Histone acetylation plays a central role in gene regulation and is sensitive to the levels of metabolic intermediates. However, predicting the impact of metabolic alterations on acetylation in pathological conditions is a significant challenge. Here, we present a genome-scale network model that predicts the impact of nutritional environment and genetic alterations on histone acetylation. It identifies cell types that are sensitive to histone deacetylase inhibitors based on their metabolic state, and we validate metabolites that alter drug sensitivity. Our model provides a mechanistic framework for predicting how metabolic perturbations contribute to epigenetic changes and sensitivity to deacetylase inhibitors.The online version of this article (10.1186/s13059-019-1661-z) contains supplementary material, which is available to authorized users. Saccharomyces cerevisiae and human cell lines have shown that levels of acetyl-CoA directly affect protein acetylation [Protein acetylation is a highly conserved mechanism to regulate many cellular processes including transcription and metabolism. The substrate for acetylation, acetyl-CoA, is a central metabolic intermediate at the crossroads of anabolic and catabolic pathways . Proteintylation –5. Hundrtylation , 7. Acettylation , 8.Given its pervasive regulatory role, altered acetylation is believed to play a part in a variety of diseases including cancer and metabolic disorders such as diabetes, obesity, dyslipidemia, and hypertension , 9–11. SCreating a model of metabolism and protein acetylation can enable the prediction of the impact of nutrient shifts or mutations in metabolic enzymes on the epigenome. This can shed light on metabolic and chromatin dysregulation during tumorigenesis , 13. ComTo address this challenge, here we develop a computational model of metabolism and protein acetylation using constraint-based modeling (CBM). CBM makes use of metabolic network reconstructions that represent the mechanistic relationships between genes, proteins, and metabolites within a biological system. CBM has been successfully used to predict the metabolic state of various mammalian systems, including cancer cells and stem cells –17. We hWe demonstrate that our metabolic model can explain known acetylation changes associated with nutrient excess and starvation based on the availability of carbon units. We then apply our acetylation model to predict and validate the impact of cellular metabolic state on sensitivity to drugs that disrupt acetylation, specifically protein deacetylase inhibitors that are currently used in the clinic for anticancer therapy. Our approach allowed us to predict the variation in sensitivity between deacetylase inhibitors based on their unique impact on cellular metabolism.To simulate the influence of metabolism on acetylation, a nuclear protein acetylation reaction (protein + acetyl-CoA → acetyl-protein + CoA) was incorporated into the human metabolic network reconstruction by Duarte et al., which contains 3747 reactions, 1496 ORFs, 2004 proteins, and 2766 metabolites . A nucleTo predict the impact of the cellular metabolic state on acetylation, we subjected the metabolic model to different nutrient environments and simulated the impact on acetylation Figs.  and 2a. The metabolic model recapitulated known acetylation changes occurring due to a shift in the metabolic state. Switching to high or low glucose significantly affected acetylation levels, which are known to change with glucose flux , 19 Figa. Bulk hThe ability of the model to reproduce these diverse observations provided new insights on the interaction between acetylation and metabolism. Our analysis suggests that bulk acetylation reflects excess carbon flux that is not used for biomass synthesis. Hence, the model predicted acetylation even in the absence of growth, which was observed experimentally in conditions with a carbon source but without a nitrogen source . In contrast, growth conditions without excess carbon, such as those with amino acids alone, did not display histone acetylation Fig. c.The inconsistent observation between the model and experiment arose in a media condition lacking the carbon source—glucose. The model did not predict any acetylation, while it was observed experimentally. Acetylation in this condition was only possible in the model if there was an additional carbon source such as acetate or fatty acids. A recent study has found significant levels of acetate in DMEM media, which is usually not accounted for in biochemical studies . This acSince FBA correctly identified the impact of distinct metabolic conditions on acetylation levels, we next tested if FBA can predict more nuanced differences in the basal metabolic state and acetylation levels between different cancer cell lines. We used bulk histone acetylation levels from LeRoy et al.’s study, which measured acetylation levels using quantitative proteomics across a panel of diverse cell lines representing lung, liver, colon, and brain tumors .To predict cell-type-specific changes in acetylation levels due to their underlying metabolism, we inferred their metabolic state from gene expression data . MetabolR = 0.6, p value = 0.022, FDR < 0.05, Fig. R = 0.25, and H3K23, R = 0.35). Given the small sample size of our dataset (14 cell lines), the predictive power on other acetylation marks might be discernable in a larger dataset in the future. Overall, our analysis suggests that genome-scale modeling can predict the impact of the cellular metabolic state on bulk histone H3K9 acetylation.The transcriptional state of each cell line resulted in distinct metabolic states and acetylation levels. The predicted acetylation flux of these 14 cell lines was compared to the net acetylation levels measured using proteomics in these cell lines. The acetylation levels predicted by the model correlated significantly across all the cell lines with bulk H3K9 acetylation levels, the major acetylation mark known to be sensitive to metabolism . Further, we compared the extent of overlap with acetylases and deacetylases separately. We observed a significant overlap between acetylation-enhancing genes with protein deacetylases but not with acetylases . In contrast, acetylation-impacting genes have a significant number of interactions with both protein acetylases and deacetylases . Thus, acetylases predominantly interact with enzymes that lead to the synthesis of acetyl units. For example, the acetylation-impacting enzyme ACLY had physical interactions with several acetylases. ACLY is known to be transported to the nucleus to facilitate acetylation [Using data from the Biogrid database , which ctylation , 43. TheOur analysis so far suggests that genome-scale modeling can predict the impact of the metabolic state on global protein acetylation. We next predicted the impact of the cellular metabolic state on susceptibility to drugs that disrupt cellular protein acetylation, specifically protein deacetylase inhibitors. The human genome encodes 18 different lysine deacetylases (KDACs) that regulate numerous biochemical pathways . KDACs aDeacetylase enzymes catalyze the removal of acetylation marks from histones and other proteins. They are sensitive to, and directly impact, the metabolic state of the cell . DeacetySince genome-scale modeling allowed us to predict metabolic conditions that increased protein acetylation, we next used it to predict conditions that enhance sensitivity to deacetylase inhibitors. Specifically, we explored the use of metabolic network modeling to identify cell types that are sensitive to KDAC inhibition based on their metabolic and acetylation state. This can enable in silico identification of tumors most sensitive to these drugs.To validate our hypothesis, we experimentally measured the sensitivity of the ovarian cancer cell line (HeLa) to vorinostat ). Vorinostat was the first approved histone deacetylase inhibitor. HeLa cells were cultured in 92 different metabolic conditions using Biolog phenotype microarrays and exposed to vorinostat or control (DMSO). The culture conditions in the Biolog arrays included a wide range of carbon sources that result in distinct patterns of metabolic activity in the cell . This brR = − 0.66, p value = 0.0051, Fig. R = − 0.3, p value > 0.05).The growth inhibition by vorinostat, quantified by area under the growth curve (AUC) relative to control, changed significantly with different nutrient conditions . This is consistent with the observation across metabolic conditions using Biolog phenotype arrays. The low throughput Biolog assays revealed a strong quantitative relationship with the model predictions. However, these were observed with a single cell line. In contrast, the high-throughput drug-screening assays from Seashore-Ludlow et al. involve hundreds of cell lines. Our results across this large dataset suggest that this is a statistically robust phenomenon.We compared the sensitivity of the cell lines with high acetylation flux state with those with low acetylation flux. Cell lines with high acetylation flux were found to be significantly more sensitive to vorinostat treatment than those with low acetylation flux  before and after treatment from UKN1 cells . Severalp value = 10− 62, t-test, Fig. We compared the extent of acetylation flux change caused by each drug in a cell line to the sensitivity of each of these drugs. Cell lines showing higher acetylation flux reduction for a drug relative to others displayed significantly greater growth inhibition to that drug, with an average of 25.3% difference in growth . Overflow metabolism has also been proposed to drive acetylation in prokaryotes , 57. ConOur analysis also identified known and novel metabolic enzymes that can impact acetylation. These predictions were supported by numerous physical interactions between the acetylation-impacting metabolic enzymes predicted by our model with proteins in the acetylation machinery. This suggests that the activity of these metabolic enzymes can impact protein acetylation and are in turn regulated by protein acetylation. This reciprocal regulation to maintain homeostasis has also been observed between metabolic pathways and signaling pathways –60 .p value < 0.05) [Since acetylation plays a central role in signaling and chromatin regulation, mutations in the acetylation-impacting metabolic genes can significantly affect cellular homeostasis. The acetylation-impacting genes, IDH2, SDHA/B/C, and FH, are annotated as being frequently mutated in cancers in the COSMIC database . Aberran < 0.05) . These gWe then demonstrated that our model can predict the impact of the metabolic state on sensitivity to deacetylase inhibitors. We hypothesized that conditions that favor increased acetylation should enhance sensitivity to these drugs, which cause cell death by blocking deacetylation. Consistent with this hypothesis, we were able to predict and validate both metabolic conditions and cell types that show increased sensitivity to these drugs. Our experimental screen across diverse metabolic conditions revealed that sensitivity to vorinostat changed significantly with the metabolic state. Notably, our biochemical model accurately predicted the sensitivity to vorinostat by predicting the acetylation flux in diverse nutrient conditions. Nutrients that were modeled in this study such as glucose, acetate, amino acids, and lactate are also metabolized by tumors in vivo , 64. WhiAnalysis of KDAC inhibitor sensitivity across 860 cancer cell lines revealed that differences in basal metabolic state among cells can lead to variation in sensitivity. Using metabolic modeling, we were able to group cell lines based on their acetylation state and predict those that show increased sensitivity to deacetylase inhibition. Identifying tumors that are sensitive to specific KDAC inhibitors is a significant clinical challenge . Our appFurthermore, unique differences in the transcriptomic pattern induced by each KDAC inhibitor correlate with variation in sensitivity between these inhibitors. By analyzing sensitivity to four clinically used KDAC inhibitors across all CCLE cell lines, we found that cell lines that showed higher acetylation flux reduction after treatment with a KDAC inhibitor relative to others were more sensitive to the corresponding drug. Our approach complements machine-learning and high-throughput screening approaches  by proviWhile we have focused on the impact of metabolism and nutrition on acetylation in this study, the activity of acetylases and metabolic enzymes can also be regulated by signaling pathways which can subsequently impact bulk acetylation levels . FurtherHistone acetylation links gene regulation with metabolism, and aberrant acetylation is associated with cancers and metabolic disorders. Here we developed a genome-scale biochemical network model to predict the impact of metabolism on acetylation. Our model revealed that histone acetylation levels change predictably depending on cellular carbon and nutrient availability. We identified several novel metabolic genes that can impact acetylation when deleted. Our approach provided two key insights related to cellular metabolism and sensitivity to deacetylase inhibition. Firstly, our experimental screen across diverse metabolic conditions and analysis across 860 cancer cell lines revealed that sensitivity to deacetylase inhibitors can be predicted from the cellular metabolic state. Secondly, unique rewiring of metabolic pathways induced by each KDAC inhibitor correlates with variability between these inhibitors. This is potentially relevant for tumor treatment stratification based on the metabolic state. Overall, our study demonstrates the strong and predictable interconnection between metabolism and acetylation.In FBA, an optimal metabolic flux state is determined that maximizes an objective . We used the biomass composition from Shlomi et al.  for the − 6 does not influence the value of acetylation flux and the accuracy of our approach . Acetylation flux is optimized after biomass synthesis is maximized. We used a parameter (“epsilon”) to incorporate the relative weights for optimizing biomass flux relative to acetylation. Changing the value of epsilon  over a 10,000-fold range from 0.01 to 109 molecules per hour in each cell. Assuming a total of 109 acetylation sites in a mammalian cell [Using data from total potential acetylation sites in the human genome , we findian cell , redirecian cell . The mitian cell . This suTo integrate transcriptomic data with the metabolic network model, we used a linear version of the iMAT approach  implemenTo assess the robustness of our results to the method of transcriptome integration, we repeated all our analyses with an alternative approach for transcriptomic data integration called GIMME . This apArea under the growth curve (AUC) values for the small molecule therapeutic screening data for 481 compounds against 860 cell lines were obtained from Seashore-Ludlow et al. along with media used for each of the 860 cell lines. The media composition and transcriptomic data for these cell lines from CCLE was used to infer the metabolic network state for these cell lines as described above. In order to estimate the impact of the cellular doubling rate on drug sensitivity, we also used data from Hafner et al. that controls for this effect . The groThe phenotype microarray (PM) plates from Biolog Inc.  contain diverse energy sources to profile the metabolic capabilities of a cell. Each well in a PM plate contains a single chemical as the sole energy source and production of NADH per well is monitored using a colorimetric redox dye chemistry. As the cells metabolize the energy source, tetrazolium dye in the media is reduced, producing a purple color according to the amount of NADH generated. The PM-M1 plate used in this study contains 92 different carbon energy sources along with negative control wells.2, using the modified Biolog IF-M1 medium [Biolog PM assays were performed as described in Boccuto et al. . Viable 1 medium . HeLa ceTo control for the impact of slow or no growth, we used only those conditions that supported any growth above negative control (Background). Using various thresholds for growth did not impact the strong correlation between the predicted acetylation flux and growth inhibition


Streptomyces coelicolor strain A3(2) strain to convert valencene to the grapefruit metabolite nootkatone, and confirmed its enzymatic activity by gas chromatography-mass spectrometry. This enzyme re-positioning approach may offer an entirely new way of screening enzymes that cannot be achieved by most of other conventional methods, and it is applicable to various other metabolites and may enable microbial production of compounds that are currently difficult to produce industrially.Plant-biosynthesised secondary metabolites are unique sources of pharmaceuticals, food additives, and flavourings, among other industrial uses. However, industrial production of these metabolites is difficult because of their structural complexity, dangerousness and unfriendliness to natural environment, so the development of new methods to synthesise them is required. In this study, we developed a novel approach to identifying alternative bacterial enzyme to produce plant-biosynthesised secondary metabolites. Based on the similarity of enzymatic reactions, we searched for candidate bacterial genes encoding enzymes that could potentially replace the enzymes in plant-specific secondary metabolism reactions that are contained in the KEGG database (enzyme re-positioning). As a result, we discovered candidate bacterial alternative enzyme genes for 447 plant-specific secondary metabolic reaction. To validate our approach, we focused on the ability of an enzyme from   •We developed ‘bacterial enzyme gene re-positioning’ that is a method to search for enzyme genes based on reaction similarity.•We identified candidate bacterial alternative enzymes for 447 plant-specific secondary metabolism reactions.•An enzyme for synthesising nootkatone from valencene was discovered. For exaTo overcome the challenges of extracting metabolites from plants, several means of synthesising metabolites artificially have been developed. Chemical synthesis is popular methods of stably obtaining metabolites that do not involve extraction from plants. Nonetheless, organic synthesis is not always readily possible, because plant secondary metabolites have complex structures and large molecular sizes. In such cases, organic synthesis requires many steps to obtain target metabolites from simple substrates, constituting a great hurdle for industrial large-scale synthesis of plant-specific secondary metabolites . On the 2), which has an environmental impact  (Mucor (fungi) (Rhodococcus (bacteria)  . Further   and meta (fungi)  and Rhodacteria)  have beeEscherichia coli, identified CYP109B1 from Bacillus subtilis that produces nootkatone from valencene  and producing plant-specific secondary metabolites, yet this approach is extremely difficult because of decreasing expression level and enzyme activity due to differences in biological function . In receIn this study, we developed a method to search for genes that encode enzymes based on similarity of enzyme reactions and not on gene sequences. In other words, we aimed to search for enzymes with similar metabolic reactions but with dissimilar gene sequences. Furthermore, in order to validate the approach, we discovered an enzyme for synthesising nootkatone from valencene that has no sequence similarity with the known plant enzyme.22.1We used KEGG OC  database2.2Streptomyces lividans TK64 (NBRC 15678), which was purchased from National Institute of Technology and Evaluation , was used as the host organism for bioconversion. S. lividans TK64 was cultured in TSB medium ; BD, Heidelberg, Germany) supplemented with 50 μg/mL of thiostrepton at 28 °C and 200 rpm for 72 h.Escherichia coli JM109  was used as the host organism for constructing plasmid clones. Escherichia coli JM109 was cultured in LB medium  at 37 °C for 16 h.2.3Streptomyces coelicolor A3(2) (GenBank No. NC_003888), SCO5223, SCO3099, SCO3770 and SCO3636 were cloned. The genomic DNA of S. coelicolor A3(2) was acquired by phenol-chloroform extraction. The coding sequences of four genes were amplified with primers (S. coelicolor A3(2) genomic DNA as a template. PCR was performed under the following conditions: 94 °C for 2 min, followed by 30 cycles of 98 °C for 10 s and 68 °C for 1.5 min . The PCR products were purified and digested with SphI, except for the SCO3636 PCR product, which was digested with EcoT22I. pIJ702D, a derivative of pIJ702SSMP from which melC1 and melC2 have been removed (SCO3636)  . The PCRSCO3770 partially-knockout vector, nucleotides 97 to 1090 of SCO3770, which encode an inactive form of the enzyme, were amplified with primers (S. coelicolor A3(2) genome as a template. PCR was performed under the following conditions: 98 °C for 30 s, followed by 30 cycles of 98 °C for 30 s, 55 °C for 30 s, and 68 °C for 1 min . The PCR product was purified and digested with EcoRI and KpnI. pk18melC, a derivative of pk18mob carrying melC1 and melC2 was digested with the same restriction enzyme, and the fragments were ligated together  supplemented with 10 μg/mL of thiostrepton and incubated at 28 °C and 160 rpm. After 72 h, glucose and valencene  were added at final concentrations of 10% and 0.025%, respectively. Cultivation was then continued for another 168 h.2.6g for 20 min. The cell pellet was resuspended in 1.5 mL ethanol, and 0.25 mL distilled water and 0.5 mL n-hexane were added to 1.0 mL of the supernatant and mixed by shaking. The n-hexane layer was collected by centrifugation at 14,000×g for 1 min. Nootkatone in the extract was analysed by GC/MS . The peak of nootkatone was at approximately 12.0 min. Measurements were performed under the conditions indicated in Following culture of the P450-overexpressing strains, cells were harvested from 2 mL whole broth by centrifugation at 14,000×2.7S. lividans TK64, S. lividans TK64/pIJ702D:SCO3770, S. lividans TK64 ΔSCO3770, and S. lividans TK64 ΔSCO3770/pIJ702D:SCO3770) were cultured, and cells were harvested from 2 mL whole broth by centrifugation at 14,000×g for 20 min. Next, 0.5 mL n-hexane was added to 1.0 mL of the supernatant and mixed by shaking, after which the n-hexane layer was separated by centrifugation at 14,000×g for 1 min. The cell pellet was resuspended in 1.5 mL ethanol, and 0.25 mL distilled water and 0.5 mL n-hexane were added to 1.0 mL of the supernatant and mixed by shaking. Nootkatone in both extracts was analysed by GC/MS  under the conditions indicated in Four strains , which is a representative Streptomyces species and generally used for enzyme screening, exhibited 365 reactions with a similarity score ≥ 0.4, and 43 reactions with a similarity score ≥ 0.9 , which belong to the CYP170A, CYP107U, CYP107P and CYP107T subclasses of the P450 family, respectively, as alternative enzyme candidates for nootkatone biosynthesis according to their similarity scores (E1B2Z9 (Cichorium intybus) and B8ZIU7 (Pleurotus sapidus), the total scores (BLAST bit score) compared to four genes were low, less than 54.6 and identity was also low, less than 30%. For the prokaryotic-derived gene U5U1Z3 (Bacillus subtilis), the BLAST bit score was 99–229, and some homology with four genes was observed, even though identity was only 24–36%. Thus, it could never be considered that these scores were top hits for sequence similarity based screening.We detected four y scores . Our enzy scores  . First, SCO3770 overexpressing (S. lividans TK64/pIJ702D:SCO3770), genomic SCO3770 homolog partially-knockout (S. lividans TK64 ΔSCO3770) and SCO3770 complementation (S. lividans TK64 ΔSCO3770/pIJ702D:SCO3770) strains were constructed. Next, these three strains and wild-type S. lividans were cultured in medium containing valencene for 168 h, the culture supernatant was extracted with hexane solvent, and the nootkatone in hexane was detected by GC-MS . These results indicate that SCO3770 is involved in the conversion of valencene to nootkatone.To confirm the involvement of by GC-MS . Althoug4In this study, we developed ‘bacterial enzyme gene re-positioning’ that is a method to search for enzyme coding genes based on similarity of enzyme reactions, and identified candidate bacterial alternative enzymes for 447 plant-specific secondary metabolism reactions. In addition, an enzyme for synthesising nootkatone from valencene, SCO3770 was discovered by our approach, and SCO3770 had low sequence homology with existing enzymes. This result showed that our ‘bacterial enzyme gene re-positioning’ approach has a novel enzyme screening space which is not considered by sequence based similarity approach, and it may enable us to produce compounds that are currently difficult to produce industrially by microbial fermentation.Our bacterial enzyme gene re-positioning approach detected candidate bacterial alternative enzymes for 447 plant-specific secondary metabolism reactions, and 41 of 447 (9.2%) of the plant-specific secondary metabolism reactions for which re-positioning candidates were identified involved “orphan enzymes”, whose reactions are reported but the genes are not discovered . AlthougOf the plant-specific orphan enzymatic reactions for which we found alternative enzymes in this study, about half of the 19 reactions belonged to flavone-related metabolic pathways. Flavone-related compounds reportedly have anti-tumour  and antiOur result of phylogenetic distribution analysis for discovered candidate bacterial alternative enzymes indicated that the bacterial enzyme candidate genes clustered into a few taxa. The bacterial enzyme candidates were phylogenetically biased, with Pseudonocardiaceae, Streptomycetaceae, Mycobacteriaceae, Myxococcales and Burkholderiaceae possessing more alternative enzyme candidates than other taxa. Since Streptomycetaceae and Burkholderiaceae have particularly many secondary metabolic functions among all of bacteria, it is possible that such bacterial secondary metabolism related enzymes have been detected as alternative candidates for plant secondary metabolism. Moreover, all these bacteria live in soil , and sinIn this study, we applied this method to plant secondary metabolism, however the scope of application of this method is not limited to plant reactions. It is possible to search for the enzyme reactions of all organisms. Not only that, it is possible to search for reactions in which no enzyme has been found if we have only a substrate-product pair. Therefore, applying this method may enable us to flexibly search for the enzyme genes for the desired reaction. This method may be used to search for enzymes for producing industrially valuable compounds from inexpensive compounds without considering whether the reactions are catalysed by the enzymes. the reactions.5Taken together, we developed a novel method, bacterial enzyme gene re-positioning, to efficiently screen bacterial alternative enzymes for plant-specific secondary metabolism based on reaction similarity and found a nootkatone biosynthetic enzyme and many alternative enzyme candidates for other reactions. This bacterial enzyme gene re-positioning method may offer an entirely new way of screening enzymes that cannot be achieved by most of other conventional methods. Overall, this method will enable the production of compounds that are difficult to synthesise. In the future, the discovery of new alternative enzymes through application of this methodology will enable microbial fermentation-mediated mass production of various compounds.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.Y. M., S. H. and T. Y. designed this study. Y. N. and Y. M. performed the bioinformatic screening and other bioinformatic analysis. Y. T. performed the bacterial culture and other experiments. T. Y. and S. H. provided senior guidance. Y. N. wrote the manuscript with assistance from other authors. All authors reviewed and approved the final version of the paper.No conflict of interests is declared.


Modern biological tools generate a wealth of data on metabolite and protein concentrations that can be used to help inform new strain designs. However, learning from these data to predict how a cell will respond to genetic changes, a key need for engineering, remains challenging. A promising technique for leveraging omics measurements in metabolic modeling involves the construction of kinetic descriptions of the enzymatic reactions that occur within a cell. Parameterizing these models from biological data can be computationally difficult, since methods must also quantify the uncertainty in model parameters resulting from the observed data. While the field of Bayesian inference offers a wide range of methods for efficiently estimating distributions in parameter uncertainty, such techniques are poorly suited to traditional kinetic models due to their complex rate laws and resulting nonlinear dynamics. In this paper, we employ linear-logarithmic kinetics to simplify the calculation of steady-state flux distributions and enable efficient sampling and inference methods. We demonstrate that detailed information on the posterior distribution of parameters can be obtained efficiently at a variety of problem scales, including nearly genome-scale kinetic models trained on multiomics datasets. These results allow modern Bayesian machine learning tools to be leveraged in understanding biological data and in developing new, efficient strain designs. Genetic engineering of microbes is a promising strategy to enable more efficient and environmentally friendly production routes for chemicals and materials traditionally produced from petroleum. While the tools to both edit microbial genomes and measure the resulting changes to cellular physiology are growing increasingly efficient, our ability to predict which genetic interventions will have the greatest likelihood of achieving the desired phenotype is still lacking. In particular, computational methods are needed that are able to efficiently ingest the increasing amount of data generated from large biological datasets to guide subsequent rounds of experiments. This study presents an efficient algorithm coupled to modern computational tools that permits a closer integration of modeling in the design, build, test, and learn cycle of genetic engineering. Microbial metabolism offers a promising route for the sustainable production of fuels and chemicals. Fine-tuning enzyme expression to optimize fluxes within these metabolic networks for maximum titer, rate, and yield is a critical step in improving bioprocess economics . TowardsCentral to this question is determining how steady-state metabolic fluxes are controlled. These fluxes arise through a vast network of enzymes with complex regulation and nonlinear kinetics. Constraint-based models offer one strategy for predicting metabolic fluxes by investigating feasible steady-state phenomena by placing constraints on reaction fluxes in accordance with stoichiometric , thermodin vitro experiments have characterized the most common enzymes, the vast majority of enzymes lack explicit kinetic information [Enzymatic rate rules involve a number of  parameters: variables which must be determined from experimental data. While ormation . Alternaormation –16. In aormation –20. For ormation .A major limitation of ensemble-based modeling has been its ability to scale both to larger datasets as well as larger kinetic models, since larger datasets cause a higher fraction of samples to be discarded and larger kinetic models increase the computational cost of each simulation. Computation times on the order of hours per parameter sample have been encountered even for relatively small systems , 21, andi.e., changes to enzyme expression) to changes in the resulting steady-state concentrations and fluxes [in vitro example, showing that the method is flexible enough to capture allosteric interactions between metabolites and enzymes. We next show that the method appropriately captures uncertainty in estimated parameters, revealing significant flux control coefficients (FCCs) for only the most likely enzyme perturbations in the case of limited biological data. Finally, we employ the method to integrate thousands of individual metabolomic, proteomic, and fluxomic data-points with a large-scale model of yeast metabolism. We therefore show that the field of metabolic modeling can take full advantage of recent advances in the fields of probabilistic programming, machine learning, and computational statistics, and that ensemble-based approximate kinetic modeling approaches are capable of scaling to genome-sized models and datasets to provide interpretable and actionable insight for strain engineers.In this study, we develop a scalable analog of metabolic ensemble modeling, capable of inferring posterior distributions in kinetic parameters of large metabolic models with multiomics-sized datasets. We sidestep many of the previously discussed computational bottlenecks through the use of linear-logarithmic (linlog) kinetics as an approximate reaction rate rule , 25. Lind fluxes , 27. Mosd fluxes , 29. We The kinetic models we consider in this study are parameterized with a matrix of elasticity values, where rows correspond to enzymes and columns correspond to metabolites. Values in this matrix reflect how an increase in a given metabolite’s concentration will affect the reaction rate of the corresponding enzyme. Elasticities are unitless parameters defined as the normalized derivative of reaction rate with respect to metabolite concentration. Positive elasticities therefore indicate that higher metabolite concentrations will increase reaction rate, while negative elasticities indicate that higher metabolite concentrations will decrease reaction rates. For a reactant, a small yet positive elasticity implies the enzyme is saturated and further increases in metabolite concentration will not effectively increase the rate. A substantial negative elasticity associated with a reaction product might indicate a reaction close to equilibrium, where changes to product concentration are significant in changing the forward rate. Since the elasticities are represented by a dense matrix, other regulatory interactions including substrate-level inhibition or activation can be captured through non-zero elasticity values associated with the enzyme-regulator pair. We therefore seek to find distributions in the values of this elasticity matrix that are consistent with experimentally observed metabolite, flux, and enzyme measurements. While this approach allows the possibility that all metabolites could affect all reaction rates, we constrain metabolites not participating in a reaction to have a very low probability of affecting flux while still allowing for a small chance of allosteric regulation. An overview of the methodology is presented in in vitro flux and concentration data for a reconstructed subsection of lower glycolysis [While the primary purpose of the proposed modeling framework is to parameterize genome-scale kinetic models from large, multiomics datasets, we first demonstrate the method on a simple linear pathway. We re-fit a simple three-reaction model  to steadycolysis . A schemBayesian inference is a technique that uses Bayes’ theorem to construct probability distributions in model parameters from experimental data. Inputs to Bayesian inference include both a likelihood model, which describes the probability of the observed data occurring as a function of model parameters, and a prior distribution that encompasses all values that model parameters are likely to take before the experimental data is considered.Numerical techniques then invert these functions to find the posterior distribution: the conditional probability of the parameter after observing the experimental data. The choice of prior distributions can also be used for regularized regression. In this study, Laplace priors (with a sharp peak near zero) are placed on elasticities for metabolite-reaction pairs in which the metabolite does not directly participate, resulting in a posterior elasticity close to zero unless sufficient evidence is present to indicate activation or repression.The likelihood model in this example assumed the experimental errors were normally distributed, and prior distributions ensured that estimated enzyme elasticities were reasonable. Specifically, we assumed elasticities associated with reactants to be predominately positive, those associated with products to be predominately negative, and those for metabolites not participating in a given reaction to be close to zero . More dei.e., lots of parameters) can be numerically difficult to sample. As an alternative, variational Bayesian methods approximate the true posterior with an analytically tractable distribution , and minimize the dissimilarity between the true and approximate posterior through parameter optimization. While the estimated posterior is only an approximation of the true distribution, variational approaches have been shown to be capable of scaling to neural-network sized models with millions of parameters [Computational methods for Bayesian inference typically fall into two broad categories. Markov chain Monte Carlo (MCMC) methods exactly sample the posterior distribution by constructing a stochastic process that ultimately converges to a stationary distribution, representing the true posterior. However, convergence of these methods is not guaranteed, and high dimensional posteriors , y values . Strong et al., 2004, indicating that systems-level properties are relatively insensitive to the particular parameterization used to capture allosteric regulation.Once appropriate parameter distributions that fit the data have been found, we can determine which enzymes in the pathway are rate-limiting by using the posterior predictive distributions in flux control coefficients (FCCs). In this example, since steady-state fluxes are constrained to be equal for all three reactions, the FCCs are a vector of three coefficients that determine whether increasing enzyme concentration will increase or decrease pathway flux. in vivo examples. We therefore rely only on ADVI for subsequent examples that deal with larger reaction networks.The close agreement of the estimates provided by the approximate ADVI method to the more accurate NUTS traces in elasticities and FCCs is an important result. As most applications in metabolism involve a larger reaction network, approximate inference methods are likely the only techniques that will scale to biologically-relevant E. coli strains. The experimental data consists of lysine flux measurements (in mol L−1 week−1) from six sequential enzyme overexpression experiments, all of which were observed to improve L-lysine yields [et al., 2009. A schematic of the reaction network is shown in We next demonstrate how the inference framework can be used to suggest enzyme targets in a many-reaction network that includes branching and shared co-factors. The problem we consider was previously examined through ensemble metabolic modeling , and inve yields . The metin vitro example, with the optimization taking under three minutes (as compared with days for a comparable ensemble-modeling based approach [Posterior distributions in the elasticity matrix were estimated using ADVI as with the approach ). The poapproach , indicatWe next calculated prior and posterior distributions in FCCs. Because only a limited selection of data was available to constrain the elasticity values, only 6 of the 44 reactions had a confidently nonzero FCC. However, five of these reactions were the same as previously specified as successful modifications for improving lysine flux  . The remThe main strength of the proposed method is its ability to constrain kinetic parameters using multiomics data, even for large-scale metabolic systems. We therefore demonstrate the method using literature data on metabolomics, proteomics, and quantification of exchange fluxes for 25 different chemostat experiments with yeast . The datIn fitting the observed steady-state phenotypes, the model has to account for not only experimental error in measured enzyme concentrations, but also for potential changes in gene expression in unmeasured enzymes. We therefore place prior distributions on log enzyme concentrations for each condition that drive enzyme changes towards their measured values, or, if the reaction is not measured, towards zero (unchanged). Thus, we allow unmeasured enzyme concentrations to deviate from zero only if there is sufficient evidence. The model parameters therefore include 915 elasticities associated with direct kinetic interactions, 23,684 elasticities associated with potential off-target allosteric regulation, 5,760 enzyme expression levels (240 enzymes over 24 experiments), and 192 external metabolite concentrations (8 metabolites over 24 experiments), for a total of 30,551 parameters. While this number is far greater than the number of experimental data points, regularization forces roughly 85% of these parameters to be zero.The model was fit using ADVI, with the 40,000 iterations completing in approximately 5 hours on a single compute node. Posterior distributions in parameter values indicate that the model is able to fit the observed experimental data while using relatively few of the additional regulatory parameters. Of the 23,684 regulatory elasticities, only 153 (0.65%) were confidently nonzero. However, we note that determining mechanistically accurate regulatory interactions from observations of steady-state flux behavior is inherently difficult. For instance, for a regulatory pathway in which A regulates B and B regulates C, identifiability issues might cause the pathway to be modeled as A regulates B and A directly regulates C. While poorly identifiable, the impacts of these alternative regulatory topologies on FCCs are largely similar. Of the 50 unmeasured enzymes, only half were nonzero in at least one experimental condition, and overall only 35% of the available unmeasured enzyme expressions differed from their reference state value. Since reaction flux can be controlled through both changes in enzyme expression and metabolite concentrations, these results indicate that the model is overly relying on changes in enzyme expression to capture the observed metabolic phenotypes.α = 0.05 confidence level; non-significant correlations were masked from the array. In this map, hierarchical clustering is used to reveal clear groups of metabolites and enzymes that vary together in the experimental data. A larger version of this image, with labelled axes, is shown in A common goal in strain engineering is to find gene targets for increasing the yield of a given metabolic product. We therefore look at relationships between enzymes with measured protein concentrations and measured boundary fluxes as a way to identify putative targets. In a traditional statistical approach, correlations between enzyme levels and metabolite fluxes might be used to further enhance production of a desired metabolite. i.e. glycerol-3-phosphate dehydrogenase enhancing glycerol production, are direct upstream enzymes for the boundary flux in question. However, since linear pathways can have an uneven distribution of FCCs, determining the most rate-limiting step in biosynthesis pathways is an important result. Other confident FCCs represent more indirect effects: for instance, the consumption of the upstream phosphoenolpyruvate in 3-phosphoshikimate 1-carboxyvinyltransferase reduces the export of pyruvate. These results therefore show that the method, after considering experimental data, is able to suggest reasonable enzyme targets for improving the flux to a desired metabolite.We compared this traditional statistical correlation approach to our framework. FCCs that are estimated through Bayesian inference and linlog kinetics offer an alternative approach for determining potential enzyme targets that more systematically considers the effects of metabolic connectivity, stoichiometry, and kinetics compared to the correlation analysis which views the system as a black box. Before considering posterior distributions in FCCs, we first look at whether the prior assumptions on enzyme elasticities and model stoichiometry result in any confidently nonzero values. From the prior predictive distribution, only 6 enzyme-boundary flux pairs have a significantly nonzero FCC, and typically involve reactions directly associated with metabolite production. For instance, a positive FCC is associated with asparagine synthase and valine transaminase on asparagine and valine export, respectively. A heat map of FCCs calculated from the fitted posterior elasticity matrix is shown in In this study we demonstrate how kinetic models of microbial metabolism can be analyzed through modern probabilistic programming frameworks. In doing so, we have invoked approximate formalisms for enzymatic kinetics; however, we note that similar trade-offs between modeling fidelity and computational efficiency are common throughout biology and chemistry. For instance, while small-scale pathways might be better modeled at a higher level of kinetic theory, a complete kinetic description of a genome-scale kinetic model is likely currently infeasible given available data and computational resources. As biological experiments are becoming increasingly easy to iterate with modeling results, a complete kinetic description of a given pathway may not be as valuable as a reasonable guess as to how to improve a desired phenotype. Computational methodologies that quickly converge to generate a list of potential targets, such as the one proposed in this study, may therefore be essential in keeping up with the growing ease of multiomics experiments. The proposed method can also be run efficiently on consumer-grade hardware, an important factor for applications in industrial microbiology where access to large-scale high performance computing resources is limited.As the field of variational inference is rapidly evolving, this technique could likely be made more robust or efficient through the use of alternative inference algorithms. For instance, correlations between elasticities were demonstrated through a Hamiltonian Monte Carlo trace but were missed by the corresponding mean-field Gaussian approximation. While fitting a full-rank Gaussian is likely impractical at larger data set sizes, reduced-rank approximations , 38 mighWith the presented approach, genome-scale metabolic models and omics-sized datasets can be integrated to generate actionable recommendations for further strain engineering. Data at this scale has typically been analyzed through statistical “black-box” approaches that do not consider the nature of the relationship between reaction fluxes and enzyme and metabolite concentrations. Bayesian inference with linlog kinetics naturally includes stoichiometric and kinetic constraints in a scalable form. The method is also well-suited to the specific types of omics data that are currently being collected. In particular, linlog kinetics only requires relative quantification of enzyme and metabolite concentrations (rather than absolute), which are easier to collect. Additionally, the method is able to gracefully handle missing data and estimate the resulting confidence in model predictions. Despite the increasing amount of data being collected on cellular metabolism, it remains challenging to integrate this data to draw actionable conclusions. Bayesian inference with linlog kinetics is therefore broadly useful for modeling metabolism and as a tool for metabolic engineering. Future work will leverage this methodology to make predictions for subsequent experimental validation, with subsequent omics data used to iteratively refine model predictions.x, quickly reach a pseudo-steady state by balancing fluxes v through each reaction.n reactions and m metabolites, where Nij indicates the stoichiometry of metabolite i in reaction j. Linlog kinetics approximates a reaction rate v(x) as a sum of logarithms [G = ΔG° + RT log Q, expressing the reaction rate as a linear combination of the logarithm of metabolite concentrations is justified. While many biochemical reactions are far from equilibrium, this relationship remains linear over a wide range of reaction affinities for enzymatic reactions [We begin with a review of the relevant equations from dynamic flux balance analysis and the linear-logarithmic kinetic framework, which together form the theoretical basis for the methodology discussed in this study. In flux balance analysis, we assume that metabolite concentrations, garithms . Linlog garithms . Since Δeactions , 43. As eactions . Howevereactions , and foreactions . As a reeactions –47. Mosteactions .A → B + C, the reaction rate is modeled ase represents the enzyme concentration, and with coefficients ka > 0; b, c < 0. This approximation is most accurate in the vicinity of an introduced reference state, e*, v*, x* [x is the concentration of intracellular (dependent) metabolite species, y is the concentration of p external (independently controllable) metabolite species, and a, b, and c in For the reaction , v*, x* . As the In metabolic control analysis, elasticity parameters are defined that capture local effects of metabolite concentration on reaction rate . These px* , a much more difficult task for ODE integration .conserved moieties, or metabolite quantities which can be expressed as linear combinations of other metabolites (e.g. ATP + ADP = constant). The stoichiometric matrix N, and as a result the A matrix defined above, will therefore not be full row rank. In effect, this means that L, and a reduced set of metabolites with conserved moieties removed [A can be transformed to a full-rank, square matrix and a unique steady-state can be determined that corresponds to the dynamic system’s true steady-state. However, in most biological experiments, changes to steady-state enzyme expression correspond with separately cultured cell lines for which the assumption that total cofactor pools would remain constant is not necessarily valid. Instead, we propose that a more biologically relevant solution to χ‖2: i.e., the solution that results in the smallest deviation of metabolite concentrations from the reference state. This assumption has experimental support in that intracellular metabolite concentrations tend to be buffered from drastic changes through feedback circuits at the genetic and enzyme level [A can be made full row-rank prior to the least-norm linear solve. We can therefore replace N with A matrix (with more columns than rows) prior to performing the least-norm linear solve in N v = 0, this change can be made without affecting the final solution.However, in general a metabolic system will contain  removed , 51. Thrme level . We therDue to the changes to traditional MCA theory introduced by the altered steady-state calculation defined above, we also slightly modify the traditional calculations of metabolite and flux control coefficients.Since flux and metabolite control coefficient matrices describe the response of the steady-state to changes in enzyme expression, our altered versions describe the flux response at the particular steady-state in which metabolite concentrations are as close as possible to the unperturbed state. In practice, this has the effect of improving the identifiability of FCCs in the numerical experiments described below. A plot of FCC values obtained via both traditional and modified methods for the following genome-scale model is shown in likelihood model, p(z|θ), is constructed for the probability of observing the measured data, z, given particular values for each parameter, θ. Combined with a prior distribution, p(θ), for each parameter that represents generally feasible values, numerical approaches use Bayes theorem,posterior parameter distribution p(θ|z): the probability a parameter takes the given value after accounting for the observed data. With a suitable kinetic framework for calculating steady-state fluxes and concentrations as a function of enzyme expression, we next discuss the prior distributions and likelihood function required for Bayesian inference. The prior distributions represent our belief of possible parameter values before any experimental data is collected. For metabolite elasticity matrices we assume that for any given reaction, reactants are likely to be associated with a positive elasticity, while products likely have a negative elasticity . Alternatively, we assume that if a metabolite does not directly participate in a reaction, it can only regulate the reaction if it appears in the same sub-cellular compartment. We denote the vectors cm and cr of metabolite and reaction compartments, respectively. Since regulation of enzymatic reactions by otherwise nonparticipatory metabolites is relatively rare, we place a sparsity-inducing prior on its elasticity value. This distribution encourages elasticities for off-target metabolites to take values near zero, unless strong experimental evidence for a regulator interaction is present. The combined priors for enzyme elasticities can then be expressed through the following functional form, also depicted graphically in In Bayesian inference, a We note that the assumption that reactants and products must take positive and negative elasticity values, respectively, can be relaxed by replacing the half-normal distribution in An explicit likelihood function can be formed by constructing a statistical model for the observed data. We assume that observed data are normally distributed around the calculated steady-state metabolite and flux values.σx and σv, can either be set explicitly or estimated from the data. For smaller-scale examples, we place half-normal priors on these variables, while for larger datasets we set these values explicitly to improve numerical stability. We also note that for genome-scale multiomics data, computational stability can be improved by fitting log-transformed normalized fluxes,13C labeling studies, the reaction could be decomposed and modeled separately as irreversible forward and reverse reactions.Experimental errors, Once the prior distribution and likelihood model have been specified, the remaining task is to numerically estimate posterior distributions in elasticity parameters. Two inference algorithms were used, the No-U-turn sampler (NUTS) and Automatic differentiation variational inference (ADVI). NUTS , as a vaσ values in σ = 1, α = 5) distribution was used in place of the HalfNormal when Nij ≠ 0. This distribution allows a small chance of substrate inhibition, where higher concentrations of a reactant in an enzyme-catalyzed reactions actually reduces reaction rate. However, this distribution was not used in larger examples as it introduced additional numerical instability. A comparison of the HalfNormal, SkewNormal, and Laplace distributions (with parameters used in this work) is shown in Since all metabolites  are present in the same compartment, all elasticities are allowed to have allosteric interactions normalized with Laplace priors. Measurement errors in fluxes and metabolite concentrations were fit by the inference algorithm by placing a half-normal prior distribution on the Using NUTS, stable traces were found across four independent chains, indicating that each trace converged to the true posterior distribution , S3 Fig.Comparing the mean and variance of the elasticity posterior distributions from the two different approaches, we notice that while the mean values agree closely, ADVI underestimates the variance for many parameters . This un−1week−1. As the resulting enzyme concentrations following overexpression were unknown, prior distributions were placed on these parameters. Since enzyme concentrations were specified relative to the overexpressed reference state, uniform priors between zero and one were placed on the relative concentrations of each of the 5 modulated enzymes. The resulting inferred distributions in enzyme expression for the 5 enzymes are shown in As the goal of the inference approach is to estimate targets for subsequent lysine flux improvement, we chose the reference state for linlog kinetics to be the final, optimized strain with 5 overexpressed enzymes. Since the reference state was chosen to be the final, optimized strain, perturbed strains had lower relative enzyme concentrations and lysine flux. Values for target lysine fluxes were taken from the published yields for the W3110 strain, with a calculated glucose uptake flux of 1.243 mol Lϵy values were needed. Prior distributions in elasticities associated with stoichiometric metabolite-reaction pairs (kinetic elasticities) used a half-normal distribution with σ = 1 and had a 95% HPD that spanned from 0 to 2. Kinetic elasticities were therefore flagged as constrained by the data if they had a 95% highest posterior density that spanned less than 0.75 elasticity units. Regulatory elasticities and FCCs were deemed confidently nonzero if their 95% HPD did not overlap zero.When analyzed with metabolic ensemble modeling, each successive enzyme overexpression was required to increase lysine flux over the previous base strain. However in our framework, we require a continuous and differentiable likelihood function, and are also able to directly incorporate the experimentally measured yields. Prior distributions in enzyme elasticities were specified as described in −1 dilution rate. Reference fluxes (v*) were calculated via flux balance analysis by minimizing error with the experimental boundary measurements while enforcing a nonzero flux through each reaction. In this example, relative metabolite concentrations are given as log2-transformed values [A, relative concentrations χ can be calculated from log2-transformed concentrations a and b:As the goal in this example is to demonstrate that linlog kinetics are able to consume large amounts of multiomics data, a reference state near the center of the considered data was chosen, specifically the chemostat with phosphate-limiting media at a 0.11 hrd values . Even wiNij = 0) were given a b = 0.01, which was found to have an optimal trade-off between regularization and flexibility for the larger model. The effect of this regularization for several values of b was explored, as shown in b from 0.01 to 0.1.Distributions of the transformed data are shown in et al., 2016 have previously shown that metabolic control is mainly determined by metabolite concentrations, some mechanism for adjusting enzyme levels is required to buffer against errors in model formulation and experimental measurements. By placing a Laplace prior on unmeasured enzymes, we create a regularizing effect that penalizes an over-reliance on enzymatic control:Allowing all enzyme concentrations to vary induces a trade-off where steady-state fluxes are controlled through changes to enzyme expression instead of changes to steady-state metabolite concentrations. While Hackett σx = 0.2 for the metabolite data and σv = 0.1 for the log-transformed fluxes. To improve numerical stability, we also clip the log-transformed, relative experimental data to ±1.5, such that log-transformed experimental data and model predictions greater than 1.5 or less than -1.5 are replaced by ±1.5. This process has the effect of reducing the influence of extreme points, especially in regimes far from the reference state that are unlikely to be fit well by the linlog approximation. However, the model is still required to predict the directionality and high-magnitude of these points correctly. Fitting the model using ADVI required 40,000 iterations of stochastic gradient descent, taking approximately five hours on a single compute node Click here for additional data file.S2 FigThe HalfNormal distribution is used when a metabolite directly participates in a reaction, and the directionality is known. The SkewNormal distribution is similar to the HalfNormal, but also allows for the small possibility of substrate inhibition. Laplace distributions were used to specify potential regulatory interactions with an unknown direction.(EPS)Click here for additional data file.S3 Figet al. [(left) kernel density estimates of each parameter. Vertical bars indicate the values obtained using the multiple linear regression technique of Wu et al. . (right)(EPS)Click here for additional data file.S4 Fig(EPS)Click here for additional data file.S5 Figin vitro dataset as estimated by NUTS (solid lines) or ADVI (dashed lines). ADVI posteriors have a similar mean but smaller variance.Comparison between posterior distributions for the (EPS)Click here for additional data file.S6 Fig(EPS)Click here for additional data file.S7 Figb parameter is the Laplace prior for enzyme elasticities. The ability of the model to reproduce the data is quantified through the use of the median absolute error (MAE). (B) Percent of confidently inferred regulatory (off-target) elasticities. Elasticities were deemed confidently inferred if their 95% HPD did not include zero.(A) Posterior predictive distributions as a function of the (EPS)Click here for additional data file.S8 Fig(EPS)Click here for additional data file.S9 FigFull names for the reaction IDs shown can be found in the detailed model description.(EPS)Click here for additional data file.S10 Fig(EPS)Click here for additional data file.S1 Text(PDF)Click here for additional data file.


The isolation of Candidatus “Nitrosopumilus maritimus” strain SCM1, which represents the globally distributed AOA in the ocean, provided an opportunity for uncovering the contributions of those AOA to carbon and nitrogen cycles in ocean. Although several ammonia oxidation pathways have been proposed for SCM1, little is known about its ATP production efficiency. Here, based on the published genome of Nitrosopumilus maritimus SCM1, a genome-scale metabolic model named NmrFL413 was reconstructed. Based on the model NmrFL413, the estimated ATP/NH4+ yield (0.149–0.276 ATP/NH4+) is tenfold lower than the calculated theoretical yield of the proposed ammonia oxidation pathways in marine AOA (1.5–1.75 ATP/NH4+), indicating a low energy production efficiency of SCM1. Our model also suggested the minor contribution of marine AOA to carbon cycle comparing with their significant contribution to nitrogen cycle in the ocean.Marine ammonia-oxidizing archaea (AOA) play an important role in the global nitrogen cycle by obtaining energy for biomass production from COThe online version of this article (10.1186/s13568-018-0635-y) contains supplementary material, which is available to authorized users. Thaumarchaeota constitute about 40% of total prokaryotes in the deep ocean . However, it is well recognized that the real ATP production efficiency of a respiratory chain is often smaller than the theoretical value. In heterotrophic microorganisms, 3 ATP can be theoretically produced from 1 NADH oxidized through the oxidative phosphorylation respiratory chain. Whereas in real cells the ATP/NADH yield is normally less than 2  have been developed for quantitative prediction of intracellular metabolic flux distributions based on mass balance constraints coined in the stoichiometric matrix of a metabolic model. Up to now, about 200 GEMs have been reconstructed, covering three domains of life   was used to calculate the optimal pathways in a genome-scale metabolic network for the production of biomass or other metabolites from a carbon source . Further, relevant literature provided data to calculate the biomass yield from ammonium oxidation (Biomass/NH4+ yield). To calculate efficiency of the respiratory chain, biomass yields from ammonium oxidation were normalized to be Biomass/NH4+ yield (gDW mol−1). Efficiency of respiratory chain were obtained by multiplying these two yields (ATP/Biomass yield and Biomass/NH4+ yield).Estimating the efficiency of the respiratory chain of strain SCM1, which uses ammonium oxidation as the sole energy source, began by the reconstruction of a GEM for strain SCM1. This was followed by calculating the cost  of synthesizing 1-g biomass from COi, that is, the growth requirement of metabolite Ri (often in mmol) for the production of 1 g dry cell weight. j. Since all the coefficients of biomass components are determined based on 1-g dry cell weight, the biomass reaction was satisfied with the mass balance constraint and was written as Eq. i and Bj, respectively. Stoichiometric coefficients in the biomass equation of our model was corrected to ensure mass balance.Biomass production equation can be written as Eq. entclass1pt{minima2, the ATP and reducing equivalents were determined by performing FBA on the NmrFL413 model. For the calculation, the biomass production reaction rate was set to be 1 h−1 and the lower bound and upper bound of reactions in ammonia oxidation pathway was set to be zero to block the ATP/NADH production from ammonium oxidation. Artificial reactions for ATP/NADH input were introduced in the model and the ATP input flux was minimized using FBA analysis. The ATP and NADH requirement for the production of 1 g biomass were obtained from the calculated ATP and NADH input rates. Here, we use NADH as the representative for the reducing equivalents during the calculation. NADH can be converted to other reducing equivalents  through existing reactions in the model to meet the need of other reducing equivalents, for example one molecule NADH can be converted to one molecule NADPH, the conversion of NADH with NADPH is similar to the conversion in well-characterized E. coli model iJO1366. AOA ferredoxin transcripts and proteins were detected in high abundance in environmental samples, suggesting the importance of the low reduction potential ferredoxin in the metabolic network of marine AOA. In our model, one molecule NADH can be converted to two molecules ferredoxin, which is also in consistent with model iJO1366 and other archaeal models.The method used here is an extension of the method used by Mangiapia and Scott . Instead2, growth-associated maintenance energy (GAM) reaction consume ATP, which reflects the ATP consumption required for the organism to grow and is incorporated into the biomass reaction. In the calculation, the value of GAM in model NmrFL413 was set as 25 mmol ATP/gDW according to a published model iTU515 for S. solfataricus which is the most closely related organism to strain SCM1 in all archaeal models.Apart from the ATP requirement for biomass synthesis from CO4+ transportation, CO2 transportation, metal ions transportations, H2O transportation    the pathways for the synthesis of biomass components; (3) and the ammonia oxidation pathway, which supplies the energy required for carbon fixation.Although necessary transport reactions were added, most pathways from CO2 fixation  was missing in the draft model  cycle for COdel Fig. . Argininway Fig. . These fway Fig. . Furtherway Fig. .Fig. 2Th4+ oxidation, the theoretical ATP/NH4+ yield for each pathway was calculated to be in the range from 1.5 to 1.75 as shown in Table Three different ammonia oxidizing pathways of AOA have been suggested during the past few years and can be represented as sets of reaction equations as shown in Table Nitrosopumilus maritimus SCM1 containing 765 reactions and 825 metabolites was reconstructed after the transport reactions and the reaction equation for biomass production were manually added and gaps were filled  for SCM1 have not been reported yet due to the difficulty in measuring the intracellular ATP production rates  calculated from the model with published data for SCM1 Biomass/NH4+ yields in different experiments . This value is in the same range with previous reports showing 0.195 mol ATP/gDW for reductive citric acid cycle (rCAC) and 0.238 mol ATP/gDW for Calvin–Benson–Bassham (CBB) cycle  and the experimentally measured biomass/NH4+ yields, the ATP/NH4+ values representing the requiring energy for SCM1 growth, were calculated to be 0.149, 0.213, 0.276 and 0.217 based on different reported biomass/NH4+ yield values . The ATP/NH4+ ratio for N. europaea (a model strain of AOB) hydrolysate was measured to be 0.16  and Thaumarchaeota largely unexplored. A high-quality genome-scale metabolic model NmrFL413 for Nitrosopumilus maritimus SCM1 was reconstructed in this work. Reconstruction of the NmrFL413 model offers the possibility to give significant insights into the metabolism and growth of SCM1 and other organisms in the phylum Thaumarchaeota.Using genome scale metabolic network analysis to investigate the biochemical and physiological properties of archaea is still a developing effort. So far, only 15 GEMs for 10 archaea have been reconstructed , sulfate reduction (e.g. Archaeoglobus fulgidus), nitrate reduction (e.g. Pyrobaculum aerophilum) and also can conserve energy combining with methanogenesis (Methanosarcina acetivorans). The existence of diverse energy conservation and production pathways will likely come with diverse electron transport systems. GEMs offer a wonderful platform to understand these unique characteristics. In the existing GEMs, only the energy efficiency involving methanogenesis of methanogen and bioenergetics for the extreme halophile Halobacterium salinarum have been thoroughly investigated. By combining the GEM for strain SCM1 and easily measured data, we predicted the energy efficiency of SCM1 that represents an autotrophic Archaea, which may shed light on estimating the energy efficiencies of other chemoautotrophs.In this paper, we mainly focused on using the model NmrFL413 to estimate the energy generation efficiency of the ammonia oxidation pathway in SCM1 which is difficult to measure directly. The results indicated that the energy production efficiency might be far less than the theoretical value but similar to the energy production efficiency of −1 of NH4+ produced by the mineralization process in the meso- and bathypelagic zones of the ocean are needed to be oxidized. Using the average Biomass/NH4+ yield of 1:25 in Table −1. This value is in general agreement with the values of 0.11 Gt·C year−1 estimated by Middelburg (Herndl et al. −1 obtained by Wuchter et al. (−1 by photosynthetic organisms (Field et al. Wuchter et al.  estimater et al. . CompareAdditional file 1: Table S1. Transport reactions in the model for the exchange of metabolites between the cell and the environment. Table S2. Biomass components and their coefficients.Additional file 2. Model NmrFL413 in SBML format.Additional file 3. Model NmrFL413 in excel format.


The process of anaerobic digestion in which waste biomass is transformed to methane by complex microbial communities has been modeled for more than 16 years by parametric gray box approaches that simplify process biology and do not resolve intracellular microbial activity. Information on such activity, however, has become available in unprecedented detail by recent experimental advances in metatranscriptomics and metaproteomics. The inclusion of such data could lead to more powerful process models of anaerobic digestion that more faithfully represent the activity of microbial communities. We augmented the Anaerobic Digestion Model No. 1 (ADM1) as the standard kinetic model of anaerobic digestion by coupling it to Flux-Balance-Analysis (FBA) models of methanogenic species. Steady-state results of coupled models are comparable to standard ADM1 simulations if the energy demand for non-growth associated maintenance (NGAM) is chosen adequately. When changing a constant feed of maize silage from continuous to pulsed feeding, the final average methane production remains very similar for both standard and coupled models, while both the initial response of the methanogenic population at the onset of pulsed feeding as well as its dynamics between pulses deviates considerably. In contrast to ADM1, the coupled models deliver predictions of up to 1,000s of intracellular metabolic fluxes per species, describing intracellular metabolic pathway activity in much higher detail. Furthermore, yield coefficients which need to be specified in ADM1 are no longer required as they are implicitly encoded in the topology of the species’ metabolic network. We show the feasibility of augmenting ADM1, an ordinary differential equation-based model for simulating biogas production, by FBA models implementing individual steps of anaerobic digestion. While cellular maintenance is introduced as a new parameter, the total number of parameters is reduced as yield coefficients no longer need to be specified. The coupled models provide detailed predictions on intracellular activity of microbial species which are compatible with experimental data on enzyme synthesis activity or abundance as obtained by metatranscriptomics or metaproteomics. By providing predictions of intracellular fluxes of individual community members, the presented approach advances the simulation of microbial community driven processes and provides a direct link to validation by state-of-the-art experimental techniques. Being a suitable building block in a renewable energy landscape, biogas production is a popular topic in research and development , μ(S) is the substrate concentration dependent specific growth rate defined as max (1/d), substrate concentration S (g/L) and half-saturation constant SK (g/L). I is the product of inhibitory terms nI having values ranging from 0 (complete inhibition) to 1 (no inhibition), and dk is the specific biomass decay rate (1/d). ADM1 considers methanogenesis via the acetoclastic and the hydrogenotrophic pathway, with each pathway being described by an ODE of the form of Eq. 1. For the acetoclastic methanogens, the growth-limiting substrate in Eq. 1 is acetate, while it is hydrogen for the hyrogenotrophic methanogens. In our coupled model, we model one or both pathways by FBA models of specific methanogens. For this, we need to specify the maximal substrate uptake rate maxUptakev, which depends on the substrate concentration S in the reactor:where maxv (mmol/gDW/h). Note that we use the same inhibitory term(s) I as in Eq. 1 to restrict substrate uptake to replicate ADM1’s implementation of growth inhibition. Using maxUptakev, the FBA model is then used to predict the current specific growth rate μFBA, and microbial growth can then be modeled as:with maximal uptake rate SK as in Eq. 1 and select maxv so that in absence of substrate limitations and inhibitory processes, the maximal growth rate becomes identical to the value used in ADM1, that is μFBA = μmax. For describing the impact of microbial activity on substrates and products in the standard ADM1, Eq. 1 is multiplied by a yield factor. This is not necessary in the coupled model for those steps which are replaced by FBA models, as these directly predict uptake and excretion rates of substrates and products, only requiring the conversion of these fluxes given in mmol/gDW/h to g/L/d, including a multiplication with the current biomass X of the respective microbial population. For acetoclastic methanogenesis, we couple methane and acetate directly. The compounds CO2  and NH4 are linked to ADM1’s state variables for inorganic carbon and inorganic nitrogen. To implement the coupled model, we use the direct approach in which calls to the FBA solver are placed in the function which is used by the numerical solver to evaluate the right-hand side of the ODE system. The Matlab solver ode15s  is used to numerically solve the coupled model. The fundamental coupling concept and transfer of state variable values between ADM1 and FBA models is illustrated in For parameterizing Eq. 2, we use the same numeric values for M. barkeri and M. maripaludis, were used to simulate methanogenesis in ADM1 (M. barkeri (M. barkeri (GS)” from here on, to identify possible benefits of such comprehensive models. M. barkeri can perform both acetoclastic and hydrogenotrophic methanogenesis, while M. maripaludis can only produce methane from hydrogen. Maximal substrate uptake rates (maxv in Eq. 2) were set for FBA growth prediction to match ADM1’s μmax values, as described above  laboratory-scale reactor at mesophilic temperatures at a hydraulic retention time of 185 d (qin = 0.2 L/d)  was implemented in a continuously operated 45 L (V0.2 L/d) . Phase 10.2 L/d) .To ensure sufficient nitrogen supply the input concentration for inorganic nitrogen was set to 1.5 g per L substrate added. All remaining input concentrations of additional state variables considered in ADM1  were set to zero.maxv for FBA simulations was chosen accordingly . If NGAM demand is increased to 2.5 and 5 mmol ATP/gDW/h, a larger fraction of the consumed substrate needs to be transformed to energy and is no longer available for biomass synthesis. As a consequence, predicted specific growth rates become smaller as NGAM demand is increased. Additionally, growth becomes infeasible below a critical substrate concentration. As a fraction of consumed substrate is used for fulfilling cellular maintenance requirements, the observed biomass yield X/SY becomes a function of the growth rate.We first compared the prediction of specific growth rates and yields under varying substrate concentrations using either ADM1’s ODE for acetoclastic and hydrogenotrophic methanogenesis or the respective FBA models. If setting the non-growth associated maintenance (NGAM) demand to zero, the FBA-predicted specific growth rate matched ADM1’s prediction  as the mX/SY. At high substrate concentrations and fast growth, in contrast, the yield approaches the constant yield assumed in ADM1 and, depending on chosen values for the maintenance requirement, surpasses this value . We simulated the coupled models until the steady state was reached. To evaluate the impact of the chosen NGAM demand, we systematically varied the demand between 0 and 5 mmol ATP/gDW/h and compared resulting steady states with the standard ADM1 model predictions.M. barkeri, as from there on, acidification with a subsequent process breakdown was predicted by the coupled model. The general tendency to first approach ADM1 predictions, but then overshooting or undershooting them as NGAM demand is increased was also true for the predicted methane production rate, pH values, and the contribution of both methanogenesis pathways toward methane production  remains unchanged. Once the feeding regime is switched, a regular oscillatory behavior results after a transient phase . Mean prAnaerobic Digestion Model No. 1’s and the coupled model’s predictions regarding process performance agree very well, but differ considerably regarding biomass concentrations of both methanogenic populations and their dynamics . The couM. barkeri as predicted by the coupled model remains fairly constant  and a genome-scale FBA model (816 reactions). Simulation results agreed very well qualitatively (M. barkeri very well and is sufficient to model this organism as part of an anaerobic digestion microbial community.To model tatively –4, and oM. maripaludis, and 3.6 mmol ATP/gDW/h for acetate converting M. barkeri [collected in (Syntrophobacter fumaroxidans and 0.025 mmol ATP/gDW/h for Methanospirillum hungatei (For the coupled model, we observed predicted reactor breakdowns for NGAM values beyond 1.4 mmol ATP/gDW/h, when simulated under constant conditions. For the dynamic simulation, we selected a value of 0.5 mmol ATP/gDW/h as this value led to steady-state predictions close to those of the standard ADM1. While higher values have been estimated before, including 0.9 mmol ATP/gDW/h for ected in . A combiected in . Fittinghungatei . Under shungatei .Methanoculleus marisnigri and Methanosaeta concilii, it will be possible to include exactly those species in the model, which have been found to be dominant in the anaerobic digestion process to be simulated, for example based on 16S rRNA gene- and/or mcrA-based community analysis. Such tailor-made models offer the most faithful representation of the actual microbial community at hand and are expected to surpass current modeling approaches in their predictive power for simulating industrial biogas processes.To add species-specific state variables to ADM1, we started by replacing ODE descriptions of both methanogenic pathways by species-specific FBA models. Methanogenesis is the archaea-driven last of four steps in anaerobic digestion. It is associated with a low microbial diversity, which increases toward the first steps of the process . As onlyWe are only at the beginning to understand the complex interplay at work in microbial communities in natural or engineered systems. Community systems biology and quantitative modeling are instrumental in advancing our understanding . Here, fThe raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.FC introduced the initial idea and coordinated the study. SW, SKo, FB, DP, SKl, and FC designed the study. SKo, DB, and SKl developed metabolic models, SW implemented the ADM1 model. FC implemented the metabolic flux modeling component, performed simulations and analyzed the data. All authors read and approved the final manuscript.Anaerobic digestion is a naturally occurring process that is harnessed in biotechnological settings to produce biogas as a flexible and renewable energy source. It is a multi-step process which is brought about by a complex microbial community. Modeling this process to simulate industrial-scale biogas plants has been done for many years by the model ADM1, which is based on ordinary differential equations. In this approach, the activity of microbes is considered by their Input–Output behavior, that is, how much substrate is how fast transformed into products and cellular growth. Metabolic activity within the cell is not considered. However, the intracellular activity of microbial cells has been elucidated to a level at which networks of thousands of enzymatic reactions and metabolites detail, how substrates are converted to products and biomass. Furthermore, current experimental techniques deliver data on the activity on individual enzymes and pathways part of these networks. To make use of such data, we combine ADM1 with the Flux-Balance-Analysis modeling technique, which works on the level of species-specific metabolic networks. Our coupled models are a first step toward models that more faithfully represent microbial activity on the single species-level in complex community simulations. Such models can take advantage of current experimental techniques and hence promise to surpass current models in their predictive power.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Determining the value of kinetic constants for a metabolic system in the exactphysiological conditions is an extremely hard task. However, this kind ofinformation is of pivotal relevance to effectively simulate a biologicalphenomenon as complex as metabolism.E. Coli, by analyzingfive different experimental conditions associated with the ECC2comp model recentlypublished by Hädicke and collaborators.To overcome this issue, we propose to investigate emerging properties ofensembles of sets of kinetic constants leading to the biological readout observedin different experimental conditions. To this aim, we exploit informationretrievable from constraint-based analyses (i.e. metabolic flux distributions atsteady state) with the goal to generate feasible values for kinetic constantsexploiting the mass action law. The sets retrieved from the previous step will beused to parametrize a mechanistic model whose simulation will be performed toreconstruct the dynamics of the system (until reaching the metabolic steady state)for each experimental condition. Every parametrization that is in accordance withthe expected metabolic phenotype is collected in an ensemble whose features areanalyzed to determine the emergence of properties of a phenotype. In this work weapply the proposed approach to identify ensembles of kinetic parameters for fivemetabolic phenotypes of Our results suggest that the parameter values of just few reactions areresponsible for the emergence of a metabolic phenotype. Notably, in contrast withconstraint-based approaches such as Flux Balance Analysis, the methodology used inthis paper does not require to assume that metabolism is optimizing towards aspecific goal.The online version of this article (10.1186/s12859-018-2181-7) contains supplementary material, which is available to authorizedusers. Advances in the understanding of biological processes has revealed that livingorganisms must be analyzed by taking into account the complex network ofinteractions among different entities such as genes, transcripts, proteins andmetabolites in order to decipher emergent behaviors and regulatory processes. In thecontext of Systems Biology , thestuHigh throughput information allowed the generation of detailed genome-scalemetabolic reconstructions, defined ad hoc for different cell types :  anextenDue to lack of information on kinetic constants, either with FBA or eeFBA itis not possible to determine metabolic concentrations at steady state. To overcomethis limitation, in a recent paper , we propWith the above described procedure, we have been able to determine steadystate metabolic concentrations that satisfy the definition of a given metabolicresponse to changing experimental conditions. It is worth to underline that, thisreadout was obtained without defining an OF, thus avoiding the assumption that thecell is performing an optimization towards a certain objective.In this work we slightly modify the approach in order to take into account thefact that kinetic constants may assume different values under various experimentalconditions due to enzymatic regulation. In order to associate a set of specificrate constants to the phenotype associated to each experimental condition, thekinetic constants are retrieved from a set of parameterizations of a mechanisticmodel that, when dynamically simulated with those constants, is able to generatetime courses in agreement with the phenotype definition.Strikingly, our method can be used to predict ensembles of rate constants thatare in agreement with a given metabolic phenotype of interest only by providingits definition and a flux distribution for the same condition, obtained by meansof FBA.S.cerevisie and filtering trajectories accordingly to a definition ofthe Crabtree phenotype. In the present paper, we aim at investigating a morerealistic metabolic reconstruction focusing on Escherichiacoli, the prokaryotic model organism for which a number of coremodels have been built in a bottom-up fashion and are currently retrievable fromthe literature. A notable example, due to its wide exploitation, is the E. coli core model illustrated in Orth et al. of species wcomputed over S the number of specieskept constant throughout the simulation and θis a tolerance threshold.where vi arecalculated for every reaction (when the dynamic reaches the steady state) by meansof the relation expressed by the mass action law illustrated in Eq.  built oTo evaluate the effectiveness of the procedure in discriminating the 5phenotypes and in selecting corresponding ensembles of kinetic constants andsteady state metabolic concentrations, we used ECC2comp . We spliE. coli model, we set them accordingly to theaverage values illustrated in the E. coliMetabolome Database (ECMDB)  metabolism is robust towards kinetic constantvariation. This parameter insensitivity has been further investigated in[Overall, we underline that standard deviation values  and a flux distributionobtained by means of a constraint-based simulation (for which no kinetic parametersare needed).For what concerns perspectives, we plan to better characterize the metabolicsteady state by exploiting more efficient strategies to calculate whether the systemreaches a stationary condition. Among these strategies a promising approach includesthe use of the NLEQ2 non-linear root-finding algorithm . MoreoveAdditional file 1E. coli used for the analysis. (XML 69. 8kb)ECC2C.xml. SBML file for the ECC2comp model of Additional file 2X0etc.xlsx. In tab “conc” are listed initial concentrations ofmetabolites for the 5 different phenotypes. In tab “FeedNoFilt” arelisted metabolites provided at constant concentration throughout thesimulation and metabolites not evaluated to verify the steady state.(XLSX 14.8 kb)Github. The generated dataset(ECcoliExpsParam_10_Filter_0.001.h5) and python scripts implemented forthis study are deposited on a GitHub repository at http://github.com/riccardocolombo/kineticensemble (ZIP 1.52e+7 kb)