Integrative Genome-Scale Metabolic Modeling Reveals Versatile Metabolic Strategies for Methane Utilization in Methylomicrobium album BG8

ABSTRACT Methylomicrobium album BG8 is an aerobic methanotrophic bacterium with promising features as a microbial cell factory for the conversion of methane to value-added chemicals. However, the lack of a genome-scale metabolic model (GEM) of M. album BG8 has hindered the development of systems biology and metabolic engineering of this methanotroph. To fill this gap, a high-quality GEM was constructed to facilitate a system-level understanding of the biochemistry of M. album BG8. Flux balance analysis, constrained with time-series data derived from experiments with various levels of methane, oxygen, and biomass, was used to investigate the metabolic states that promote the production of biomass and the excretion of carbon dioxide, formate, and acetate. The experimental and modeling results indicated that M. album BG8 requires a ratio of ∼1.5:1 between the oxygen- and methane-specific uptake rates for optimal growth. Integrative modeling revealed that at ratios of  >2:1 oxygen-to-methane uptake flux, carbon dioxide and formate were the preferred excreted compounds, while at ratios of <1.5:1 acetate accounted for a larger fraction of the total excreted flux. Our results showed a coupling between biomass production and the excretion of carbon dioxide that was linked to the ratio between the oxygen- and methane-specific uptake rates. In contrast, acetate excretion was experimentally detected during exponential growth only when the initial biomass concentration was increased. A relatively lower growth rate was also observed when acetate was produced in the exponential phase, suggesting a trade-off between biomass and acetate production. IMPORTANCE A genome-scale metabolic model (GEM) is an integrative platform that enables the incorporation of a wide range of experimental data. It is used to reveal system-level metabolism and, thus, clarify the link between the genotype and phenotype. The lack of a GEM for Methylomicrobium album BG8, an aerobic methane-oxidizing bacterium, has hindered its use in environmental and industrial biotechnology applications. The diverse metabolic states indicated by the GEM developed in this study demonstrate the versatility in the methane metabolic processes used by this strain. The integrative GEM presented here will aid the implementation of the design-build-test-learn paradigm in the metabolic engineering of M. album BG8. This advance will facilitate the development of a robust methane bioconversion platform and help to mitigate methane emissions from environmental systems.

Methylomicrobium album BG8 (formerly known as Methylobacter albus, Methylomonas albus, or Methylomonas alba) is an obligate aerobic, Gram-negative, gammaproteobacterial methanotroph that uses methane or methanol as its sole source of carbon and energy (17). A DNA-DNA hybridization study revealed high levels of similarity between its genome and those of Methylomicrobium agile ATCC 35068 (99.16%), Methylotuvimicrobium alcaliphilum 20Z (75.69%), and Methylotuvimicrobium buryatense 5G (76.64%) (18). Recent phylogenomic analyses based on the average amino acid identity and average nucleotide identity have shown that M. album BG8 is also closely related to Methylomicrobium (formerly Methylosarcina) lacus LW14 (19). M. album BG8 has been isolated from swampy soils and freshwater sediments (18,20) and has been widely studied due to its importance in environmental microbiology for bioremediation of different environmental pollutants (21)(22)(23). Through recent physiological and omics analyses, M. album BG8 has also been identified as a promising microbial cell factory (24,25) for applications in the methanebased biotechnology industry (26).
Despite the potential of M. album BG8 as a tool in environmental and industrial biotechnology, no GEM of this methanotroph has been developed; therefore, an integrative system-level understanding of methanotrophy in this strain remains lacking. In this study, a high-quality GEM of M. album BG8 was constructed by stringently following well-established systems biology protocols (42,43). Furthermore, an integrative modeling framework was applied, wherein experimental time-series growth and compound uptake and excretion data collected under different initial methane and oxygen headspace percentages and biomass concentrations were integrated with the initial GEM to construct parametrized GEMs. Subsequently, the metabolic states that promote biomass production and carbon dioxide, formate, and acetate excretion were identified through a flux balance analysis (FBA). The study findings provide novel insight into the metabolic versatility of M. album BG8 and highlight the associations between biomass production and organic compound excretion.

RESULTS
Conversion between the OD and DCW. A linear regression model was established between gram of dry cell weight (gDCW) liter 21 and optical density at 600 nm (OD 600 ) to calculate the DCW from a measured OD 600 value. The model with a y intercept at the origin produced the best fit (see Fig. S1 in the supplemental material), yielding the equation gDCW liter 21 = 0.26 Â OD 600 .
Excess methane did not favor metabolite production. Aerobic methane oxidation, which is catalyzed by the particulate methane monooxygenase in M. album BG8, requires an equimolar ratio of oxygen to methane. We first hypothesized that excess methane in a batch culture of M. album BG8 favors growth. To test this hypothesis, we characterized the effects of two initial methane (20% [0.41 mmol] or 45% [1.0 mmol]) and oxygen (20% [0.43 mmol]) headspace ratios on metabolite excretion and biomass production. The time-series profiles in Fig. 1A demonstrate that a notable amount of methane remained in the culture with 45% initial methane, and that the final concentrations of biomass and excreted products were not significantly different between the cultures grown under different headspace ratios (t test, 5% threshold for P value) (Fig. 1A). Contrary to our hypothesis, excess methane significantly reduced (t test, P , 0.05) not only the biomass yield but also the oxygen uptake and carbon dioxide and acetate excretion yields (Fig. 1B). Although the formate yield was also reduced, this difference was not statistically significant.
Oxygen availability strongly influenced biomass production and organic compound excretion. After determining that excess methane did not favor metabolite excretion, we tested the effects of oxygen availability (range, 5% to 25%) on the metabolism and growth of M. album BG8 under 20% methane. The time-series profile in Fig. 2A shows that the initial oxygen headspace percentage significantly affected the dynamics of biomass production and organic compound excretion. The highest concentration of oxygen led to an increased consumption of methane and the highest concentration of excreted organic compounds in culture ( Fig. 2A). Interestingly, acetate was only detected after approximately 50 h in cultures subjected to all conditions except 5% oxygen (;36 FIG 1 Effects of different initial methane headspace percentages on Methylomicrobium album BG8 in culture. (A) Time-series concentration profiles of biomass production, compound consumption, and compound excretion. The gray-shaded region indicates the estimated exponential phase (;16 h to 40 h). (B) Biomass yields, oxygen uptake, and metabolite excretion throughout the culture period. P values were determined using the two-sided t test. In all panels, the data are shown as the mean values from biological triplicates, and the error bars represent the standard errors. The initial conditions with 20% methane and 20% oxygen (C20_O20) or 45% methane and 20% oxygen (C45_O20) are indicated in blue and red, respectively. In all panels, the same labeling notation is used to denote the experimental conditions, with C representing methane, O representing oxygen, and the following number indicating the initial percentage (vol/vol) in the headspace.
Integrative Modeling of M. album BG8 Metabolism mSystems h; Fig. 2A). The final biomass, carbon dioxide, formate, and acetate concentrations were significantly affected by the initial oxygen headspace percentage (analysis of variance [ANOVA], P , 0.05; Fig. 2B). In terms of yields, all were significantly affected (ANOVA, P , 0.05) except biomass concentration (Fig. S2). Oxygen was practically depleted from all of the cultures at the end of the experiment (120 h; Fig. 2B). The growth kinetics of the cultures, assuming oxygen was the only limiting substrate, were determined by fitting a Monod kinetic model, resulting in a maximum growth rate (m max ) of 0.11 h 21 (95% confidence interval [CI 95 ] = 0.09 to 0.12) and a half-saturation constant (K m ) of 1.69 mM (CI 95 = 0.78 to 2.60) (Fig. 2C). The change in oxygen concentration as a function of the initial ratio of oxygen to methane in the culture headspace (i.e., oxygen-to-methane headspace ratio; slope of the oxygen curve) was greater than the change in the methane concentration (i.e., slope of the methane curve) (Fig. 2D), suggesting that the effects of the initial availability of oxygen and methane on the respective proportions (E) Specific methane and oxygen uptake rates in each culture. Error bars represent the upper and lower bounds of the estimate (99% confidence interval). (F) Comparison of the ratio between the changes in the concentrations of oxygen and methane with the ratio of oxygen-to-methane specific uptake rates. For panels A, B, and D, the data are shown as the mean values from biological triplicates, and the error bars represent the standard errors. In all panels, the color gradient represents the different initial percentages of oxygen (5% to 25%) in 5% increments with 20% methane.
Integrative Modeling of M. album BG8 Metabolism mSystems of both substrates were mainly mediated by higher oxygen consumption (Fig. 2D). The specific uptake rate of oxygen tended to be higher than that of methane under all experimental conditions except the culture containing the lowest initial oxygen headspace percentage (Fig. 2E). In the cultures with initial oxygen headspace percentages ranging from 10% to 25%, the ratio between the specific uptake rates of oxygen and methane remained similar (1.2:1 to 1.4:1), while the ratios between the changes in the concentrations of oxygen and methane varied from 0.75:1 to 1.3:1 (Fig. 2F). Interestingly, only the culture with the lowest initial oxygen headspace percentage had a low ratio (;0.5:1) between the specific uptake rates of oxygen and methane (Fig. 2F) and a noticeably lower rate of specific growth (Fig. 2C).
Features of the GEM of M. album BG8. Given the strong effect of the initial oxygen headspace percentage on the growth rate and metabolic yields, we next aimed to elucidate the metabolic states induced by different levels of oxygen availability in M. album BG8. To achieve a system-level understanding of M. album BG8 metabolism, we constructed a high-quality GEM that incorporated all of the central metabolic pathways contributing to methane oxidation (Fig. 3) and many other pathways that provide energy (ATP is produced by aerobic respiration through oxidative phosphorylation) and precursors for biomass production in M. album BG8 (Fig. 4). The final GEM was established after manually curating the gene-protein-reaction (GPR) associations and biomass compositions in the draft model generated by KBase (43), which led to the addition of 16 genes, 33 metabolites, and 181 reactions. The final curated GEM comprises 803 genes, 1,367 metabolites, and 1,358 reactions ( Fig. 4A), uses the nutrient parameters described in Materials and Methods, and constrains only methane and oxygen uptake fluxes by default (Fig. 4B). The differences in metabolic reactions between the draft and curated versions of the model are detailed in Table S2. Although the final model does not seem underdetermined at steady state (more metabolites than reactions), many metabolites in the model are not directly involved in FBA solutions to maximize the biomass production reaction (e.g., only ;550 metabolites were involved at an oxygen flux of 15 mmol/gDCW/h and a variable methane uptake flux). Furthermore, the final model purposely includes five blocked reactions (i.e., flux is not allowed) (Fig. 4C), of which four are involved in alternative biomass production (containing different growth-associated ATP maintenance assumptions) and one involves an alternative methanol dehydrogenase, and 171 orphan reactions (i.e., with no GPR associations) that were added through the automatic gap-filling of the draft GEM. Among the orphan reactions, 72 are exchange reactions required to interact with the external compartment of the model, and the rest are required to sustain biomass production in the model. However, homologs for their GPR associations could not be detected through genome (re)annotation.
By applying the FBA (44) and minimization of metabolic adjustment (MOMA; linearized version) (45) approaches to the model simulations, 281 essential genes were identified in which a single in silico gene knockout resulted in growth inhibition (Fig. 4D). Consequently, the high-quality final version of the iJV803 GEM included 45 metabolic pathways containing more than five reactions (Fig. 4E). In descending order, (i) the glycerophospholipid metabolism, (ii) fatty acid metabolism, (iii) exchange/demand and transport reactions, (iv) nucleotide interconversion, and (v) cell wall biosynthesis pathways contained the largest numbers of reactions (Fig. 4E). However, reactions that cannot be assigned to specific metabolic pathways accounted for a large proportion of the total reactions, and these remain to be classified in future studies (Fig. 4E).
Metabolic modeling capabilities of the GEM of M. album BG8. We next tested the modeling capabilities of the GEM for M. album BG8 using FBA. We first evaluated the growth rate obtained in the FBA based solely on the experimentally derived methane specific uptake rates. The lower and upper 99% CIs of the methane specific uptake rates derived from cultures with different initial oxygen-to-methane headspace ratios (Fig. 2E) were used as the uptake flux constraint. As shown in Fig. 5A, the growth rates in the FBA were similar to the experimental results, demonstrating the accuracy of the GEM. We also evaluated the ratio obtained in the FBA between the oxygen and methane specific uptake rates that would maximize the growth rate and found that the flux ratio of ;1.5:1 matched the specific uptake rate ratios observed in the cultures with a higher initial oxygen headspace percentage (Fig. 5B).
In the same experiment (Fig. 2), the initial oxygen-to-methane headspace ratio and the specific oxygen and methane uptake rates strongly influenced the growth rates and the final excreted metabolite yields and concentrations. To investigate the variations in growth rate under different oxygen-to-methane uptake flux ratios, a phenotype phase plane analysis was performed while controlling the oxygen and methane uptake flux reactions and maximizing the biomass production reaction (Fig. 5C). Consistent with the experimental results (Fig. 2), the GEM showed a range of ratios of oxygen-to-methane uptake flux within which growth was feasible (above the line showing slope of 1 in Fig. 5C). The highest growth rate was obtained in the FBA at a slope of ;1.5 (Fig. 5C), indicating that although biomass production is possible at an oxygen-to-methane uptake flux ratio slightly greater than 1:1, the ideal oxygen uptake flux is ;1.5 times that of  (Fig. 5C). Interestingly, most of the experimentally determined specific uptake rate ratios (Fig. 2F) were within the range of feasible growth obtained in the FBA; the experiment with the lowest initial oxygen headspace percentage (5%) was the only exception ( Fig. 5C). This result suggests that the specific oxygen and methane uptake rates are not optimal for M. album BG8 growth when oxygen availability is very low.
GEM revealed the role of oxygen availability in balancing formaldehyde oxidization and assimilation. Given the apparent effect of oxygen on methane oxidation and subsequent biomass production and metabolite excretion (Fig. 2), the GEM was used to further investigate the effects of oxygen on system-level metabolism in M. album BG8. Using time-series data from the experiments conducted under various initial oxygen headspace percentages (Fig. 2), the growth rates, methane and oxygen uptake fluxes, and carbon dioxide, formate, and acetate excretion fluxes in the exponential phase were computed (Fig. 5D). The mean growth rate increased with the initial oxygen headspace percentage (Fig. 5D). The methane and oxygen uptake fluxes and carbon dioxide excretion flux were significantly different in the culture with the lowest oxygen-to-methane headspace ratio compared to the rest (Fig. 5D). Similar to the experimental results obtained for yields (Fig. S2), no clear positive associations were observed between the formate excretion fluxes and the initial oxygen headspace percentage in the model (Fig. 5D). Nevertheless, the experiment with the highest initial oxygen-to-methane headspace ratio exhibited the highest formate excretion flux (Fig. 5D). Acetate flux was only detected in the culture with the lowest initial oxygento-methane headspace ratio (although the concentration was low and the uncertainty was high; Fig. 5D).
The use of the upper and lower bounds of the measured fluxes as constraints on the respective reactions in the GEM enabled the construction of a parametrized GEM for each experimental condition. Subsequently, the distribution of flux in the key central metabolic pathways was analyzed in detail ( Fig. 5E to G). The parametrized GEM revealed significant with the highest values obtained in the cultures with initial oxygen headspace percentages of 25% and 10% (Fig. 5E). Significant differences (t test, P , 0.05) were observed in the methane oxidation pathway, the H 4 MPT pathway, the folate metabolism, the partial serine cycle, the RuMP cycle, the RuMP EDD variant, and the RuMP EMP variant (Fig. 5F). Notable formaldehyde dehydrogenase (FDH, rxn00371_c) ( Fig. 3) activity was detected in the experiments initially provided with 15% and 25% oxygen (Fig. 5G), while the NADHconsuming glycerate production reaction (rxn01280_c) (Fig. 3) was only highly active in the culture initially provided with 10% oxygen (Fig. 5G).
Overall, the results of the parametrized GEM-based system-level analysis of M. album BG8 cultures provided with different initial oxygen headspace percentages reveal that these cultures differ mainly in the regulation of formaldehyde oxidization and assimilation. At an initial oxygen-to-methane headspace ratio of 1.25:1, formaldehyde can be efficiently oxidized through the H 4 MPT pathway and assimilated mainly through the RuMP cycle and its EMP variant ( Fig. 3 and 5F and G). However, at an initial oxygen-to-methane headspace ratio of ,0.75:1, the folate metabolism pathway contributes to the oxidation of formaldehyde, which is then assimilated through the EDD variant of the RuMP cycle ( Fig. 3 and 5F and G). Interestingly, the FBA showed that some methanol must be excreted to perform efficient methane oxidation under the condition of low initial oxygen availability (5%) (Fig. 5G). Furthermore, the FBA showed that the culture with the highest biomass yield (20% methane and 20% oxygen) carried a relatively lower mean absolute flux through its metabolic network (Fig. 5E) and high activity throughout the tricarboxylic acid (TCA) cycle ( Fig. 3 and 5G).
Regulation of organic compound excretion by the oxygen-to-methane uptake flux ratio. Because the initial oxygen headspace percentage had a system-level effect on the metabolic state of M. album BG8, a potential mechanistic link to organic compound excretion and biomass production was further investigated. Because the GEM cannot account for absolute concentrations, we focused our analysis on the oxygento-methane uptake flux ratio. The GEM was used to perform over 700 simulations in which the lower and upper bounds of the methane uptake flux were set to an arbitrary value of 10 mmol h 21 gDCW 21 and the lower and upper bounds of the oxygen uptake flux were set to be the same and allowed to vary from 0 to 30 mmol h 21 gDCW 21 . The large volume of simulation results provided insight into the effects of different combinations of methane and oxygen uptake fluxes on the production of biomass and ATP and the excretion of organic compounds, including carbon dioxide, formate, acetate, lactate, and succinate.
The FBA showed that oxygen-to-methane uptake flux ratios in the range of .0:1 to ,2.5:1 were feasible to support biomass and ATP production (Fig. 6A) and organic compound excretion (Fig. 6B). The optimal ratio for biomass and ATP production was ;1.5:1 (Fig. 6A). At high (.2:1) oxygen-to-methane uptake flux ratios, carbon dioxide and formate were preferentially excreted (Fig. 6B), consistent with the experimental results measured in the exponential growth phase ( Fig. 1A and 2A). By limiting the analysis to excreted metabolites that could be experimentally detected (i.e., carbon dioxide, formate, and acetate), the simulation demonstrated that when the oxygen uptake flux decreased (i.e., a lower oxygen-to-methane uptake flux ratio), formate and (eventually) acetate accounted for a larger fraction of the total excreted flux, whereas the carbon dioxide excretion flux was reduced (Fig. 6C). These results are consistent with the experimental phenotypes measured during the late-exponential and stationary phases ( Fig. 1A and 2A).
Metabolic modeling of a high-acetate-excreting phenotype identified a mixed mode involving both respiration and fermentation. Studies (46-50) have determined that the initial biomass concentration can affect microbial growth and metabolic capabilities. Here, we further investigated the effects of two relatively different initial biomass concentrations (low and high) on system-level metabolism in M. album BG8. Both biomass concentrations were tested under the initial oxygen-to-methane headspace ratios that promoted the highest biomass and organic compound excretion yields (1:1 [20% methane and 20% oxygen] and 1.25:1 [20% methane and 25% oxygen]). Under both ratios, the initial biomass concentration had a significant (P , 0.05) and specific effect on the formate and acetate yields (Fig. 7A). In the cultures with a lower initial biomass concentration, a higher formate yield was achieved under the 1:1 oxygen-to-methane headspace ratio compared with the 1.25:1 ratio (Fig. 7A). However, the acetate yield was higher in the cultures with a relatively higher initial biomass concentration under both oxygen-to-methane headspace ratios (Fig. 7A).
No consistent trends in the methane and oxygen uptake fluxes were observed between the cultures with high and low initial biomass concentrations grown under different initial oxygen-to-methane headspace ratios (Fig. 7B). Furthermore, the biomass concentration had a significant effect on formate and acetate excretion (Fig. 7B, the accuracy of the sample mean estimator was determined by the 99% confidence intervals represented by the error bars) but not on carbon dioxide excretion. Acetate excretion flux was observed during the exponential phase under a relatively higher initial biomass concentration and an initial oxygen-to-methane headspace ratio of 1:1 (Fig. 7B). However, these conditions led to a significantly lower growth rate than those of the other three cultures (Fig. 7B).
Although the effects of changing the initial biomass concentration in the experiments cannot be directly simulated using FBA, we approached the metabolic effects of different initial biomass concentrations by constraining the GEM with the experimentally measured growth rates, uptakes of methane and oxygen, and excretion of carbon dioxide, formate, and acetate of the different cultures. The parametrized GEMs were then used to model the metabolism of M. album BG8, revealing that only the culture with a relatively higher initial biomass concentration and an initial oxygen-to-methane headspace ratio of 1:1 exhibited significantly higher (t test, P , 0.05) mean absolute fluxes in the overall metabolic network (Fig. 7C) and in several metabolic pathways, including H 4 MPT, folate metabolism, the partial serine cycle, RuMP cycle, the EMP variant of the RuMP cycle, and the tricarboxylic acid (TCA) cycle (Fig. 7D). In the cultures grown under an initial oxygen-tomethane headspace ratio of 1.25:1, we identified significant effects of the initial biomass concentration (P , 0.05) on the mean absolute fluxes in the metabolic pathways of H 4 MPT and the EMP and EDD variants of the RuMP cycle (Fig. 7D).
A detailed analysis of affected pathways and reactions in the acetate-excreting phenotype indicated that the BS variant of the RuMP cycle, the reactions of which are linked to fermentation-like reactions, exhibited a high level of flux (Fig. 7E). In fact, high levels of flux (Fig. 7E) were observed in the reaction that converts fructose-6P plus glyceraldehyde-3P to xylulose-5P and erythrose-4P (rxn00785_c) and the subsequent reaction that converts xylulose-5P to acetyl-P (rxn01187_c) (Fig. 3). Acetyl-P and acetate can be interconverted through the reactions rxn00230_c and rxn00225_c (with ATP generation), both of which exhibited high levels of flux in this phenotype (Fig. 7E). Furthermore, the parametrized GEM of this acetate-excreting phenotype indicated a second pathway leading to acetate excretion. Specifically, high flux was observed in the pathway that converts pyruvate to acetyl-coenzyme A (CoA) (rxn05938_c) and acetyl-CoA to acetate (rxn00175_c) (Fig. 3 and 7E) and also generates ATP (Fig. 3). Intriguingly, the reactions that convert malate to malyl-CoA (rxn00934, Fig. 3) and malyl-CoA to acetyl-CoA plus glyoxalate (rxn00331_c) (Fig. 3) both exhibited high levels of flux, suggesting that this pathway replenishes acetyl-CoA at the expense of ATP and connects the TCA cycle with the partial serine cycle. In turn, the active production of malate and subsequent generation of acetyl-CoA would explain the high flux in the TCA cycle in this phenotype (Fig. 7E). Interestingly, the flux analysis of this acetateexcreting phenotype also revealed that the entire TCA cycle was used to produce one molecule of ATP, three molecules of NADH, and one molecule of ubiquinol and to excrete carbon dioxide ( Fig. 3 and 7E). Taken together, the results of integrative modeling in this study suggest that the high acetate-excreting phenotype uses a mixed metabolic mode in which the pathways required for respiration and fermentation are simultaneously active. Metabolic versatility of M. album BG8 and coupling between biomass production and organic compound excretion. After separately analyzing and describing the effects of the initial methane (Fig. 1), oxygen (Fig. 2), and biomass (Fig. 7) concentrations on the metabolism of M. album BG8, we quantitatively investigated the associations of these factors with the oxygen-to-methane uptake flux ratio, an important parameter used to define phenotypes (Fig. 6). In all of the experiments, the relationship between the initial oxygen-to-methane headspace ratio and the calculated oxygen-to-methane uptake flux ratio could be described using a bounded exponential model (Fig. 8A). At an initial oxygen-to-methane headspace ratio of .0.5:1, the maximum oxygen-to-methane uptake The oxygen-to-methane uptake flux ratio as a function of the initial oxygen-to-methane headspace ratio under all of the experimental conditions. A bounded exponential model was fitted to the data; the gray-shaded region represents the 95% confidence interval. (B) Results of a principal-component analysis (PCA) of the overall metabolic flux in each experimental culture. Five simulated constrained models were included in the PCA to represent phenotypes optimized for growth, ATP generation, carbon dioxide production, formate excretion, or acetate excretion. The top 5 reactions that contributed the most to the ordination of the phenotypes based on the loadings in dimension 1 of the PCA are shown in the inset. (C) Multiple FBA wherein the acetate, carbon dioxide, or formate excretion reaction was controlled and the biomass production reaction was maximized. The lines indicate the coupling between the rate of growth and the excretion flux of a metabolite. Five hundred simulations were performed for each metabolite.
Integrative Modeling of M. album BG8 Metabolism mSystems flux ratio was 1.3:1 to 1.4:1 (Fig. 8A), consistent with the FBA result of an optimal oxygento-methane uptake flux ratio of ;1.5:1 for growth and ATP generation (Fig. 6A). A PCA was applied to the results of the parametrized GEM to compare the metabolic flux between different cultures (Fig. 8B). Based on the results, most of the experimental phenotypes were clustered together, except the phenotype grown under 20% methane, 25% oxygen, and a relatively high biomass (C20_O25_ODH) (Fig. 8B). Interestingly, this phenotype also yielded an oxygen-to-methane uptake flux ratio of 1.4:1 (the highest observed in all our cultures), which deviated from the confidence interval of the bounded exponential model (Fig. 8A). Cultures with different methane and oxygen headspace percentages but similar initial oxygen-to-methane headspace ratios also had similar oxygen-to-methane uptake flux ratios (Fig. 8A) but slightly different metabolic fluxes, as indicated by their separation on the PCA plot (Fig. 8B).
The results of GEM simulations of phenotypes optimized for growth, ATP generation, or carbon dioxide, formate, and acetate excretion were also included in the PCA as reference values (Fig. 8B). Although the metabolic fluxes resulting from the FBA tended to differ between the experimental cultures, these values were relatively closer to the reference phenotypes optimized for growth, acetate excretion, and ATP generation and clearly distant from the phenotypes optimized for carbon dioxide and formate excretion (Fig. 8B). This metabolic versatility may have enabled M. album BG8 to optimize for growth and ATP generation under different conditions by using different pathways. A closer examination of the top five reactions that contributed the most to the ordination of the phenotypes, based on the loadings in dimension 1 of the PCA (inset in Fig. 8B), revealed that reactions involved in energy generation (rxn10042_c, ATP synthase; rxn05468_c, oxygen transport via diffusion; rxn00519_c, oxaloacetate carboxy-lyase; rxn10122_c, NADH dehydrogenase; and EX_H2O_e, water exchange) were most relevant to define the phenotypes.
An analysis of the metabolic fluxes in the optimal phenotype for acetate production revealed a cluster that included the phenotypes optimized for growth and ATP generation and the phenotypes indicated by the FBA of the experimental cultures. Acetate may be a highly relevant metabolite that balances the pathways contributing to energy and biomass production in M. album BG8. In fact, we hypothesized that a trade-off existed between biomass production and acetate excretion in this strain. This hypothesis was partially supported by the observation of a reduction in the growth rate when acetate was excreted during the exponential phase (Fig. 7B).
To test our hypothesis, we applied multiple FBA in which the acetate excretion reaction was controlled and the biomass production reaction was maximized. The lower and upper bounds of both the methane and oxygen uptake fluxes were set to 210 mmol h 21 gDCW 21 and 0 mmol h 21 gDCW 21 , respectively. This enabled the GEM to automatically adjust the oxygen-to-methane uptake flux ratio to maximize the growth rate under every acetate excretion condition. Consistent with the hypothesis, the multiple FBA revealed a trade-off between the biomass production and acetate and formate excretion (Fig. 8C) and a coupling between biomass production and carbon dioxide excretion (Fig. 8C). In fact, a carbon dioxide excretion flux between 0 and 2 mmol h 21 gDCW 21 (Fig. 8C), which matched the experimentally measured range, favored the growth rate ( Fig. 5D and 7B).

DISCUSSION
The aim of this study was to elucidate the system-level metabolism of M. album BG8 using an integrative systems biology framework. The integration of time-series growth and compound uptake and excretion data into a newly developed, high-quality GEM yielded novel insights into the metabolic mechanisms of this methanotrophic bacterial strain. Furthermore, the experimental data collected in this study enabled the construction of parametrized GEMs, and the application of an FBA enabled the systemlevel understanding of the metabolism of M. album BG8 under different initial concentrations of oxygen, methane, and biomass. The conversion factor of 0.26 gDCW liter 21 derived between the OD 600 and DCW of M. album BG8 in our study differs from a previously reported conversion factor of 0.33 gDCW liter 21 (51). Although a linear regression of our data with a y intercept of 20.044 yielded a conversion factor of 0.32 gDCW liter 21 (see Fig. S1 in the supplemental material), this model was not used due to a lower adjusted R 2 and a less significant P value than those of our selected model. These results highlight the need for caution regarding potential variability in the conversion factor between OD 600 and DCW when studying M. album BG8. However, the Monod model was used to estimate growth kinetics as a function of the initial oxygen headspace percentage, and the calculated m max value (0.11 h 21 ) is similar to other reported growth rates for M. album BG8 (e.g., 0.10 h 21 to 0.18 h 21 with different concentrations of methane [24,51], 0.09 h 21 to 0.13 h 21 with different concentrations of chloromethane [52], and 0.11 h 21 with methanol [53]). However, the Monod model assumed that oxygen was the only limiting substrate, which may not be true in a real-life scenario.
We identified oxygen as the key driver of methane oxidation by M. album BG8, as it exerted strong effects on both biomass production and organic compound excretion. In our analysis, optimal growth could be sustained at a ratio of ;1.5:1 between the specific uptake rates of oxygen and methane. In agreement with our results, a ratio of ;1.5:1 between oxygen and methane uptake rates has also been found by FBA to be optimal for growth for the methanotroph Methylomicrobium buryatense 5GB1 after careful correction of pathways in the GEM (54). Biomass production was maximized under culture conditions of 20% methane and 20% oxygen, with a yield of 0.021 gDCW mmol-CH 4

21
. This was the only culture indicated by the parametrized GEM to have a completely active TCA cycle and to exhibit a low mean level of absolute flux throughout its metabolic network. We speculate that these results of integrative M. album BG8 modeling indicate an optimal methanotrophic state for the allocation of molecular and metabolic resources in which optimal biomass production is preserved and enzyme use is minimized. Future work is required to further explore this notion. These results also complement the findings of recent work in which M. album BG8 was identified as the bacterium with the highest biomass yield (nearly double that of the others tested) among a group of industrially relevant methanotrophs (25).
Intriguingly, the GEM showed the excretion of methanol as a by-product of growth under the condition with the lowest initial oxygen availability (5%). The GEM was parametrized (based on the experimental data) with an uptake rate bounded at 1.52 to 3.16 mmol h 21 gDCW 21 for methane and an uptake rate bounded at 0.05 to 2.24 mmol h 21 gDCW 21 for oxygen. A possible explanation for this methanol-excreting phenotype from the FBA is that methanol works as an additional control for the metabolic branching at low oxygen concentrations, leading to tetrahydrofuran-based oxidation of formaldehyde in addition to metabolic flux through the EDD variant of the RuMP cycle and partial serine pathways. Hence, instead of actual methanol release to the extracellular environment (which was not detected in the medium), M. album BG8 could be using the mentioned pathways to more efficiently oxidize methanol to gain biomass. A recent transcriptomics and metabolomics study of M. album BG8 grown on methanol (55) yielded a phenotype that is similar to the condition with low availability of oxygen. Increased transcription of genes related to carbon metabolism through the RuMP EDD variant and pentose phosphate pathways as well as formaldehyde detoxification through the glutathione dependent pathway, of which formate is the product, were observed (55). Taking the reported transcriptomics and metabolomics data (55) together with the GEM and FBA results presented here, they suggest that M. album BG8 favors methanol oxidation over methane as oxygen availability diminishes.
Although carbon dioxide and formate are usually excreted during aerobic methanotrophy (27), these metabolites have recently become valuable by-products (56,57) and are used as carbon sources in synthetically constructed methanotrophic modular microbial consortia to produce value-added compounds (58). In our study, the highest carbon dioxide yield (0.39 mmol mmol-CH 4 21 ) was achieved under culture conditions of 20% methane and 20% oxygen, and the highest formate yield (0.025 mmol mmol-CH 4 21 ) was obtained under conditions of 20% methane and 25% oxygen. In contrast to a recent report (25), formate excretion was detected in all of the cultures in this study. The phenotype with the highest formate yield exhibited the highest mean absolute flux through its metabolic network and the second highest flux through the H 4 MPT formaldehyde oxidation pathway. In other words, by actively using the complete H 4 MPT pathway, this phenotype can generate two reducing equivalents [NAD(P)H]. Based on these results, developers of metabolic engineering strategies that aim to optimize carbon dioxide and/or formate excretion by M. album BG8 during methane metabolism may consider directing carbon flux toward the H 4 MPT pathway. Nevertheless, future attempts to optimize formate production by M. album BG8 should consider the achievement of significantly larger formate yields by other methanotrophs grown on methanol instead of methane (59)(60)(61). Although a previous study investigated the effects of methane and methanol on formate excretion by M. album BG8, the authors did not detect formate under the tested conditions (25), likely because the samples collected in the reported experiments corresponded to the early stages of M. album BG8 growth in our experimental setup.
Acetate is a key precursor in high-value chemical production (62). Therefore, the biotechnological potential of M. album BG8 in the conversion of methane to valuable compounds depends on the ability to produce a high acetate yield. Among the different culture conditions in this study, the highest acetate yield (0.072 mmol mmol-CH 4 21 ) was unexpectedly obtained under the conditions of 20% methane, 20% oxygen, and a relatively high initial biomass concentration (Fig. 7A). This culture of M. album BG8 excreted acetate during the exponential phase (Fig. S3) but resulted in a relatively lower growth rate at this phase (Fig. 7B), indicating a trade-off between biomass production and acetate excretion (Fig. 7) that was further supported by the model FBA (Fig. 8C). However, the molecular and metabolic mechanisms behind this trade-off remain unclear and need to be further investigated. Previous reports have described acetate excretion by other gammaproteobacterial methanotrophs under prolonged oxygen starvation (63) and oxygen-limited growth (64). Our experimental results agree with those findings, as acetate excretion was detected in all cultures in which oxygen was present at a very low concentration or completely depleted. Similarly, the FBA showed a high acetate excretion flux in M. album BG8 at a low (,1.5:1) oxygen-to-methane uptake flux ratio (Fig. 6C). Overall, we expect that the metabolic characterization of acetate excretion presented here will support future attempts to increase acetate yields and achieve the metabolic reprogramming of acetyl-CoA conversion in M. album BG8.
Both the oxygen-to-methane headspace ratio and specific uptake ratio have been explored intensively in methanotrophy studies (59,63,(65)(66)(67)(68), as these variables are thought to control the differential activation of pathways required for the production of biomass, generation of energy, and induction of fermentation-like metabolism (63,64). The M. album BG8 genome encodes homologs of enzymes found in the EDD and EMP RuMP cycle variants in M. alcaliphilum 20Z and M. buryatense 5G(B1) (64). However, M. album BG8 lacks 3 of the 18 key enzymes [i.e., phosphate acetyltransferase, D-fructose 6phosphate phosphoketolase, and NAD(P)-dependent malic enzyme] required for fermentation-like metabolism in M. alcaliphilum 20Z (64) and M. buryatense 5G(B1) (63) at low oxygen-to-methane concentration ratios. Nevertheless, the M. album BG8 cultures exhibited a fermentation-like metabolism with high acetate excretion and low carbon dioxide and formate excretion mainly during the stationary phase when the oxygen-to-methane concentration ratio was very low. However, in terms of energetic investigations with the current version of the GEM, it is important to note that the growth-associated and nongrowth-associated ATP maintenance have not been specifically determined for M. album BG8. Thus, future work is required to experimentally determine these parameters for M. album BG8, as has been described elsewhere (69,70). Finally, we identified a nonlinear relationship between the initial oxygen-to-methane headspace ratio and the oxygen-to-methane uptake flux ratio in batch cultures of M. album BG8, which will facilitate control of the oxygen-to-methane uptake flux ratio in batch systems.
In summary, the experimental results and the FBA presented in this study elucidate some of the characteristics of M. album BG8. However, many other aspects of metabolism in this strain remain to be explored in detail. The newly developed GEM of M. album BG8 is a valuable tool that will aid future investigations of this important methanotroph in the context of methane conversion applications in biomanufacturing or methane emission mitigation in environments that experience dynamic fluxes of methane and oxygen.

MATERIALS AND METHODS
Strain. M. album BG8 was purchased from the American Type Culture Collection (catalog number 33003D). The genome of this strain has been sequenced (71) and is publicly available in the National Center for Biotechnology Information (NCBI) repository (assembly ASM21427v3), the Integrated Microbial Genomes (IMG) system (IMG genome ID 2508501010), and the KBase Central Store (source ID 686340.3).
Experimental procedures. For all of the experiments, M. album BG8 was cultured in 20 mL of nitrate mineral salts (NMS) medium (72) in a 160-mL serum bottle capped with a butyl rubber stopper. The initial bacterial cell concentration was adjusted according to the experimental specifications. For experiments with a relatively higher and lower initial biomass concentration (Fig. 7), the initial bacterial cell concentration was increased by 1.6-fold and decreased by 3.8-fold compared to all other experiments. The culture bottles were incubated at 30°C with agitation at 200 rpm, and CuCl 2 (5 mM) was used as the copper source (73). The headspace was filled with high-purity (99.995%) nitrogen, and the desired initial mixing ratio between oxygen and methane in the headspace was obtained by injecting appropriate volumes of the respective high-purity (99.7%) gases with a syringe. Here, the initial headspace volume-pervolume percentage refers to the reported percentages of oxygen and methane. All the experiments were performed with three biological replicates. Uninoculated controls were set up in parallel to assess abiotic losses (which were insignificant). For downstream analyses, the cells were collected on 0.22-mm filters (47 mm, MF-Millipore; MilliporeSigma, USA) and washed twice with sterile NMS medium.
Analytical analysis. To determine the headspace concentrations (mM) of hydrogen, oxygen, methane, and carbon dioxide, samples were collected using a gas-tight syringe (Hamilton, USA) and analyzed on a gas chromatograph (GC-2010; Shimadzu, Japan) as described previously (74). After withdrawing a gas sample, an equal volume of nitrogen gas was inserted into the headspace to make up the volume to avoid a vacuum effect (75). Excreted metabolites in the aqueous phase were measured using a high-performance liquid chromatography (HPLC) system (Waters Corporation, USA) equipped with an Aminex ion exclusion HPX-87H column (Bio-Rad, USA) as described previously (74).
Experimental measurement of biomass composition. The concentrations of cellular amino acids and total lipid fatty acids in bacterial cells were analyzed during the exponential growth phase. Seventeen amino acids were measured quantitatively using HPLC at the Proteomics and Metabolomics Facility, Center for Biotechnology, University of Nebraska-Lincoln (USA) by following standard protocols. The total levels of 15 lipid fatty acids were measured quantitatively using thin-layer chromatography, which was performed by a commercial laboratory (AminoAcids.com) by following standard protocols.
Conversion between the optical density and dry cell weight. To determine the conversion factor between the observed optical density at 600 nm (OD 600 ) and the dry cell weight (DCW), 13 cultures of M. album BG8 were grown under 20% methane and 20% oxygen to various cell densities (OD 600 of 0.2 to 1.0), and the corresponding lyophilized cell masses were weighed. OD was measured using a UV-visible spectrophotometer (UV-1800, Shimadzu, Japan), and DCW was determined using an MS-TS analytical balance (MS204; Mettler, Toledo, OH).
Calculations of yield, rate, and flux. The yields of total biomass (gDCW mmol-CH 4

21
) were calculated by considering the changes in concentration per total methane consumed throughout the experiment. The growth rate (per hour) was calculated over the exponential phase as the log-linear regression between the biomass concentration and time. The specific uptake rate and excretion rate were considered equivalent to the uptake flux and excretion flux, respectively, when integrated as constraints into the GEM. To meet the steady-state assumption of the FBA, both rates or fluxes were calculated for each metabolite (in mmol h 21 gDCW 21 ) in each experiment by linear regression of only those data points that were collected during the exponential phase, as described in a previously published protocol (76). Briefly, the growth rates were calculated using a linear regression between the log-biomass concentration and time, with the growth rate being the regression coefficient. The uptake/excretion of metabolites was calculated by using a linear regression between the metabolite concentration and the biomass concentration that was divided by the growth rate. The resulting regression coefficient was the flux, with a positive value indicating excretion and a negative value indicating uptake (76). The computed confidence intervals of the slopes in the linear regression model informed the uncertainty of the measured data and were applied as upper and lower constraints to the reactions in the GEM.
Reconstruction of a draft GEM. The GEM for M. album BG8 was reconstructed based on its genome sequence (71). A draft version of the model was reconstructed using KBase (43) and converted into Systems Biology Markup Language (SBML) for further curation and processing using the Sybil package in R (77), the COBRApy library in Python (78), and the COBRA Toolbox 3.0 in MATLAB (42).
In silico growth medium. An in silico recipe of the chemical compounds required to produce biomass (i.e., growth medium) must be inputted into a GEM. All of the components in the experimental NMS medium (72) were mapped to the KBase compounds database using the tools in the Known Media Database (KOMODO) (79). In the GEM, methane and nitrate were set as the sole carbon and nitrogen sources, respectively. The oxygen exchange reaction was set at a lower limit of 210 mmol h 21 gDCW 21 to ensure an aerobic growth condition.
Integration of experimentally determined biomass compositions into the GEM. In a GEM, an accurate representation of the biomass composition enables better representations of the associated cellular biology and biochemistry. The biomass composition is specified using a metabolic reaction that accounts for the mass fraction of the different macromolecules that constitute 1 g of DCW. However, the automatically reconstructed GEM in KBase only generated a draft biomass production reaction in which the default biomass composition was generated according to the Gram classification of the bacterium of interest. To account for the experimentally determined biomass composition, the M. album BG8 biomass production reaction was manually edited using Python on the Jupyter Notebooks (80) interface of KBase. Briefly, the reaction was updated by adding the experimentally measured concentrations of amino acids and fatty acids and the intracellular organic metabolite, trace element, and cofactor concentrations used in the GEM of M. buryatense 5G(B1) (34). Pyrroloquinoline quinone (PQQ), a cofactor specific for methanol dehydrogenase, was added manually to the biomass production reaction. Other biomass components were obtained from the automatic KBase GEM reconstruction. The biomass production reaction in the GEM was then formulated using the stoichiometric coefficients of all of the metabolites required to generate 1 g of DCW. The following assumptions were made: growth-associated ATP maintenance of 59.8 mmol gDCW 21 , which is used in the GEMs of Escherichia coli (81) and other methanotrophs (34,37), and non-growth-associated ATP maintenance of 3.5 mmol gDCW 21 h 21 , as reported elsewhere for the methanotroph M. parvus OBBP (39). These ATP maintenance parameters have not been experimentally determined for M. album BG8; thus, they are a limitation of the current GEM.
Gap filling and model refinement. After the biomass production reaction in the GEM was edited as described in the previous section, automatic gap filling of the draft GEM was performed using KBase and components of the in silico NMS medium as the nutrient source. All of the reactions added in the gap-filling step were manually checked to determine their essentiality in the GEM using a leave-one-out approach, wherein single reactions were excluded and an FBA was applied to maximize the biomass production reaction. Reactions that were not essential to in silico biomass production were discarded.
The KBase-generated draft GEM in SBML format did not contain the chemical formulae of metabolites. The formulae from the KBase biochemistry database were manually integrated into the GEM. The balance of carbon, hydrogen, oxygen, and nitrogen was checked using the checkBalance function in the COBRA Toolbox 2.0. The final version of the M. album BG8 GEM was named iJV803 according to standard convention (86), where i stands for in silico, J and V are the initials of the name of the GEM builder, and 803 represents the number of included metabolic genes.
Gene locus tags in the GEM. M. album BG8 genes found in KBase (source ID 686340.3) were identified using locus tags that differed from those in the NCBI (accession no. NZ_CM001475) and Joint Genome Institute (genome ID 2508501010) depositories. To reconcile these differences and facilitate the use of the GEM in future research applications, all of the genes present in the GEM were aligned against genes identified in different repositories using Blast (87) (identity cutoff, 99%) to identify the corresponding locus tags. The annotations of all of the key genes involved in methane oxidation were further verified against the reported functions in the literature (24,71), with no discrepancies. The locus tags of all of the genes in the GEM and their corresponding annotations in the different repositories are summarized in Table S1 in the supplemental material.
Quality control and quality assurance. The quality of the iJV803 GEM was checked using the MEMOTE platform (88), and a report of the model can be obtained at https://juanvillada.github.io/iJV803/ docs/index.html.
Genome-scale metabolic modeling and FBA. FBA (44) was performed using the R package Sybil (77). To avoid infeasible metabolic cycles, the cycle-free FBA method (cfFBA) was also applied to metabolic modeling using the R package CycleFreeFlux (89). Linear programming problems were solved using the GNU Linear Programming kit (version 4.65). Although the objectives of optimization varied according to the objective of each analysis (90), the biomass production reaction was the default objective function in the GEM. The FBA method was applied in all phenotype phase plane analyses (91), whereas the cfFBA method was used to optimize parametrized GEMs. After normalizing the metabolic flux of each reaction to the methane specific uptake rate of each parametrized GEM, a principal-component analysis (PCA) of the metabolic fluxes of all reactions in the parametrized GEMs was performed using the R function prcomp.
Statistics. The t test was applied to test the difference between the mean of two groups, and analysis of variance (ANOVA) was applied to test the difference between more than two groups. The parametric tests were applied based on three criteria: (i) the Shapiro-Wilk test indicated a normal distribution, (ii) the variance of the samples was within the same order of magnitude, and (iii) the same number of independent samples was in each group. The majority approach was adopted when the criteria for parametric testing did not apply perfectly for some sample groups (as in the case for some of the data presented in Fig. 5F).
Data availability. The final version of the model can be downloaded in RData, SBML, JSON, and XLS formats from https://juanvillada.github.io/iJV803.

SUPPLEMENTAL MATERIAL
Supplemental material is available online only.