Heavy and wet: evaluating the validity and implications of assumptions made when measuring growth efficiency using 18O water

How microbes allocate carbon to growth vs. respiration plays a central role in determining the ability of soil to retain carbon. This carbon use efficiency (CUE) is increasingly measured using the 18O-H2O method, in which heavy oxygen incorporated into DNA is used to estimate growth. Here we evaluated the validity of some of the assumptions of this method using a literature search, and then tested how violating them affected estimates of the growth component of carbon use efficiency in soil. We found that the 18O method is consistently sensitive to assumptions made about oxygen sources to DNA, but that the effect of other assumptions depends on the microbial community present. We provide an example for how the tools developed here may be used with observed CUE values, and demonstrate that the original conclusions drawn from the data remain robust in the face of methodological bias. Our results lay the foundation for a better understanding of the consequences to the 18O method underlying assumptions. Future studies can use the approach developed here to identify how different incubation conditions and/or treatments might bias its CUE estimates and how trustworthy their results are. Further wet-lab work dissecting the assumptions of the 18O method in soil will help justify the scenarios under which it is reasonable to trust its results.

. For many years, the study of CUE was limited to looking at one substrate type at a time, as a single heavy-labeled carbon source was added to the soil. Under this method, heavy carbon is partitioned by the cell into respiration and biomass, and carbon use e ciency can be calculated as the fraction of heavy carbon collected from biomass compared to the sum collected from biomass and CO 2 respiration. However, this method is believed to overestimate "true" e ciency by measuring the uptake of simple labile compounds, and not their integration into biomass [5,6]. 13 C methods may also overestimate CUE if the target compound preferentially enters anabolic pathways while non-labeled substrates are used to generate ATP [7,8]. Finally, 13 C methods measure substrate use e ciency on a specific compound, and do not capture the repertoire of substrates microbes are faced with in natural environments such as soil.
Due to these known biases there has been a recent push towards using substrate-agnostic growth-based measures of biomass increment, such as 18 O-H 2 O incorporation into DNA. This method provides more realistic and reproducible measures of CUE than the other dominant methods [5]. To complete this assay, 18 O-H 2 O is added at 5-50% of the total soil moisture and the soil is incubated in a sealed container for 12-72 hours [5,9].
At the end of the incubation, a gas sample is taken to measure the dissimilatory carbon losses, and the incubated soil is extracted for DNA. The amount of 18 O incorporated into the DNA is then determined using Isotope-Ratio Mass Spectrometry (IRMS), and converted into new DNA produced assuming 31% of DNA is oxygen. This DNA "growth" is then converted into microbial biomass carbon produced using either a sample-specific [5,10,11] or a cross-sample average ratio between total DNA yield and chloroform fumigation-extractable microbial biomass carbon [12]. CUE can then be calculated as for the 13 C and 14 C labeled methods.
For the 18 O-H 2 O method to provide an accurate estimate of CUE, a number of assumptions must be made. These include extracellular water being the sole source of oxygen in DNA; unbiased DNA and microbial biomass carbon extraction, and the actively growing community being representative of the total community ( Figure 1).
Here we explore the validity of these assumptions, the e ects of violating them, and the subsequent consequences for the conclusions made. We focus primarily on how the sensitivity of conclusions changes as a function of the fungal:bacterial DNA ratio of soil, both because proxies for this value are often determined during routine soil analyses, and because relevant physiological di erences between these two groups are relatively well studied.

Methods:
We generated models to simulate the e ects of ine cient DNA and MBC extraction, the active community not representing the total community, alternative oxygen sources to DNA, and di erential growth rates between bacteria and fungi on measured MBC accumulation. All analyses were completed in R v3.4.0 [13], and results were plotted using ggplot2 [14]. Other packages used for the analysis included: plyr [15], Shiny [16], and ggpubr , and the assumptions made (letters). 1. Soil collected from the environment is subject to chloroform fumigation extraction to determine total microbial biomass carbon. All taxa are assumed to have their biomass extracted with equal and complete e ciency (a). 2. A subfraction of the soil is incubated with 18 O-H 2 O, which is assumed to be incorporated into new DNA (3) to comprise a fraction of the oxygens equal to its abundance as a fraction of total soil water (b). 4. The DNA is extracted and quantified, so that a relationship between the DNA and microbial biomass carbon content of the community can be established. It is assumed that this community-level MBC:DNA ratio is representative of the community which grew during the incubation with 18 O-H 2 O, such that the new DNA growth can be converted to new microbial biomass carbon (c). Image made in BioRender©-biorender.com [17].

Model development:
First, we explored the existing literature for reported values regarding each parameter corresponding to the underlying assumptions that could impact CUE estimates (Table 1). Second, we generated a Shiny app [16] to interactively explore the e ect of violating the assumptions of microbial growth measurements over a range of fungal:bacterial ratios. It is available at: https://gracepold.shinyapps.io/18OSimulations/ until 25 hours/month server time have been used, and also as supplementary file S1. These simulations were run either assuming identical growth rates for bacteria and fungi (which were generated as a function of the fungal:bacterial DNA ratio), or that bacteria and fungi formed groups with distinct growth rates. Within each of these scenarios, we evaluated subsets where just DNA was extracted ine ciently, where MBC was extracted ine ciently, or where both were incompletely extracted. This app was additionally used for error checking the code used in subsequent steps, as predicted responses and test cases could be readily screened than when embedded in sensitivity analyses.
Next, we completed a sensitivity analysis by running simulations where a single parameter was changed to the minimum or maximum value observed in the literature (supplementary file S1 and 1), while keeping all the remaining parameters at a best-estimate value. Since "true" MBC di ered between simulations, we divided the resultant "apparent" or "observed" microbial biomass carbon by the true microbial biomass carbon in order to standardize results. Sensitivity values were subsequently recorded as per Allison et al. [1,6]: where high output is the ratio of the true CUE to the observed CUE under the high parameter value, and low output is the ratio of the observed CUE under the low parameter value. Simulation parameters and the underlying assumptions can be found in Table 1, and references are available as a part of our Shiny app.

Empirical validation:
We used a soil microbial diversity manipulation experiment to explore how removing fungi from inocula impacts estimates of carbon use e ciency under a range of methodological errors. Briefly, microbial communities were extracted from temperate deciduous forest soil and either the complete ("fungi + bacteria") or less than 0.8uM fraction ("filtered"; "bacteria only") was used to inoculate an artificial soil matrix. This matrix consisted of 70% acid-washed sand, 20% mu ed and acid-washed silt, and 10% calcium chloride-treated bentonite clay, initially amended with mixed deciduous leaf litter DOC, 2X roller media [18], VL55 minerals and yeast extract. The communities were grown for four months, with weekly additions of 0.5mg g soil -1 cellobiose and 0.05mg g soil -1 ammonium nitrate solutions as sources of C and N, respectively, for the first three months. CUE was then measured by adding 18 O-H 2 O to 20% of the final water present to subsamples of the soil. Samples were prepared identically, only using 16 O-H 2 O, as controls for background heavy oxygen incorporation. The samples were then placed in sealed tubes for 24 hours and the CO 2 produced during this time measured using an IRGA. The soil samples were stored at -80C until DNA extraction using the Qiiagen Powersoil HTP kit. The resultant DNA was quantified using PicoGreen (Invitrogen), and its 18 O enrichment was measured using IRMS at the UC Davis Stable Isotope Facility. CUE was calculated as per [12]. The abundance of total bacteria and total fungi was assessed by real-time quantitative PCR (qPCR) using 16S rRNA primers [19] and ITS primers [20], respectively. The abundance in each soil sample was based on increasing fluorescence intensity of the SYBR Green dye during amplification. Preceding qPCR assay an inhibition test was performed by running serial dilutions of DNA extractions and no amplification inhibition was detected. The qPCR assay was carried out in a 15 ul reaction volume containing 2 ng of DNA, 7.5 ul of SYBR green (QuantiFast SYBR Green PCR Master Mix) and 1 uM of each primer. Two independent qPCR assay were performed for each gene. The qPCR e ciencies for both genes ranged between 85 and 105%. 16S qPCR conditions were: 15 minutes at 95C; 40x 15s @ 94 o C, 30s @ 55 o C, 30s @72 o C; and a melting curve. ITS qPCR conditions were: 15 minutes at 95 o C; 40x 15s @ 94 o C, 30s @ 46 o C, 30s @ 72 o C; and a melting curve. These values were corrected to a genome counts basis using median values from [21] for ITS copies and from [22] for bacterial 16S ribosomal RNA operon copy number.

Shiny app and theoretical sensitivity simulations:
Each simulation was set up under a series of biologically-plausible scenarios. Fungal:bacterial ratio and total community size are presented in terms of DNA, as this is the unit of growth measurement for the 18 O method.
Definitions for parameters are found in Table 1, and for variables defined in the equations below in Table 2. Values without subscripts denote true MBC, DNA, and MBC:DNA ratios, while values with subscripts denote observed values were DNA (d), MBC (c), or both (dc) to be extracted ine ciently: A community of size totalDNA was generated as a function of the fungal fraction of the total DNA pool (FBratio), where 30 was used as an arbitrary multiplier to determine the amount of DNA, and 3 as an additive factor to ensure that bacteria-only (FBratio of zero) still had DNA.
The corresponding amount of microbial biomass carbon (MBC ) is calculated as the sum of the biomass carbon of bacteria and fungi, which are the products of their DNA and MBC:DNA ratios.
Since the MBC:DNA ratio of bacteria (MBCDNAratB) is generally larger in fast-growing and well-fed cells [42,43], we also added the option to allow this ratio to vary as a function of bacterial growth rate. This was done by scaling the ratio between the minimum and maximum MBCDNAratB values observed in the literature over the range of bacterial growth rate (GRbact) values observed (Table (1)), and assuming a linear relationship: which is the solution of The MBC:DNA ratio of the starting community is therefore: However, DNA is not completely extracted from soil microbes, with some evidence for a higher extraction The true total mass of the microbial biomass carbon pool in the soil ug g -1 soil

MBCc
The apparent total mass of the microbial biomass carbon pool in the soil, given ine cient microbial biomass carbon extraction ug g -1 soil totalDNAd The apparent total size of the true DNA pool in the soil, given a DNA extraction ine ciency ug g -1 soil MBCDNA True microbial biomass carbon to DNA mass ratio of starting community; Used to convert the DNA growth increment into microbial biomass carbon growth. dimensionless MBCDNAc Apparent microbial biomass carbon to DNA mass ratio of starting community, given that microbial biomass carbon is not completely extracted; Used to convert the DNA growth increment into microbial biomass carbon growth.
dimensionless MBCDNAd Apparent microbial biomass carbon to DNA mass ratio of starting community, given that DNA is not completely extracted; Used to convert the DNA growth increment into microbial biomass carbon growth.
dimensionless MBCDNAdc Apparent microbial biomass carbon to DNA mass ratio of starting community, given that both DNA and microbial biomass carbon are not completely extracted; Used to convert the DNA growth increment into microbial biomass carbon growth.
dimensionless GRmean Growth rate for simulations when bacteria and fungi are assumed to grow at the same community-level mean day -1

TrueMBCsame
The true new microbial biomass carbon produced during the CUE incubation, assuming bacteria and fungi grow at the same rate (GRmean) ug C day -1

MBCsamed
The apparent new microbial biomass carbon produced during the CUE incubation, given that not all the DNA is extracted from the growing community and assuming that bacteria and fungi grow at the same rate (GRmean) ug C day -1

MBCsamec
The apparent new microbial biomass carbon produced during the CUE incubation, given that not all the microbial biomass carbon is extracted from the growing community and assuming that bacteria and fungi grow at the same rate (GRmean) ug C day -1

MBCsamedc
The apparent new microbial biomass carbon produced during the CUE incubation, given that not all the DNA and microbial biomass carbon are extracted from the growing community and assuming that bacteria and fungi grow at the same rate (GRmean) ug C day -1

DNAbias
The fraction of new oxygen in DNA which comes from extracellular water (ie the 18O-water added) rather than other sources dimensionless

TrueMBCdi↵
The true new microbial biomass carbon produced during the CUE incubation assuming bacteria and fungi grow at di↵erent rates ug C day -1

MBCdi↵d
The apparent new microbial biomass carbon produced during the CUE incubation assuming bacteria and fungi grow at di↵erent rates, given that not all the DNA is extracted from the growing community ug C day -1

MBCdi↵c
The true new microbial biomass carbon produced during the CUE incubation assuming bacteria and fungi grow at di↵erent rates, given that not all the microbial biomass carbon is extracted from the growing community ug C day -1

MBCdi↵dc
The true new microbial biomass carbon produced during the CUE incubation assuming bacteria and fungi grow at di↵erent rates, given that not all the DNA and microbial biomass carbon are extracted from the microbial community ug C day -1  [31]. Spores may be extracted with even lower e ciency [54], but do not contribute to growth so do not play into our calculations. The observed total DNA observed assuming ine cient DNA extraction (totalDNA d ) is then: The corresponding MBC:DNA ratio assuming ine cient DNA extraction (MBCDNA d ) is: MBC is also ine ciently extracted, with chloroform fumigation extraction capturing the true fungal (MBCexte F ) and bacterial (MBCexte B) biomass carbon present with di erent e ciencies [48]. MBCc represents the total amount of microbial biomass observed after accounting for this chloroform fumigation extraction ine ciency: And the corresponding MBC:DNA ratio is: If ine ciencies in both MBC and DNA extraction must be accounted for, then the apparent MBC:DNA ratio (MBCDNA dc ) is: Steps 4-6 therefore show the MBC:DNA ratios a researcher converting the new DNA produced to MBC would use if they were unaware of extraction biases and did not account for di erences in bacterial and fungal growth rates (below).
We assume growth during the incubation is representative of overall community growth. In other words, the community is assumed to be in a steady state and the rate of turnover of a given taxon matches its growth.
In turn, the turnover of DNA in the environment is proportionate to its abundance [55]. If bacteria and fungi grow at the same rate, then the community-level growth rate (GRmean) can be set to vary as a function of the community composition: The corresponding true increase in MBC for bacteria and fungi when they are assumed to grow at the same rate (TrueMBCsame) is: (13) However, we may not "see" all this growth because extracellular water is not the sole source of oxygen in DNA. Rather, anywhere from 4-70% of oxygen in DNA may come from metabolic water [27,26,28]. We refer to this bias towards using extracellular rather than intracellular water as DNAbias, which is the fraction of DNA oxygen derived from extracellular water.
Subsequently, if just DNA is extracted ine ciently then the corresponding apparent new MBC produced (MBCsame d ) is: If just MBC is extracted ine ciently, then the corresponding apparent new MBC produced (MBCsamec) is: If both MBC and DNA are extracted ine ciently, then the apparent new MBC produced (MBCsame dc ) is: When bacterial growth rate (GRbact) and fungal growth rate (GRfun) di er, the true MBC produced (TrueM-BCdi ) is: (17) And the values for the true MBC produced under the various extraction bias scenarios are: One of the assumptions of the 18 O-CUE method is that the turnover of labeled biomass is negligible over the course of the incubation. Assuming a steady microbial community biomass, the corresponding bulk turnover rates of 0.3 to 7% per day above indicate that this expectation is reasonable. However, the true DNA growth rate is likely to be higher, and the impact on estimates of microbial carbon growth to be mixed. Dormancy estimations vary widely, from 6 to 96% of the community observed as dormant [25,23]. Considering a scenario in which 96% of the community is dormant leads to a 24-fold underestimation of growth rate (0.96/(1-0.96)) due to dilution with the bulk pool, but only minimal underestimation if 6% are. Furthermore, factors such as predation could decrease apparent growth rate through the ine cient re-allocation of labeled nucleic acids from primary to secondary consumers, particularly if predators selectively consume community members [56] within a narrow size range [57]. Finally, as a result of the "live fast, die young" adage often attributed to copiotrophs, CUE is likely to be particularly underestimated when growth is concentrated in a small but rapidly growing fraction of the population compared to a larger but slower growing fraction. Our simulations accounted for an active community fraction varying from 1 to 99 GRf un = GRf un ⇤ activeF ractionF (21) GRbact = GRbact ⇤ activeF ractionB (22)

Sensitivity of CUE to fungal removal
We assessed the sensitivity of observed CUE to various methodological assumptions using a few modifications to account for observed fungal:bacterial ratio. Unlike the simulations above, we wished to retain the inter-sample di erences in MBC:DNA ratio and growth. Therefore we applied modifying factors to the original data using expected ratios between bacterial and fungal parameters, rather than imposing fixed values for these organism classes as above.
First, we converted the observed fungal:bacterial DNA ratio based on qPCR to a F:B DNA ratio. To do this, we assumed 82 ITS copies per genome (ITSpergenome) ( Table 1) and a median genome size of 5x10 8 bp for fungi [21,58], and 2.25 16S copies per genome (16Spergenome) and a genome size of 5x10 6 bp for bacteria [22,58]. To get the true fungal:bacterial DNA ratio FBratio, we had to back-calculate from the observed ITS copies copiesITS and 16S ribosomal RNA copies copies16S from qPCR. We then accounted for ine ciencies in DNA extraction as follows: And then convert the 16S and ITS copies to fungal (FDNA) and bacterial (BDNA) DNA mass per gram of soil as follows: BDN A = copies16S ⇤ 5x10 6 ⇤ 650 ⇤ 10 6 6.02214 ⇤ 10 23 Where 650*10 6 is the molecular weight of the average DNA basepair in µg and 6.02214*10 23 is Avogadro's constant. So the corresponding extraction-e ciency and marker gene per genome base pair corrected fungus DNA: bacteria DNA ratio (FBratio) is: The corresponding corrected total DNA (totalDNAActual) in the initial pool (active and inactive) used for MBC:DNA ratio calculation is: We can then calculate relative fungal and bacterial contributions to the MBC pool for fungi (fcont) and bacteria (bcont), the actual amount of MBC (MBCactual) and the MBC:DNA ratios for each group as follows: Now we calculate the FBratio active, which is the fraction of new growth attributed to fungi during the incubation. It is a function of the relative growth rates of bacteria and fungi, as well as their FBratio in the starting bulk community and the fraction of the cells which are active, rather than dormant.
We can then account for DNA extraction (in)e ciency and the use of intracellular water/other sources of DNA oxygen for the growing community: Finally, we convert these DNA growth to the MBC growth which occurred after applying our methodological bias corrections: And calculate CUE using the observed respiration rate (per day): 4 Results and Discussion:

Growth bias depends on extraction bias and FB ratio
Our Shiny app simulations showed that observed microbial growth deviated most from true microbial growth at intermediate fungal:bacterial ratios, and when fungi and bacteria grew at di erent rates ( Figure 2). If only bacteria or fungi are present the active community is better represented by the total community and the MBC:DNA ratio of the active community is as well represented as possible in the MBC:DNA ratio of the starting community. We also found that if groups of microbes with distinct MBC:DNA ratios grow at the same growth rate, then the ability of the 18 O method to reliably estimate the increase in MBC is insensitive to any di erences in the DNA extraction e ciency. This is demonstrated as the observed and actual MBC growth falling on the 1:1 line over all FB ratios, and can be explained by the DNA being underestimated by equivalent amounts in both the total community used for MBC:DNA conversion and the active community extracted. However, mis-estimating the MBC extraction e ciency leads to incorrect microbial growth values whether or not bacteria and fungi grow at the same rate (Figure 2, center column). While a mathematically simple scenario to explain, this is particularly alarming because CFE extraction e ciency depends on a wide range of experimentally-relevant features. This includes the ratio of intracellular (cytoplasm) to extracellular (membrane, extracellular polysaccharides, proteins) carbon, which is known to di er with community structure and growth rate [48,50] and edaphic parameters such as soil pH, water and clay contents [59,60].

CUE estimates are sensitive in the presence of metabolic water
Using a sensitivity analysis and varying one factor at a time, we found that the deviation of observed microbial growth from true growth was most sensitive to metabolic water content across all extraction scenarios ( Figure 3); the sensitivity value was 1 throughout. The first uses of the 18 O method for CUE assumed that all DNA oxygen came from extracellular water [12], but it is known that E. coli only derives around 30% of its DNA oxygen from intracellular water when grown on rich media in the lab [26,29]. Under the less-than ideal conditions in the soil, the value is likely to be higher -from 70-98% of oxygen from extracellular water -as the contribution of intracellular water to DNA oxygen is lower in slower growing E. coli [26] and B. subtilis [28]. The degree of 18 O enrichment in the phosphate backbone also decreases with temperature [61]; since growth rate often increases with temperature, this is another mechanism by which growth may be underestimated in the fastest growing communities. On the other hand, the recycling of nucleotides and "cryptic growth" may be more important in slow-growing and nutrient-starved organisms, preferentially hiding growth in these communities. Moreover, we observed the suppression of respiration after addition of 18 O H 2 O compared to 16 O water in three temperate deciduous forest soils ( Figure S6), which could indicate that 18 O-H 2 O undersestimates growth by suppressing metabolism. We still lack precise estimates of how important non-extracellular water sources are for DNA oxygen under in-situ conditions for bacteria or any conditions for fungi, making them important areas for future research.

Sensitivity of growth to methodological bias depends on heterogeneity in growth rates
With the exception of intracellular water contribution, MBC sensitivity to changes in the other parameters depended on both assumed extraction biases and whether bacteria and fungi grew at same or di erent rates ( Figure   3). In general, estimates were more sensitive to changes in the parameters when bacteria and fungi grew at different rates rather than some community-level mean, in large part because the MBC:DNA ratio observed for the whole community was no longer representative of the growing population. Fungal MBC:DNA extraction e ciency had a similar e ect on how far expected growth deviated from observed growth independent of whether bacteria and fungi grew at the same rate. Errors were also sensitive to bacterial MBC extraction e ciency, but less so. This is because despite slow DNA-based growth in the baseline condition, fungi have a very large MBC:DNA ratio and so contribute disproportionately to the MBC estimate. In a similar thread, errors were less sensitive to fungal DNA extraction e ciency because their growth rate is minimal under baseline conditions. To address this slow growth, researchers sometimes add di erent amounts of 18O-water to soils or incubate for di erent periods based on the growth rates of soils [5].  The plotted scenario assumes that DNA and MBC are both under-extracted, and that F and B grow at di↵erent rates. Results for the remaining scenarios in (Figure 3) can be found in figures S1-S5. Parameters are defined in Table 1 4

.4 Sensitivity of errors in MBC estimations depend on FBratio
Fungal to bacterial DNA ratio a ected which parameters MBC estimates were most sensitive to, with these sensitivities also di ering in their sensitivity to F:B ratio. For instance, MBC error had a sensitivity of approximately 0.5 over all intermediate values of fungal and bacterial growth rate, but decreased precipitously towards zero at FB ratios approaching 0 or 1. By contrast, sensitivity to bacterial DNA extraction e ciency was greatest around a FB ratio of 0.7, and to fungal DNA extraction e ciency at an FB ratio of 0.1-0.2. Sensitivity of MBC extraction e ciency for bacteria was almost zero, except at F:B ratios below 0.1, but almost 1 for fungal MBC extraction e ciency under these same scenarios. Assuming the DNA content and rrN/ITS copy numbers in table 2, the F:B DNA ratio in both soil metagenomic sequences [62] and qpcr [63,22] datasets are often less than 10%. As such, many soil samples are within the range of F:B DNA ratios where deviations in CUE estimates are highly sensitive to even small changes in fungal dominance, such that related samples within a study may di er in the kinds of methodological assumptions they are most sensitive to.

E↵ect of fungal removal on CUE
Fungal:bacterial ratio is one of the oldest and coarsest ways of di erentiating microbial communities, with the ratio typically decreasing with depth and increasing with carbon content [64,63]. We found that our conclusions achieved with our simulations regarding the e ects of fungal removal on CUE were confirmed by empirically excluding fungi from an artificial soil inocula. This is despite the observation that microcosms with bacteria only or both bacteria and fungi di ered in the parameters they were most sensitive to ( Figure 6). For instance, bacteria only microcosms were 2.9x more sensitive to bacterial biomass carbon extraction e ciency, but less than 1% as sensitive to dormancy than were the microcosms with both bacteria and fungi. This led to CUE estimates responding di erently to the same assumption in the two community types ( Figure 5). The observed, "uncorrected" CUE was on average only 25% as high in communities with fungi excluded than those with fungi for the raw data ( Figure 5, solid grey line). No scenarios led CUE in bacteria-only microcosms to approach that of the mixed fungal and bacterial microcosms (ratio = 1; dashed line). This is likely because bacteria dominated in both bacteria-only and mixed microcosms, and was estimated to account for greater than 99% of the DNA.
This imbalance in fungal abundance is much greater than the MBC:DNA ratio for fungi would need to be in order to overcome their much slower growth rates compared to bacteria in our simulations.
Increasing the mean bacterial rrN per genome or decreasing the mean fungal ITS copies per genome increased the ratio of bacteria to bacteria + fungi CUE by decreasing the bacterial contribution to the total DNA pool.
However, because fungal DNA was either absent or nearly absent from bacteria-only microcosms, this impacted the mixed community microcosms much more strongly. Since bacteria grow much faster than fungi by default in   Table 1 the model, reducing bacterial contribution to growth in the mixed microcosms enabled the high MBC:DNA ratio fungi to contribute more, and, in turn, increasing estimated MBC increment and CUE. All together, these results indicate that the observation of reduced CUE in communities where fungi were filtered out is not due to a single methodological bias.
Early studies of bacterial vs. fungal CUE proposed that bacteria should be less e cient than fungi because of their lower biomass CN ratio. Our results do not dispute that bacteria are less e cient than fungi, as the pattern held even with extreme corrections to CUE. Furthermore, recent work explicitly accounting for di erences in bacterial and fungal growth rates and biomasses have found lower CUE in fungal-dominated communities [65]. However, our results do illustrate the benefits of sample-specific conversion factors. Microcosms di ered in the assumptions their CUE estimates were most sensitive to (Figure 6), and biological di erences between samples can alter the degree of methodological correction required. In other words, there are a number of possible methodological biases introduced by the act of using a single set of conversion factors for communities with and without fungi. First is that the bacterial communities are dissimilar in composition between the two treatments, with more Gram-positive Actinobacteria in bacteria-only microcosms than bacteria+fungi microcosms.
The MBC:DNA ratio of the bacteria-only microcosms was very low, sometimes below 1, indicating that the bacterial biomass carbon was not e ciently extracted. By contrast, observed MBC:DNA ratios of natural soil communities generally fall between 3 and 60 [9,45], with values as low as 3.6 for bacteria and as high as 3300 for filamentous fungi in the lab (File S1). In addition, the true MBC:DNA ratio of bacteria is lower for small, slowgrowing and starving or oligotrophic cells [42,43,66]. Small cells have a large amount of membrane (which CFE does not e ectively capture [48,50]) relative to cytoplasm (which it does), therefore exacerbating the genuinely lower MBC:DNA ratio. Although we lack empirical evidence for smaller bacterial cells in the absence of fungi, this could explain the apparently low MBC:DNA ratio and necessitate using di erent extraction e ciencies and MBC:DNA conversions in the two communities. However, we also note that the 18 O method of microbial growth determination already requires a number of assumptions to be made, so making additional assumptions should be done with care.

Shortcomings:
Many of the values used to parameterize these simulations are based on isolates grown in the lab under ideal conditions. However, microbes are known to grow very di erently in the lab compared to in soil. For instance, well-fed bacterial cultures will have lower dormancy and less starvation-induced reductive cell division than those found in soil [66]. Cultivation bias towards fast-growing organisms only exacerbates this, as the (CFE-measureable) cytoplasm:(CFE-ignored) cell membrane ratio will be greater in the copiotrophic organisms we tend to study in the lab [40]. The DNA:MBC ratio has been observed to be higher in small, slow-growing cells in communities extracted from soil [42], but to remain constant over a wide range of growth rates in E. coli [67,68]. Given how poorly-defined this relationship is, we did not include it as a component in our simulations, although the sensitivity of biomass increment estimates to this parameter indicate that -should such a pattern exist -it should have been accounted for. Furthermore, we note that the contribution of intracellular water to DNA oxygen was 70% for fast compared to 4% in slow-growing bacterial culture on rich media. Therefore, it is likely important to account for intersample di erences in the contribution of 18 O-H 2 O to DNA water as a function of growth rate. However, in the absence of knowledge about where bacterial and fungal growth in soil fit on this intracellular water spectrum, we did not include this parameter in our simulations. Finally, determining the true contribution of di erent groups of microbes to the soil DNA pool remains challenging; accurate predictions based on metagenomes are limited by both database biases and the abundance of non-coding DNA in eukaryote genomes, while imperfect primers and di erences in ribosomal RNA operon copy number limit the utility of QPCR. As such, correction factors for microbial biomass carbon estimates will always be limited by the accuracy of fungal to bacterial ratios in the present simulation framework.

Conclusion:
CUE is an essential descriptor of soil carbon cycling, with interesting ramifications for both the ecology and biogeochemistry of soil. There is great interest in measuring this parameter, but also a growing awareness of the various shortcomings in its quantification. Here we focused on one method -18 O water incorporation into DNA, arguably the most reproducible [5] -to examine how assumptions about what it actually measures a ects the conclusions drawn from its estimation. We evaluated how ine cient biomolecule extraction, deviations in microbial growth rate from the population mean, and heterogeneity in microbial community composition a ected how far o observed microbial growth values are from their true values. We found that measurements are particularly sensitive to the use of oxygen sources other than extracellular water, a value which has been shown to change with experimental variables such as temperature and growth rate under controlled conditions in the lab.
Despite this and other possible biases a ecting the CUE we observed in our lab study, our conclusions regarding reduced CUE following fungal removal held. Nonetheless, our results do not account for the possibility that the biology underlying the observed di erences in CUE may necessitate sample-specific correction factors, for instance assuming lower MBC extraction e ciencies in clay-rich or nutrient-poor soils compared to more organic soils.
However, a more complete understanding of the constraints on and biological factors driving the importance of the biases proposed here is needed if these sample-specific correction factors are to improve -rather than worsen -the degree of measurement bias in CUE. For the time being, we therefore strongly encourage other studies to use the model script that we developed here as a springboard for evaluating how robust their own conclusions are to the various 18 O-H 2 O CUE method assumptions.

Data availability:
All data and scripts used to generate the figures in this paper are provided in the supplement.

Acknowledgements:
Funding for this project was provided by the Department of Energy grant DE-SC0016590 to KMD, and an American Association of University Women American Dissertation fellowship to GP. We would also like to thank Eric Morrison for fungal MBC:DNA ratio data, and to Kevin Geyer and Xiaojun Liu for conversations about the 18 O-water method.

Supplementary files and figures
Supplementary file S1 -review of current knowledge on pathways for water oxygen incorporation into DNA and isotopic fractionation.