Evaluating the contribution of methanotrophy kinetics to uncertainty in the soil methane sink

The oxidation of atmospheric methane by soil microbes is an important natural sink for a potent greenhouse gas. However, estimates of the current and future soil methane sink are highly uncertain. Here we assessed the extent to which methanotrophy enzyme kinetics contribute to uncertainty in projections of the soil methane sink. We generated a comprehensive compilation of methanotrophy kinetic data from modern environments and assessed the patterns in kinetic parameters present in natural samples. Our compiled data enabled us to quantify the global soil methane sink through two idealized calculations comparing first-order and Michaelis–Menten models of kinetics. We show that these two kinetic models diverge only under high atmospheric CH4 scenarios, where first-order rate constants slightly overestimate the soil methane sink size, but produce similar predictions at modern atmospheric concentrations. Our compilation also shows that the kinetics of methanotrophy in natural soil samples is highly variable—both the V max (oxidation rate at saturation) and KM (half-saturation constant) in natural samples span over six orders of magnitude. However, accounting for the correlation we observe between V max and KM reduces the range of calculated uptake rates by as much as 96%. Additionally, our results indicate that variation in enzyme kinetics introduces a similar magnitude of variation in the calculated soil methane sink as temperature sensitivity. Systematic sampling of methanotroph kinetic parameters at multiple spatial scales should therefore be a key objective for closing the budget on the global soil methane sink.


Introduction
Aerobic microbial methane oxidation, or methanotrophy, is the only known Earth surface process that removes methane from the atmosphere.Today, methanotrophy is thought to account for roughly 5% of the total sink for atmospheric methane (Saunois et al 2020).However, estimates of the soil methane sink size span a wide range: for example, in the range of bottom-up estimates reported by Saunois et al (2020) of 11-49 Tg CH 4 yr −1 , the low and high estimates differ by almost a factor of five.Minimizing the uncertainty in estimates of the global methane cycle, including the soil methane sink, is crucial to accurately projecting and effectively managing ongoing climate change.
Several sources contribute to the uncertainty in estimates of the soil methane sink.Estimates based on upscaled field data rely on observations from specific locations at specific times, and these datasets may not fully capture the large spatial and temporal heterogeneity that is characteristic of biogeochemical processes in soils (Nunan et al 2020, Lacroix et al 2023).Bottom-up estimates also hinge on correlations between methane flux and environmental variables such as climate or soil properties, but these correlations are often relatively weak.For example, a statistical model considering ecosystem type, soil texture, and climatic zone explained at best only 29% of the variation in observed methane flux (Dutaur and Verchot 2007).Process-based models estimate global methane fluxes by defining mathematical relationships between methane flux and environmental conditions based on theoretical considerations or field-based observations, but these mathematical definitions are similarly hampered by limited mechanistic understanding and small datasets (Murguia-Flores et al 2018).In order to improve ongoing modeling efforts, it therefore is important to identify which processes contribute the most to uncertainty in the modeled soil methane sink.
Many existing models of the soil methane sink employ linear rate constants to calculate methane uptake rate as a function of atmospheric methane concentration (Ridgwell et al 1999, Curry 2007, Murguia-Flores et al 2018).The rate constants among three canonical models vary by a factor of ∼50 (Murguia-Flores et al 2018).While these models calculate soil methane uptake rate as a linear function of methane availability, many experimental studies have found that methanotrophy in natural soils follows Michaelis-Menten kinetics (e.g.Bender andConrad 1992, 1993).Accordingly, a subset of soil methane sink models implement Michaelis-Menten kinetics (Shu et al 2020).The Michaelis-Menten model supports quantitative descriptions of cellular and ecosystem-level processes wherein the rate is sensitive to the concentration of available substrate, but reaches some theoretical maximum when the enzyme or community is saturated with substrate (Liu 2007, Alvarez-Ramirez et al 2019).In contrast to Michaelis-Menten kinetics, first-order rate constants allow for infinitely large oxidation rates as the concentration of substrate (e.g.methane) increases.
Previous work has shown that methanotrophs have variable kinetic properties.Methanotrophs from environments with substantial local methane sources, such as wetlands or landfills, are known to have a lower apparent affinity to methane than methanotrophs with reliable access to only atmospheric methane (Knief and Dunfield 2005).Studies commonly divide methanotrophs into two classes according to their kinetic properties: low-affinity and high-affinity methanotrophs, where only the high-affinity populations are capable of oxidizing methane at atmospheric abundance.The effect of kinetic variability at the enzymatic and the population level on the soil methane sink has not yet been assessed.
Here, we assessed the potential for variation in methanotrophy kinetics to contribute to uncertainty in soil methane sink estimates.We first characterized the variability in kinetic parameters observed in natural soil samples through a comprehensive literature compilation.We then performed an idealized calculation informed by our literature review to test the sensitivity of the modeled methane sink size under different scenarios.We compared the calculated sink size under Michaelis-Menten and linear kinetics models to assess whether the assumption of first-order kinetics substantially affects model outputs.We also quantified the sensitivity of the calculated sink size to the range of kinetic properties observed in natural soils.Finally, we calculated the sink size under future changes in methane concentration (via kinetic parameters) and temperature (via Q 10 values).Our results highlight important considerations for future observations and models of the soil methane sink.

Literature compilation
To evaluate the range of methanotrophy kinetics in Earth surface environments, we generated a comprehensive compilation of published Michaelis-Menten kinetic data for methanotrophy in natural soils (data set S1).The equation to describe Michaelis-Menten kinetics is: where V is the reaction rate, V max is the maximum reaction rate observed at saturation, [S] is the concentration of substrate (in this case methane), and K M is the substrate concentration where 1 /2 V max is attained.K M values are often discussed in terms of affinity, where low K M values indicate high affinity for methane and vice versa.
We extracted 542 observations of V max and/or K M values (supplementary information S1, data set S1).At least 1 observation was reported for 5 continents, but the vast majority of these (441) were from Europe and North America, exhibiting strong regional bias (figure 1).Observations spanned diverse environments including forest, grassland, peat, and shrubland vegetation, although no data were available for desert or high-latitude sites.Treatment of the soil samples before and during the kinetic incubations varied among studies, as did the units for reported K M and V max values (supplementary information S1, data set S1).To standardize the dataset for analysis, we converted all K M values to the mixing ratio of methane in the headspace in units of ppbv and all V max values to nmol CH 4 h −1 g soil −1 (supplementary information S1).

Soil methane sink calculations
We used data from our literature compilation to inform an idealized calculation of the soil methane sink size.Our calculation is based on a soil layer of constant thickness covering a fixed percentage of Earth's surface area.In contrast to studies with spatially resolved models (e.  did not implement diffusion limitation within the simulated soil layer for two reasons: First, an accurate model of methane diffusion in soils must account for in situ methane production within anoxic microsites and/or below the water table, mechanisms that are beyond the scope of this work.Second, and more importantly, we are not using this calculation to produce an accurate value for the soil methane sink size, but rather to test the sensitivity of the calculated sink size to kinetic parameters. We selected the following parameters for our calculation: (1) we assumed an average soil bulk density of 1.41 g cm −3 (Sequeira et al 2014).( 2) We used MODIS data to estimate the total area of Earth's land surface where methanotrophs contribute to atmospheric methane drawdown (Friedl et al 2022).We included all land area from ecosystem types in our dataset without persistent local sources of methane: forest, shrubland, grassland/meadow, and cropland (supplementary information S2).(3) To select default K M and V max values for the model, we selected the median values for each ecosystem, and weighted them by the global extent of the respective ecosystem to calculate global median values.(4) We specified the average thickness of the soil layer where methanotrophy may occur as 5.36 cm [4.96, 6.30].We calibrated this value for soil depth to produce a calculated sink size at the modern methane mixing ratio (1850 ppbv) of 40 Tg yr −1 (range: 37-47 Tg yr −1 ), matching the average and uncertainty for top-down models in 2017 (Saunois et al 2020).Process-based models of methanotrophy have chosen soil depths ranging from 1 to 10 cm (Ridgwell et al 1999, Curry 2007, 2009 and references therein), while a recent global model allows the depth of methanotrophic soils to vary as a function of methane diffusion and uptake rates (Murguia-Flores et al 2018).Although methanotrophy may certainly occur at a wider range of depths in natural soils, our calibrated value for soil depth partially accounts for the fact that our calculation does not otherwise account for limitations on vertical transport.Values for each parameter are summarized in Supplementary information table S1.

Compiled K M and V max values support physiological or evolutionary adaptation of methanotrophs
In this dataset, K M and V max values each varied over several orders of magnitude: K M from 10 3.2 to 10 9.4 ppbv and V max from 10 −2.7 to 10 4.9 nmol CH 4 g dry soil −1 h −1 (figure 2).All but 1 of 413 K M values exceeded modern atmospheric methane abundance, and the maximum K M value exceeded atmospheric abundance by 6 orders of magnitude.These high K M values indicate that soil methanotrophy at ambient methane concentration is generally slow, but that rising methane availability can stimulate large increases in rate.Both K M and V max values related to the environmental source of the sample.Most low-affinity, high-V max measurements were from landfill or compost soil samples (categorized here as 'waste').These samples come from environments where methanotroph communities experience persistently high local methane concentrations.Meanwhile, most high-affinity, low-V max measurements came from forest and grassland sites.These findings align with previous laboratory experiments showing that the methane concentration available to an enrichment culture can affect the kinetics displayed by that culture, with lower methane However, substantial variation was also evident within each ecosystem type (figure 2).For example, K M values spanned 7 orders of magnitude within the full dataset; up to 4 orders of magnitude in ecosystems with limited local methane sources (e.g.grasslands); and up to 6 orders of magnitude in ecosystems with substantial local methane sources (e.g.peat bogs).Similarly, the range of V max values within individual ecosystems spanned up to 6 orders of magnitude, an equivalent range to the full dataset.Within-ecosystem variability may partially be explained by variability in local methane concentrations that is not captured by ecosystem type.Additionally, recent work has shown that the kinetics of methanotrophy can also change within a single strain: some methanotroph strains harbor two distinct types of the particulate methane monooxygenase enzyme used to mediate methane oxidation, each with distinct kinetic properties (Baani and Liesack 2008, Tikhonova et al 2021).These findings suggest that a single methanotroph community in a single environment may express distinct kinetic properties under different conditions, for reasons that are not yet understood.
The studies included in our data compilation employed varied sample handling strategies before and during kinetic analyses (supplementary information text S1).These methodological differences could partially account for differences in observed K M and V max values between studies.A Mann-Whitney U-test showed a statistically significant difference between the K M and V max values of samples that underwent preincubation, but no significant difference due to amendments.Samples that underwent preincubation were also dominantly from waste sites (82%), unlike samples that did not receive preincubation treatment (23%), making it impossible to conclude whether preincubation caused the observed difference.Other aspects of sample treatment including soil moisture adjustments were not reported with sufficient consistency to perform statistical tests.We suggest that the effect of sample handling on kinetic measurements is a worthwhile topic for future investigation.
Across the wide range of K M and V max values in our compiled dataset, we found that the two parameters were positively correlated when log 10 -transformed, demonstrated by a standardized major axis (SMA) regression (r 2 = 0.44, slope = 10 −2.94 nmol g soil −1 h −1 ppbv −1 ) (figure 3).This correlation is not an inherent property of the methods for deriving or measuring K M and V max values.Few similar compilations of kinetic data are available to investigate the prevalence of this trend; however, a study of the kinetics of nitrification did not reveal a correlation between K M and V max values (Kits et al 2017), indicating that this trend is not ubiquitous in biological systems.A study that investigated in vitro k cat and K M values across several 1000 enzymes showed a weak correlation between these two parameters (r 2 = 0.09) (Bar-Even et al 2011).Because V max is a function of k cat and the concentration of active sites, a similarly weak correlation between K M and V max values might be expected across diverse enzyme classes.The study noted stronger correlations in enzyme classes with simple catalytic mechanisms and particularly low correlations for many monooxygenase enzymes.
The correlation we observed between methanotrophy kinetic parameters may reflect physiological or evolutionary processes through which methanotrophs adapt to the availability of methane in their ecological niches.A low K M value suggests a high affinity for methane, an advantageous trait in environments where methanotrophs subsist on primarily atmospheric methane, like forests and grasslands.Conversely, a high V max value paired with a higher K M value implies rapid methane oxidation at elevated methane levels, enabling faster methane turnover and possibly faster growth in methane-rich environments such as landfills or peatlands.If methanotrophs have adapted their enzymatic properties according to substrate availability, they are not alone among biological systems.For instance, the oxygen reductase enzyme families involved in aerobic respiration demonstrate a tradeoff between oxygen affinity and proton pumping capacity (Han et al 2011).Methanotrophy may offer another example where ecological niche partitioning drives enzymatic adaptations.This possible evolutionary mechanism, alongside the grouping of variability in kinetic parameters by ecosystem type in our dataset, supports that ecosystem type may be a useful constraint for predicting methanotrophy kinetics.
Previous studies have found that laboratory cultures can develop a higher affinity for methane under extended incubation with low methane availability (Dunfield et al 1999, Dunfield andConrad 2000).These changes could result from a change in the expression of methane monooxygenase enzymes with distinct kinetic properties (Baani and Liesack 2008, Tikhonova et al 2021).In enrichment cultures, kinetic changes could also reflect the selective enrichment of taxa with higher methane affinity.However, in these culture studies, the decrease in K M was accompanied by a decrease in V max values only under starvation conditions (Dunfield and Conrad 2000), and not when samples were methane-replete (Dunfield et al 1999).Dunfield and Conrad suggested that concomitant decreases in K M and V max may have resulted from limitation in a cosubstrate, such as NADH.This provides an additional explanation for the correlation between K M and V max in natural samples: methanotrophs may frequently be limited for substrates other than methane.It may be that physiological adaptations, evolutionary adaptations, and cosubstrate limitation all contribute to the correlation evident in this compiled dataset.

Comparing Michaelis-Menten kinetics to linear rate constants
We calibrated our idealized calculation to yield a methanotrophy sink of 40 Tg yr −1 [37, 47] at 1850 ppbv methane.By calibrating our parameters to produce a realistic methane sink size under a modern methane mixing ratio, we were able to test the effect of different kinetic models and kinetic parameter values on the calculated soil methane sink size relative to a reasonable baseline.To test the importance of the choice of kinetic model, we quantified the effect of implementing Michaelis-Menten versus linear kinetics on the calculated soil methane sink size.We identified the first quartile, median, and third quartile K M and V max values for each ecosystem (figure 2), and calculated area-weighted average kinetic parameters for each quartile.For each set of K M and V max values, we calculated the corresponding first-order rate constants by solving equation ( 1) for [S] = 1850 and dividing the result by [S].
Both kinetic models agreed closely at modern and historical pCH 4 values (figure 4).This results from the fact that most K M values substantially exceed the atmospheric abundance of methane: Michaelis-Menten kinetics produce a near-linear response when [S] is much smaller than K M .The soil methane sink size calculated from the two models diverged most at high pCH 4 and low values of K M .At 4000 ppbv methane, linear kinetics using 1st quartile kinetic values yielded a sink of 75 Tg yr −1 , while Michaelis-Menten kinetics yielded a sink of 70 Tg yr −1 , a 1.1fold difference.As pCH 4 reached closer values to K M , the linear and Michaelis-Menten models reached a 1.2-fold difference of 22 Tg yr −1 at 8000 ppbv.Our findings indicate that under very high-emissions projections such as Shared Socioeconomic Pathway (SSP) 3-7.0 (Kleinen et al 2021), a linear rate constant may overestimate the size of the soil methane sink.However, in all cases, results of the two kinetic models overlapped when accounting for the uncertainty in the modern methane sink size used to calibrate our calculation.The difference between the two kinetic models was greatest for the lowest K M values, where Michaelis-Menten kinetics produce a saturation effect at lower values of pCH 4 .Therefore, models focusing on the methane sink in forest environments, where K M and V max values are typically low (figure 2), may derive a benefit from implementing Michaelis-Menten kinetics.Generally, however, differences between the calculated soil methane sink size were far more pronounced between quartiles of kinetic values than between linear and Michaelis-Menten kinetic models.As a result, the selection of kinetic parameters may be more important to accurate modeling results than the choice of kinetic model.

Quantifying the effect of kinetic variability
We found that the soil methane sink size calculated under the Michaelis-Menten model was highly sensitive to the K M and V max values used as model inputs.We first calculated the sink size across all combinations of K M and V max values between the 1st and 3rd quartiles for the ecosystem types without persistent local methane sources.K M values ranged from 18 000 to 141 000 ppbv and V max values from 0.71 to 3.83 nmol g soil −1 h −1 .Within this range of kinetic parameters, the calculated soil methane sink varied from 11 [10,12] to 410 [378,481] Tg year −1 , a 37fold difference between the minimum and maximum values (figure 5).
We also tested whether the correlation between K M and V max values constrained the possible range for the soil methane sink strength.As noted in section 3.1, the K M and V max values from natural samples covaried (r 2 for log-transformed data = 0.44).We first calculated the soil methane sink size using K M and V max values that were limited to ordered pairs from natural samples, including only pairs where both K M and V max values were between the 1st and 3rd quartile values from low-methane ecosystems.The calculated soil methane sink values ranged from 15 [14,18] to 415 [384,488] Tg year −1 , a 28-fold difference between minimum and maximum values.We also calculated the soil methane sink size when pairs of K M and V max values all fell within the 95% confidence interval of the SMA regression slope (10 −2.97 -10 −2.91 ).This calculation yielded a sink size ranging from 52 [48,61] to 76 [70, 89] Tg year −1 , a 1.5-fold difference between minimum and maximum predicted sink sizes-much smaller than the 37-fold difference where the correlation was not accounted for.This finding suggests that the correlation between K M and V max values can lend certainty to estimates of the soil methane sink, and that a deeper understanding of the controls on methanotroph kinetics can support more accurate models.

Comparing kinetic and temperature sensitivity of the soil methane sink
Finally, we compared the sensitivity of our calculated methane sink size to atmospheric methane (via kinetics) versus its sensitivity to global temperature.To assess the temperature sensitivity of soil methanotrophy, we used a temperature coefficient, or Q 10 .Q 10 values are commonly used to express the rate of biological reactions as an exponential function of temperature, including for methanotrophy (e.g.Segers 1998).Only 14 studies in our compiled dataset reported Q 10 values, of which 8 measured exclusively landfill samples, making it difficult to predict expected Q 10 values for soils globally.For this reason, we elected to use a previously published Q 10 value of 1.95 (Murguia-Flores et al 2018).This value was calculated from a compilation of global methanotrophy rates and was used in a recent process-based model of methanotrophy; additionally, it fell within the range of observations from low-methane environments in our compiled dataset (data set S1).We used this Q 10 value to calculate the estimated soil methane sink size for 5 SSPs based on the predicted atmospheric where ∆T is the projected near-surface air temperature increase (Tebaldi et al 2021).Although methanotrophy is located in the soil, where temperatures are often offset from air temperatures, the projected changes in air and soil temperatures are expected to be similar in magnitude (e.g.Soong et al 2020).
Our calculations yielded increased soil methane sink values in proportion to both temperature and atmospheric methane concentration, as has been found in previous work (Oh et al 2020) (figure 6).The combined kinetic and temperature response to the SSPs resulted in a 2.8-fold increase in the soil methane sink strength from SSP1-1.9 to SSP5-8.5, while the kinetic response alone produced a 1.8-fold increase, indicating that kinetics may be of equal or greater importance to future changes in the soil methane sink than the temperature response.The variation in soil methanotrophy kinetics produced variability in the predicted soil methane sink size across all five SSPs.Further, the variability under each SSP between quartiles of kinetic data was of a similar magnitude to the uncertainty introduced by the 90% confidence interval of CMIP6 temperature projections.Calculations based on bootstrapped 90% confidence intervals on kinetic median values produced a similar range of variability as the range between quartiles, but bootstrapping calculations were limited by the sparsity of shrubland data (supplementary information figure S1).In total, these results support that the uncertainty in methanotrophy kinetics may be an important contributor to uncertainty in models of the soil methane sink.

Summary and recommendations
This work provides the first comprehensive compilation of methanotrophy kinetics, lending support to modeling efforts for the soil methane sink which are often data-limited (Murguia-Flores et al 2018).The compiled dataset revealed a correlation between methanotrophy K M and V max values in natural samples, which could result from physiological and/or evolutionary adaptations according to ambient methane mixing ratios, or from cosubstrate limitation.In an idealized calculation of the soil methane sink based on our compiled kinetic data, our results indicated that linear and Michaelis-Menten kinetics closely replicate the modeled soil methane sink size over a modest range of CH 4 mixing ratios.In extreme scenarios, linear kinetics slightly overestimate the size of the sink.This overestimation is primarily relevant in environments where highaffinity methanotrophy dominates, such as forests and grasslands.Nevertheless, the choice of kinetic parameters had a larger effect on the calculated soil methane sink size than the choice of kinetic model.Additionally, the correlation between K M and V max values substantially constrained the range of possible values for the calculated soil methane sink, indicating that a clearer understanding of the mechanisms driving methanotrophy kinetics can reduce modeling uncertainty.Our calculations comparing the effects of future atmospheric methane concentrations and temperature indicated that kinetic variability may introduce a significant source of uncertainty into models of the soil methane sink.
The values reported here are spatially and temporally unresolved, and were calculated using globally averaged parameters rather than a process-based model.By taking this simplified approach, we were able to efficiently test a wide range of input parameters and understand their impact on the outcomes.While a process-based model may amplify or dampen the magnitude of the trends we observe here due to interactions between variables, our results illustrate that methanotrophy kinetics are likely to exert a significant effect on the projected soil methane sink size.This finding highlights the potential value of thoughtfully implementing methanotrophy kinetics in future process-based models.Accordingly, we make several recommendations for ongoing work that can build on our findings.
We recommend that researchers prioritize further kinetic measurements of natural soils, focusing on environments that are underrepresented in our data compilation (e.g.high and low latitudes and sparsely vegetated environments).Our findings also indicate the importance of ongoing experimental work to better determine controls on the kinetics exhibited by methanotroph populations, including the effect of sample preparation methods.More complete datasets and improved mechanistic understanding will support modelers in selecting appropriate kinetic parameters for their models.The choice of linear versus Michaelis-Menten kinetics may be less consequential than the selection of accurate kinetic parameters or rate constants, and modelers may consider assigning different kinetic parameters for different ecosystems.Overall, our results highlight the value in better understanding the mechanisms underlying microbial methane oxidation kinetics, and indicate that a stronger understanding will improve the accuracy of process-based models of the methane cycle.

Figure 1 .
Figure 1.Global map visualizing distribution of methanotrophy kinetic observations.Point size is proportional to the number of observations at a given location.Basemap courtesy of NASA.

Figure 2 .
Figure 2. Compiled Michaelis-Menten kinetic measurements from natural soil samples sorted by environment type (data set S1). Categories are ordered from low to high median values, which are indicated by heavy gray lines.For termite mounds, only KM values were available in the literature.

Figure 3 .
Figure 3. Compiled Michaelis-Menten kinetic measurements from natural soil samples (data set S1).Point shape and color correspond to the environment where the measured soil sample was obtained.Dark gray line represents a standardized major axis regression performed on the log10-transformed KM and Vmax data using the Python package plyr2 (r 2 = 0.44).

Figure 4 .
Figure 4. Comparison of calculated soil methane sink size for linear and Michaelis-Menten kinetics across a range of atmospheric CH4 mixing ratios and quartiles of kinetic data.Shaded regions represent calculated results across the range of soil depth values [4.96 cm, 6.30 cm] calibrated to match uncertainty in the soil methane sink [37 Tg yr −1 , 47 Tg yr −1 ] under the modern methane mixing ratio, as described in section 2.2.

Figure 5 .
Figure 5. Sensitivity of the modeled methane sink size to the kinetic parameters of methanotrophy.Black points are the kinetic measurements from natural soil samples that fall within the interquartile range of the data compilation, shown in greater detail in figure 3. Black solid line is a standardized major axis regression on the log10-transformed KM and Vmax values.

Figure 6 .
Figure 6.The combined effects of kinetic variability, globally averaged near-surface air temperature increases, and atmospheric methane concentrations from Shared Socioeconomic Pathway projections on the calculated soil methane sink size for 2100.Bars represent uncertainty ranges and lines represent average values for projected global mean near-surface air temperatures from CMIP6 (Tebaldi et al 2021).Open circles indicate the effect of atmospheric methane increases in the absence of temperature sensitivity.