool sizes over the course of the incubation. To take these changing pool sizes into account, it is necessary to know the CH 4 concentration over time, its isotopic composition, as well as the size of the DIC pool and its isotopic composition. The reaction representing the degradation of cellulose into CH 4 and CO 2 follows the predictable stoichiometry (Eq. 3).
The CH 4 and CO 2 produced during this reaction have stable isotopic abundances that are close to that of the organic matter. Although there are isotope fractionations associated with this reaction, they only play a minor role in the resulting partition of stable isotopes when considering the large variations caused by the insertion of labeled 13 C-CH 4 . For this exercise, the isotopic partitioning occurring during methanogenesis was neglected. However, the mass fluxes do influence the net isotopic composition of the pools.
A depletion of 13 C-CH 4 during the incubation is caused by the intense 12 C-CH 4 production of methanogenesis which may dilute the tracer that was inserted. Moreover, the isotopic ratio of the DIC can also be imprinted by methanogenesis because it also produces DIC (Eq. 3). For example, in Big Trail Lake, a marked increase in DIC concentrations was observed over the course of incubations (Supporting Information Fig. S2). The dynamic calculation method is fully described in Supplementary Methods and Supporting Information Fig. S3.

Molecular analysis of microbial communities
We assessed the microbial community in a sediment profile from Big Trail Lake, site S, by the analysis of natural samples. We sampled and immediately froze sediments from six different depths along the core (Table 2). Total genomic DNA was extracted by DNeasy PowerLyzer PowerSoil Kit (QIAGEN), Genomic DNA was eluted by 50 μL of elution buffer. The 16S rRNA gene of archaea and bacteria was amplified by polymerase chain reaction (PCR; with Taq PCR MasterMix DNA Polymerases, Tiangen) following the Earth Microbiome Project (http://www.earthmicrobiome.org) protocol for Illumina sequencing (Thompson et al. 2017; primers are described in Supporting Information Table S4). Illumina sequencing was performed by Hylabs, Rehovot, Israel. Demultiplexed pairedend reads were analyzed by QIIME2 V2020.6 (Bolyen et al. 2019). By applying the DADA2 pipeline (Callahan et al. 2016; implemented in QIIME2), reads were truncated according to their quality plots, chimeras were removed and reads were merged and grouped into amplicon sequence variants (ASVs). Taxonomy was assigned to ASVs by Silva 138 99% classifier (Quast et al. 2013;Yilmaz et al. 2014). The relative abundance analyses and plots were conducted in Rstudio (Team 2020) by using phyloseq (McMurdie and Holmes 2013), ampvis2 (Andersen et al. 2018), and ggplot2 (Wickham 2011) libraries.
Eukaryotes, chloroplast, mitochondria-derived reads and ASVs with unassigned kingdom or phylum were removed from the dataset. Heatmaps of the relative abundance of the remaining taxa were produced using ampvis2 default settings, the relative abundances were calculated separately for the bacterial and archaeal communities.

Results
Here, we present the AOM rates measured from long-term incubations in the deep (50-90 cm) sediments of four lakes, and the rates along $ 1-m sediment profiles of two different sampling sites in Big Trail Lake. We also describe the response caused by the addition of naturally abundant electron acceptors and inhibitors. Finally, the relative abundance of aerobic and anaerobic methanotrophs in the microbial community along a $ 1-m sediment profile is presented.

AOM rates in deep (50-90 cm) sediments
The two different calculation methods showed the same magnitude of AOM rates, and in some cases, very similar rates (Fig. 1). Apart from Vault Lake 50-80 cm, the static calculation had lower AOM rates than the dynamic calculation (20-80% lower). According to the dynamic calculation, the rates measured in the 10 individual incubation bottles varied from 0.002 to 0.077 nmol cm À3 d À1 , while the static calculation ranged between indicated AOM rates of 0.001-0.058 nmol cm À3 d À1 . In both methods, the highest AOM rates were observed in Big Trail Lake, site D-0.074 AE 0.004 nmol cm À3 d À1 by the dynamic calculation, and 0.057 AE 0.001 nmol cm À3 d À1 by the static calculation (rates are reported as the mean of the duplicates AE standard deviation). In Vault Lake, sediments from 80 to 90 cm showed AOM rates of 0.002 AE 0.0001 nmol cm À3 d À1 according to the dynamic calculation and 0.001 AE 10 À5 nmol cm À3 d À1 by the static calculation. Sediments of the same lake from a shallower depth (50-60 cm) showed AOM rates of 0.004 nmol cm À3 d À1 , by both approaches (0.004 AE 0.0003 and 0.004 AE 0.0001 nmol cm À3 d À1 for the dynamic and static calculations, respectively). Doughnut Lake showed AOM rates of 0.016 AE 0.001 nmol cm À3 d À1 by the dynamic calculation and 0.003 AE 0.0001 nmol cm À3 d À1 by the static calculation. In Oxbow Lake, the AOM rates were 0.015 AE 0.010 nmol cm À3 d À1 according to the dynamic calculation, and 0.010 AE 0.009 nmol cm À3 d À1 by the static calculation. The R 2 fit of the dynamic model to the data of each incubation bottle is noted in Supporting Information Table S5. The methanogenesis rates in these lakes, reported in previous studies (Martinez-Cruz et al. 2018;Pellerin et al. 2022), are at least two orders of magnitude higher than the AOM rates (Supporting Information  Table S6; Fig. 2).

AOM rates along sediment profiles in Big Trail Lake
While the previous section focused on the AOM in deep sediments (50-90 cm), in this section, AOM rates along the entire upper meter profile of Big Trail Lake sediments were measured. Replicates from six sampling depths in two sites were kept at 4 C and 16 C for $ 90 d, to examine the temperature sensitivity of AOM relative to the temperature sensitivity of methanogenesis. The temperature of 4 C represents a typical temperature of thermokarst sediments during the warm season (Heslop et al. 2020), whereas 16 C is slightly higher than the maximum temperature measured for Vault Lake's marginal sediments (14.45 C; Heslop et al. 2020).
The methanogenesis rates in both temperatures (4 C and 16 C) were in the range of 4-36 nmol cm À3 d À1 , with the exception of the peat horizon. In the peat horizon, methanogenesis rates of 70-100 nmol cm À3 d À1 were measured in incubations stored at 16 C (Fig. 2). The AOM rates ranged from 0.004 up to 0.4 nmol cm À3 d À1 , both in 4 C and in 16 C (Fig. 2), according to the static calculation, where for some sampling depths the rates in 16 C were slightly higher than in 4 C, fitting also the slight increase in methanogenesis. At the lower temperature (4 C), the uppermost sampling point (4 cm) at site S showed the highest AOM rates (0.2-0.4 nmol cm À3 d À1 ). Over all the results show that the relative AOM (AOM as a fraction of methanogenesis) was scarcely affected by variations in temperature. Interestingly, the relative AOM negatively correlates with sediment depth (Fig. 2). This trend was more prominent in site S than in site D. The relative AOM varied from 0.02% to 5% of the methanogenesis rate. The highest relative AOM occurred in unit 1, site S, where the AOM rates were 2-5% of the methanogenesis rates. In all other samples, the relative AOM did not exceed 2% of the methanogenesis rate. The dynamic calculation resulted in AOM rates of the same magnitude, presented in Supporting Information Fig. S1.

Long-term incubations amended with electron acceptors or inhibitors
Since CH 4 concentration in the upper meter of thermokarst sediments is high (Martinez-Cruz et al. 2018;Pellerin et al. 2022), CH 4 is not the limiting factor of AOM. To determine if electron acceptors are in low abundance and limit  Table S5). AOM, we amended the sediment with high concentrations of electron acceptors (10 mM, Supporting Information Table S3) to examine their potential to promote AOM. Long-term (245-377 d) sediment incubation experiments of four different lakes were conducted, spiked with 13 CH 4 , and stored at 16 C. The results show that the DIC pool of the natural treatment (no electron acceptors or inhibitors additions) was enriched in 13 C during all incubations (Fig. 3). This indicated that in the natural treatments, a portion 13 C-CH 4 was oxidized to 13 C-DIC. All amendments yielded equal or lower 13 C enrichment than the natural treatment. The addition of iron oxides (hematite and magnetite) did not enhance the 13 C enrichment. Additional treatments were also amended with inhibitors which are specific for the reduction of a particular electron acceptor or a certain mechanism. Molybdate, a sulfate reduction inhibitor, did not affect the 13 C enrichment, implying that the AOM is not coupled to sulfate reduction in these incubations (Fig. 3). Green circles denote no external addition besides 13 C-CH 4 , yellow squares denote magnetic addition, blue inverted triangles denote hematite addition, maroon triangles denote molybdate addition, and orange diamonds denote killed controls. The beige background color in (A) and (B) denotes the δ 13 C-DIC range of other additions (manganese[IV] oxide, AQDS, amorphous iron and BES) which showed similar results to the killed control. The black arrows (B-D) denote the day of molybdate injection to the experiment bottles. Duplicate bottles were set for every treatment, each duplicate is presented individually (the symbols may overlap). Note the differences in Y-axis scales.
We also amended Big Trail sediments with natural humic acids extracted from a nearby thermokarst lake (Goldstream Lake). The results show that the addition of natural humic acids did not enhance AOM rates (Supporting Information Fig. S4). However, in contrast to the amendments in Vault and Doughnut Lakes with AQDS, the addition of natural humic acids yielded a similar 13 C enrichment to the natural treatment-it did not inhibit CH 4 oxidation.

Methanotrophs abundance
In order to evaluate the abundance of methanotrophs in the microbial community, and to detect specific microbes which can potentially mediate CH 4 oxidation, the microbial communities of six different depths along a sediment core from Big Trail Lake, site S (shallow water column) were examined. Among the bacteria orders, bacteroidales were detected in the highest relative abundance in most depths (with one exception of the topmost sample), ranging between 12% and 17% of all bacteria reads. At the topmost sample (4 cm depth), Campylobacterales were slightly more abundant (14% of bacteria reads). The archaea analysis reflected the dominance of the Woesearchaeales, with the exception of the topmost sample, where Marine Benthic Group D and DHVEG-1 were more abundant (64% of archaea reads). In all other five sampling depths, Woesearchaeales abundance ranged between 49% and 89% of archaea reads, while maximum abundance was detected at the deepest point (Supporting Information  Fig. S5).
Known anaerobic methanotrophs were found in low abundance (Table 2) in all depths. Members of ANME-1 and ANME-3 clusters were not detected in all six sampling points (0 reads). Methanoperedenaceae (ANME-2d) were detected only in 1 out of the 6 sampling points, in an abundance of 0.2% of the archaea reads (0.03% of the total reads, depth of $ 28 cm). Methylomirabilales (NC10 phylum), which are capable of mediating nitrite-dependent AOM (Ettwig et al. 2010), were detected in 5 out of the 6 points, in abundance of 0.9-0.1% of the bacterial reads (0.7-0.1% of the total reads). Their highest abundance was measured at the topmost samples (4 cm), while at all other points it did not exceed 0.2% of the bacteria reads.
Aerobic methanotrophs were detected in the topmost sediment samples, but not in deeper depths, with the exception of one point (70 cm, 0.2% of bacteria reads). At the topmost samples (4 cm), two families of aerobic methanotrophs were detected; Methylomonadaceae (Methylococcales order, 1.1% of bacteria reads) and Beijerinckiaceae (Rhizobiales order, 0.7% of bacteria reads). Together, their abundance was near 2% of all bacteria reads. Besides the topmost sample, Methylomonadaceae were not detected in all other five depths, and Beijerinckiaceae were detected at the depth of 70 cm, 0.2% of all bacteria reads (Table 2).

Discussion
AOM was first identified in marine sediments because of the evident signature it produces in diffusion-controlled sediment porewater profiles. There, the upwards diffusion of CH 4 meets the downward diffusion of sulfate from the overlying water column and when both overlap in high enough concentrations, are simultaneously consumed by anaerobic CH 4 oxidizers in a zone referred to as the sulfate CH 4 transition zone (Martens and Berner 1977;Hoehler et al. 1994). The evidence for CH 4 oxidation is also in the corresponding isotopic enrichment of the light 12 C isotope transferred from CH 4 in the DIC, as well as other signatures that are a result of the diffusion-controlled nature of these system (Alperin et al. 1988;Martens et al. 1999). In freshwater systems, AOM was also detected by porewater trends, and AOM rates were evaluated by diffusive controlled diagenetic models (Sivan et al. 2011;Segarra et al. 2015). In thermokarst lakes of this study, AOM activity did not influence the porewater profile with a quintessential signature (Pellerin et al. 2022). The reason for this may be the high rate of methanogenesis, a low rate of AOM or the dynamic nature of these systems. Moreover, in thermokarst sediments the dissolved δ 13 C-CH 4 values can be imprinted by advective transport of ex situ bubbles (Pellerin et al. 2022), and therefore signals of local metabolic processes could be easily masked. Thus, in order to quantify AOM in thermokarst lakes, it was necessary to measure the rates experimentally.

AOM rates
The low AOM rates observed in the investigated thermokarst lakes points to a small role for this type of metabolism in the studied sediment zones (top 1-m sediments in Big Trail Lake, 50-90 cm depth in Vault, Oxbow, and Doughnut). In many of these sediment zones, high CH 4 production rates were measured (Supporting Information Table S6; Martinez-Cruz et al. 2018;Pellerin et al. 2022), but these do not appear to be accompanied by concomitant high rates of AOM. When comparing the AOM rates of Doughnut, Vault, and Big Trail Lakes (Fig. 1), to the methanogenesis rates of these lake sediments published in previous studies, the relative AOM (AOM rate/methanogenesis rate Â 100%) varies between 0.01% and 0.57%, following the static calculation method, or 0.04-0.74% by the dynamic calculation (Supporting Information  Table S6). For Oxbow Lake, the relative AOM could not be evaluated due to the lack of methanogenesis rate data; however, the absolute AOM rates of this lake were within the range of the other three lakes (Fig. 1). The highest absolute and relative AOM rates of the deeper sediment sections (50-90 cm; Fig. 1) were observed in Big Trail Lake, where AOM rates were 0.57% AE 0.01% of the reported methanogenesis rates (or alternatively 0.74% AE 0.04% by the dynamic calculation). However, it is important to note that although these relative AOM estimations are based on methanogenesis rates measured in incubations of similar temperatures (4 C), the incubated sediment was sampled from different locations and depths within the lakes, and thus they may not accurately represent the sediment in which AOM was quantified. To evaluate the relative AOM with higher confidence, in sediment profiles of two sites in Big Trail Lake, both the methanogenesis and AOM rates were measured per individual incubation bottles (Fig. 2).
In the 1 m profiles of Big Trail Lake sediments, slightly higher AOM rates were observed, where the relative AOM rates were at most, 5% of the methanogenesis in the topmost sediments (2-6 cm), and less than 2% in all other sampling points (Fig. 2). In comparation with Big Trail Lake, in the other studied lakes the proportion of AOM relative to methanogenesis was very low ($ 0.2% or less, Supporting Information Table S6). In Big Trail Lake, the relative AOM was not affected by changes in temperatures, remaining minor in 16 C. Therefore, our results imply that in scenarios of a warmer arctic, the role of AOM in attenuating CH 4 production in the top 1-m lake sediments (which experience the largest temperature fluctuations) is likely to stay minor.
Previous studies of thermokarst sediments suggested that AOM consumed a large portion of the CH 4 production. For example, incubation experiments in the top sediment of Vault and Doughnut Lake's (0-25 cm) suggested that 12-87% of the CH 4 produced is anaerobically oxidized (Martinez-Cruz et al. 2018). These different AOM measurements might be a result of the different sampling locations within Vault Lake, the different horizon that was examined in the incubation experiments (as in this study, only sediment from 50 to 90 cm depth was examined in these specific lakes), or of the different approach for calculating the AOM rates. In both studies, the incubations were amended with 13 C-CH 4 at the beginning of the experiment, but different parameters are used in the AOM calculation. Martinez-Cruz et al. (2018) measured the depletion in 13 C-CH 4 (considering the changes in CH 4 pool that occur during both methane production and AOM). Measuring the 13 C-CH 4 depletion can result an overestimation of the AOM rates, particularly under high CH 4 production rates which may dilute the 13 C signal in the CH 4 pool. Our AOM rates were calculated based on the 13 C-DIC enrichment measured over time. Tracing the 13 C-DIC may lead to an underestimation of AOM rates because the accumulation of 13 C-CO 2 in the gas phase is not considered. However, it is unlikely that these effects induce large variations in AOM rates and they cannot explain the large discrepancy between the studies. Nonetheless, to better constrain AOM rates, future incubation experiments should consider the entire mass balance of the 13 C amendment and attempt to measure simultaneously the δ 13 C-CH 4 , δ 13 C-DIC, and δ 13 C-CO 2 values over time.
Based on the natural variations of δ 13 C-CH 4 , it was concluded that in Vault Lake, 41-83% of the dissolved CH 4 must be consumed within the anoxic sediments (Winkel et al. 2019). However, the measured AOM rates based on incubation experiments of the same profile, were 0.001-0.003 nmol cm À3 d À1 (Winkel et al. 2019), which could not account for the large role of AOM based on porewater isotope calculations. Interestingly, these small reported AOM rates are comparable to those measured in this study (Fig. 1). Furthermore, a study of a different thermokarst lake (Utqia _ gvik, formerly Barrow, Alaska) did not detect any AOM activity in 13 C-amended sediment incubations (de Jong et al. 2018). These observations may suggest that AOM rates are small, perhaps negligible, in many thermokarst lakes (Table 3).
A decrease in AOM with depth was observed in Big Trail Lake. This may be the result of AOM with electron acceptors that were formed and deposited in the oxic water column that have high reactivities. In site D (Big Trail Lake), it is unlikely that the sediment water interface is exposed to oxic conditions since water chemistry is anoxic year-round (Supporting Information Fig. S6). In contrast, in the shallow region of the lake, near site S, the sediment surface is in contact with oxic waters, at least for a portion of the year (Supporting Information Fig. S7). Moreover, in site S aquatic macrophytes were observed, and their roots may supply O 2 to the surface sediments. This potential O 2 supply may also be related to the relatively high abundance of aerobic methanotrophs ($ 2% of bacteria) in the topmost sediments of this site, in contrast to the other depths, where they were not detected (Table 2). Consequently, the proximity to the oxic zone may result in larger amounts of oxidized species with high reactivity towards AOM. Future studies should consider focusing on the topmost sediments (< 20 cm) of numerous thermokarst lakes, as here we examined this sediment section only in one lake (Big Trail Lake).

AOM mechanism
The addition of electron acceptors that are found naturally in thermokarst lake sediments did not appear to stimulate AOM (Fig. 3). This implies that although iron oxides, manganese(IV) oxides and humic substances are abundant in thermokarst lakes (Martinez-Cruz et al. 2018;Pellerin et al. 2022), their abundance is not the factor limiting AOM, as shown in other, non-thermokarst lakes (Friese et al. 2021;Vigderovich et al. 2022). In Big Trail Lake, the dissolved iron(II) porewater concentrations do not appear to co-vary with the measured AOM rates along the sediment profiles (Supporting Information Fig. S8), which could suggest that AOM is not the factor controlling iron reduction in these sediments. It was recently shown that ferric iron and high methane concentrations coexist in sediments of a ferruginous lake, suggesting the lack of iron-AOM in this lake (Friese et al. 2021). As dissolved iron concentrations in thermokarst lake sediments are in a similar range as in ferruginous lakes (up to mM levels), and both are sulfate depleted (Supporting Information Table S2; Friese et al. 2021), the carbon-iron interplay in these environments might be similar. The low AOM rates observed in the studied thermokarst lakes, together with the inhibition or inert response to ferric iron addition, may suggest that iron-AOM does not play a major role in thermokarst lakes as well.
The addition of molybdate did not inhibit the AOM (Fig. 3), suggesting AOM is not coupled to sulfate reduction. This aligns with the micromolar-level sulfate concentrations measured in all four sites (Supporting Information Table S2). The pore water concentrations of nitrate and nitrite, which can also be utilized as electron acceptors during AOM, were very low as well (Supporting Information Table S2). Hence, the participation of most plausible inorganic electron acceptors in the AOM process was ruled out.
An inert behavior toward the addition of various electron acceptors or molybdate was also recently shown in the methanogenic sediments of a monomictic lake in Israel, where AOM rates ranged between 3% and8% of the CH 4 production rates (Vigderovich et al. 2022). In our study, such high relative AOM rates were achieved only in the topmost sediments of Big Trail Lake, site S (Fig. 2B). Similarly, the specific electron acceptor supporting AOM at this point was not identified.
The conventional AOM pathway relies on the reverse enzymatic pathway of CH 4 production (Wang et al. 2014). AOM can therefore be suppressed by the methanogenesis inhibitor BES (Nauhaus et al. 2005). In our study, addition of BES also prevented AOM (Fig. 3), indicating that the mechanism of AOM is related to the mechanism of CH 4 production. This is consistent with other freshwater sediment incubations (Bar-Or et al. 2017;Vigderovich et al. 2022). However, BES addition was only tested on deeper sediments (50-90 cm) of Vault and Doughnut Lakes, and not on the topmost sediments of Big Trail site S, where the relative AOM appeared to be highest. The bacteria present in shallow depths can perform nitrite-dependent AOM or aerobic CH 4 oxidation ( Table 2). The metabolic pathways of these processes do not rely on reverse methanogenesis, but on converting methane to methanol (Ettwig et al. 2010), hence they should not be inhibited by BES. Therefore, at this point, CH 4 oxidation may still be related to bacterial methanotrophic communities which were more abundant in this depth, and not necessarily to ANME or methanogens. Activity of aerobic methanotrophs in the surface sediments was also observed to be possible at Vault Lake (Martinez-Cruz et al. 2017), and in Lake Qalluuraq, Alaska (He et al. 2021). However, it is important to emphasize that in this study, aerobic methanotrophs were present only at the topmost sediments (4 cm), beneath shallow waters ($ 0.6 m).
The microbial community analysis in Big Trail Lake supports the low AOM rates measured in this study, as they suggest that the metabolic potential for AOM is limited. Members of ANME, which are known for performing AOM in marine, terrestrial, and freshwater environments (Hinrichs and Boetius 2002;Takeuchi et al. 2011;Timmers et al. 2017), were scarcely detected (Table 2). Nevertheless, this analysis was performed only on Big Trail Lake, the youngest lake in this study. The ANME abundance in the three other lakes may be different, as the establishment of ANME communities may be a very slow process, and strongly dependent on the age of the CH 4 source (Thurber et al. 2020). For example, a previous study of Vault Lake reported high abundance of ANME-2d in its taberite deep (3.5-5 m) sediments (Winkel et al. 2019). However, the reported AOM rates were not concomitantly high, as they did not exceed 0.003 nmol cm À3 d À1 (Winkel et al. 2019). This observation may question the metabolic activity of ANME-2d in these sediments.
Besides the typical anaerobic methanotrophic archaea, some bacteria are capable of oxidizing CH 4 under anaerobic conditions. The methanotrophic bacteria Methylomirabilales (of the NC10 phylum) which can perform nitrite-dependent-AOM (Ettwig et al. 2010), were detected in the sediment, although their abundance did not exceed 1% of bacterial reads. Noting that the activity of a specific group does not necessarily correlate with their abundance, these low abundances alone do not rule out a potential role for nitrite-dependent AOM, and perhaps complimentary analyses (e.g., metatranscriptomics) could provide deeper insights regarding the activity of this metabolism. However, from a geochemical perspective, it is unlikely that nitrite-AOM plays a significant role in the sediments, since nitrite concentrations were < 2 μM along the porewater profile (Supporting Information Table S2). The abundance of aerobic methanotrophs in the topmost sediments was slightly higher (near 2% of bacteria reads). Since the incubations were kept in anaerobic conditions, total CH 4 oxidation (aerobic and anaerobic) may be underestimated in this horizon. Furthermore, it is possible that the microbial community composition has shifted from its original in situ composition during the incubation experiments. Nonetheless, focusing on the anaerobic processes, under laboratory anoxic conditions, the overall CH 4 oxidation in this horizon was less than 5% of the CH 4 production. This suggests that the presence of aerobic methanotrophs in the topmost sediments is not correlated with significant anaerobic methane oxidation, but only slightly higher than other depths. Essentially, the microbial community along the sediment profile was dominated by fermenters and methanogens (Supporting Information Fig. S5), while methanotrophic communities were scarce.
The low AOM rates, together with the unidentified electron acceptor, low abundance of anaerobic methanotrophs and the mechanistic relation to CH 4 production may call into question the assumption that AOM is the mechanism controlling the 13 C-DIC enrichment observed during the 13 C-CH 4 amended incubations.

AOM is near the limit of detection
Since the dead controls did not show a 13 C-DIC enrichment (Fig. 3), it is clear that the transformation of the 13 C label into the DIC pool is microbially mediated. Previous studies suggest two different interpretations for CH 4 oxidation signals during a net reaction of CH 4 production: either Trace-AOM or methanogenesis enzymatic back-flux (Timmers et al. 2017). Here, the term trace-AOM refers to CH 4 oxidation coupled to an electron acceptor, which yields a metabolically efficient overall reaction (ΔG < 0), under conditions of net CH 4 production. In some environments, AOM is occurring simultaneously with CH 4 production, and the microbial community of natural samples often includes both methanotrophs and methanogens (Beulig et al. 2019).
The other interpretation relies on the enzymatic back-flux during CH 4 production (Valentine et al. 2004;Timmers et al. 2017). It has been shown that the individual enzymatic reactions that together assemble the CH 4 production pathway are reversible (Holler et al. 2011;Wang et al. 2014), and that pure cultures of methanogens can oxidize small amounts of labeled CH 4 to DIC under net CH 4 production (Harder 1997;Moran et al. 2005). In incubations of natural samples which show net CH 4 production, it is not easy to distinguish trace-AOM from methanogenesis enzymatic back-flux, since the sediments include a diverse microbial community with a wide array of metabolic capabilities as well as the presence of potential electron acceptors for AOM. Therefore, solid evaluations of methanogenesis enzymatic back-flux can be made only from identified cultures in a controlled medium (Timmers et al. 2017). A pure culture of Methanosarcina barkeri grown on CO 2 + H 2 (without other electron acceptors) oxidized 0.15% of the CH 4 it produced (Moran et al. 2005). Our experimental results of sediment retrieved from Vault, Doughnut and Oxbow Lakes, showed a similar relative oxidation of CH 4 to DIC (0.1-0.3%; Fig. 1). Given the similar magnitude, in these experiments, the observed 13 C-enrichment may very well be a result of enzymatic back-flux during CH 4 production, rather than trace-AOM.
Furthermore, even when AOM appears to be higher than 1%, such as in Big Trail Lake, enzymatic back-flux may still account for the larger flux of carbon from CH 4 to CO 2 . Contrary to laboratory cultures, substrates for methanogenesis in the environment may be limited, resulting in lower free energy yields. According to the differential reversibility hypothesis (Valentine et al. 2004), the degree of enzymatic back-flux is thermodynamically controlled, with less negative ΔG giving higher reversibility. For example, in cultures mediating sulfate-AOM, a catabolic process with a very low energetic yield, the carbon reversibility reached up to 5% of the net AOM rate (Holler et al. 2011). Although the current discussion focuses on the opposite process (reversibility during CH 4 production), in some conditions, an enzymatic back-flux of 5% can be achieved and still provide enough energy for microbial maintenance and growth (Gropp et al. 2022). Thus, the 13 C-tracer may not necessarily indicate active AOM metabolism.
Although we cannot indicate if the 13 C-tracer transformation in the incubations was caused by trace-AOM or by enzymatic back-flux of methanogenesis, the experimental AOM rates are near the limit of detection. In the overall carbon budget of thermokarst lakes, AOM appears negligible.

Conclusions
The formation of new thermokarst lakes and the expansion of existing ones will continue as Arctic temperatures rise, potentially exacerbating CH 4 emissions. However, the oxidation of CH 4 , both aerobic and anaerobic, may offset this increase. Our study, which focused on quantifying AOM suggests that in the anoxic, upper 1-m sediments of thermokarst lakes, AOM rates are two orders of magnitude lower than CH 4 production, indicating it is not a significant sink for CH 4 . Amending the sediment with some of the naturally abundant electron acceptors did not stimulate AOM rates, suggesting that the electron acceptors available in the sediments (e.g., iron oxides) cannot be efficiently utilized towards AOM. We suggest this finding might be valid in many inland thermokarst landscapes due to similar geochemical conditions. Thermokarst lakes in regions with different geochemical settings may have higher AOM rates.
Nevertheless, it is important to consider the limitations of this study. Although AOM rates were obtained from various depths along the top 1-m sediment column in two different sites in Big Trail Lake, in the other three lakes only sediments from 50 to 90 cm were examined. We cannot rule out the possibility that AOM occurs at higher rates in deeper sediment sections which were not sampled, or in the upper sediments (< 50 cm) of three of the four studied lakes. Additional studies on these sediment horizons could better constrain the extent of AOM in thermokarst settings. Since there are indications that aerobic methanotrophy in the water column is more dominant than AOM, future studies should also quantify the aerobic CH 4 oxidation to constrain the overall CH 4 sinks in thermokarst lakes.

Data availability statement
The data that support the findings of this study are openly available in Figshare at http://doi.org/10.6084/m9.figshare. 22351381