In this research, we applied 13C-MFA to identify bottlenecks in the bioconversion of glycerol into acetol by Escherichia coli. Valorization of glycerol, the main by-product of biodiesel, has contributed to the viability of biofuel economy.Bioprocessing offers a sustainable and green approach to manufacture various chemicals and materials. Development of bioprocesses requires transforming common producer strains to cell factories. 13C-MFA and measured intracellular pyridine nucleotide pools in a first-generation acetol producer strain (HJ06) and a non-producer strain (HJ06C), and identified that engineering the NADPH regeneration is a promising target. Based on this finding, we overexpressed nadK encoding NAD kinase or pntAB encoding membrane-bound transhydrogenase either individually or in combination with HJ06, obtaining HJ06N, HJ06P and HJ06PN. The step-wise approach resulted in increasing the acetol titer from 0.91 g/L (HJ06) to 2.81 g/L (HJ06PN). To systematically characterize and the effect of mutation(s) on the metabolism, we also examined the metabolomics and transcriptional levels of key genes in four strains. The pool sizes of NADPH, NADP+ and the NADPH/NADP+ ratio were progressively increased from HJ06 to HJ06PN, demonstrating that the sufficient NADPH supply is critical for acetol production. Flux distribution was optimized towards acetol formation from HJ06 to HJ06PN: (1) The carbon partitioning at the DHAP node directed gradually more carbon from the lower glycolytic pathway through the acetol biosynthetic pathway; (2) The transhydrogenation flux was constantly increased. In addition, 13C-MFA showed the rigidity of upper glycolytic pathway, PP pathway and the TCA cycle to support growth. The flux patterns were supported by most metabolomics data and gene expression profiles.We performed 13C-MFA can be applied to drive the cycles of design, build, test and learn implementation for strain development. This succeeding engineering strategy can also be applicable for rational design of other microbial cell factories.This research demonstrated how The online version of this article (10.1186/s13068-019-1372-4) contains supplementary material, which is available to authorized users. The shortage of non-renewable energy sources and their negative impacts on the environment have inspired interests in the field of bio-based economy . The use13C-MFA can accurately determine the flux configuration with the help of isotope tracers, providing information on relative contributions of different metabolic routes, in particular, for the generation of energy and cofactors -labeled isotope isomer . If necessary, 50 µg/mL kanamycin was added to the media.The acetol-producing and non-producing 600) of E. coli cultures. Glycerol, acetate, and acetol concentrations were determined by high-performance liquid chromatography (HPLC)  equipped with a refractive index detector as described previously [Cell density was monitored by measuring the optical density at 600 nm . The method was adapted from the studies of Wu et al. [13C-MFA, IS was not added to the methanol. After sonication and vortexing with chloroform and Milli-Q water (72:28), the mixture was centrifuged for 5 min at 4600×g and 4 °C. The top layer was transferred into 5-kDa cutoff filters  and then centrifuged to improve the extraction efficiency. The samples were completely lyophilized  and stored at − 80 °C.The quenching and extraction procedures for metabolome analysis and eviously –51. 10 mu et al.  and Weinu et al.  with sliDried metabolite extracts were resuspended in 50 μL of methanol–water  and analyzed using a method as described previously . Metabolt test with Microsoft Excel 2016. The principal component analysis plots were generated using SIMCA 14.1 . PCA was applied to the data after mean centering and UV scaling.Significant differences were analyzed by a two-tailed Student’s 13C-MFA was performed using the elementary metabolite unit (EMU)-based software, INCA [χ2-statistical test for goodness-of-fit was performed. The nonlinear 95% confidence intervals were computed for all estimated fluxes by computing the sensitivity of the minimized variance-weighted sum of squared residuals to flux variations [The network model used for flux calculation was modified from our previous research  by exclure, INCA , 55. Fluriations .RNA was extracted from mid-exponential growing cells to perform qRT-PCR as previously described . The seqAdditional file 1. Metabolic pathways for acetol biosynthesis in E. coli.Additional file 2. Measured and simulated mass isotopomer distributions of intracellular metabolites.Additional file 3. Best fit-fluxes and flux confidence intervals.Additional file 4. Goodness-of-fit analysis for 13C-MFA.Additional file 5. Metabolomic data corresponding to the heat map in Fig. Additional file 6. Primers used in this study.Additional file 7. Metabolic network model used for 13C-MFA.


Listeria monocytogenes is a microorganism of great concern for the food industry and the cause of human foodborne disease. Therefore, novel methods of control are needed, and systems biology is one such approach to identify them. Using a combination of computational techniques and laboratory methods, genome-scale metabolic models (GEMs) can be created, validated, and used to simulate growth environments and discern metabolic capabilities of microbes of interest, including L. monocytogenes. The objective of the work presented here was to generate GEMs for six different strains of L. monocytogenes, and to both qualitatively and quantitatively validate these GEMs with experimental data to examine the diversity of metabolic capabilities of numerous strains from the three different serovar groups most associated with foodborne outbreaks and human disease. Following qualitative validation, 57 of the 95 carbon sources tested experimentally were present in the GEMs, and; therefore, these were the compounds from which comparisons could be drawn. Of these 57 compounds, agreement between in silico predictions and in vitro results for carbon source utilization ranged from 80.7% to 91.2% between strains. Nutrient utilization agreement between in silico predictions and in vitro results were also conducted for numerous nitrogen, phosphorous, and sulfur sources. Additionally, quantitative validation showed that the L. monocytogenes GEMs were able to generate in silico predictions for growth rate and growth yield that were strongly and significantly  correlated with experimental results. These findings are significant because they show that these GEMs for L. monocytogenes are comparable to published GEMs of other organisms for agreement between in silico predictions and in vitro results. Therefore, as with the other GEMs, namely those for Escherichia coli, Staphylococcus aureus, Vibrio vulnificus, and Salmonella spp., they can be used to determine new methods of growth control and disease treatment. L. monocytogenes to the food industry, there is a continuous interest in new methods of control and treatment. The development of rapid, relatively cheap genome sequencing techniques in recent years has led to the emergence of genomic tools for identifying more properties of microorganisms through the field of systems biology and its associated computational techniques.Due to the importance of Escherichia coli O157:H7, Salmonella, Vibrio vulnificus, Staphylococcus aureus, Listeria monocytogenes . The semi-automated process uses publicly available genomic information alongside online database tools to generate draft GEMs. The draft GEMs are then curated and expanded through an iterative process to validate computational predictions by comparison to experimental data. GEMs generated through use of KBase have been used to elucidate the metabolic profile of Candidatus Homothermaceae, to reveal niche adaptation of Sinorhizobium meliloti, to reveal diverse metabolic functions used in plant-bacterial interactions of Pseudomonas fluorescens, and to analyze central metabolism across all microbial life through analysis of > 8,000 different prokaryotic organisms . Ea. Ea15]. L. monocytogenes strains. In the work of Schauer et al. (2010), a condensed central metabolic network was reconstructed to model listerial metabolism, and the GEM contained 155 reactions (30 are transport reactions) and 167 metabolites  that is built with the same bioinformatics pipeline as the ModelSeed [Six database ,33,34. TodelSeed . In the odelSeed  and impoL. monocytogenes and nearly all free living bacteria. Therefore, using KBase, gap-filling was performed on the draft L. monocytogenes models for D-glucose under both aerobic and anaerobic conditions. Then the draft models were downloaded in systems biology markup language (SBML) file format, curated through comparison to experimental data, and provided here as validated SBML Level 3 fbc format files  were used for all in vitro nutrient utilization experiments. When preparing Biolog™ plates, three isolated colonies from each refrigerated culture plate were inoculated into separate test tubes containing 9 mL of BHI broth. The BHI tubes were then incubated at 37°C overnight. After incubation, two tubes for each strain were chosen and 300 μL from each tube were taken and inoculated onto separate Biolog Universal Growth plus sheep’s Blood (BUG+B) agar plates in triplicate (6 plates per strain). The BUG+B plates were then incubated at 37°C overnight. After incubation, one BUG+B plate was harvested using a sterile cotton swab, and cells were placed in 15 mL conical tubes containing 1.8 mL of IF-0 solution, prepared as directed by the manufacturer. 150 μL of cell suspension was removed, placed in a new 15 mL conical tube, and the OD590 was then adjusted to 0.171 ± 0.020 by diluting with fresh IF-0 solution. After OD590 adjustment, 1.8 mL of the diluted cell suspension was added to 15 mL conical tubes containing 9 mL of IF-0+ solution that had been prepared according to manufacturer instructions. For PM3 and PM4 plates, 108 μL of 100X ferric citrate/sodium succinate solution was added to each conical tube containing cellular suspension. The resulting solution was then transferred to a sterile reservoir, and then transferred to separate wells of Biolog™ plates, separate plates for each replicate of each strain , in 100 μL aliquots. 640 nm absorbance values were then taken at 0, 12, 24, 48, and 72 hour time points using a ChroMate® Microplate Reader .BiologGAMS is an optimization software package and was used to perform flux balance analysis (FBA) on each of the models to determine predicted nutrient utilization capabilities using methods previously described . FBA is ™ plates that did not already have corresponding transport reactions in the draft GEMs. After identifying the missing compounds, the models were manually curated to add the required reactions in order to generate predictions for in silico nutrient utilization. These predictions were then compared to in vitro nutrient utilization experiments using Biolog™ plates.After the initial nutrient utilization predictions, the metabolites contained in the GEMs were surveyed to identify compounds matching those present on Biologin silico predictions to in vitro results generated a list of disagreements necessary to reconcile for validation of GEMs predictive accuracy. The GEMs were then manually curated to remove transport reactions associated with compounds for which in vitro results showed no growth but in silico predictions predicted growth . Compounds for which in silico simulations predicted no growth, but in vitro experiments showed growth  were reconciled by first using KBase to gapfill the draft models on those compounds to identify any necessary missing metabolic reactions. The reactions in the resultant secondary draft models were then used as templates by which the manually curated models could be updated. This step was necessary because the manually curated models could not be re-uploaded to KBase and repeatedly gapfilled. The gapfilling, manual curation, and Biolog™ experimental validation techniques presented here are common methods used to validate and optimize GEMs [Comparisons of ize GEMs ,37,39,40in silico by adding additional constraints to the FBA simulations of GEMs. The constraints introduced during essential reaction prediction simulations serve to restrict the flux through each metabolic reaction one at a time. FBA then re-optimizes the objective function (biomass production) while the single reaction is restricted. If, lacking the specific metabolic reaction, the predicted biomass is zero, the restricted reaction is deemed essential. This approach for predicting essential reactions with GEMs is well established [et al. were able to identify successful metabolite-mimicking drugs that had a bactericidal effect on the opportunistic foodborne pathogen, Vibrio vulnificus [Essential reactions are those required by a microorganism for viability and/or growth in a given environmental condition. Therefore, determination of essential reactions identifies metabolic reactions and corresponding genes as ideal targets for control of viability and growth. Predictions of essential reactions can be accomplished ablished ,41. Usinlnificus .in silico predictions and in vitro experimental results. GAMS was used to simulate gene knockouts, eliminating one metabolic reaction at a time by constraining the flux to zero in order to identify which of those reactions were essential to the survivability and viability of each of the six strains of L. monocytogenes. Essential reactions were determined by a prediction of zero biomass generation associated with the removal of the reaction. Essential reaction predictions were first performed in conditions reflecting the nutrients present in a minimal media with glucose as the sole energy source alamin, Na+, Fe2+, Fe3+, O2, and D-glucose). Subsequently, the chemical composition of five of the foods most commonly recalled for L. monocytogenes contamination was obtained from the United States Department of Agriculture (USDA) nutrient database. Using this chemical composition, compounds that were both present in the foods and present in the models were added to the environmental simulations in reported analytical amounts . Three chemically defined media were tested. The first was an improved minimal medium (IMM) described by Phan-Thanh et al. [et al. [600 was adjusted to 0.040 ± 0.010 using fresh media. After the OD600 adjustment, 200 μL of each sample was placed into separate wells of a 96 well plate, along with triplicate wells of fresh, uninoculated media as the negative growth control. The 96 well plate was then placed in the plate reader, where OD600 measurements were taken every 10 minutes for 48 hours at 37°C. Every six readings were then averaged to generate a growth curve with hourly time points. Inconsistent growth was observed with the first two chemically defined media tested (IMM and MWB), but growth was supported by MWB supplemented with 3% BHI.The strains of lidation . To ensuh et al. . The sec [et al. . The finL. monocytogenes in sufficient quantities to perform dry cell weight measurements, batch spargers, as described by Sutton et al. [L. monocytogenes strain to be tested. The tubes were incubated overnight at 37°C with shaking at 250 rpm.In order to grow n et al. , were us600 was 0.040 ± 0.010. Then, the remaining overnight culture was used to inoculate the three batches of 600 mL MWB3 such that the dilution was equivalent to the dilution required to obtain the desired OD600 in the 100 μL sample. A sample from each of the batch spargers was then taken, and its OD600 measured. Subsequent OD600 measurements were taken hourly for each of the batches for the duration of the run.MWB3 was prepared fresh prior to the start of each experiment and 600 mL aliquots were placed into three separate, sterile 1 L glass sparger bottles. Additionally, 50 mL were prepared for use as spectrophotometer blanks. A 100 μL sample of the overnight culture was taken and diluted so that the OD™ glass microfiber filters  were labeled and placed in an 80°C oven and left overnight to dry. One hour prior to beginning dry cell weight experiments, the dry filter weight was measured and recorded as described by Baumler et al. [600 of the batch growth spargers reached 0.100.Dry cell weight measurements were performed in conjunction with the aerobic batch growth experiments. 12 (3 batches x 4 time points) Whatman600 reached 0.100, approximately 60 mL was extracted from each batch. 50 mL of each sample was vacuum filtered through its corresponding pre-weighed filter paper. After the culture was filtered, the paper was washed with approximately 5 mL of sterile DI water, left to dry for two minutes, and washed again with approximately 5 mL of sterile DI water. When all three of the filter papers for the time point were finished, they were placed in an 80°C oven to dry for a minimum of 24 hours. This process was repeated hourly for a total of four time points. 24 hours after the last time point, the filters were re-weighed, and the dry cell weight was determined from the difference between the pre-weighed filter mass, and the post-filtration mass.When the OD−9. The six highest dilutions (10−4–10−9) were then plated on BHI agar plates, incubated at 37°C for 24 hours, and enumerated.At the second dry cell weight time point, a CFU/mL count was determined for each of the three batches. Duplicate samples from each batch were taken and serially diluted to 10in silico predictions for biomass corresponding to growth rate. First, the data was used to generate conversion factors between biomass and optical density and between biomass and viable cell counts. Subsequent analysis of the data generated experimental growth rates (h-1), which were compared to in silico predicted growth rates to generate a scaling factor as previously described for the E. coli K12 GEMs [in silico growth predictions. Initial in silico growth rates were determined by adjusting in silico glucose uptake rates until the duration of the batch growth matched experimental values. These glucose uptake rates were then held constant when the scaling factor was introduced, allowing the scaling factor to increase the accuracy of predictions of biomass used to generate values for growth rate and growth yield.Following the completion of the batch growth dry cell weight experiments, the experimental data was used to adjust the models and improve the accuracy of the K12 GEMs . This scStudent’s t-test and Pearson correlation statistics in this study were conducted using Microsoft Excel.S1 FileL. monocytogenes strain J2-031 for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S2 FileL. monocytogenes strain JO161 for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S3 FileL. monocytogenes strain J2-064 for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S4 FileL. monocytogenes strain R2-502 for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S5 FileL. monocytogenes strain F2365 for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S6 FileL. monocytogenes strain ScottA for distribution and use in other modeling environments.SBML format of the final model of (XML)Click here for additional data file.S1 Dataset(XLSX)Click here for additional data file.S2 Dataset(XLSX)Click here for additional data file.S3 Dataset(XLSX)Click here for additional data file.S4 Dataset(XLSX)Click here for additional data file.S5 Dataset(XLSX)Click here for additional data file.S1 Fig(DOCX)Click here for additional data file.


Mucor circinelloides (M. circinelloides) strain with mitochondrial malate transporter (mt) gene overexpression was increased by 70%, while that of strain with mt gene knockout was decreased by 27%. However, the mechanism of malate transporter promoting the transport of mitochondrial malate and citrate related to lipid accumulation is not clear. Therefore, 13C-labeled glucose metabolic flux analysis was carried out to identify the metabolic network topology and estimate intracellular fluxes of genetically engineered M. circinelloides strains for the purpose of better understanding the roles of malate transporters in citrate transport systems and lipid accumulation.Mitochondrial and cytoplasmic malate transporter proteins are responsible for transmembrane transport of malate, thereby linking malate metabolism in various subcellular regions of the cell. These transporters play an important role in fatty acid biosynthesis of oleaginous microorganisms. Our previous studies have found that lipid content of the recombinant mt-overexpression strains was decreased compared to that of the control strain, but in contrast, glyoxylic acid (GOX) cycle flux ratio was increased. Accordingly, the mt-knockout strain showed an opposite phenomenon with a higher TCA cycle flux ratio and a lower GOX cycle flux ratio than the control strain. GOX cycle might be more effective than TCA cycle in producing malate and oxaloacetate replenishment. Moreover, a relatively higher flux ratio of the pentose phosphate (PP) pathway was obtained in mt-overexpression strains, but no significant difference in the malic enzyme flux between recombinant strains and the control strain. Our results confirmed that PP pathway might play an important role for supplying NADPH and malic enzyme is not a limiting factor for fatty acid synthesis in oleaginous fungus M. circinelloides strains.The metabolic flux distribution analysis suggested that tricarboxylic acid (TCA) cycle flux ratio of mt-overexpression strains had higher flux in PP pathway and GOX cycle, lower flux in TCA cycle, and no difference in malic enzyme cycle. Together, the role of malate transporter was assumed to further participate in transporting cycle of acetyl-CoA and drive PP pathway to supply NADPH required for lipid accumulation in recombinant M. circinelloides strains.Intracellular metabolic flux information suggested that  Oleaginous microorganism can synthesize a large amount of triglycerides, accounting for 20–80% of cell dry weight (w/w) . Among tKm value of transporters in non-oleaginous yeast was 2-fold higher than that of oleaginous yeast  glucose labeling experiment, The fractional label of the different derivatized fragments should be consistent with the labeling content of the input substrate which could be determined according to Eq For the [U-M. circinelloides cells, which was performed using Metran [13C labeled metabolic flux analysis, tracer experimental design and statistical analysis. Each experiment was performed in triplicate. All data were represented as means ± standard deviations and were analyzed with ANOVA. Validation of the fit was accomplished by a χ2-statistical test for the goodness-of-fit between the experimental values of the mass isotopomers and those simulated from the estimated flux distribution [In our study, metabolic fluxes and the confidence intervals were determined to simultaneously fit the external fluxes and the mass isotope abundances of intracellular amino acids to a detailed metabolic network model of g Metran . The Metribution .Additional file 1: Table S1. Measured and estimated MDV of control and recombinant strains using proteinogenic amino acid.Additional file 2: Table S2. Metabolic network model for 13C metabolic flux analysis.Additional file 3: Table S3. The minimum mass spectrometric fragments of amino acids.Additional file 4: Table S4. Abundance of natural stable isotopes for biologically relevant elements.


A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.Saccharomyces cerevisiae, with fluxes derived from simulated and real concentration data sets, are presented to highlight the benefits of this dynamic modelling.Two methods are introduced here: dynamic elementary mode analysis (dynEMA) and dynamic elementary mode regression discriminant analysis (dynEMR-DA). The former is an extension of the recently proposed principal elementary mode analysis (PEMA) method from steady state to non-steady state scenarios. The latter is a discriminant model that permits to identify which dynEMs behave strongly different depending on the experimental conditions. Two case studies of This methodology permits to analyse metabolic fluxes at early stages with the aim of i) creating reduced dynamic models of flux data, ii) combining many experiments in a single biologically meaningful model, and iii) identifying the metabolic pathways that drive the organism from one state to another when changing the environmental conditions.The online version of this article (10.1186/s12918-018-0589-3) contains supplementary material, which is available to authorized users. Data analysis methods are widely used in Systems Biology to interpret different kinds of data. In the field of fluxomics, principal component analysis (PCA)  models hThe drawback of PCA and MCR is that the components do not represent metabolic routes connecting substrates with end-products, but separate groups of concatenated reactions in the network. To enhance the interpretability of PCA and MCR, principal elementary mode analysis (PEMA)  was propIn non-steady state conditions, the state of the network at a particular time point of the biological process is defined by the concentration of each metabolite in the cell, and metabolites may interact via one or more reactions. Each reaction is represented by an ordinary differential equation (ODE) relating chemical compounds. Since metabolic networks may have hundreds of reactions, it is hard to build kinetic models requiring kinetic parameters. When given the initial concentrations of metabolites and the full kinetic model , the concentration of the metabolites along time can be simulated to produce a state transition path or trajectory, i.e. the succession of states adopted by the network over time . MethodoOnce the kinetic model is built and the data is gathered, either simulated or  measured, a comparison between experimental conditions can be performed to discover which groups of metabolites, reactions or pathways show differences between substrates, environment, etc. For this purpose, partial least squares regression discriminant analysis (PLS-DA)  can be uThe Goeman’s test was proposed in  to tacklTo solve the aforementioned drawbacks of PLS-DA and the Goeman’s global test, a novel framework is proposed to analyse non-steady state metabolite concentrations, based on an extension of the PEMA model. For this, we introduce the concept of dynamic EMs (dynEMs), i.e. EMs activated partially at each time point of the experiment. The dynEMs are used in a discriminant model to identify which metabolic routes have different activations depending on the initial conditions, i.e. which pathways discriminate between experimental conditions (as for example different substrate concentrations). As opposed to PLS-DA, dynEMR-DA integrates topological information to make the model more interpretable, as the set of candidates are drawn from the elementary mode matrix of the metabolic network; and, as opposed to Goeman’s test, includes all metabolic routes connecting substrates with end-products and all time points of the experiment in the same discriminant model.http://www.bdagroup.nl/content/Downloads/software/software.php, with instructions about how to use the method with own data. This way, practitioners are guided through the procedure, from the definition of the inputs, elementary mode matrix and concentration or flux data (either can be used), to the outputs, i.e. coefficients for the dynamic elementary modes to reconstruct the flux data. The N-way toolbox [efmtool [The MATLAB code for dynEMR-DA, related functions and example data are freely available in  toolbox  and efmt[efmtool  for MATLS. cerevisiae are presented and the adaptation of the PEMA model from a steady to a non-steady state environment is introduced, describing dynEMA, dynEMR-DA and the validation scheme. In Results, the output of dynEMR-DA is analysed using simulated and real concentration data. Finally, some conclusions are drawn in the last section.The structure of the article is as follows. In Methods, the metabolic models and data sets of S. cerevisiae are used here to build the multivariate discriminant models  cycle c0, where c is the concentration used in the analysis, c0 is the concentration given by COPASI and ε follows a Normal distribution with mean 0 and standard deviation 1. In the first 32 experiments the initial glucose concentration is set to 10mMol/l (plus noise), while in the last 32, this concentration is set to 2.5 mMol/l . These two values are indeed interesting, since they mimic the glucose concentrations used in the real case study (see paragraph below). The other common metabolites between metabolic models have comparable values in both concentration data sets. The set of EMs is obtained in this case using efmtool software [The aim in the simulated study consists of discriminating between scenarios using a high software .S. cerevisiae along 24 time points were obtained experimentally using liquid chromatography–mass spectrometry (LC-MS) [In the real case, the concentrations of  (LC-MS) , 23 at t (LC-MS) . 12 diffThe aim in the real case study consists of discriminating between i) high and low glucose concentrations (i.e. experiments 1-4 vs 5-8), and ii) aerobic and anaerobic conditions (experiments 5-8 vs 9-12).N) and indices will appear as italic lower-case letters (e.g. j). Vectors are represented as bold lower-case letters (e.g. v). Data matrices are represented as bold capital letters (e.g. X). Superindex T denotes the transpose of a matrix. Observations or individuals within matrices are represented by rows, while variables are represented as columns. 3-dimensional arrays will be denoted as underlined bold capital letters (e.g. X). The mathematical operator × is used here to denote the size of the modes of a matrix (e.g. Y is a N×M matrix). No mathematical operator is used for products between scalars, vectors and matrices. Operator ∘ denotes the Hadamard element-wise product between vectors or matrices. Finally, operator ⊗ denotes the Kronecker tensor product between vectors or matrices, that is: Scalar values are represented here as italic capital letters  can be decomposed as a positive linear combination of a set of E EMs [Any steady state flux distribution of E EMs : 2\docuK is the number of fluxes (matching the number of reactions in the network), eth EM, λe is the positive weighting factor of the eth EM, and E is the number of EMs needed to reconstruct the flux distribution x. The set of E EMs is a subset of the complete set of Z EMs of the metabolic network.where M=5 metabolites and K=8 reactions. There are Z=3 EMs in the network: ,  and . Let us assume that there is only flux on reactions 1 to 6. A linear combination of the first E=2 EMs will reconstruct the flux carried by the reactions in the system in Fig. 2Figure 2N flux distributions are considered, coming from different experiments or cultures, a PEMA model can be built: When X is the N×K flux data matrix, P is the K×E principal elementary mode (PEM) matrix, formed by a subset of E EMs; Λ is the N×E weighting matrix; and F is the N×K residual matrix. A schematic representation of a PEMA model is shown in Fig. where Non-steady state flux distributions cannot be decomposed as linear combinations of EMs, as in steady state. When the biological system has not reached yet the steady state, the system is not in equilibrium and fluxes can change over time. However, the EMs are indeed the simplest pathways along which the non-steady state fluxes have to flow, but not in a constant fashion. Thus, the EMs must be modified or adapted to fit this dynamical system. These are the so-called dynamic elementary modes (dynEMs).Λ values in PEMA): To adapt an EM, there is not only a single coefficient multiplying the EM  the flux at each reaction  is different. High values are registered at the beginning of the experiment in the first reaction  model: Considering non-steady state flux distributions along A is the EJ×K coefficients matrix, IJ is the J×J identify matrix, P is the K×E principal elementary mode (PEM) matrix, 1E and 1J represent column vectors of E and J ones respectively, F is the J×K residual matrix (containing the fluxes not explained by the set of dynamic elementary modes) and ⊗ is the Kronecker matrix product. In this case, X is a J×K data matrix representing the non-steady state fluxes from a single experiment along J time points; while in the PEMA model, X is a N×K matrix representing the steady state fluxes of N different experiments. Figure where A in the previous equation is, in fact, a E×K×J 3-way matrix unfolded reaction-wise, and each entry in the matrix k of EM e to reconstruct the flux at time point j. Using this modelling it is possible to study the time evolution of a dynEM, i.e. how the dynEM is adapted or dynamically used along all measured time points for a given experimental condition.The coefficients matrix K×ZEM matrix in a step-wise fashion. After selecting an EM, the coefficients multiplying it (thus creating the dynEM) are obtained solving Eq. P). Afterwards, this first dynEM is set, and the search for the second one starts, recalculating the coefficients in matrix A for both the first and the second dynEMs at each evaluation. In this way, the dynEMA model is built in a greedy way, explaining as much variance as possible at each step.This system of equations is solved similarly to PEMA. The candidates for first dynEM are selected from the complete Regarding the number of dynEM extracted, this depends on the aim of the analysis, as explained in  with theThe dynEMA model is useful to identify the dynEMs active in an experiment and how each dynEM is used in the culture at different time points of the experiment.When the aim is to establish differences between environmental or experimental conditions, e.g. presence/absence of a compound or case/control studies, a discriminant model is needed. For this, dynamic elementary mode regression discriminant analysis (dynEMR-DA) is proposed here. This model focuses on finding which are the dynEMs with a strongly different time evolution or performance between conditions. In essence, dynEMR-DA is a two-step procedure. First, it projects the flux data into the space defined by each single dynEM. Then, fits a NPLS-DA  model wiX we consider N experiments, measuring K fluxes along J time points. Therefore, it is mandatory to have the same time points in all experiments.To build a dynEMR-DA model, the set of different experiments are combined in a single N×K×JX matrix in Fig. JN×K matrix X.Unfold reaction-wise the A using the dynEMA model: Calculate the coefficients matrix p denotes the candidate EM from step 1.where Reconstruct the flux data Fold the reconstructed data to build again a three-way data structure y data, where y denotes the class of experiments (having 1s and 0s).Fit an NPLS-DA model between the reconstructed data and the For each EM in the metabolic network (candidate to dynEM): y is classified as the first dynEM.The dynEM whose NPLS-DA model explains most variance in Check the predictions of NPLS-DA model. If the current model discriminates perfectly, stop. If not, set the first dynEM and repeat steps 1-3 to extract the second dynEM following the dynEMR-DA procedure.The algorithm of dynEMR-DA has the following steps: N-dimensional data structures with discriminant purposes. NPLS is the natural extension of PLS to N-way structures, which tries to maximize the covariance between the Y data arrays. Y is denoted as y when one variable is predicted. NPLS-DA models in this paper have been computed using the N-way toolbox for MATLAB [NPLS-DA was proposed for studying r MATLAB .The dynEMR-DA algorithm can select many dynEMs until attaining a perfect discrimination. However, in practice, individual dynEMs are able to discriminate between two experimental conditions, so there is no need of considering two dynEMs simultaneously active to obtain a discriminant model. Moreover, some dynEMs are discriminating between initial conditions, but some of their reactions are not used at any time point of the experiment (so the flux does not flow through the metabolic pathway from the beginning to the end). These dynEMs do not represent actual metabolic pathways, so they should be removed when they are selected.Proper validation of multivariate models is a subtle issue in Systems Biology. When enough data are available, single cross-validation procedures may lead to too optimistic models, especially when the aim is discrimination between classes. As commented in , when diDivide the data set in four groups: calibration, test, selection, and validation. The latter is left out of the analysis until the final external validation.K components (as many as fluxes).Fit a dynEMR-DA model using the calibration set, using a maximum of K NPLS-DA calibration models. At this point, the minimum number of components, A, needed to classify each experiment in its corresponding class, is selected.Project the test set, first to the corresponding dynEM, and then to each of the A NPLS-DA components and evaluate the predictive power of each dynEM.Project the selection set into the previous dynEMR-DA model with Steps 2-4 are repeated three times, changing the roles of the subsets. That is, the models are built using, in steps 2 to 4 respectively: calibration-test-selection, test-selection-calibration and selection-calibration-test sets.The dynEMs with perfect classification rates using the selection set in the three rounds are used finally for validation, so the discrimination power of each dynEM is evaluated with completely external data. This prediction is performed substituting the selection group by these validation samples in the three models previously fitted.In this work, though, we need an extra round of validation. dynEMR-DA models involve the projection, as first step, of the flux data into the space defined by each single dynEM. Afterwards, an NPLS-DA model is fitted, determining at the end which dynEMs are discriminating between groups. Therefore, we propose here a triple cross validation (3CV) scheme see Fig. . This prA 2CV strategy is used for the NPLS-DA section of the dynEMR-DA models, but an extra validation round is needed to assess the performance of the selected dynEMs in terms of discrimination. Therefore, the 3CV procedure is built basically replacing the validation step, in the original 2CV, by the selection step, and performing the external validation in the last step.S. cerevisiae in Fig. 1The metabolic model of N-way Toolbox for MATLAB [To validate the discriminant models, the 3CV scheme is used here, using the r MATLAB  to fit tWhen applying the dynEMR-DA procedure described in the previous section, only one dynEM (from the whole set of 26 EMs) is able to discriminate perfectly between both experimental conditions: dynEM 8. Finally, the remaining 16 cultures are used for the final validation of this dynEM see Fig. . Again, 8. This mode covers the whole glycolytic pathway, starting from glucose (GLCo), producing all the intermediate products until reaching pyruvate (PYR), acetate (ACE) and finally ethanol (ETOH). The coefficients multiplying the EM are visualized in Fig. 8Figure 8versus red bars). The usage of all reactions in the dynEM, i.e. the coefficients in A matrix, are higher in the high glucose concentration experiments than in the low glucose. This implies that these scenarios take advantage of the higher amount of glucose to carry more flux through the glycolysis until reaching ethanol.The differences between both experimental conditions can be seen in Fig. 8It is worth mentioning that the system is close to steady state from the first time point. However, we used this set up to have a simulated case as close as possible to the real case, in order to find out i) whether there are differences between the initial concentrations of glucose, and ii) if the discriminant dynEM resembles the real case one(s) (see next section).S. cerevisiae are used to discriminate between experiments using a high or a low initial glucose concentration. Unfortunately, the number of available cultures is low for this case study (4 in each class), so no 3CV, neither 2CV, is possible. Therefore, single CV is applied here: 3+3 experiments are used for dynEMR-DA model building and selection of NPLS-DA components, and the remaining 1+1 experiments are used for validation. This procedure is repeated 4 times, leaving out a couple of cultures each time.To assess the performance of dynEMR-DA in a real case study, a set of cultures of The dynEMR-DA model has to be built using fluxes, not concentrations. Therefore, we computed the fluxes based on the changes in the concentrations between two consecutive time points solving an optimization problem (similarly as in ). SpecifM=12 metabolites are measured in 24 time points within 2 min (1 measurement every 3 s). The metabolic network  flux data matrix. The quadratic optimization problem needs an initial guess on X, i.e. X0. This guess is obtained solving k and j denote flux number and time point, respectively, S denotes the 12×20 stoichiometric matrix (metabolites × reactions), and C is the 24×12 concentration matrix (time points × metabolites). It is worth noting that, since fluxes are computed based on the differences between concentrations at consecutive time points, there is one time point less in the flux data matrix (J=23) than in the concentration data (24).where The objective function used in the optimization problem resembles the MOMA function (minimize the squared difference of the reaction rates with steady state) used in , with th9 (from the set of 20 EMs) is able to discriminate the left out experiments. This dynEM can be visualised, jointly with the coefficients in matrix A, in Fig. In this case, only dynEMThe results in this example follows the scheme described in Fig. 8 of the simulated case study. Both dynEMs are describing the same phenomena, the glycolysis until reaching pyruvate. They are not exactly the same because the metabolic models are different: acetate and ethanol were not measured in experimental conditions. However, when comparing the simulated and the actual data, the dynEM discriminating between experimental conditions is basically the same one.It is worth noting the similarity between the dynEM identified here and dynEMFinally, it is difficult to assess when the system reaches the steady state in the real case study. In the simulated case, steady state was reached clearly at 36 s (since fluxes did not change anymore). In the real case, after 24 s see Fig.  fluxes dversus four more in anaerobic conditions are compared. As in the previous example, fluxes are calculated from the real concentration data using the optimization framework  can be visualized in Fig. In this case study, dynEMAs in , it is wFigure Figure The computation time with these case studies is 17 s (dynEMR-DA model) versus 0.5 s (NPLS-DA model). In the dynEMR-DA algorithm, as many NPLS-DA models as EMs  are fitted to find the most discriminant one, therefore it is clear that one single NPLS-DA model will be faster than dynEMR-DA. However, the time needed to interpret the output of NPLS-DA is longer than the pathway-oriented result that dynEMR-DA provides.dynEMR-DA, as opposed to NPLS-DA, can be strongly affected by the size of the EMs matrix. When having several hundreds of EMs, a pre-selection of EMs can be performed to speed up the analysis. One strategy would be to study the reactions that are active in all EMs and include only those EMs with different active reactions (i.e. coefficient different from zero). For example, if many elementary modes use the same reactions with the same directionality for the reversible ones, only one EM can be included in the set of EMs to test. Another possibility would be to use the set of extreme pathways of the network instead of the EMs .p-value indicating which pathways were different depending on the groups at discrete time points. Their results showed that glycolysis and TCA cycle were significant but not for all time points when comparing high versus low initial glucose. For the aerobic versus anaerobic case, both the glycolysis and TCA were significant for all time points.The Goeman’s global test was applied in  to find This approach is not directly comparable to dynEMR-DA, as all pathways are tested simultaneously in dynEMR-DA, instead of individual pathway testing. No EM containing TCA was significant here, which can be also due to i) all time points are used simultaneously in dynEMR-DA, instead of discrete time point analysis (4 time points in ), and iiFinally, authors stated in the Goeman’s test article  that a dThe approach for dynamic elementary mode modelling proposed here permits decomposing non-steady state flux distributions into a set of active dynEMs. This way, dynEMA can be used to study the active dynEMs in an experiment, or a set of experiments, extending the PEMA model to a dynamic environment. For discrimination purposes, the main interest in this article, dynEMR-DA allows identifying which dynEMs have different patterns of activation depending on the culture initial conditions.S. cerevisiae have been used here to evaluate dynEMR-DA. When changing the amount of glucose present in the experiment in both data sets, dynEMR-DA is able to identify that the dynEM flowing through the glycolytic pathway from glucose to pyruvate is discriminating between high and low initial glucose concentration experiments. Even considering two different metabolic models, for data availability reasons, the results of dynEMR-DA seem coherent between case studies. When analysing data from aerobic versus anaerobic conditions, dynEMR-DA indicates that the most discriminant dynEM drives the initial glucose concentration to the glycerol production. Previously published research confirms the results obtained using this new methodology.Actual and simulated concentration data of The framework presented here will serve to create reduced dynamic models of flux data while preserving biological and thermodynamical meaning, as a tool to analyse non-steady state flux distributions in many experiments and to identify the hidden metabolic patterns that drive the organism from one state to another when changing the environmental conditions. dynEMA and dynEMR-DA have potential applications in bioprocess engineering to understand the small changes in cell metabolism at early stages of cultures.Additional file 1An additional file is provided with the detailed metabolic models. (PDF 105 kb)


Aspergillus fumigatus. The healthy human immune system is capable to ward off A. fumigatus infections however immune-deficient patients are highly vulnerable to invasive aspergillosis. A. fumigatus can persist during infection due to its ability to survive the immune response of human DCs. Therefore, the study of the metabolism specific to the context of infection may allow us to gain insight into the adaptation strategies of both the pathogen and the immune cells. We established a metabolic model of A. fumigatus central metabolism during infection of DCs and calculated the metabolic pathway . Transcriptome data were used to identify pathways activated when A. fumigatus is challenged with DCs. In particular, amino acid metabolic pathways, alternative carbon metabolic pathways and stress regulating enzymes were found to be active. Metabolic flux modeling identified further active enzymes such as alcohol dehydrogenase, inositol oxygenase and GTP cyclohydrolase participating in different stress responses in A. fumigatus. These were further validated by qRT-PCR from RNA extracted under these different conditions. For DCs, we outlined the activation of metabolic pathways in response to the confrontation with A. fumigatus. We found the fatty acid metabolism plays a crucial role, along with other metabolic changes. The gene expression data and their analysis illuminate additional regulatory pathways activated in the DCs apart from interleukin regulation. In particular, Toll-like receptor signaling, NOD-like receptor signaling and RIG-I-like receptor signaling were active pathways. Moreover, we identified subnetworks and several novel key regulators such as UBC, EGFR, and CUL3 of DCs to be activated in response to A. fumigatus. In conclusion, we analyze the metabolic and regulatory responses of A. fumigatus and DCs when confronted with each other.Dendritic cells (DCs) are antigen presenting cells which serve as a passage between the innate and the acquired immunity. Aspergillosis is a major lethal condition in immunocompromised patients caused by the adaptable saprophytic fungus  Aspergillus fumigatus is an airborne fungal pathogen which can cause a hypersensitive reaction, mucosal colonization, and even life-threatening invasive infection in the immunocompromised host  serve as a bridge between the innate and the acquired immunity. DCs are antigen presenting cells that express several pattern recognition receptors (PRRs) that recognize A. fumigatus by comparing different Aspergillus genome sequences and their well-curated metabolic enzyme annotation, followed by a flux balance analysis  using RT-PCR measurements on the key enzymes identified.Our We created a large network as an initial genome-scale network which includes not only the reactions from the central metabolism but also reactions from propanoate metabolism, seleno-compound metabolism, terpenoid biosynthesis, and others.However, calculation of all EFMs (elementary flux modes) becomes computational challenging for such a huge network, there is combinatorial explosion. The initial network was decomposed into subnetworks .We then calculated flux strengths for individual enzymes . Apart fA. fumigatus (GSE69723) was used to create a context dependent network. Mining information from publications was useful to create links between the metabolic and regulatory pathways. NetDecoder was used to identify the key regulators in DCs during infection.For the dendritic cell expression data from the dendritic cell infected by Finally, we re-checked several of the expression predictions by independent RT-PCR experiments and collected these data. Such a second validation by experiments is typical in modeling studies, for instance  revealed alterations in pathogen metabolic pathways contributing to circumvention of host immune mechanisms. Our approach  tests fiAll the subnetworks which actually run for metabolic flux calculation are given in YANAsquare compatible dat files . The bigS involved 13 reversible and 66 irreversible reactions  is lacking , aldehyde reductase and alcohol dehydrogenase demonstrate upregulation of enzyme activity ranging from 30 to 50 percent. This indicates that fungal cells survive in anaerobic conditions in DCs. The activity for alcohol dehydrogenase increases from 17% at 3 h to 33% at 6 h, 40% at 9 h and 43% at 12 h, respectively. During the course of the DC challenge, the down regulated activity for pyruvate kinase and the upregulated activities of phosphoenolpyruvate carboxykinase (PEP carboxykinase) and pyruvate decarboxylase (pdcA) indicates that the fungal cells suffer starvation and hence enter the gluconeogenesis cycle where phosphoenol pyruvate is converted to glucose instead of pyruvate.The gene expression data-set (GSE22053) we analyzed hence enables a view on the time course of changes at 3, 6, 9, and 12 h  when The activity of inositol oxygenase in ascorbate and aldarate sugar acid metabolic pathway was found to be very high, close to the maximum activity of flux strength  at 3 h, and reaching maximum activity at 6 h. This activity was reduced slightly to 99% at 9 and 12 h. Acyl CoA dehydrogenase was also highly active with the activity values ranging from 80 to 85% at different time points. In the pathway valine-leucine-isoleucine degradation the activity for the enzyme branched amino acid transferase was decreased at all the time points with the lowest activity of 40% at 3 h. The enymes catalase and aldehyde dehydrogenase were also significantly positively regulated with 66 and 69% activity for aldehyde dehydrogenase at 6 and 9 h, respectively.A. fumigatus during infection in the dendritic cell. During the pathway enrichment analysis based on the gene expression data set (GSE69723), we did, however, not notice any significant change in other redox pathways.Aldehyde dehydrogenases (ALDHs) are known to metabolize endogenous and exogenous aldehydes and thus mitigate oxidative stress in both prokaryotic and eukaryotic organisms  and analyzed which enzymes are strongly changing under the challenge. To compare by this the affected metabolic or regulatory pathways and how far the challenge modified more regulation or metabolism in DCs we considered links between the affected enzymes according to literature . Among the proteoglycans, chondroitin sulfate and heparan sulfate has been reported as modulators of the innate immune response  signaling pathway, RIG-I-like receptors, and Nucleotide-binding Oligomerization Domain (NOD)-like receptors as depicted in Regarding concomitant signaling and regulation of the activation of DCs can be induced by a various receptors for pathogen-associated molecular patterns (PAMPs) as well as alarmins. By these signals, DCs become active in infection or to cope with other environmental challenges  glycolysis and anerobic (Warburg) metabolism becomes more important  to inhibit the mitochondrial respiration. In macrophages activated by LPS and IFN-gamma or bacterial infection, extracellular arginine is imported into the cell and it is metabolized to NO and citrulline by iNOS as in A. fumigatus challenged DCs. Additionally, the increased expression of hexokinase 2 (HK2) that phosphorylate glucose to produce glucose-6-phosphate (G6P) mediates an increased rate of glycolysis in DCs against A. fumigatus challenge. LDHA is induced by Hif-1α and hence pyruvate is turned into lactate, and far less ends up in acetyl-CoA for the TCA cycle. The expression of LDHA was significantly enhanced to ~1.5 fold at 6 h of infection. Moreover, Hif-1α activates pyruvate dehydrogenase kinase (PDK) that inhibits pyruvate dehydrogenase, which consequently inhibits the pyruvate decarboxylation. This inhibits the use of acetyl-CoA in the citric acid cycle and cellular respiration by interfering with the transformation of pyruvate into acetyl-CoA. The expression of PDK was significantly increased to >3 fold while no significant change in expression of Hif-1α was detected at 6 h.However, the hypoxia-inducible factor 1-alpha (Hif-1α) transcription factor facilitates the metabolic switch toward anaerobic glycolysis by targeting hypoxia response element containing genes . Hypoxic conditions induce expression of egl-9 family hypoxia inducible factor 1 (EGLN1) and factor 3 (EGLN3). Under re-oxygenation they terminate the HIF response rapidly by regulating the stability of HIF-α subunits  are necessary for the successful eradication of infection Coppens, . MMPs inA. fumigatus infected DCs at 6 h by inducing both the metabolic shift toward glycolysis and energy production by metabolism of fatty acid.Taken together, the complex interplay between several genes regulate the energy requirement of the A. fumigatus using NetDecoder program  is usually very low and transient in somatic cells , epidermal growth factor receptor (EGFR), cullin-3 (CUL3), neddylin (NEDD8), obscurin-like protein 1 (OBSL1), F-box only protein 6 (FBXO6), TNF receptor-associated factor 2 (TRAF2), amyloid-beta A4 protein (APP) plays important regulatory roles in the infected DCs . ExtendiA. fumigatus-human interaction, we investigated an early stage of the confrontation (6 h) using qRT-PCR. The results from qRT-PCR revealed a considerable response of A. fumigatus genes, however, the human host responded more moderately. The A. fumigatus infection of DCs induced upregulated expression of 4-aminobutyrate transaminase GatA (AFUA_5G06680- GATA) and alcohol dehydrogenases . The same experiment revealed a decrease of alkaline phosphatase (AFUA_6G08710 – ALP), branched-chain amino acid aminotransferase (AFUA_1G01680 – BCAAA), and GTP cyclohydrolase I (AFUA_5G03140 - GTPCH)  , which aWe included 10 enzymes in our test and our analysis revealed a moderate increase of each examined enzyme , in accoA. fumigatus is surprisingly well adapted to the challenge of stress due to DCs: most redox responses are quite, but catalase and alcohol dehydrogenase is active. Moreover, the differential activity of enzymes PEP carboxykinase, pdcA, LDHA, and aldehyde reductase A. fumigatus survive well in the anaerobic and nutrient deficient conditions in dendritic cell. Overall the metabolism is remarkable stable and well-adapted to environmental challenges, this could be a general feature of A. fumigatus a world-wide distributed and flourishing saprophyte. In contrast, the DCs reveal a number of specific features as fatty acid synthesis crucial for activating toll like receptor, glycosaminoglycan biosynthesis forming proteoglycans which can modulate immunological functions and active NOD like and RIG-I like receptor. Among the top 40 high impact genes we found polyubiquitin-C (UBC), epidermal growth factor receptor (EGFR), cullin-3 (CUL3), neddylin (NEDD8), obscurin-like protein 1 (OBSL1), F-box only protein 6 (FBXO6), TNF receptor-associated factor 2 (TRAF2), amyloid-beta A4 protein (APP) plays important regulatory roles in the infected DCs  of key importance during DCs challenge and maintaining full growth potential in A.fumigatus. Enzymes arginase, inositol oxygenase, GTP cyclohydrolase, catalase, and others were found to be most active during dendritic cell challenge. Flux activity calculations from our model also suggest the important role of glucuronic acid for immune activation and host cell adaptation.The present study delivers a curated model of A. fumigatus confrontation include UBC, EGFR, and CUL3 with involved defense signaling networks.DCs rapidly get metabolically ready to sense and fight fungal cells, utilizing enzymes such as PPARα/PPARγ/PPARδ involved in lipid metabolism for getting their receptors and defenses ready. Besides well-known responders in DCs such as maturation markers CD80, CD83, and CD86 and interleukins, novel regulators in human DCs as identified by differential co-expression of genes in DCs during A. fumigatus challenge   to support steady state operation of a metabolic network with irreversible reactions to proceed in appropriate directions”  of infection in DCs. A least square fit method used YANAsquare and next an R routine to calculate optimal pathway fluxes matching optimally the constraints for key enzyme activities. The latter were estimated according to significant elevated or lowered absolute gene expression intensity . Resulting cDNA was diluted to a final concentration of 40 ng/μl. Gene expression was analyzed by qRT-PCR. The primers for selected A. fumigatus and human genes were designed by Geneious 9.0.5  as reference genes. Results were expressed as mean ± standard deviation (SD) and the data were evaluated using the GraphPad Prism 3.00 software by one sample t-test.The total RNA was isolated separately from DCs from human, A. fumigatus from gene expression data  between phenotype 1 and phenotype 2, which is independent of the magnitude of gene expression correlations with the same directionality.”where giTFMS and SG performed the bioinformatics analyses. EB and EW carried out all validation experiments. EB performed the statistical analysis. MS and TD were involved in drafting the manuscript. JL and TD conceived the project and supervised the work. All authors were involved in manuscript writing and agreed to the final version of the manuscript.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.


Chromobacterium violaceum, an opportunistic human pathogen, was reconstructed using legacy data. Experimental constraints were used to represent antibiotic susceptible and resistant populations. Model predictions were validated using growth and respiration data successfully. Differential flux distribution and metabolic reprogramming were identified as a response to antibiotics, chloramphenicol and streptomycin. Streptomycin resistant populations (StrpR) redirected tricarboxylic acid (TCA) cycle flux through the glyoxylate shunt. Chloramphenicol resistant populations (ChlR) resorted to overflow metabolism producing acetate and formate. This switch to fermentative metabolism is potentially through excess reducing equivalents and increased NADH/NAD ratios. Reduced proton gradients and changed Proton Motive Force (PMF) induced by antibiotics were also predicted and verified experimentally using flow cytometry based membrane potential measurements. Pareto analysis of NADH and ATP maintenance showed the decoupling of electron transfer and ATP synthesis in StrpR. Redox homeostasis and NAD+ cycling through rewiring metabolic flux was implicated in re-sensitizing antibiotic resistant C. violaceum. These approaches can be used to probe metabolic vulnerabilities of resistant pathogens. On the verge of a post-antibiotic era, we foresee a critical need for systems level understanding of pathogens and host interaction to extend shelf life of antibiotics and strategize novel therapies.In the post genomic era, high throughput data augment stoichiometric flux balance models to compute accurate metabolic flux states, growth and energy phenotypes. Investigating altered metabolism in the context of evolved resistant genotypes potentially provide simple strategies to overcome drug resistance and induce susceptibility to existing antibiotics. A genome-scale metabolic model (GSMM) for  Chromobacterium violaceum is abundantly present in the soil and water as microbiota in tropical and subtropical regions around the world. For many years, it was mainly known as a producer of violacein and as a reporter for the discovery of quorum sensing molecules. In recent years, C. violaceum, primarily a neglected zoonotic pathogen, has emerged as an important model of an environmental opportunistic human pathogen, with a current low incidence of about 150 cases worldwide [C. violaceum [orldwide ) of infeorldwide . Its higorldwide . Furtheriolaceum  mandatesiolaceum –9. Such C. violaceum. It also highlighted the utility of a core model of metabolism integrated in the context of systems-level data, to generate hypothesis and predict emergent properties of antibiotic resistance.Antibiotic resistance has become a grand challenge for society and a multipronged approach that addresses surveillance, awareness and scientific mechanisms are required to combat it . Our preC. violaceum genome sequence was used to develop a GSMM through an initial automated draft reconstruction using the Model SEED server. The draft reconstruction was translated into a functional mathematical model after manual curation with legacy data and customized biomass macromolecular composition. The model was validated (prediction accuracy of 89%) using legacy BIOLOG data for respiration. Growth on thirty metabolites were predicted and validated experimentally. Glucose uptake rates (GUR), violacein secretion rates (VSR) and ATP maintenance (ATPM) were used as constraints to customize models to represent antibiotic resistant and susceptible phenotypes. Flux variability analysis (FVA) showed metabolic flux redistribution associated with antibiotic resistance in reactions involving redox factors NADH, TCA cycle, glyoxylate shunt and overflow metabolism. FVA also identified fold changes in proton motive force through ATP synthesis proportional to that observed in PMF using flow cytometer. Pareto front analysis was performed to identify tradeoffs between ATP and NADH maintenance using an in silico NADH oxidase reaction (NOX) in the growth of the resistant populations vis a vis wild type (WT). This study represents C. violaceum in silico and correlates it’s metabolic features to antibiotic resistance and predicts related metabolite vulnerabilities. Such approaches could lead to scalable pipelines using OMICS derived constraints-based flux balance models for clinical isolates.In this study, the C. violaceum metabolism. The curation involved systematic literature mining. Data mining through PubMed search engine resulted in 750 research articles related to C. violaceum  [iDB858 was able to predict metabolic phenotypes of C. violaceum with a prediction accuracy of 89% (iDB858.The summarized metabolic reconstruction and modeling process is iterative . The GSM™) –17. Faily of 89% . Sensitiy of 89%  to identiDB858 predicted growth on 24 out of 27 exogenous metabolites tested  growing on glucose with violacein secretion decreased the maintenance costs (45%) for biomass synthesis from 12.59 to 6.96 mmol ATP per g of biomass. As a consequence if the violacein demand decreases, the ATP maintenance costs would increase. For wild type and resistant strains (ChlR and StrpR) and experimental conditions described here  and streptomycin (WT+strep) were delineated using FVA and analysed  complex, represented by cytochrome oxidase bo3 carries a 12 fold lower flux compared to WT. Experimentally measured PMF using flow cytometry based membrane potential measurements is 10 fold higher measured  was used to show perturbed central metabolism and redox balance in the presence of antibiotics and reprogrammed metabolism as compensatory mechanisms in resistant populations. To understand the effect of antibiotics on d Tables  and 6. Ameasured  in the pin silico as well as in vitro, confirms modulation of flux involving NADH. FRD7 is reduced 2.5 fold. ATP generation is almost three fold lower through the ETC-PMF route similar to that of WT. The PMF is a third of that observed in the wild type  . Lysine,ild type  and corrSalmonella and resistance in Mycobacterium [de novo antibiotic resistance [+2 indicates lower probability of Fenton reaction and DNA mutations. The lowered oxygen uptake rate and the increased flux towards NADH, potentially represent a pseudohypoxic state. Lowered ratios of NAD+/NADH increase pyruvate dehydrogenase (PDH) phosphorylation and modulate pyruvate and acetate levels. In the presence of chloramphenicol, the ChlR population growing on glucose maintained the NAD/NADH ratio at 0.28 while in the presence of streptomycin, the StrpR population maintained the NAD/NADH ratio at 2.47. Potentially, the PDH must be completely dephosphorylated in the ChlR (supporting acetate and formate overflow) as compared to StrpR (only acetate overflow) to evoke such a response.The metabolic reprogramming due to antibiotic selection pressures was analysed by FVA using customized models to represent WT, ChlR and StrpR Tables  and 8. Dacterium  shunts iacterium . The flusistance ,22. The The NAD/NADH ratios in the wild type were around 0.25 for glucose and pyruvate, while it was 0.73 for succinate and oxoadipate. The ChlR strain shows major 7 fold reduction indicating high levels of NAD recycling provided by pyruvate. Concurrently, PMF/membrane potential is higher for the resistant populations in pyruvate as compared to the wild type. This suggests potential incapability to maintain ATP homeostasis under these conditions and an eventually complete decoupling of electron transfer and ATP synthesis. Similar results were observed for succinate, maleate and 2-oxoadipate.NADH oxidase (NOX) allows dissecting the role of redox imbalance and ATP synthesis deficiency in ETC function . The fluFVA of the three populations  in presence of NOX provided an insight into NAD+ recycling associated metabolic reprogramming in the resistant populations. Based on the feasible flux distributions, the resistant populations behaved very similar to the wild type . MetabolGene essentiality analysis for growth and biomass precursors  identifitpiA had the highest connectivity. CV_1071 involved in utilization of 2oxoadipate (resensitisation candidate) utilization was synthetically lethal with two genes from the TCA cycle (CV_1075 or CV_1076). This might explain the criticality of TCA  in resensitising the resistant population to 2 oxoadipate. The synthetic lethal pairs can be utilized for predicting drug targets that would otherwise be extremely challenging  to test experimentally. All the simulation results and iDB858 model have been provided in supporting information.Double gene deletion (DGD) analysis  led to iAntibiotic lethality may be initiated by altered cellular redox state. The redox stress potentially rewires central metabolism, cellular respiration, and iron resulting in cellular damage . Our worChromobacterium violaceum, iDB858 was generated that predicted response to antibiotics and metabolic reprogramming in resistant populations. FVA identified rewired central and redox metabolism in the presence of antibiotics and resistant populations all represented by in silico constraints. The relative contributions of redox imbalance and ATP insufficiency contributing to antibiotic action were delineated. iDB858 showed all redox coupled reactions carried uniquely determined flux confirming the critical role of redox homeostasis in maintaining viability and cellular function in C. violaceum as seen experimentally [iDB858 as a response to chloramphenicol or streptomycin resulted in overflow metabolism. Compensations in resistant populations included overflow metabolism to acetate and formate in ChlR but only acetate in StrpR. StrpR bypassed the oxidative branch of TCA and redirected metabolism to the glyoxylate shunt  seen in Salmonella persisters.A whole genome-scale metabolic model of mentally –29. Thismentally . The metiDB858 also captured for the first time the metabolic flux distributions related to NAD+ recycling. This is key for survival of ChlR and StrpR in silico. The Pareto optimality analysis of ATP and NADH maintenance in iDB858 identified decoupled electron transfer and ATP synthesis in case of StrpR but not in ChlR. This is first of a kind study that shows such decoupling in ETC function in aminoglycoside antibiotic resistant populations.Addition of NOX  to C. violaceum.Although we were able to understand re-sensitization of resistant population in presence of 2-oxoadipate by synthetic lethal pair analysis, further experimental validation is critical to identify more such candidates for inducing death in Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacter species). Such approaches are scalable and show promise to identify candidate substrates for re-sensitization and understand complex emergent phenomena like antibiotic resistance.Quite recently constraints-based flux balance analysis of metabolic models is gaining momentum to understand “emergent phenomena” of antibiotic resistance ,30–32. IChromobacterium violaceum strain ATCC 12472,wild type, (C. violaceum or WT) was obtained from the American Type Culture Collection Center (ATCC), USA and routinely cultured on Luria- Broth  at 30 °C with continuous aeration in a shaker incubator set at 180 revolutions per minute (rpm). Antibiotic resistant strains ChlR and StrpR of C. violaceum were evolved in our previous study [us study  under coC. violaceum according to the manufacturer’s instructions. Briefly, stationary cells cultured in presence of different metabolites were diluted to 106 CFU/mL and stained with 10 μL of 3 mM DiOC2 (3), incubated for 30 min. Samples were analyzed using a BD LSR Fortessa SORP cell analyzer flow cytometer  with optimized settings. The membrane potential was normalized as the intensity ratio of red fluorescence  and green fluorescence . The measurements were made for Glucose, Pyruvate, 2oxoADP, Maleate and Succinate. Seven replicates were used for glucose with a standard deviation of 0.075 whereas three replicates were used for the other substrates with standard deviations of 0.14, 0.35, 0.095 and 0.145 respectively. Relative PMF was determined in test samples compared to positive control samples (with glucose) and negative control samples (+CCCP).BacLight Bacterial Membrane Potential Kit  was used to measure changes in PMF induced by antibiotic for all three population of C. violaceum ATCC 12472, GenBank accession number AE016825.1 [http://www.ncbi.nlm.nih.gov) was imported into the RAST server (http://rast.nmpdr.org/) for gene calling and annotation with subsequent manual inspection and curation. This information was used in the metabolic network reconstruction and validation processes.The complete genome sequence and annotation of C. violaceum. The protocol for reconstruction of genome-scale metabolic models (GSMM) [iDB858, was based on existing convention for naming GSMMs [s (GSMM)  was follng GSMMs , 858 repng GSMMs –17. ReacC. violaceum was built using the RAST server and Model SEED Server (http://www.theseed.org/models/) [An initial draft genome-scale reconstruction of models/) ,36. The in silico were identified through manual curation. The manually added reactions begin with “rDB” prefix in the model.The initial draft reconstruction downloaded from Model SEED, was not able to generate biomass using minimal media or a richer chemically defined media. 27 precursors of biomass not forming http://www.kegg.jp/) or to the IDs available on BiGG database (http://bigg.ucsd.edu/) to maintain acceptable and clear standards of constraint-based models [The SEED reactions and metabolites were matched with KEGG reaction IDs represented in KEGG database  Toolbox 2.0.2 [https://opencobra.github.io/). The function optimizeCbModel, in COBRA toolbox was used to simulate for growth (maximize biomass objective function) and violacein production as reported earlier [Implementation of the GSMM for ox 2.0.2  with MAT earlier  using fliDB858 was performed in part by simulating for growth and respiration on metabolites that are potential carbon and nitrogen sources. The predictions were validated using legacy (BIOLOG) substrate utilization data. Predictions of the model for simultaneous growth and violacein production on 30 substrates were validated experimentally.Validation of Chromobacterium. The constraints used were experimentally measured in our previous study [A set of constraints that define the antibiotic susceptible WT and the evolved populations (ChlR and StrpR) were used to customize the models to represent antibiotic susceptible and resistant us study  as shownC. violaceum to different environmental perturbations such as oxygen uptake, NADPH, tryptophan, ATP demand.Robustness analysis, using robustnessAnalysis was used to better understand the sensitivity of growth and violacein phenotype of FVA (set up using fluxVariability) calculates minimum and maximum flux values for each reaction in the model subject to constraints for specific objectives . DiffereA reaction representing NADH oxidase (water forming) was added to the model to delineate the role of NADH imbalance and show decoupling of electron transfer via Electron Transport Chain (ETC) and proton pumping for ATP synthesis . This reAnalysis of Pareto fronts and trade-off between ATP and NADH maintenance reactions was performed by constraining the GUR, VSR and the growth yield to experimental values and maximizing the fluxes through the generic ATPase (ATPM) and NADH oxidase reaction (NOX).In silico virulent genes are those that are essential for C. violaceum growth. Non-essential or avirulent genes and attenuated genes lower growth vis a vis wild type on deletion [Gene essentiality or lethality was predicted using the function singleGeneDeletion, . In silideletion . EpistatS1 FileiDB858.Supporting figures, tables and additional information regarding manual curation, model features and selected simulations of (PDF)Click here for additional data file.S1 TableC. violaceum, iDB858 using COBRA Toolbox as described in material and methods.Supporting information related to the simulations done using the genome scale metabolic model of (XLSX)Click here for additional data file.S1 ModelC. violaceum, iDB858 used on MATLAB platform for all the simulations reported in this manuscript.The .mat file for the genome scale model of (MAT)Click here for additional data file.


Yarrowia lipolytica, an oleaginous yeast, is a promising platform strain for production of biofuels and oleochemicals as it can accumulate a high level of lipids in response to nitrogen limitation. Accordingly, many metabolic engineering efforts have been made to develop engineered strains of Y. lipolytica with higher lipid yields. Genome-scale model of metabolism (GEM) is a powerful tool for identifying novel genetic designs for metabolic engineering. Several GEMs for Y. lipolytica have recently been developed; however, not many applications of the GEMs have been reported for actual metabolic engineering of Y. lipolytica. The major obstacle impeding the application of Y. lipolytica GEMs is the lack of proper methods for predicting phenotypes of the cells in the nitrogen-limited condition, or more specifically in the stationary phase of a batch culture.Y. lipolytica under the nitrogen-limited condition and identifying metabolic engineering strategies to improve lipid production in Y. lipolytica. Several well-characterized overexpression targets, such as diglyceride acyltransferase, acetyl-CoA carboxylase, and stearoyl-CoA desaturase, were successfully rediscovered by our eMOMA-based design method, showing the relevance of prediction results. Interestingly, the eMOMA-based design method also suggested non-intuitive knockout targets, and we experimentally validated the prediction with a mutant lacking YALI0F30745g, one of the predicted targets involved in one-carbon/methionine metabolism. The mutant accumulated 45% more lipids compared to the wild-type.In this study, we showed that environmental version of minimization of metabolic adjustment (eMOMA) can be used for predicting metabolic flux distribution of Y. lipolytica and potentially other oleaginous microorganisms.This study demonstrated that eMOMA is a powerful computational method for understanding and engineering the metabolism of The online version of this article (10.1186/s13068-019-1518-4) contains supplementary material, which is available to authorized users. Yarrowia lipolytica has drawn a great attention as a model oleaginous yeast [Y. lipolytica strains can be an efficient production platform for a variety of fuels and oleochemicals [In recent years, environmental crises caused by massive use of fossil fuels raise urgent needs for developing renewable ways to produce fuels and chemicals. One of the promising solutions is a use of heterotrophic oleaginous microorganisms to produce lipid feedstocks for biofuels and oleochemicals , 2. Produs yeast , 8. Up uhemicals .Y. lipolytica start to accumulate lipids in response to nutrient depletion. Typically, nitrogen-limited conditions are employed to produce lipids in oleaginous yeasts, and the general mechanism of how nitrogen limitation leads to lipid production had been suggested before [Oleaginous yeasts including d before . The lipd before . Then, td before . The citd before , 12. Find before . Howeverd before –16. TherEscherichia coli and Saccharomyces cerevisiae [Y. lipolytica, have recently been developed [Y. lipolytica  and existing CSOMs. Various CSOMs were tested in the two recent studies, e.g., OptGeneKnock [Systems biology provides essential tools for modern biotechnology to effectively design, build, test, and learn the engineered microbial strains , 18. Esprevisiae . In an eeveloped . The fir (iNL895  and iYL6L619_PCP ) were re, iMK735  and iYal [iYali4 , respectoduction , and iYatabolism . The fouils, see ). Brieflrevisiae , iYL619_ as KEGG  and BiGG as KEGG , and iMKrevisiae , as a screvisiae  and Mishrevisiae  exploredeneKnock  and APGCeneKnock  for TAG eneKnock  and cofaY. lipolytica is because there is still a lack of suitable constraint-based modeling methods for predicting metabolic behaviors of oleaginous yeasts. In particular, when considering a typical batch culture scenario for lipid production using oleaginous yeasts, there is no proper method for predicting flux distribution, including lipid production rate, in nitrogen-limited condition . Flux balance analysis (FBA) is the most popular constraint-based modeling method for predicting metabolic fluxes using GEMs by optimizing an evolutionary objective function [Here, we argue that the lack of successful application of GEMs for metabolic engineering of function . In genefunction . Howeverfunction , 37; howY. lipolytica under nitrogen-limited conditions, we applied eMOMA for predicting metabolic engineering strategies to improve the lipid production in Y. lipolytica. Using our eMOMA-based design method, we successfully identified both known and novel genetic intervention targets for improving the lipid production and experimentally validated the model predictions by constructing knockout strains using the recently developed CRISPR/Cas9 system.In this work, we demonstrated that minimization of metabolic adjustments (MOMA), another very popular constraint-based modeling method developed to find a flux distribution for a perturbed condition by minimizing the Euclidean distance from a reference flux distribution , can be μmax) of the cells under non-limited growth conditions. Due to the degeneracy of FBA solutions, there are infinite number of flux vectors which can support the maximum specific growth rate [We implemented eMOMA to predict metabolic fluxes of the cells in nutrient-limited conditions. The procedure of making eMOMA prediction, which consists of three optimization problems, is schematically represented in Fig. wth rate . Howeverwth rate . Thus, pwth rate , was intY. lipolytica in nitrogen-limited conditions, it was applied to a published GEM for Y. lipolytica, iMK735 [To test whether eMOMA can be used for predicting phenotypes of , iMK735 . We used, iMK735  for a noY. lipolytica physiology. Under the non-limited condition, the cells consume balanced amounts of glucose, ammonium, phosphate, sulfate, and oxygen to produce biomass. No byproduct production except for tiny amounts of zymosterol and inositol was predicted for the cells in the non-limited condition. Following the nitrogen starvation (applied by the blockage of ammonium uptake), consumption and production profiles of nutrients and metabolites, respectively, were predicted to completely change as the cells could not produce biomass anymore while still consuming the glucose. Most strikingly, eMOMA successfully predicted TAG and citrate as the major products produced by Y. lipolytica during nitrogen limitation, which is the representative characteristic of the wild-type Y. lipolytica strains. In addition, production of ergosterol was predicted for the nitrogen-limited condition as some previous studies had reported [Y. lipolytica following the nitrogen starvation, some quantitative discrepancies between the predicted and measured exchange fluxes were observed. In the previous report, it has been shown that 54% and 13.5% of the carbon utilized during the nitrogen-limited condition were converted into citrate and TAG, respectively [Y. lipolytica by just using eMOMA. This success is somewhat in accordance with the reported lack of direct regulatory controls for lipid metabolism in response to nitrogen limitation in Y. lipolytica, e.g., no significant changes in transcript levels for the genes in lipid biosynthetic pathway [Firstly, predicted changes in exchange fluxes between the non-limited and nitrogen-limited conditions  result. Recently, Wasylenko et al. have reported the metabolic flux distribution of a Y. lipolytica strain  in nitrogen-limited conditions by parallel labeling experiments [13C-MFA flux data . Note that only the fluxes for the reactions in the central metabolism were compared due to the limited coverage of 13C-MFA  even though there existed some quantitative discrepancies.To further investigate whether eMOMA can also predict intracellular fluxes of eriments . The eMOoversial . More spFA study ), cytosoussed in ), and otY. lipolytica including lipid production, we next used the method to design mutant strains for improved lipid production. Figure After confirming that eMOMA can be used for predicting metabolic phenotypes of Y. lipolytica under nitrogen-limited conditions. Toward this end, we first identified candidate reactions which can be genetically overexpressed or deleted without significantly harming cell growth (see “We employed a brute force approach to find target reactions for overexpression or knockout that may increase the lipid production in wth see “”. In resY. lipolytica by pushing and pulling metabolic fluxes toward lipid biosynthetic pathway [Y. lipolytica by a recent reverse engineering study [Y. lipolytica [n0COA), and citrate synthase (CSm), were identified as overexpression targets. Although these targets seem to be apparent and play similar roles on the production of lipids, the eMOMA prediction provides an additional aspect, i.e., the predicted yield improvements for each target. It is notable that the predicted yield improvements were not directly related to the distances from the TAG node in the metabolic pathway map or basal flux levels of the reactions. It could be thought that the eMOMA prediction reflects complexity of intertwined structures of metabolic pathways. Even though it was yet to know that the actual lipid production yields would meet the predicted tendency at this moment, the prediction was still meaningful since it could be used for deciding a priority of conducting experiments.Interestingly, several experimentally validated, well-characterized overexpression targets were successfully called by the eMOMA-based design method Table . Overexp pathway . Furtherng study . ATP:citpolytica . Along wThe remaining top ten overexpression targets, i.e., homoserine dehydrogenase (HSDxi), aspartate-semialdehyde dehydrogenase (ASADi), and aspartate kinase (ASPKi), were all involved in the threonine biosynthesis Table . At a glY. lipolytica that showed significant upregulation of urea carboxylase and arginase in nitrogen-limited conditions [For the deletion targets, reactions involved in one-carbon/methionine metabolism  and arginine metabolism  were predicted as top targets Table . In the nditions . HoweverRest of the predicted deletion targets were also quite interesting Table . DeletioY. lipolytica metabolism was considered as a design space [Y. lipolytica metabolism, the lack of ATP/NADPH-related targets in the lists is in a good agreement with the existing reports. Nevertheless, in future studies, it would be interesting to expand the search space of eMOMA-based design method, i.e., to include synthetic/heterologous pathways in the design space, and to see what kinds of new targets could be predicted.While our eMOMA-based design method successfully rediscovered many experimentally validated targets, some well-known knockout targets involved in lipid degradation, such as PEX10 (peroxisome biogenesis factor), TGL3 (lipase), and MFE1 , were not identified by the eMOMA-based design method. This is because we employed pFBA for predicting flux distribution of the wild-type strain in the non-limited growth condition. As pFBA does not allow futile cycles, zero fluxes through lipid/fatty acid degradation pathways were predicted for the wild-type cells in the non-limited condition. Subsequently, eMOMA also predicted zero fluxes through such pathways for the wild-type cells in the nitrogen-limited condition. Therefore, knockouts of reactions in such lipid/fatty acid degradation pathways were predicted to have no effects as the fluxes were already zero in both non-limited and nitrogen-limited conditions. On the other hand, top targets predicted by the eMOMA-based design method did not include the reactions directly related to cofactors such as ATP and NADPH, which are keys to lipid production. Indeed, strategies like “push and pull” showed the most pronounced effects when only the native gn space , 49. Howgn space . As the Y. lipolytica have focused primarily on lipid biosynthesis and degradation pathways [Y. lipolytica [So far, engineering efforts to improve the lipid production in pathways –54. Our polytica . In contY. lipolytica are particularly hard to manipulate using the CRISPR/Cas9 system [Three genes, YALI0F30745g, YALI0E01056g, and YALI0E07271g, which are associated with the top knockout target reactions in Table 9 system , and YALY. lipolytica.We profiled growth and lipid accumulation of the knockout mutants in a batch culture using CN75 medium and compared them to that of the wild-type strain Fig. . CN75 meY. lipolytica in nitrogen-limited conditions, which cannot be predicted by conventional FBA, could be predicted by eMOMA. We also demonstrated that eMOMA could be further applied to identify metabolic engineering strategies for improving lipid production in Y. lipolytica. Our eMOMA-based design method successfully predicted not only well-known engineering targets but also novel and non-intuitive targets. We experimentally tested some of the novel knockout targets, and deletion of YALI0F30745g in Y. lipolytica showed 1.45-fold increase in lipid accumulation compared to the wild-type strain. Altogether, eMOMA is a powerful method for identifying metabolic engineering strategies for improved lipid production in Y. lipolytica.In this study, we showed that metabolic flux distributions of There are multiple avenues of further research for broadening the applicability of eMOMA-based design method. First, although our work was limited to the batch culture scenarios, eMOMA could also be applied to chemostat scenarios  once a method for finding appropriate reference flux distribution is established for such cases. Second, even though our work was focused on the lipid production case to clearly demonstrate the effectiveness and usefulness of eMOMA-based design method, our method could further be applied for predicting metabolic engineering strategies for overproducing other chemicals if they are also produced in response to nutrient limitation. It would be very interesting if future studies could provide experimental validation of newly predicted strategies for production of other chemicals, including fatty acid-derived oleochemicals nes, and esters), terpenoids, and organic acids. Third, as more GEMs are becoming available for diverse oleaginous microorganisms, the applicability of eMOMA-based design method could be tested in other oleaginous fungi, oleaginous bacteria, and even in oleaginous algae. Lastly, expanding the search space of eMOMA-based design method, e.g., exploring the effects of multiple interventions and synthetic/heterologous pathway introduction, would be the most interesting topic for the following computational work.S is the stoichiometric matrix in which rows represent metabolites and columns represent reactions, v is the flux vector, a is the vector of lower flux bounds, b is the vector of upper flux bounds, and c is the vector of objective coefficients representing the objective function, herein maximization of biomass production. By solving this linear programming (LP) problem, a unique optimal value (fopt) for the given objective function, herein maximum specific growth rate (μmax), can be obtained although there exist a number of flux vectors which satisfy the optimality .Prior to apply eMOMA to identify flux distribution of the cells under nutrient-limited conditions, FBA was first utilized to predict flux distribution of the cells under non-limited growth conditions which will serve as a reference state for eMOMA. FBA requires an evolutionary objective function, such as maximization of biomass production, to simulate flux distribution in the cells . MathemaTo further select a particular flux vector to be used as a reference state for eMOMA, FBA with parsimonious enzyme usage  was empfopt is the optimal value of the objective function from the previous LP problem  any longer, try to reallocate metabolic resources as minimally as possible with respect to the reference state. To account for such behavior, eMOMA for nutrient-limited conditions was formulated as follows:vref is the flux vector for reference state (flux distribution for non-limited growth conditions) obtained by solving the previous pFBA problem  production, aforementioned optimization problems for FBA Eq. , pFBA E and eMOMFlux distributions for the mutant strains under nitrogen-limited conditions were calculated for each mutant by sequentially solving Eqs.  2) and  and 2) aDepending on the roles and implicated network structures of the reactions, manipulation of some reactions could exert severe damages to the cell growth. Since the fast cell growth is a prerequisite for high lipid productivities, we only sought for the reaction manipulations which can sustain specific growth rates more than 90% of that of the wild-type. In addition, by default, twofold increased fluxes were constrained for simulating overexpression mutants Eq. . HoweveriMK735 [Y. lipolytica, was used for this study. Although the quality of the model is reasonably fair, the model has many loops and lacks some important genes for the lipid production pathway which might lead to significant prediction errors for our case. Therefore, we slightly modified iMK735 to remove the loops and revise several apparent errors. The MATLAB code for revising iMK735 is provided in Additional file iMK735 , a GEM fiMK735 was used without any modifications. Even exponentially growing Y. lipolytica cells in a non-limited growth condition possess a small amount of TAG in their biomass, and such growth-associated production of TAG was modeled in the biomass equation [For all the simulations, default biomass equation  in equation . The bioequation . In summiMK735 were used for all the simulations. Following the standard [iMK735. GAM was included in the biomass equation, and NGAM was modeled using a separated ATP hydrolysis reaction (“ATPM”). Note that GAM was applied to only non-limited growth condition , while NGAM was applied to both non-limited and nutrient-limited conditions.Default ATP maintenance costs in standard , growth-https://people.ee.ethz.ch/~cohysys/cplexint.html) and Gurobi (Gurobi Optimization) were used as optimization solvers.All the simulations were performed using COBRA Toolbox v2.0 for MATLAB  and in-hEscherichia coli DH5α and Y. lipolytica Po1g ku70∆ were used in this study. E. coli DH5α was used for vector construction for genetic manipulation of Y. lipolytica. Y. lipolytica Po1g ku70∆ strain was a generous gift from Professor Matthew Wook Chang in National University of Singapore. Strains used in this study are listed in Additional file Y. lipolytica, YPD medium containing glucose 2%, peptone 2%, and yeast extract 1% was used. Desired genotype of Y. lipolytica was selected or enriched in SD media containing glucose 2%, Yeast Nitrogen Base without amino acids 6.8 g/L, and 430 mg/L of amino acids and nucleotide mixture without appropriate amino acids for selection. CN75 medium, a minimal medium to induce lipid accumulation in Y. lipolytica, was composed of glucose 4%, ammonium sulfate 1 g/L, and 1.7 g/L of Yeast Nitrogen Base without ammonium sulfate and amino acids. To measure growth and lipid accumulation of the knockout mutants in CN75 medium, the cells were first inoculated in the SD medium for seed culture and grown for 2 days at 30 °C. Then, the inoculums from the seed culture washed with CN75 medium once were added to 50 mL of CN75 medium in 250 mL baffled flask to give an initial OD600 = 0.1. Flask culture was performed for 3 days. All the experiments were performed in biological duplicates.For non-selective cultivation of Y. lipolytica to construct the knockout mutants more easily and rapidly. We used Y. lipolytica Po1g ku70∆ strain to avoid non-homologous end joining [Y. lipolytica, gRNA scaffold, and auxotrophic marker were purchased from Addgene [https://www.atum.bio/eCommerce/cas9/input) and cloned into pCRISPRyl. Primers used in this study are listed in Additional file CRISPR/Cas9 system was applied to  joining  and refe Addgene . Then, sY. lipolytica cells. Cells and DNAs were mixed with a buffer containing 45% of PEG 4000, 100 mM of dithiothreitol, 0.1 M of lithium acetate pH 6.0, and 0.2 μg/μL of single strand carrier DNA purchased from ThermoFisher Scientific. The mixture was incubated in 37 °C water bath for 1 h and plated on selective agar plates.Constructed plasmids for gene deletion and relevant editing templates for HR were transformed into Y. lipolytica was described elsewhere. Lipids accumulated in Y. lipolytica were first transesterificated into fatty acid methyl esters (FAMEs) via acid-catalyzed methanolysis [Quantification of neutral lipids in anolysis . In shorQuantification of the extracted FAMEs was performed using Trace GC Ultra system coupled to an ion trap mass detector ITQ 1100 . The transesterificated samples were analyzed using a non-polar capillary column  and a linear temperature gradient . Standard curves for each FAME were obtained using analytic standards purchased from Sigma-Aldrich Chemical Co. .Additional file 1: Methods. MATLAB codes for revising metabolic model of Y. lipolytica Table S1. Comparison of eMOMA-predicted fluxes and 13C-MFA fluxes Table S2. List of candidate reactions for overexpression and knockout Table S3. Full list of predicted overexpression targets for increasing lipid production by more than 10% Table S4. List of strains and primers used in this study.