Microorganisms produce and secrete many primary and secondary metabolites to the surrounding environment during their growth. Therefore, extracellular metabolites provide important information about the changes in microbial metabolism due to different environmental cues. The determination of these metabolites is also comparatively easier than the extraction and analysis of intracellular metabolites as there is no need for cell rupture. Many analytical methods are already available and have been used for the analysis of extracellular metabolites from microorganisms over the last two decades. Here, we review the applications and benefits of extracellular metabolite analysis. We also discuss different sample preparation protocols available in the literature for both types  of extracellular microbial metabolites. Lastly, we evaluate the authenticity of using extracellular metabolomics data in the metabolic modelling of different industrially important microorganisms. Extracellular metabolomics is the study of low molecular weight extracellular metabolites that are secreted by microbial cells into their environment, namely the culture media. The entire complement of these metabolites is often referred to as the exometabolome. It includes all of the metabolites secreted outside the microbial cell, as well as those components of the microbial culture media that are found in the supernatant .Analysis of the exometabolome yields information about microbial activities under different culture conditions which, coupled with the intracellular metabolic profile, provides a comprehensive overview of microbial metabolism. There are some advantages of extracellular metabolite analysis (metabolic footprinting) over the analysis of intracellular metabolites (metabolic fingerprinting). The separation of extracellular metabolites from microbial cells and their intracellular metabolites can be achieved by simple techniques such as centrifugation and filtration, while the extraction of intracellular metabolites from microbial cells is a complex process ,3. SamplExtracellular metabolites are mainly produced as by-products of the metabolic activities of microorganisms growing in a specific environment. There are various environmental factors which can affect the uptake and secretion of metabolites from and into their environment  such as temperature, pH, the concentration of nutrients, and others. Consequently, the level of extracellular metabolites can be easily modified by changing any one, or more, of these factors . ExometaMetabolic footprint analysis provides valuable information about the metabolism of different microorganisms that change in response to different environmental conditions. Therefore, this approach has been extensively applied in different areas, such as bioprocess monitoring, bioremediation, biomarker discovery, and functional genomics. Due to the rapid development of different technical platforms, the popularity of extracellular metabolite analysis has increased considerably in the last ten years. In the near future, analysis of extracellular metabolites will provide more substantial biological information because of the rapid advancement and accessibility of a wide range of different analytical approaches.The availability of different analytical tools and high-throughput methods has made extracellular metabolite analysis an invaluable technique for monitoring bioprocesses. These technologies have been shown to be useful for the quality control of fermentation processes since they enable the monitoring of changes in metabolite levels during fermentation ,8. Metab2 and H2O) or producing hazardous and more recalcitrant compounds [In addition to monitoring bioprocesses, metabolic footprint analysis has also been used to monitor and assess the mineralization process of xenobiotic compounds , both in the environment  and in tompounds . Potentiompounds ,17.Fusarium oxysporum. They identified extracellular organic and amino acids, and found that the activation of the GABA shunt caused the inhibition of the fungus’ Kreb’s cycle. Using both metabolic footprinting and fingerprinting, they described a novel fungal metabolic pathway (Phosphoketolase pathway) involved in xylose metabolism [Besides the usefulness of extracellular metabolomics in important areas like bioprocess and bioremediation, the integration of metabolic footprinting with other “omics”  has also been undertaken successfully. These integrated approaches were applied efficiently for the identification and characterization of unknown genes responsible for the production of important enzymes involved in expedient and novel pathways. For instance, there is currently great interest in the industrial production of ethanol (biofuel) from agricultural waste ,19,20. Ttabolism ,23. Thertabolism ,25,26.Escherichia coli tryptophan mutants) have also been differentiated after analyzing the exometabolome [Clostridium proteoclasticum B316T has been shown by analyzing extracellular metabolites [Metabolic footprinting has also gained popularity in microbial functional genomics because of its utility in discriminating between microbial strains. It has been used, for instance, to discriminate between yeast strains by identifying extracellular metabolites related to insertion and deletion mutations ,28. In atabolome . This apabolites .Pseudomonas aeruginosa can cause a chronic lung infection by producing QS molecules that enable this microorganism to form biofilm and develop a resistance to antibiotics [Furthermore, analysis of extracellular metabolites that are secreted by the microorganisms into the culture media allows the identification of quorum sensing (QS) molecules,  ,31. Thesibiotics . Microbiibiotics .Given that metabolic footprinting has already been successfully applied to various types of biotechnological research, this approach has already proved to be very powerful in unraveling innovative and novel information ,34,35,36Recently, dynamic or time-resolved metabolic footprinting has gained considerable interest from the scientific community because this approach allows a better understanding of metabolites secreted by different microbial cells at different time intervals due to the changes in environmental conditions ,41. TradThe changes in growth media due to the presence of contaminants can also be easily determined by analyzing samples at different time intervals rather than at a single point. For example, Sue et al.  reportedBurkholderia cepacia complex. They also employed a similar approach to determine the differences between Pseudomonas aeruginosa wild type and its mutant (mucA22), and identified metabolites associated with osmotic tolerance  that caused the main difference between wild-type and mutant strains [The main benefit of the dynamic or time-resolved metabolic footprinting approach is the ability to capture the changes in the metabolism of microorganisms with different growth rates . Therefore, it is possible to discriminate between mutants and also among the same microbial species. Behrends et al.  successf strains .The data analysis platform for handling large datasets obtained from dynamic or time-resolved metabolic footprinting has also been updated in recent years ,44,45. FSample preparation is a crucial part of any experimental procedure. In metabolomic analyses the first, and perhaps most critical, step is quenching to halt any biochemical reactions beyond the time of sampling. The microbial culture is then separated from the cells by centrifugation or filtration . The nex5–106 C.F.U per mL are usually recommended for inoculation during extracellular metabolite analysis [Prior to performing experiments, several factors need to be considered carefully. Especially, the numbers of inoculated cells relative to culture medium volume is particularly of interest so that metabolites are secreted into the surrounding environment in a detectable amount. Microbial cells in a concentration of 10analysis ,48. Moreanalysis .Extracellular metabolites can be present in solution or in the gas-phase . The sam(a)liquid-liquid separation where metabolites of interest are separated into an immiscible solvent,(b)using a column or solid-phase matrix to trap the metabolites, and(c)selective solubilization, which is the complete evaporation of the solvent to concentrate the sample and the metabolites are then dissolved with suitable solvents.Extracellular metabolites are present in the microbial culture media. The composition of liquid media and the possible presence of interferences (matrix), such as a high amount of salts, sugars, proteins, lipids, and sometimes even water, can cause problems with the operation of analytical equipment. As a result, metabolites that are present in low concentrations may not be detected in the biological samples. Therefore, problems caused by the sample matrix need to be identified and resolved to ensure the acquisition of informative and accurate extracellular metabolite profiles . There aThe use of solvents in the liquid-liquid separation of metabolites from extracellular media is very laborious and time consuming, making it unpopular for metabolite profiling. This approach is also known to result in incomplete phase separations and lower recovery rates. In addition, this type of separation also requires the use of large amounts of glassware and organic solvents. A better separation of metabolites, however, is achieved via solid-phase extraction to trap metabolites of interest  and seleSolid-phase extraction (SPE) is a sample separation and extraction method, which causes the exhaustive removal of metabolites from a liquid sample resulting in targeted analytes being retained on a solid sorbent . SPE is Different types of SPE sorbent materials, such as silica, alkylated silica , carbon-based sorbents, ion exchange materials, polymer materials, and restricted access materials (RAM) are commercially available for different types of metabolite extraction. Mixed-mode sorbents are a newer development and are based on multiple retention mechanisms due to incorporating diverse ligands in the same sorbent .The SPE cartridge, or stationary phase, is contained in a glass or plastic column above a frit or glass wool. The column has a frit on the top and there is a stopcock that controls the flow of solvent in the column. The cartridges are placed on a vacuum manifold which is used to control the solvent flow rate through the cartridge. Collection tubes are placed under the cartridge to collect the waste liquid after washing the column. During elution, clean tubes replace those waste tubes to collect the final sample containing the metabolites of interest . The traThree different SPE stationary phases, such as normal, reversed, and ion-exchange, are available with SPE cartridges and disks. These stationary phases are mainly silica-based and commonly used in the preparation of samples for metabolomics analysis, allowing the separation of metabolites according to their chemical properties .● Normal PhaseA non-polar matrix and polar stationary phase are used to extract non-polar analytes. The retention of analytes depends on chemical interactions  between functional groups of analytes and sorbents. The trapped analytes are eluted by a more polar solvent which is able to break up the binding mechanism.● Reversed PhaseReversed phase SPE has a mobile phase with a polar or moderately polar matrix and a non-polar stationary phase. This non-polar stationary phase is derivatized with hydrocarbon chains that allow the retention of non-polar metabolites because of the hydrophobic effect. Non-polar forces involved in this phase are known as van der Wals or dispersion forces. A non-polar solvent is also used to elute the analytes.● Ion-Exchange PhaseMetabolites which are charged while in solution can be extracted by using an ion-exchange phase. The retention of analytes is due to the electrostatic attraction of the charged functional group of the metabolite to the charged group of the matrix. A solvent with a pH level that neutralizes these charged groups is used to elute the analytes.SPE is a sensitive method that enables the simultaneous analysis of a number of metabolites by limiting possible ion suppression effects . The maiSolid-phase microextraction (SPME) is a portable small sample preparation technique invented by Pawliszyn and colleagues which is both fast and simple ,58,59. TThe first SPME device consisted of coated fibers in a micro-syringe referred to as a fiber SPME. A polymer-coated fused-silica fiber was exposed to a sample for a predetermined time until equilibrium was reached. The fiber was then removed from the solution to desorb the analytes into the injector of an analytical instrument . DiffereEven though the use of SPME allows the separation of many metabolites, this technique has both advantages and disadvantages. For instance, it is resource efficient in that it does not require solvent for the elution of analytes and the fibers are reusable. Furthermore, SPME is portable so that it can be used in the field, as well as in the laboratory. However, the coated fibers are expensive, fragile, and have a limited extraction capacity, resulting in poor sensitivity ,59. AlthVolatile compounds, or gaseous metabolites, present in extracellular samples provide precious information on different properties of microorganisms and/or their phenotypes and their metabolic pathways. Metabolites already in gas phase are easy to analyze by GC-MS and require no further derivatization . Thus, tSeveral methods have been developed in recent years to trap and concentrate volatile compounds in extracellular samples. SPME methods using adsorptive materials, such as porous carbon, or sorptive polymers, are often used to analyze volatile compounds. Headspace analysis coupled with SPME is another alternative technique employed to analyze these compounds.Direct headspace analysis where volatile compounds are collected into a syringe and analyzed by GC.Headspace SPME (HS-SPME) which is a coupled technique in which the gas sample in the headspace is trapped on the SPME fiber .SPME is considered a promising sample preparation technique for the extraction of volatile compounds from microorganisms because of its ability to separate metabolites with a wide range of properties (both in liquid and solid samples) at a very low concentration (ppt to ppm) . SPME anIn headspace analysis, a liquid sample is collected and heated to vaporize in the headspace. Both manual and automated systems can be applied; however, automated systems show better reproducibility . The heaSample concentration is an important aspect of metabolome analysis because metabolites are diluted in both intracellular and extracellular samples. Concentration of the samples is necessary before analysis by analytical tools to improve the limit of detections ,71. If tFreeze-drying is a widely used sample concentration method in metabolomics where samples are immediately frozen and then dried by sublimation to remove all of the frozen solvents. Freeze-drying is considered a non-destructive sample concentration and dehydration process that avoids the thermal degradation of compounds. A variety of manual and completely automated freeze-dryers are commercially available these days, including facilities to dry samples under a very low temperature (–65 °C). Some “smart” freeze-drying instruments, for example, a manometric temperature measurement (MTM), measure the metabolite temperature by rapidly isolating the freeze-drying chamber from the condenser while also monitoring the pressure . Recent The nature of the metabolites and the sample matrix need to be considered carefully while concentrating the metabolomics samples. Moreover, appropriate precautions also need to be followed to overcome problems, e.g., the thermal and oxidative degradation of labile metabolites. Factors such as the solution pH and sample matrix are very important and these may cause problems while freeze-drying the samples. For instance, extracellular samples with a high sugar concentration are almost impossible to dry completely, leaving only sticky undried samples. To avoid this, such samples must be diluted prior to freeze-drying. Moreover, samples containing a high volume of organic solvent cannot be frozen and must have water added to increase the water:solvent ratio. This then enables the sample to be frozen but also increases the drying time. After freeze-drying, another issue is the resuspension of samples because metabolite losses may occur due to the incomplete recovery of the dried samples ,75. HoweThe vaccum-drying procedure using a speed-vac instrument makes use of a combination of the centrifugal force, heat, and vacuum to remove moisture from a given sample. This process dries a sample through evaporation, mainly by converting the liquid to vapor. It is mostly used to concentrate a small amount of sample to complete dryness. Therefore, vacuum-drying, being faster and comparatively less aggressive than freeze-drying, is preferable in some cases . For insOnce extracellular samples have been extracted and concentrated, the next step is to store them under appropriate conditions prior to analysis. To avoid any unwanted changes during the storage, necessary precautions need to be undertaken. Storage conditions and time are, however, dependent on the types and stability of metabolites. Even though metabolomic samples are quenched before the separation and extraction of extracellular metabolites, it is better to ensure that no chemical reaction is taking place during the storage. Therefore, it is highly recommended that the extracellular samples must be stored in the dark and at a very low temperatures  to avoid the degradation caused by light and heat. This way, it is possible to retain the original properties of metabolites.Some metabolites can lose their functionality during storage at low temperature and can be oxidized easily, and this may completely alter their characteristics. To protect them, they must be kept under vacuum . Stable The genome-scale reconstruction of entire organisms and modelling of their physiology in a predictive manner is a comparatively new approach and has been successfully used in systems metabolic engineering to design microbial cell factories ,80,81,82Recent developments in profiling extracellular metabolites are now allowing us to gather a large amount of information on microbial systems. These extracellular metabolites are either present in the culture media or secreted by the microorganisms during growth due to experimental perturbations. Therefore, these data contain valuable information about the cell metabolism and how the environment can affect the utilization and production of various metabolites, indicating the alteration of intracellular status. The generation of intracellular metabolites data is comparatively troublesome, mainly because of the need to rupture the cell in order to release the metabolites ,26,86. TSaccharomyces cerevisiae iMM904 to determine how the variation in extracellular metabolite levels is associated with changes in intracellular metabolites fluxes [The integration of extracellular metabolomics data into genome-scale models is now allowing the prediction of the intracellular status of microorganisms. For instance, Cakir et al. (2007) incorporated small-scale extracellular metabolomics data with a genome-scale metabolic model of yeast to predict the oxygen consumption and ethanol production ability of mutant strains with respiratory deficiencies . A few ys fluxes . They alA comprehensive and detailed protocol entitled “MetaboTools” is now available for integrating extracellular metabolomics data obtained from microorganisms, plants, and animals . This toThe analysis of extracellular metabolites from a microbial culture provides crucial information about the intracellular status of a microbial system that occurs in response to the surrounding environment. Therefore, this approach has already been used widely in both fundamental and applied research ,89,90,91


Dissolved oxygen tension (DOT) is hardly constant and homogenously distributed in a bioreactor, which can have a negative impact in the metabolism and product synthesis. However, the effects of DOT on plasmid DNA (pDNA) production and quality have not been thoroughly investigated. In the present study, the effects of aerobic (DOT ≥30% air sat.), microaerobic (constant DOT = 3% air sat.) and oscillatory DOT (from 0 to 100% air sat.) conditions on pDNA production, quality and host performance were characterized.Microaerobic conditions had little effect on pDNA production, supercoiled fraction and sequence fidelity. By contrast, oscillatory DOT caused a 22% decrease in pDNA production compared with aerobic cultures. Although in aerobic cultures the pDNA supercoiled fraction was 98%, it decreased to 80% under heterogeneous DOT conditions. The different oxygen availabilities had no effect on the fidelity of the produced pDNA. The estimated metabolic fluxes indicated substantial differences at the level of the pentose phosphate pathway and TCA cycle under different conditions. Cyclic changes in fermentative pathway fluxes, as well as fast shifts in the fluxes through cytochromes, were also estimated. Model-based genetic modifications that can potentially improve the process performance are suggested.DOT heterogeneities strongly affected cell performance, pDNA production and topology. This should be considered when operating or scaling-up a bioreactor with deficient mixing. Constant microaerobic conditions affected the bacterial metabolism but not the amount or quality of pDNA. Therefore, pDNA production in microaerobic cultures may be an alternative for bioreactor operation at higher oxygen transfer rates.The online version of this article (doi:10.1186/s12896-017-0378-x) contains supplementary material, which is available to authorized users. E. coli, causing a metabolic rearrangement from aerobic to fermentative metabolism and leading to the accumulation of partially oxidized byproducts like organic acids and ethanol. The production of byproducts results in a decrease in the growth rate and yield of products and biomass [E. coli from aerobic to anaerobic conditions, and the supercoiling was maximum after 20 min of the shift. This was attributed to a decrease in the DNA relaxing activity of topoisomerase I and the constant activity of gyrase after the shift to anaerobiosis.The production of plasmid DNA (pDNA) of sufficient quality for transfection to cell cultures and therapeutic purposes requires efficient and robust culture performance. Poor mass transfer can result in oxygen limitations of cultures in shake flasks –3, singl biomass . However biomass . Namdev  biomass  reported biomass . The eff biomass , while t biomass  and tran biomass . Cortass biomass  showed tE. coli and pDNA production was studied. Fully aerobic (DOT ≥30% air sat.) and microaerobic (DOT = 3% air sat.) conditions were used. Heterogeneous DOT conditions were simulated by the cyclic variation of the stirring speed, which resulted in DOT oscillations ranging from 100 to 0% air sat. during batch cultures. To obtain insight into the metabolic effect of the growth conditions and to better understand the cellular response, flux balance analysis was performed. The pDNA supercoiled fraction (SCF) was analyzed by agarose gels and microfluidics chips. To assess the fidelity, the produced plasmid was sequenced using Illumina Technologies.The above mentioned reports focused on one-step shift anaerobiosis or constant microaerobic conditions, which are not representative of large-scale cultures. In the present work, the effect of constant and oscillating DOT on the growth of Escherichia coli W3110 recA−. In such a strain, the recA gene was interrupted by the cat (chloramphenicol acetyl-transferase) gene in our laboratory according to the methodology described by Datsenko and Wanner [GTGTAGGCTGGAGCTGCTTC, and the reverse primer, CAGAACATATTGACTATCCGGTATTACCCGGCATGACAGGAGTAAAAATGATGGGAATTAGCCATGGTCC. The underlined and non-underlined regions are the homologous sequences to the pKD3 plasmid and recA gene, respectively. The interruption of the recA gene was confirmed by polymerase chain reaction PCR. E. coli W3110 recA− was probed to double the SCF compared with wild-type E. coli W3110 (data not shown). The plasmid pVAX1  was used as a pDNA vaccine-model in our study due to its widespread use in DNA vaccine development. It is a 3-kb high-copy number vector that confers kanamycin resistance for the selection in E. coli.The strain used in this study was d Wanner . The chl2HPO4, 17; KH2PO4, 5.3; (NH4)2SO4, 2.5; NH4Cl, 1.0; Citrate-Na3·2H2O, 2; MgSO4·7H2O, 1.0; Thiamine-HCl, 0.01; and trace element solution, 2 mL/L; and 50 μg/mL kanamycin sulfate. The trace element solution composition (in g/L) was ZnCl2, 10.5; EDTA, 5.5; CoSO4·7H2O, 1.5; MnSO4·H2O, 6.4; CuSO4·5H2O, 1.1; H3BO3, 1.5; Na2MoO4·2H2O, 1; FeCl3·6H2O, 51.4; and Cit-H·H2O, 39.9. The cultures were carried out in 500 mL of medium in a 1-L Biostat A Plus stirred-tank bioreactor  at 37 °C. The pH was set at 7.2 and was controlled by the addition of 15% NH4OH. DOT was measured using a polarographic sensor . The sensor was calibrated by flowing pure N2 (for 0% air sat.) or air (for 100% air sat.) at 1 vvm. The DOT sensor was cleaned and filled with fresh electrolyte  previous to each culture. DOT was controlled at 3 or 30% air sat. by a PI controller in the agitation cascade mode  using MFCS/DA software . For oscillated DOT cultures, the stirrer speed was shifted from 100 to 1200 rpm every 10 min. Air was supplied at 1 vvm for aerobic and oscillated cultures and at 0.25 vvm for microaerobic cultures. Off-gas composition was monitored on-line through a BlueInOne Ferm  gas analyzer. Three independent cultures under each condition were performed.The medium composition (in g/L) was as follows: glucose, 10; K2SO4, and a UV detector set at 210 nm.The biomass concentration was determined as the dry cell weight. Extracellular metabolites were quantified from filtered (0.2 μm cellulose acetate membranes) supernatants. Glucose and ethanol were quantified in a YSI 2700 biochemistry analyzer . Organic acids were analyzed by HPLC using a Bio-Rad Aminex HPX-87H column  at 50 °C and 0.4 mL/min of 5 mM HOTR, oxygen transfer rate (mmol/L/h);CER, carbon dioxide volumetric production rate (mmol/L/h);p, absolute pressure of the gaseous stream, in bar;F, volumetric flow rate of the gaseous stream (L/h);−1 mol−1);R, ideal gas constant ;T, temperature of the gaseous stream (K);RI, inert ratio;i and o subscripts denote at inlet and outlet, respectively.From the off-gas composition data, OTR and CTR were calculated as follows:qO2 and qCO2 were determined by plotting OTR and CER, respectively, against the biomass concentration (X), and obtaining the slope from the line of best fit by the least squares method. Only data from the period where DOT was constant was used.The specific rates For the oscillated cultures, where such conditions were not met, the global specific uptake rates were calculated as follows:For all cases, RQ was calculated as the ratio,Numerical integrations were computed by SigmaPlot 12.5 Area Below Curves Macro.2 and H2 seems not to be a plausible reaction because the mineral media was devoid of selenium and nickel, which are required for the catalytic activity of FHL [The flux distribution in the metabolic network was calculated based on a linear programming algorithm, using the specific uptake rates and specific production rates as inputs for the calculations  . The nety of FHL .qs). Simulations to maximize the biomass by changing qS fluxes were run. The results are provided as Additional files.Sensitivity analysis was performed to evaluate the biomass function response to changes in the two measured input fluxes , and recovered in 70 μL of EB buffer at 70 °C. Such procedure enabled to maximize the amount of pDNA extracted from cells (data not shown), whereas SCF is not expected to be influenced, as indicated by the manufacturer. The extracted pDNA was quantified in a Nanodrop 2000 system. The SCF was determined from the image analysis of 0.8% agarose gels pre-stained with SYBR green safe . Additionally, pDNA samples were analyzed by chip-electrophoresis in a Bioanalyzer 2100 system  using the Agilent DNA 7500 kit. Prior to the run, the samples were concentrated by lyophilization (500–900 ng/μL) to obtain fluorescence signals within the reading capabilities of the equipment. pDNA samples from the master cell bank and the different production conditions were sequenced. pDNA sequencing and assembly were performed using the Genome Analyzer II  and Velvet 1.2.0 program, respectively. The resulting assembled sequences were aligned with the reported reference sequence of the pVAX1 plasmid  using the BLASTN 2.6.1+ suite  , as seen in Table 2 uptake  during the cultures are shown in Fig. YP/X was 30% higher under constant oxygen limitation and was similar to the oscillated case. Neither the pDNA-specific production rate (qP) nor pDNA global productivity (QP) was significantly influenced by oxygen limitation μ . In this approach, the bounds needed for the metabolic model were calculated solving a system of ordinary differential equations that accounted for the concentration profile of the extracellular metabolites , 20. The. μ Fig. , oscilla. μ Fig.  were outude Fig. .Fig. 5Esr5p) is defined as the ratio of the flux thorough the ribose-5-phosphate isomerase to the flux to the biomass objective functions. Eliminating the flux through the pyruvate dehydrogenase (PDH) resulted in a 4.84-fold increase of Yr5p and no change on the specific growth rate compared with the original background. Higher increases of Yr5p are predicted if LDH (lactate dehydrogenase), isocitrate lyase (ICL) genes or malate synthase (MALS) are combined with the PDH mutation  and wereviously . On the mentclass2pt{minimE. coli W3110 and similar growth conditions [Yp/x were greater under microaerobic than under aerobic conditions. This effect on Yp/x coincides with previous reports, which attributed such an increase to a reduction in the growth rate under microaerobic conditions [The estimated metabolic fluxes under microaerobic conditions were consistent with those previously reported using nditions . The estnditions . Therefonditions . Furthernditions , renderiquasi) steady-state under oscillating DOT, we used exhaust gas monitoring to estimate O2 and CO2 fluxes to obtain feasible solutions for maximizing biomass at each time. The results of this time-point approach yielded reasonable changes in the fermentation metabolite production rates. As expected, byproducts were low at periods of high O2 flux and vice versa. Acetate flux was less accurately predicted, and formate formation was inconsistent because almost all times were different from zero. Fluxes through the cytochromes bo and bd were also evaluated. Cytochrome bo responded fairly well to O2 flux changes, but not cytochrome bd, which behaved more like an extra supply rather than a backup for respiratory activity that was expected to switch on once cytochrome bo flux was low [bo and pyruvate formate lyase fluxes . Therefmitation .E. coli K-12 derivative strains and plasmids. Hopkins and coworkers [E. coli AB1157 strain to replicate an RK6 replicon plasmid. Namdev and coworkers [E. coli DH5α strain, a highly mutated background commonly used for pDNA amplification, to replicate a pUC replicon plasmid. In our work, we employed a much less mutated background to also amplify a pUC replicon plasmid. This opens the question of whether such discrepancies have any relation to the plasmid-host interactions.The production of pDNA was nearly unaffected by a constant low DOT. This opens the possibility for the microaerobic production of pDNA, which may be viable if strains with a lower accumulation of by-products and increased respiratory capacity are available . By contoworkers  used theoworkers  used theThe pDNA topology was strongly affected by DOT oscillations. In the model strain, the degree of pDNA supercoiling is mainly determined by the activities of topoisomerase I (an IA type topoisomerase) and gyrase (a IIA topoisomerase) , 31. BecThe impact of the process conditions on pDNA sequence, which can be a major issue, is still poorly documented. For instance, a recent study reported the contamination by 1.3 kb IS2 in a pDNA vaccine candidate, with pVAX1 as the backbone, between the kanamycin resistance cassette and BGH polyA signal . The frer5p  and thus the synthesis of ribose-5-phosphate, as evidenced by the Y5p Table . This co plasmid . TogetheE. coli to a predominantly fermentative mode. This was more evident in the case of oscillatory DOT. However, microaerobic conditions had little effect on pDNA production and quality. Therefore, the microaerobic production of pDNA may be a viable alternative, provided that engineered cells are available with a better metabolic performance. The estimated TCA and pentose phosphate pathway fluxes can help to identify cell engineering targets for such a task. Our results suggest that DOT heterogeneities may increase the topological heterogeneity pDNA and that oxygen availability does not influence pDNA sequence. This should be considered during bioreactor operation at several scales and for better strain and vector design.Microaerobic conditions shifted the metabolism of μ - Specific growth rate (h−1)X/S - Biomass on glucose yield (g/g)YACE/S - Acetate on glucose yield (g/g)YFOR/S - Formate on glucose yield (g/g)YLAC/S - Lactate on glucose yield (g/g)YSUC/S - Succinate on glucose yield (g/g)YETH/S - Ethanol on glucose yield (g/g)YO2/S - Oxygen on glucose yield (mmol/g)YCO2/S - Carbon dioxide on glucose yield (mmol/g)YqS - Glucose specific uptake rate (g/g h)qACE - Acetate specific production rate (g/g h)qFOR - Formate specific production rate (g/g h)qLAC - Lactate specific production rate (g/g h)qSUC - Succinate specific production rate (g/g h)qETH - Ethanol specific production rate (g/g h)OTR - Volumetric oxygen transfer rate (mmol/L h)CTR - Volumetric carbon dioxide transfer rate (mmol/L h)RQ - Respiratory quotient (mmol/mmol)CB - Carbon balance (C-mol/C-mol)DRB - Degree of reduction balance (e/C-mol)P - Plasmid DNA titer (mg/L)YP/X - pDNA specific yield (mg/g)qP - pDNA productivity (mg/g h)P - pDNA global productivity (mg/g h)QSCF - pDNA supercoiled fraction (%)p - Absolute pressure of the gaseous stream (bar)F - Volumetric flow rate of the gaseous stream (L/h)−1 mol−1)R - Ideal gas constant (0.0821 bar L KVL - Liquid volume (L)T - Temperature of the gaseous stream (K)RI - Inert ratio (mmol/mmol)i - Inleto - OutletX - Biomass concentration (gCDW/L)DOT - Dissolved oxygen tension (%)FBA - Flux balance analysisdFBA - Dynamic flux balance analysisCMV - CytomegalovirusAdditional file 1:μ under the different oxygen availabilities. (TIFF 512 kb)Prediction of Additional file 2:Base changes found in pVAX1. (DOCX 16 kb)Additional file 3:Response surfaces for the sensitivity analysis. (TIFF 12468 kb)


Saccharomyces cerevisiae. Notably, only uFBA predicts that stored red blood cells metabolize TCA intermediates to regenerate important cofactors, such as ATP, NADH, and NADPH. These pathway usage predictions were subsequently validated through 13C isotopic labeling and metabolic flux analysis in stored red blood cells. Utilizing time-course metabolomics data, uFBA provides an accurate method to predict metabolic physiology at the cellular scale for dynamic systems.The increasing availability of metabolomics data necessitates novel methods for deeper data analysis and interpretation. We present a flux balance analysis method that allows for the computation of dynamic intracellular metabolic changes at the cellular scale through integration of time-course absolute quantitative metabolomics. This approach, termed “unsteady-state flux balance analysis” (uFBA), is applied to four cellular systems: three dynamic and one steady-state as a negative control. uFBA and FBA predictions are contrasted, and uFBA is found to be more accurate in predicting dynamic metabolic flux states for red blood cells, platelets, and  In recent years, the availability and use of metabolite profiling has substantially increased, allowing for a functional readout of the multitude of influences on cellular biochemistryOne advantage of using metabolomics data is that high-quality, mechanistic models of metabolism are available68Saccharomyces cerevisiae during anaerobic batch fermentation and carbon starvation. In addition, one classical example of a static system was modeled: Escherichia coli during steady-state exponential growth. We find that for the dynamic systems, inclusion of intracellular metabolomics with uFBA provides different and more accurate predictions than FBA. In particular, uFBA predictions for RBC were experimentally validated with isotopic metabolic flux analysis. For the platelet and yeast systems, experimental data from the literature was used to benchmark the modeling results. Finally, the static E. coli system served as a negative control, with uFBA and FBA displaying similar predictions.In this study, we present unsteady-state flux balance analysis (uFBA), a constraint-based modeling method and workflow that integrates time-course metabolomics data to predict metabolic flux states for dynamic systems. uFBA and steady-state FBA (henceforth referred to simply as FBA) models were constructed and compared for three dynamic systems: stored human red blood cells (RBCs), stored human platelets, and The uFBA workflow integrates time-course absolute quantitative metabolomics data with a constraint-based model to predict metabolic flux states. Time-course metabolomics data is often non-linear. The first step of the workflow discretizes non-linear metabolite time profiles into time intervals of linearized metabolic states for piecewise simulation, resulting in a separate model for each metabolic state . PrincipFor each time interval, a parameterized model is constructed by (1) determining the rate of change of measured metabolites using linear regression, (2) integrating the calculated rates of change with the constraint-based model, (3) treating the model as a closed system, and (4) reconciling data measurement error and incompleteness through a metabolite node relaxation algorithm to produce a functional model.The final two steps are different than traditional FBA. uFBA is a data driven approach and aims to make flux predictions solely from time-course metabolomics data. uFBA only allows changes to metabolite levels, including extracellular metabolites for exchange, if the metabolite is measured to be significantly increasing or decreasing in the extracellular (exo) or intracellular (endo) metabolomics data. In principle, if all metabolites are accurately measured over time, the model should simulate. However, due to the experimental infeasibility of data completeness , additional metabolites will need to accumulate or deplete for proper simulation. To predict which unmeasured metabolites are changing, we developed a relaxation algorithm that makes the model simulation feasible. After all exchange reactions are removed , the metabolite node relaxation algorithm determines the minimum number of metabolites that need to deviate from steady-state for a feasible model. The algorithm and its benchmarking are detailed in the Methods and Once the uFBA model is constructed, most constraint-based modeling analyses can be used, including the maximization or minimization of an objective, flux variability analysis (FVA), and candidate flux sampling. For this study, we focused on Markov chain Monte Carlo (MCMC) samplingSaccharomyces cerevisiae during anaerobic batch fermentation and carbon starvation, and (4) Escherichia coli during steady-state exponential growth as a negative control. These cases were chosen because they represent diverse systems in terms of physiological dynamics, metabolic network complexity, cell density, data coverage, and timescales  human red blood cells (RBCs) stored up to 45 days at 4 °C; (2) human platelets stored up to 10 days at 22 °C; (3) two strains of mescales .S. cerevisiae during mixed glucose/xylose fermentation . We applied FVA to each state of each test case to determine the flux range for each metabolic reaction (flux range = maximum flux − minimum flux). The ratio of the feasible flux ranges of uFBA and FBA are shown . In the After a global comparison of uFBA and FBA, we focused on key differences in reaction flux predictions that would have consequences on biological interpretation on metabolic physiology by those investigating the metabolomics data.eq of malate dehydrogenase (Keq = 2.1 × 105) heavily favors metabolite flow in that direction. However, through intracellular metabolite profiling, we discovered that RBCs have a high concentration of intracellular malate (>1 mM). With this additional information, uFBA predicts that the secretion of malate and fumarate are due to the depletion of the large intracellular malate pool . Further, uFBA predicts the shuttling of the majority of the intracellular malate and citrate into lower glycolysis through oxaloacetate, as well as production of glutamate from citrate . We compared how well the use of uFBA or FBA fluxes were able to match the isotopic labeling pattern of intracellular metabolites that were detected to be labeled and for which we had absolute quantitation. uFBA produced quantitatively more accurate predictions ) than FBA for the isotopic labeling pattern . Alpha-ketoglutarate can then form glutamate, which was found to have increasing percentages of isotopic labeling. In this process, NADPH is generated through IDH1, which is the only known isozyme proteomically detected in RBCsFor the platelet storage data, the major discrepancy between uFBA and FBA models concerned the utilization of the electron transport chain (ETC), particularly in State 1. As this dataset did not have information on oxygen uptake, the metabolite node relaxation algorithm determined the necessary amount based on the rest of the metabolomics data. Based on the measured metabolites, the algorithm was able to accurately predict that oxygen was required for both uFBA and FBA models, but the amount of oxygen needed was only quantitatively predicted on the right order of magnitude for uFBA see . uFBA pr19S. cerevisiae strains engineered to assimilate xylose and fermented in a mixed glucose/xylose culture13C MFA studies on XI and XR yeast strains2113C MFA study was considerably different than in the study used for generating uFBA and FBA predictions.The final dynamic case study used metabolomics data for two 13C MFA studies on yeast XI and XR strains noted above. Additional systematically derived hypotheses for observations in the yeast metabolomics data are discussed in the Further, the uFBA flux predictions provide a systematic method to propose mechanisms for the observed time-course changes in metabolites, rather than use intuition. In particular, the authors postulated that the observed drain of 6-phosphogluconate (6PG) in the XI strain after glucose consumption is due to a reduced flux through the non-oxidative PPP. uFBA instead predicts 6PG decrease to be due to a significant decrease in oxidative PPP activity in State 2. The FBA model did not make a similar prediction. Further, the large decrease in flux through the oxidative PPP predicted by uFBA was confirmed with the E. coli data was used as a negative control because FBA has been traditionally successful in analyzing microbial growth processes based on exometabolomic data alone, in part due to E. coli’s balanced growth nature. As expected, uFBA flux predictions deviated less from steady-state flux predictions than did the other test cases , although more detailed, kinetic modeling and metabolic flux analysis are often difficult to construct and parameterize for large cellular networks. Constraint-based models are better suited for studying metabolism at cellular scale, but the steady-state assumption hinders studying dynamic states.S. cerevisiae. For a more traditional use of FBA , we found less difference, confirming that the uFBA is not overly sensitive. Theoretically, in a system where no intracellular metabolites change over time, uFBA and FBA would predict identical flux distributions, indicating that the use of uFBA should be considered if metabolomics measurements are available.In this study, we present unsteady-state flux balance analysis, a constraint-based modeling method, to study dynamic cellular states. uFBA provides additional utility to existing constraint-based methods that integrate metabolomics data see . We idenThe results presented here have two major implications. First, uFBA quantifies the impact of large and previously unmeasured intracellular metabolite concentration pools on network flux calculations. We experimentally validated a notable uFBA prediction for RBCs using isotopic labeling and metabolic flux analysis. The unexpected complexity of TCA metabolism in human RBCs is biologically notable. RBCs utilize TCA intermediates to produce phosphoenolpyruvate (PEP), most probably through a PEP carboxylase-like mechanism mediated by hemoglobinSecond, the common practice to allow free metabolic exchange of unmeasured metabolites out of the system can lead to erroneous predictions. For the platelet data, FBA predictions were inaccurate partly due to free exchange of L-alanine out of the system. For the yeast example, differences in FBA and uFBA predictions were partly due to the use of exchange reactions. uFBA aims to be fully data driven and only allows exchange of metabolites out of the system if they were experimentally measured or if the optimization algorithm requires the metabolite to be secreted for model feasibility. With the increasing size of metabolic networks, it requires both intimate knowledge of the cellular system and of constraint-based modeling to identify the modeling inaccuracies caused from metabolic exchanges. The uFBA approach simplifies metabolomics data integration and accurately deals with data inconsistencies through the node relaxation algorithm.Two other methods for systematically integrating intracellular metabolite concentrations with constraint-based models are available. TREM-FluxMetDFBA integrates intracellular measurements with the traditional DFBA approach. In order to deal with the huge complexity of the necessary ordinary differential equations, MetDFBA lumps and removes the majority of metabolic reactions resulting in smaller, core networks. While focusing on specific cellular processes is common in kinetic modeling, it eliminates the ability to interrogate metabolism at the whole-cell level, which is possible with FBA methods. Though uFBA is not as detailed as MetDFBA, it allows for studying metabolism at a comprehensive scale.The integration of metabolomics data using uFBA has limitations. First, the metabolomics data used to constrain the model must be absolutely quantified using internal standards. Absolutely quantified metabolomics data is often difficult to generate accurately and is more expensive. Second, the increased accuracy of uFBA predictions are determined by how large a percentage of metabolites are measured in the network. In particular, it is important to have metabolite measurements for cofactors and high flux pathways. Third, like other constraint-based methods, uFBA does not explicitly model metabolites as variables and thus total concentrations are not captured. Fourth, organelle specificity of metabolite concentrations is often lacking, requiring modelers to make assumptions on metabolite location. Finally, metabolomics data is noisier than other omics data types. To calculate significant metabolic rates of change, uFBA may require more than three replicates.uFBA provides a systematic and standardized method to generate hypotheses for the causes of detected changes in metabolite levels over time. uFBA flux predictions are based on unlabeled metabolomics but provide high quantitative accuracy in flux estimates even during dynamic metabolic conditions. These findings are not evident from statistical analysis of the time-course metabolomics alone nor from standard analysis of FBA models. We anticipate that the use of uFBA and the associated workflow will aid in deeper analysis of metabolomics data while also increasing the predictive power of constraint-based models.https://opencobra.github.io/cobratoolbox/).All analyses were performed in Matlab  using the COBRA 2.0 ToolboxS. cerevisiae during mixed culture anaerobic fermentation was taken from ref. E. coli during exponential growth was taken from ref. S. cerevisiae and E. coli. For RBC and platelet datasets, glucose and lactate were measured using a blood gas analyzer. For RBC data, ATP and 2,3 DPG were measured using enzymatic assays. In Bergdahl et al. and McCloskey et al., changes in key extracellular metabolites in S. cerevisiae  and E. coli  were also measured using HPLC. The low-throughput and HPLC measurements were prioritized over mass spectrometry measurements for use in the model. Some metabolite pools were not resolved in the original data and were manually split into individual concentrations based on known physiological ratios . Due to the rigorous quality control standards within blood banks for those two publications, there was negligible RBC and platelet cell death during storage. Thus, cell death was not included during modeling.Red blood cell (RBC) metabolomics data from normal blood banking conditions using SAGM media was taken from ref. S. cerevisiae and E. coli rates were in mmol/gDW/h.Principal component analysis (PCA) was performed on each metabolomics data set in order to objectively determine the time intervals of the discrete, linearized metabolic states. PCA was performed on the standardized Z-scores. Once the time intervals for each state were defined, linear regression was performed in order to estimate the rate of change for each metabolite during that particular state. The 95% confidence interval for each metabolite’s rate of change was calculated for integration with the model. If the 95% confidence interval for a particular metabolite’s rate of change crossed zero, the metabolite was deemed to be at steady-state as there is not enough statistical evidence for the metabolite to be changing. Rates for RBC and platelet were in mmol/L/h, while S. cerevisiae data was integrated with the S. cerevisiae metabolic model iMM904E. coli data was integrated with the E. coli metabolic model iJO1366S. cerevisiae and E. coli simulations. Platelet and S. cerevisiae metabolic models contain multiple compartments. If metabolites were known to be predominantly from a specific compartment, the metabolomics data was assigned as such. Specifically, tricarboxylic acid cycle metabolites were set to the mitochondria. If no information was available, metabolite concentrations were assumed to be in the cytosol.The endometabolomics data acquired from the literature was integrated with constraint-based models. The RBC data was integrated with a modified version of the erythrocyte model iAB-RBC-283The significant rates of change for measured metabolites for each state (as determined by linear regression) are input to the uFBA method. All four test cases are treated as closed systems, and all exchange reactions were removed from the model. Subsequent steps (see next section) determine other metabolites that can enter or leave the system. The measured metabolomics data is integrated with the model by:S is the stoichiometric matrix, v is the calculated flux vector, and  represent the 95% confidence interval for each significantly changing metabolite. All unmeasured metabolites are assumed to be at steady-state: b1 = 0 and b2 = 0.where Ideally, all model metabolites would be accurately measured. If so, the model would properly simulate, as all metabolic changes would be accounted for. However, due to experimental limitations, most metabolites cannot be measured, and often those that can be measured are done so unreliably. Optimally, one would measure metabolites that have the highest rate of change relative to the flux going through the associated pathways. However, knowing which metabolites these are may not be possible as such metabolites may change from condition to condition or the system being studied may not be well known. Thus, from any metabolomics dataset, there exists unmeasured intracellular or extracellular metabolites that are not at steady-state that are required to change in order to allow the model to simulate.To deal with this data incompleteness and data quality issue, we developed an algorithm to reconcile the metabolomics data and the network structure. In brief, the algorithm tries to parsimoniously allow unmeasured metabolites to deviate from steady-state in order to build a computable mode. The approach is detailed in the next section.Further, a standard practice in FBA is to allow all extracellular metabolites to have free exchange out of the system. As uFBA is a metabolomics driven approach, uFBA only allows exchange of extracellular metabolites out of the system if (1) it is measured to be increasing in the exometabolomics data, or (2) it is required by the metabolite node relaxation algorithm for feasibility.S. cerevisiae and E. coli to account for the generation of proteins, RNA, DNA, and lipids. Further, metabolite reserves are modeled using sinks. This is used in particular for glycogen stores for S. cerevisiae during carbon starvation.The remainder of the uFBA modeling formalism follows FBA principles. In particular, a biomass objective function is used in growing cells such as From a mathematical standpoint, the uFBA approach changes the degrees of freedom (DOF) of the system. First, for each “unsteady” metabolite incorporated, the system gains a DOF. Next, all exchange reactions are removed, reducing the DOF by the number of reactions removed. At this point, the metabolic model is most likely infeasible as the system is now over-determined. Previous approaches (i.e. TREM-Flux) deal with this issue by allowing all unmeasured metabolites to deviate from steady-state, increasing the DOF by one for each unmeasured metabolite. The uFBA approach applies a metabolite node relaxation algorithm to parsimoniously deviate unmeasured metabolites from steady-state to minimize the increase of DOF. The system’s increase in DOF is equivalent to the number of metabolites deviated by the algorithm.Because not every metabolite in the network was measured, we developed an automated method for parsimoniously deviating unmeasured metabolites from steady-state to build a computable model. We term this estimation “metabolite node relaxation”.For each metabolite that was not measured, two sink reactions are added that allow each of these metabolites to both accumulate (“up” sink reaction) and deplete (“down” sink reaction). Then, an optimization problem determines the minimal number of sinks to retain while still having a computable model. This parsimonious method was chosen under the assumption that cellular systems typically aim to maintain homeostatic levels, which has been previously shownTo exhaust potential methods, we implemented five different optimization approaches for relaxing the unmeasured metabolite nodes in the system , 5, 6, 7m is the number of unmeasured metabolites in the system and where abolites :The third technique is also an LP optimization that minimizes both the sum of the magnitude of the rate of change of the unmeasured metabolites as well as the reactions fluxes in the network :n is the number of intracellular reactions in the system and v is the reaction flux. The fourth technique is a QP optimization that minimizes the sum of the square of the rate of change of the unmeasured metabolites , the termination criterion for optimization for each iteration was set to a relative gap tolerance of 1e-6 or a time limit of 45 seconds. These criteria were chosen based on convergence properties of the solutions as the two parameters were varied.As alternative optima may exist for these optimization problems, especially for Case 1, the given optimization problem is run multiple times for a user-specified number of iterations, not allowing for previous solutions using an integer cut method. For the larger models . Sensitivity analysis of this parameter by resampling the reaction fluxes showed that the 1x scaling was too tightly constrained, yielding different results than the higher multiples. However, the higher multiples were very similar to each other. A scaling of 1.5x was used for all analyses in this study as it does not over constrain the network. A full sensitivity analysis for how varying both the cases and the scaling values affects uFBA flux predictions and the comparison of uFBA and FBA is shown in the We tested whether the various optimization approaches for parsimoniously relaxing unmeasured metabolites from steady-state was an accurate method for the data incompleteness issue. All five techniques were used to build uFBA models for the RBC metabolomics data. The relaxed nodes for each of the five approaches see  were comThe criterion for selecting the best optimization technique was minimizing the number of cases where a metabolite was incorrectly relaxed from steady-state. This criterion was chosen as it is more detrimental to over relax than to under relax, because it allows the model to have many new feasible flux states that may be erroneous. We found the MILP formulation (Case 1) to be the best method for this criterion. Further, the MILP formulation was also found to have the overall best accuracy see . For allThe FBA models constructed for control comparison against the uFBA models followed the same workflow as the uFBA model, except that only the exometabolomics data was integrated. Further, in order to satisfy the intracellular steady-state requirements for FBA, models are typically allowed to have free extracellular metabolite exchange out of the system. This practice was used for the FBA models in this study. Still, the optimization algorithms for node relaxation were required and were used in the same manner as that for uFBA. A list of relaxed nodes for the FBA models is provided see .S. cerevisiae, and E. coli models; all models were sampled until the mixed fraction was below a threshold of 0.54. The sampling distributions for each reaction were deemed significantly different between modeling formulations (uFBA vs FBA) if the two distributions overlapped by less than 5%. The correlations which are represented as histograms in S. cerevisiae, and E. coli models to account for all generated sample points. For all determining significant differences and Spearman correlations (including controls), only reactions that were in both models and were not involved in type 3 loops were compared.The FBA and uFBA models were sampled using Markov chain Monte Carlo (MCMC) sampling methodsGene essentiality predictions were completed with COBRA 2.02324A healthy donor was recruited and, after obtaining informed consent, red cells were obtained using ISO 9001:2008 certified red cell isolation protocols at the Landspitali-University Hospital Iceland Blood Bank. The study and all associated methods were approved by The National Bioethics Committee of Iceland and the Icelandic Data Protection Authority. The methods were carried out in accordance with the guidelines and regulations outlined by those committees.13C citrate  in place of unlabeled citrate in regular CPD SAGM media. Sodium hydroxide was use to match ionic strength imposed by trisodium citrate in regular CPD SAGM . As a negative control, red cells were stored in unmodified CPD SAGM. RBC units were stored at 4 °C. 5 mL samples were removed at ten time points and aliquoted accordingly for subsequent quality control assessment and metabolomics analysis. The experiment was run for 31 days, as the shift in metabolic dynamics from State 2 to State 3 occurs much earlier (day 17).Isolated red cells were added to 65 ml of modified Citrate Phosphate Dextrose (CPD) solution containing 105 mM uniformly labeled Red cell blood banking quality control assessment was performed immediately by ABL90 FLEX blood gas analyzer  determining pH, pO2, pCO2, total hemoglobin, [K+], [Na+], [Ca2+], [Cl−], [Glucose], and [Lactate]. A XN-1000 hematology analyzer  was used to record RBC count, white blood cell count, platelet count, hemoglobin, % hematocrit, total mean cell hemoglobin, mean cell hemoglobin concentration, and red cell distribution width. Labeled samples were found to have similar QC properties as control units.Metabolomic analysis was performed using a previously reported method13500 μL of RBC sample were used for metabolomics analysis and supernatant and cells were separated by centrifugation . Immediately after centrifugation, cell-free supernatant was removed from centrifuged tubes and collected in separates tubes and processed as previously described1313C isotopes using IsoCor Data integration of targeted compounds was achieved by using TargetLynx (Waters). Raw data was then corrected for natural abundance of Metabolic flux analysis (MFA) was completed using the INCA software suiteThe INCA software suite allows for two basic types of simulations: a “forward” simulation in which the labeling pattern is predicted for a given flux state, and a “reverse” simulation in which the flux state of the network is calculated based on fitting the experimentally measured labeling pattern. The traditional “reverse” MFA simulation cannot be used when both metabolite levels are changing and the labeling pattern is unsteady. Instead, the “forward” simulation was used, which takes as input: (1) measured intracellular metabolite concentrations, (2) the labeling pattern of the metabolites, and (3) the flux state of the network. The mean flux state of the network as calculated by MCMC sampling for each of the metabolic states for each of the uFBA/FBA models was used as the initial flux state labeling pattern on Day 1.The “forward” MFA simulations were completed for the first two states, where the labeling pattern approaches steady-state. First, the initial labeling pattern (Day 1) and the estimated uFBA fluxes were inputted and the labeling pattern was simulated for the duration of State 1. Next, the final predicted labeling pattern and the uFBA fluxes for State 2 were simulated for the duration of State 2. The labeling pattern reached steady-state by State 3 and is not included as there were little differences between uFBA and FBA. The same workflow was also applied to the FBA fluxes for comparison.To assess goodness of fit between the measured data and the simulated data, the residual sum of squares (RSS) was calculated for each of the four metabolites for which we had absolute concentrations and labeling data . The RSS was calculated byy is the experimental value, f(x) is the tracer simulation predicted value and the range of i contains all measured time points and each replicate is treated as a separate value. We evaluated the relative difference in RSS between the uFBA and FBA simulations to demonstrate the difference in accuracy of predictions. All RSS calculations were done with log10 transformed abundances.where Candidate flux states for the uFBA and FBA models were determined using MCMC sampling. The mean sampling vector was compared to measured flux values for the XR strain growth on glucose and xylosevmeas is the flux vector from MFA measurements and vpred is the flux vector from the uFBA and FBA models.where How to cite this article: Bordbar, A. et al. Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics. Sci. Rep.7, 46249; doi: 10.1038/srep46249 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Escherichia coli vary across 189 amino acid pairs. While most pairs display shared patterns of inter-species interactions, multiple deviations are caused by pleiotropy and epistasis in metabolism. Furthermore, simulated invasion experiments reveal possible paths to obligate cross-feeding. Our study provides genomically driven insight into the rise of ecological interactions, with implications for microbiome research and synthetic ecology.Metabolite exchanges in microbial communities give rise to ecological interactions that govern ecosystem diversity and stability. It is unclear, however, how the rise of these interactions varies across metabolites and organisms. Here we address this question by integrating genome-scale models of metabolism with evolutionary game theory. Specifically, we use microbial fitness values estimated by metabolic models to infer evolutionarily stable interactions in multi-species microbial “games”. We first validate our approach using a well-characterized yeast cheater-cooperator system. We next perform over 80,000 in silico experiments to infer how metabolic interdependencies mediated by amino acid leakage in  The rise of metabolic interdependencies among microbes is still poorly understood. Here, taking the underlying biochemical networks into consideration, Zomorrodi and Segrè integrate genome-scale metabolic models with evolutionary game theory to study the rise of cross-feeding in microbial communities. Similar interactions have also been engineered in laboratory systems, mainly based on genetically induced auxotrophies8. However, the evolutionary rise and maintenance of these interactions constitutes an unresolved puzzle, since genotypes that do not contribute to the production of costly metabolites may have a selective advantage over producers. One theory, known as the Black Queen (BQ) Hypothesis9, suggests that in communities with BQ functions  metabolic dependencies could arise through adaptive gene loss: in such communities organisms benefit from losing their own capacity to produce a costly metabolite (thus becoming “non-producers”). This could give rise to an obligate dependency of non-producers on producers9, or, in the case of more than one BQ function, to obligate cross-feeding 10. However, little is known about the conditions under which these dependencies would be established, as the rise of mutant genotypes due to adaptive gene loss does not necessarily guarantee a stable coexistence.Obligate dependencies among microorganisms through the exchange of essential metabolites have been hypothesized to be ubiquitous in microbial ecosystems14. Similarly, other studies have used evolutionary game theory (see refs. 18 for comprehensive reviews), and concepts from economics19 to better understand inter-species dependencies in microbial communities. While these approaches have provided valuable phenomenological insight into the general principles of metabolic interdependencies, they often do not take into account the specific details of the organisms, pathways, and molecules involved: behind the biosynthesis, leakiness, and utilization of these metabolites, is a complex network of biochemical reactions, which may significantly vary across different environmental conditions, metabolites, and organisms. A powerful avenue to address this gap is the use of systems biology methods, such as genome-scale network models of metabolism20. These models take into account the full metabolic circuitry of a cell and provide quantitative predictions of its growth capacity and metabolic fluxes. Recent work has started applying these approaches to model microbial communities30  and to study the evolution of adaptive diversification in long-term evolutionary experiments32. However, a systematic analysis of the possible equilibrium states of interacting species as a function of the leakiness of various metabolites, and of their underlying metabolic circuits is still lacking.A limited number of theoretical studies have recently explored this question using ecological modelsHere we propose a hybrid modeling approach that combines the theoretical insight of evolutionary game theory with the organism-specific-detailed analysis of cell-wide metabolic networks. We demonstrate how this strategy allows one to map the landscape of possible inter-species interactions, for which genome-scale metabolic models provide unique mechanistic insights. In addition to providing a genomic- and biochemistry-grounded basis for the quantitative assessment of the BQ Hypothesis, our approach can generate testable organism- and metabolite-specific predictions of inter-species interactions equilibria.33. The payoff matrix also allows one to model evolutionary dynamics 33 and to determine which of the identified Nash equilibria are evolutionarily stable  of microbes involved in metabolic interactions, and of inferring the evolutionarily stability of such interactions under diverse environmental or strategic conditions. Different microbes, identified here with their genotypes, are assumed to potentially leak specific metabolites that can be utilized by other community members. For each possible pair of genotypes in the community, we used constraint-based analysis of genome-scale metabolic models to estimate their fitness (payoff) as they engage in a specific metabolite-mediated interaction. The payoff of a genotype is set to its predicted growth rate, implicitly taking into account how this rate will be affected by the level of leakage and by the biosynthesis and possible transport cost of the specific metabolite(s) leaked , hydrolyzing sucrose into glucose and fructose, part of which leak out and serve as a public good. Since invertase production is energetically costly, a mutant strain, which has lost its suc2 gene, may emerge , and the Snowdrift game (where producers and non-producers coexist)34.As a proof of concept of our approach, we sought to reproduce the experimentally observed equilibria in the well-characterized yeast sucrose hydrolysis systemrge Fig. . Given tiAZ900 yeast metabolic model35, and inferred the Nash equilibria of the system as a function of the glucose/fructose capture efficiency and the invertase production cost . Variations in the invertase production cost were implicitly modeled by changing the stoichiometric coefficient of ATP in the sucrose hydrolysis reaction in the metabolic model. We thus explored systematically how the Nash equilibria of the system vary over a grid of possible values of the capture efficiency and the invertase production cost. This analysis showed that all three types of Nash equilibria observed experimentally34 could be reproduced , leaking a given amino acid could interact with a mutant strain  lacking the gene(s) for the biosynthesis of that amino acid  across different amino acids. With this analysis ? Four different genotypes are possible in this case  will not be able to synthesize and leak arginine, thus acting like a 00 genotype and preventing the occurrence of cross-feeding. This observation is consistent with a previous study reporting the inability of arginine and glutamate auxotrophic mutant strains to grow in a co-culture under minimal medium3. This effect is thus due to a pleiotropic metabolic gene , and illustrates how core biochemistry can impact ecological interactions.For the first anomalous pair, (arginine and glutamate), Nash equilibria in the sustainable leakiness region includes  and , but not the cross-feeding state  Fig. . Inspectthr− mutant) when facing 11, thereby preventing  from being a Nash equilibrium. This anomalous effect is due to the fact that the concurrent removal of glycine and threonine biosynthesis genes (in 00) will lead to a reduction in the capacity of metabolic network to produce a number of other essential biomass components (such as serine). Interestingly, this is a case of diminishing-return (or “negative”) epistasis, in which the effect of the double mutation (00) is less severe than expected based on the two single mutations (01 and 10). Negative epistatic interactions preventing the appearance of  as the Nash equilibrium can be observed for 34 other amino acid pairs  lead to the rise of non-intuitive ecological interactions. The analysis we presented spans over 80,000 in silico experiments (across 189 amino acid pairs and 441 leakiness level combinations), which is beyond the current experimental capabilities. This study provides testable predictions that can be used as a guideline for the design of future-targeted experiments, e.g., built upon previously established synthetic communities49: here products from the bacterial degradation of ingested food  can serve as public goods for the microbiota, potentially leading to the rise of cheaters, with major consequences for the health of the human host. In addition, our approach lays the foundation for proactively incorporating evolutionary concepts in the de novo design of stable synthetic microbial consortia for various biotechnological applications, guaranteeing that engineered communities will be resistant to invasion by competing strategies31.From a biotechnological standpoint, our study offers a basis for better understanding metabolic interdependencies in biomedically relevant natural microbial communities, such as those in the human gut microbiotak upon interacting with a partner k′. Higher-order interactions can be similarly considered. These estimated payoffs are represented in the form of a matrix, referred to as the payoff matrix of the game. (ii) Using the payoff matrix to identify the Nash equilibria—a fundamental concept in game theory, defined as a state where no player has an incentive to unilaterally change its current strategy, because it cannot improve its payoff by doing so. An “evolutionary stable strategy” is a similar concept in evolutionary game theory: It is a Nash equilibrium, which is evolutionarily stable, i.e., natural selection alone is sufficient to prevent invasion by competing mutant strategies. Evolutionary stable strategies can be found by modeling the evolutionary dynamics of the game using the computed payoffs (see the following sections). In this text , by “evolutionary dynamics,” we mean how the relative genotype abundances (frequencies or community structure) change over time. This aspect of evolutionary dynamics, as opposed to the simulation of de novo mutations and subsequent selection processes (which have been pursued in other studies50), is the main focus of our analyses.Evolutionary game theory is the application of classical game theory to model the evolutionary dynamics of mixed populations. Modeling microbial communities with evolutionary game theory involves two steps: (i) Considering all pairwise interactions among genotypes and estimating the payoff (fitness) of a microbial player 51) is a linear optimization problem that uses genome-scale metabolic models to make quantitative predictions about the cell’s growth capacity, intracellular reaction fluxes, and secretion rates of metabolites that are potentially excreted by the cell under a given environmental/growth condition. In the most common formulation, this is achieved by maximizing the flux of a pseudo-reaction called biomass reaction (vbiomass) whose reactants are precursors required for growth and whose flux is indicative of the cell’s growth capacity. This is subject to constraints imposing steady-state mass balance for each metabolite in the network (see Constraint 1 below) and lower and upper bounds on reactions fluxes reflecting known irreversibility of specific reactions and uptake and aeration conditions (see Constraint 2 below). The standard formulation of FBA is as follows:I is the set of metabolites, J is the set of reactions, sij is the stoichiometric coefficient of metabolite i in reaction j (known from the metabolic model), LBj and UBj denote lower and upper bounds on the flux of reaction j, respectively, and vj is the flux of a reaction j.FBA  is k′ when facing k (ak′k) is We used FBA to provide organism-specific estimates of the payoffs upon specific pairwise (or higher-order) interactions . In the FBA model, this gene deletion is simulated by setting vDAPDC = 0. More complex gene-to-reaction mappings could lead to more complex set of constraints. In cases where several different choices are possible for genes whose deletion would induce a given auxotrophy, we select one arbitrarily. (ii) The second type of constraints (Eqs. ei) at which a metabolite i leaks out of genotype k, we simulate such leakage by imposing a fixed secretion rate ei in the FBA calculation for this genotype. In simulating growth for genotype k, we further take into account the availability of other metabolites secreted by genotype k′, by appropriately setting the import constraints in the FBA problem. Thus, in our approximation of an interaction, the two FBA calculations for genotypes k and k′ are performed independently, each assuming availability of the metabolites leaked by the other.Each FBA problem involves two new types of constraints in addition to Constraints (1) and (2) mentioned above: (i) The first type of constraint Eq.  below imnts Eqs.  below sik is mathematically formulated as follows (superscript k is removed here for the ease of presentation):Jmutation denotes the set of reactions corresponding to specific gene mutations for the genotype under consideration. In addition, Ileaky⊂ I is the set of leaky (secreted) metabolites by the genotype under consideration and Iuptake⊂ I represents the set of metabolites that is available to this genotype for uptake and that is provided by other genotypes. vi(e)EX_ denotes the flux of exchange reaction for a metabolite i. ei > 0 and ui > 0 denote the pre-specified net export and uptake flux of a metabolite i, respectively .The general FBA problem for genotype ei and Constraint (5) allows for the uptake of metabolites available from partner genotype(s) in a pairwise or (higher-order) interaction. It is worth highlighting again that the input parameters for this FBA problem (in addition the metabolic network stoichiometry) are the list of metabolites that each genotype is leaking, and the level of leakiness for each of them.In the above FBA problem, Constraint (3) sets to zero the flux of reactions corresponding to the specific gene mutations in the genotype under consideration. Constraint (4) requires the export of leaky metabolites at the pre-specified level S. cerevisiae and E. coli are given in the Supplementary Methods. Additional environmental/strategic/genetic conditions can be incorporated through the addition of appropriately defined constraints. Alternatively, one can use a different objective function , objective function-independent approaches54, or other constraint-based community modeling tools, e.g., those in refs. 23.The payoff of the genotype under consideration is set to the optimal value of the biomass flux, or to the death rate  in the case of an infeasible problem. An infeasible FBA problem may occur due the lack of enough carbon source to satisfy maintenance ATP requirements in the model or due to imposing a high level of leakiness for leaked metabolites. Imposed leakiness level causing this infeasibility is referred to “unsustainable leakiness levels.” The details of specific formulations for the presented case studies with n-player game. Here, for ease of presentation, we describe the NashEq Finder formulation for a two-player non-symmetric game. Let P and Q denote the set of all conceivable strategies for player 1 and player 2, respectively. A binary decision variable is defined as follows to capture whether or not each entry pq of the payoff matrix satisfies the conditions of a Nash equilibrium:pq of the payoff matrix constitute 1 and LB2 are non-zero lower bounds on the payoff values of players 1 and 2, respectively, The objective function of this optimization problem maximizes the values of binary variables corresponding to entries of the payoff matrix. The definition of binary variable wpq is mathematically imposed by Constraints (6) and (7). In particular, Constraint (6) mathematically describes the conditions of a pure strategy Nash equilibrium for player 1, i.e., if player 2’s strategy is fixed at q ∈ Q, player 1 attains its maximum payoff by taking strategy p ∈ P. Constraint (7) imposes the same condition for player 2 (see Supplementary Methods for an example detailing how these constraints work). Notice that NashEq Finder is an integer linear program (ILP), which can be always solved to global optimality . Upon solving this optimization problem, any entry of the payoff matrix for which the corresponding binary variable is equal to one will be a Nash equilibrium. NashEq Finder can thus identify all pure strategy Nash equilibria of the game in one shot by solving this ILP problem. If this optimization problem is infeasible, it means that no pure strategy Nash equilibrium exists. This formulation can be easily generalized for an n-player game. A python script implementing NashEq Finder for an n-player game is available in Supplementary Software Upon constructing the payoff matrix, as described above, one can identify the Nash equilibria of the game. We developed NashEq Finder, an optimization-based procedure to automate the identification of all pure strategy Nash equilibria of an 33. To take into account interactions higher than pairwise, we used an extended form of the classical Replicator equation33. This equation predicts the changes in the relative abundance (frequencies) of genotypes over time according to their reproductive fitness under the assumption of a roughly constant population size33 (see Supplementary Note 24). The extended form of the Replicator equation can be expressed as follows55:k denotes a community member k and x = T is the composition of the community with xk being the frequency of genotype k at time t. fk(x) is the average reproductive fitness of genotype k that depends not just on other genotypes it may encounter but also on their frequencies. akk′ and akk′k″ denote the payoffs of genotype k when encountering another genotype k′ in a two-player game  or two other genotypes k′ and k″ in a three-player game, respectively. Finally, ϕ(x) is the average fitness of the entire community. Here, we use the Replicator equation to perform targeted in silico invasion experiments, in which a newly emerged low-frequency genotype invades an existing resident genotype.Following standard approaches in evolutionary game theory, we model evolutionary dynamics using the Replicator equationA python script implementing NashEq Finder is available as Supplementary Software The data sets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Software 1