Shewanella oneidensis MR-1 utilizes its resources, the metabolic network was reconstructed. The resulting network consists of 774 reactions, 783 genes, and 634 unique metabolites and contains biosynthesis pathways for all cell constituents. Using constraint-based modeling, we investigated aerobic growth of S. oneidensis MR-1 on numerous carbon sources. To achieve this, we (i) used experimental data to formulate a biomass equation and estimate cellular ATP requirements, (ii) developed an approach to identify cycles (such as futile cycles and circulations), (iii) classified how reaction usage affects cellular growth, (iv) predicted cellular biomass yields on different carbon sources and compared model predictions to experimental measurements, and (v) used experimental results to refine metabolic fluxes for growth on lactate. The results revealed that aerobic lactate-grown cells of S. oneidensis MR-1 used less efficient enzymes to couple electron transport to proton motive force generation, and possibly operated at least one futile cycle involving malic enzymes. Several examples are provided whereby model predictions were validated by experimental data, in particular the role of serine hydroxymethyltransferase and glycine cleavage system in the metabolism of one-carbon units, and growth on different sources of carbon and energy. This work illustrates how integration of computational and experimental efforts facilitates the understanding of microbial metabolism at a systems level.Shewanellae are gram-negative facultatively anaerobic metal-reducing bacteria commonly found in chemically  stratified environments. Occupying such niches requires the ability to rapidly acclimate to changes in electron donor/acceptor type and availability; hence, the ability to compete and thrive in such environments must ultimately be reflected in the organization and utilization of electron transfer networks, as well as central and peripheral carbon metabolism. To understand how  Shewanella in global carbon and nutrient cycles is implicated based on their wide distribution and their ability to link organic matter oxidation to reduction of many organic and inorganic electron acceptors both natural and artificial. These bacteria are also important in bioremediation efforts and other developing fields, including energy generating biocatalysis and the production of useful carbon containing compounds. In this study we applied a suite of systems-biology tools, including computational and high-throughput experimental approaches, to develop a predictive understanding of S. oneidensis MR-1 metabolism. We built a metabolic model and used it to analyze experimental data and to predict cellular phenotypes. Predicted cellular biomass yields on different carbon sources under aerobiosis were compared to experimental measurements, and experimental results were used to refine metabolic fluxes for growth on lactate. Computational and experimental analysis of S. oneidensis MR-1 metabolism revealed some of the reasons for a significant difference between experimental and predicted aerobic growth efficiency on lactate. The developed model provides a platform for a systematic assessment of Shewanella metabolism, which may be used for redesigning metabolic networks for chemical production.The role of members of the genus  Shewanella are common organoheterotrophic organisms in both marine and fresh water environments, particularly in those receiving high inputs of organic matter and where redox conditions fluctuate in space and time. Shewanella oneidensis MR-1 is a dissimilatory manganese-reducing bacterium isolated from Lake Oneida in upstate New York N-acetylglucosamine Shewanella is particularly well-adapted to redox interface environments 2, fumarate, nitrate, nitrite, sulfite, tetrathionate, thiosulfate, TMAO, DMSO, Fe(III), and Mn(VI). Given its propensity to transfer electrons to extracellular substrates, Shewanella has been of interest for use in microbial fuel cells Shewanella are obligately respiring bacteria; however, S. oneidensis MR-1 has recently been shown to survive by fermenting pyruvate Shewanella, unlike GeobacterAnaeromxyobacter2Shewanella on lactate under anaerobic conditions is accompanied by acetate accumulation Shewanella in catalyzing important environmental processes, as well as to assess and improve their potential for biotechnological applications. Genome-scale metabolic models allow for a systematic assessment of the metabolic capabilities of an organism. These models can be used to analyze and predict the metabolic behavior of microorganisms under different environmental conditions and in response to genetic alterations in silicoS. oneidensis MR-1 and analyzed a genome-scale constraint-based model of MR-1 metabolism to interrogate the organism's metabolic behavior and capabilities under aerobic conditions and to estimate the growth- and non-growth rate dependent ATP requirements. We made detailed biomass composition measurements for macromolecules  and amino acids. These measurements were used to construct a biomass production reaction that was included in the metabolic model iSO783. The resulting model was used to identify futile cycles, predict biomass yields on alternative carbon and energy sources, and refine intracellular flux distributions for lactate-limited growth by integrating experimental data. We also illustrate how models can be used to improve understanding of microbial metabolism by incorporating experimental data to refine metabolic pathways reconstructed from a genome annotation as well as to predict how cells will behave in response to genetic or environmental perturbations.In this work, we developed a metabolic reconstruction for S. oneidensis MR-1 grown in a lactate-limited chemostat under aerobic conditions with a dilution rate (D) = 0.095 h−1 and contained 52.8% protein, 17.5% lipids, 7.7% carbohydrates, 9% RNA, and 5% DNA on a g/g AFDW (ash-free dry weight) basis. The remaining biomass constituents  were assumed to have similar abundances as in E. coliS. oneidensis MR-1 did not excrete a significant amount of polymers under these growth conditions and that our approximations for un-measured biomass components were reasonable. The nucleotide composition of RNA and DNA were estimated based on the GC content of MR-1, and the amino acid composition of the proteins and the cellular lipid composition were based on experimental measurements. Together this information was used to formulate a biomass equation for the network  and one cytochrome d ubiquinol oxidase . The use of either Cco or Cox, in combination with ubiquinol-cytochrome c reductase , results in the translocation of 6H+/2e− across the cytoplasmic membrane as electrons move from ubiquinol to O2+/2e− as electrons are transferred from ubiquinol to O2. Previous proton translocation measurements for S. oneidensis MR-1 with oxygen as the electron acceptor found that a maximum of 2.8H+/2e− are translocated when cells are grown aerobically +/e− affects results).An important issue in the reconstruction of metabolism is the correct accounting of ATP production during substrate oxidation. Reconstructing the electron transport pathways can be challenging since energy conservation during respiration varies as a function of organism and growth condition S. oneidensis MR-1 ATP requirements, the lactate consumption rate was measured at different dilution rates in a chemostat. Analysis of cultural liquid revealed no detectable amounts of organic acids and that residual lactate concentrations were below 0.1 mM (the detection limit of the quantification method used); therefore all the lactate added to the medium (18mM) was consumed by the bacteria. Using the lactate consumption rate as a model constraint, we calculated the maximal amount of ATP that could be hydrolyzed while still maintaining the measured growth rate. A linear relationship was found between dilution rates (D) and maximum ATP hydrolysis , while at growth rates less than or equal to 0.085 h−1, the model-estimated biomass yields were in good agreement with experimental values. This may imply that at lower dilution rates the cells could be using metabolic pathways that reduce energetic efficiency.From the experimental growth and lactate consumption rates, the model estimated NGAR to be 1.03 mmol ATP/(g AFDW•h), and GAR to be 220.22 mmol ATP/g AFDW, when the transfer of electrons from ubiquinol to Organisms  [26]–[32rganisms , which iS. oneidensis MR-1 compared to other evaluated bacteria  can be used to identify what suboptimal reactions are potentially used that might explain the high GAR values. We evaluated available gene expression data for lactate aerobic and OSO3855 or SO4118) was deleted, the cells showed a ∼25% increase in biomass yield  over the wild-type strain in lactate aerobic batch cultures  than the nuo genes, which encode for the more energetically efficient proton-translocating NADH dehydrogenase. Likewise, the ABC-sulfate transporter (SO3599–3602) shows higher expression than the proton symport sulfate transporters SulP (SO2286 or SO3553), the latter being more energetically efficient.Additionally, under aerobic conditions some less energetically efficient enzymes are expressed at higher levels than their more energetically efficient counterparts. This includes two NADH dehydrogenases, Ndh (SO3517) and Nqr (SO1103–1108). These both show higher expression and higher relative changes in expression  to identify metabolites that could be used as sole carbon sources under aerobic conditions, and then experimentally tested some of those predictions. Thirty-three compounds were predicted to be able to support S. oneidensis MR-1 aerobic growth, indicating that all the necessary transporters and catabolic enzymes are present in the genome. About half of these were reported previously or were found in this study to be able to support growth of S. oneidensis MR-1 experimentally , CO2 and NH4, and then combining mlthf with another glycine molecule to produce serine  which can then be deaminated into pyruvate. Further experiments revealed that (i) addition of glycine restored aerobic growth on lactate of S. oneidensis MR-1 glyA deletion mutant  due to kinetic or transcriptional regulatory limitations.The inability of tant see  and S3, tant see  indicatiS. oneidensis MR-1's capability to use carbon sources, we found four cases where the model did not correctly predict the use of carbon sources that had been shown to support growth experimentally, including threonine, adenosine, deoxyadenosine, and inosine. We found that adding a secretion reaction for hypoxanthine to the metabolic model would allow the model to predict growth on adenosine, deoxyadenosine, and inosine, while the addition of a threonine transport reaction enabled the model to accurately predict growth on threonine.During our evaluation of + are translocated for each pair of electrons that move from ubiquinol to O2. 2 requirements (mmol O2/mmol carbon source) needed to achieve the maximal biomass yield  and to reflect the amount of O2 needed to convert a fixed amount of substrate into biomass. Substrates such as putrescine, ornithine, propionate, and acetate have the highest ratios of O2 requirement to biomass yields, while the nucleosides  have the lowest ratios.We also used FBA to evaluate the quantitative accuracy of growth phenotype predictions. Biomass yields (g AFDW/mmol carbon source) were calculated by constraining the consumption rate for carbon sources and identifying flux distributions that maximize growth rate using FBA. As with all previous simulations, the ratio of fluxes between the cytochrome oxidases was constrained so that 2.8Hield see . The O2 2 consumption rates, we fixed the substrate consumption rate for three different C3 compounds and constrained the O2 consumption rate to different values. The corresponding calculated biomass yields were significantly affected by the O2 consumption rate . In addition to the O2 consumption rate, the calculated biomass yields can also be sensitive to biomass composition measurements used to formulate the biomass reaction. To evaluate the effects of biomass composition on calculated biomass yields, the protein, DNA, RNA, and glycogen abundances were independently altered ±30% from their measured values, with corresponding reductions or elevations in the levels of other biomass components. The calculated biomass yields were most sensitive to changes in protein levels, but even a 30% decrease in protein abundance only led to a 2.5% increase in predicted biomass yield. Overall, the calculated biomass yields were more sensitive to changes in O2 consumption rates than to biomass composition.To further evaluate the sensitivity of the biomass yields to Oion rate . If O2 c2 consumption rate constraints, to experimental measurements. For most of the carbon sources, the experimentally measured biomass yields were within 15% of the model calculated values when restrictions were placed on O2 consumption rates  of 0.085 hirements , the minS. oneidensis MR-1 has two isocitrate dehydrogenases that use either NAD+ or NADP+ as electron acceptors. The model predicts that the NADP+-dependent enzyme is required for optimal biomass yield, while flux through the NAD+-dependent isocitrate dehydrogenase is optional. The periplasmic fumarate reductase is another example of an optional reaction, however, it is known to be inactive aerobically As described earlier, optimal reactions are those that can be used to achieve the maximum biomass yield. Optimal reactions can further be classified as either optional or required depending on whether the reaction has to be used to achieve the maximum biomass yield. In some cases a zero flux through an optimal reaction can still result in an optimal solution , while other optimal reactions are required to carry flux to achieve optimal biomass yield (classified as required reaction). For example, +-dependent isocitrate dehydrogenase, malate synthase, and pyruvate formate lyase activities were not detected; therefore, solutions that carry flux through these reactions and the fumarate reductase reaction were subsequently excluded from the model. The additional constraints on these four fluxes caused a small increase (∼0.7%) in the lactate consumption rate that was needed to maintain the growth rate at 0.085 h−1 ; however, the re-calculated flux values were better resolved and had less individual variability  and possibly from formate, but not from the degradation of glycine into CO2 and NH4+   molecules carrying one-carbon units  are produced during conversion of serine to glycine (by serine hydroxymethyltransferase -  SO0426) . These oild-type .glyA), and its corresponding reaction (ser+thf↔gly+mlthf) operates in the forward direction , the glyoxylate shunt, and, unexpectedly, the more energetically efficient components of the aerobic respiratory chain.In this work, we presented the development of a metabolic model for the facultative dissimilatory metal-reducing bacterium S. oneidensis MR-1 appeared to have an unusually high growth rate dependent ATP requirement (GAR). Our model directly accounts for the energy requirements needed to generate biomass components including macromolecule polymerization. The remaining GAR in our model may be attributed to membrane processes (proton leakage), protein and mRNA turnover, and other unknown costs S. oneidensis MR-1 (220 mmol/gAFDW) is 2.5 times higher than that reported for Bacillus subtilis . There are a number of possible explanations for the observed high GAR, including flux through futile cycles and use of less energetically efficient enzymes, such as components in the aerobic electron transport chain. Accounting for these inefficiencies in the model would reduce the calculated GAR and NGAR values (see details below).Based on our analysis of lactate-limited growth at different dilution rates, S. oneidensis MR-1 under the experimental conditions we tested. Futile cycles have been suggested to be beneficial for increasing network robustness and sensitivity, generating heat, reducing build-up of toxic intermediates, and providing competitive advantages in energy rich environments B. subtilis). Therefore, it seems unlikely that futile cycling is the only explanation for the high apparent GAR value.Futile cycles have been shown to be active in other bacteria S. oneidensis MR-1 has a branched electron transport chain. The S. oneidensis MR-1 genome contains annotated genes for (i) three cytochrome oxidases, which results in either translocation of 2 H+/2e−  or 6 H+/2e−  as electrons move from ubiquinol to O2, (ii) two NADH dehydrogenases translocating either 0 H+/2e−  or 4 H+/2e− , and (iii) three NADH dehydrogenases that translocate 2 Na+/2e− . As a result, the transfer of a pair of electrons from NADH to O2 can result in the translocation of 2 to 10 H+ across the cytoplasmic membrane, depending on what enzymes are used. In all aerobic simulations, we constrained the flux ratios between the cytochrome oxidases such that they result in the translocation of 2.8 H+/2e− based on experimental data S. oneidensis MR-1, Shewanella benthica KT99, and S. woodyi are the only strains among 20 sequenced Shewanella strains analyzed that have nuo orthologs and it would be expected that these three strains would grow more efficiently than those strains missing nuo orthologs. However, the presence of nuo orthologs in S. oneidensis MR-1 did not confer any growth advantage over two Shewanella strains that do not contain nuo orthologs, S. putrefaciens CN32 and Shewanella sp. strain W3-18-1. These latter two strains (CN32 and W3-18-1) both had higher growth rates and biomass production  than S. oneidensis MR-1 when grown on lactate in aerobic cultures S. oneidensis MR-1 cells under the growth conditions tested. Additionally, data published by other researchers showed that aerobic growth of E. coli mutants with disabled Nuo-type NADH dehydrogenase on minimal medium supplemented with mannitol or glycerol was undistinguishable from wild-type cultures Shewanella.Like many other bacteria, + pumping enzymes are not active , then at most, 2H+/2e− can be translocated via the electron transport chain and the GAR drops to 81. In this calculation the constraint fixing 2.8H+ per electron pair transferred from ubiquinol to O2 was not included in the simulation. Similarly, the NGAR in this case also dropped from 1.03 to 0.47, the latter value being closer to NGAR value reported for Geobacter+/2e− can be translocated across the membrane via cytochrome oxidase activity, which disagrees with previous experimental measurements ΔSO4606) deletion mutant and a double Cox and Cco (ΔSO4606/ΔSO2361) deletion mutant, both of which exhibited growth rates in batch culture that did not differ significantly from the wild-type strain, and in fact grew to higher optical densities than wild-type cultures  the energetically efficient cytochrome oxidases are not utilized and that (2) futile cycles involving malic enzymes likely operate during aerobic growth on lactate indicates that S. oneidensis MR-1, a finding that was also confirmed experimentally. Model predictions of TCA cycle fluxes in cells grown in a lactate-limited aerobic chemostat (with a growth rate of 0.085 h−1) showed that a significant fraction (∼70%) of lactate may be oxidized by TCA cycle (S. oneidensis MR-1 grown in lactate-limited aerobic chemostat (D = 0.095 h−1) displayed a high specific activity of pyruvate dehydrogenase  The integration of experimental and modeling results is extremely valuable to advance model development and biological discovery. In cases where there is agreement between data and model predictions, the models can be used to help explain observed cellular behavior , analyze experimental data, or engineer metabolism for specific applications. For example, the model predicted that the TCA cycle is important for aerobic growth on lactate by CA cycle . In agrerogenase . Additiorogenase . InteresS. oneidensis MR-1 metabolism will improve. Integrated models of metabolism and regulation for this organism  at concentration 40 mM unless stated otherwise. To grow S. oneidensis MR-1 under anaerobic conditions, NaCl was excluded from M1 medium, and sodium fumarate was added as an electron acceptor to final concentration 35 mM. Anaerobiosis was achieved by extensively purging medium with pure N2.The strains of S. oneidensis MR-1 was performed using a previously described method In-frame deletion mutagenesis in S. oneidensis MR-1 in modified M1 media supplemented with 18mM lactate. The gas flow rate and agitation were kept at 3.5 liters/min and 350 rpm, respectively, and the dissolved oxygen tension (DOT) was maintained at 20% or 1% of air saturation by automatically changing the ratio of N2 and air in the gas mix. The pH was maintained at 7.0 by addition of 2 M HCl, and composition of incoming and off-gas was constantly monitored by an in-line mass spectrometry based gas analyzer MGA iSCAN .A 15-liter New Brunswick Bioflow 3000 reactor  operated at a 7-liter working volume  at 30°C was used to grow chemostat cultures of 600 measurements using Spectronic® model 20 GENESIS™ VIS spectrophotometer , and/or further analyses when necessary.Culture growth was constantly monitored by measuring and recording optical density using a custom-made system. For this purpose, a fluorescent lamp was placed near the bioreactor wall, and a photodiode  was secured on the opposite side of the wall to quantify transmitted light. Photodiode voltages were recorded by a Keithley Model 2700 multimeter  using the ExceLinx data logging software (Microsoft Corp.). Additionally, 5- to 10-ml samples were periodically taken from the reactors for OD600 (no more than 3% variation between measurements), acid addition rate, O2 concentration in incoming gas, and O2 and CO2 concentrations in the off-gas. Samples for the following measurements were taken from reactors: (i) ash-free dry organic weight (AFDW), (ii) biomass composition, (iii) organic acids composition. Sampling procedure took no more than 4 minutes.Reactors were inoculated with 1mL/L of overnight culture grown in TSB and maintained in batch mode until late-logarithmic stage. Continuous cultures were started by pumping medium of the same composition at desired dilution rate (D). Samples for further analysis were taken after at least five volume changes at steady-state conditions. Steady-state achievement was inferred from stability of the following parameters: OD600). Cells were grown with three or more replicates in 96- or 100-well plates at 30°C. M1 minimal media supplemented with 40 mM carbon source was used in growth phenotyping experiments. Absorbance readings were taken every 15 minutes at 600 nm. A standard curve was used to convert absorbance readings in a microplate reader to a standard spectrophotometer with a 1-cm pathlength. Alternately, cultures were grown in shaken (150 rpm) 70 mL crimp-sealed serum bottles containing 10 mL of medium. If necessary, the OD measurements were converted to biomass concentration (gAFDW/L) by multiplying by 0.69 using previously established correlations between OD600 and cell concentration (g AFDW/L). All batch experiments were repeated at least 3 times, and the standard deviation of triplicate cultures never exceeded 6%, unless indicated otherwise by error bars. Under conditions used to grow cells in M1 medium supplemented with 18–20 mM lactate all substrate was consumed when cultures entered stationary phase.Batch experiments were performed at 30°C in an Infinite M200  or Bioscreen-C  microplate reader, or crimp-sealed serum bottles placed on a rotary shaker  at 30°C and 150 rpm. Growth was monitored by measuring the cultures' optical density at 600 nm (ODTo measure biomass ash-free dry weight (AFDW), a known volume of cultural liquid was centrifuged , supernatant discarded, pellet thoroughly resuspended in deionized water, transferred into a pre-weighed aluminum dish and, using Sartorius MA100 Mositure Analyzer , dried at 105°C to a constant weight (DW1). The dried biomass was then combusted at 600°C for 12 h and weighed again (DW2). The biomass concentration (gAFDW/L) was calculated as follows: (DW1–DW2)/volume.For the purpose of this work, biomass was considered to include the cell pellet following centrifugation and extracellular polymers present in the supernatant. Bacteria can produce substantial amounts of extracellular polymers (protein and carbohydrates) as well as membrane vesicles containing the above as well as membrane lipids. For the initial stages of metabolic modeling, the location of cell constituents is not critical but it is important to capture all biomass components in order for the model to be accurate. Therefore, biomass composition included analyses of culture liquid (CL) without preliminary fractionation. In all cases, a method of standard additions was used to quantify polymers in known CL volume S. oneidensis MR-1 metabolic network was reconstructed in SimPheny  initially using an automated model building process Shewanella was the subject of a reciprocal BLAST search against genes from other microorganisms with well-curated metabolic reconstructions. Metabolic reactions and gene to protein to reaction (GPR) associations from other models were included in the draft Shewanella reconstruction if a good reciprocal best hit could be found in S. oneidensis MR-1.The This draft reconstruction was manually reviewed to exclude and include additional genes and reactions. GPR associations in the draft reconstruction were reviewed to confirm that the gene's annotated functions were consistent with the associated reactions. Genes not included in the draft reconstruction were also evaluated and included in the reconstruction if their products were predicted to carry out metabolic functions. A large fraction of the anaerobic electron transport chain reactions were added to the draft reconstruction at this stage because these reactions do not occur in other reconstructed organisms. Additional reactions were added as necessary to produce known biomass constituents or utilize known growth substrates.The final reconstruction includes organism-specific reactions associated with macromolecular synthesis, which were incorrect in the draft reconstruction because they differ from other reconstructed organisms. The structure of lipopolysaccharide had been previously determined for MR-1 −1) were used for biomass composition analysis. The measured biomass composition was then used to generate a biomass reaction, which is included in the metabolic model. This biomass reaction specifies the amount of biomass components (mmol) needed to synthesize 1 g AFDW of cells. Lipopolysaccharide and peptidoglycan abundances (g/g AFDW) were estimated based on values reported for E. coliE. coliA biomass reaction was generated from measured biomass compositions  for MR-1. Cells grown in a lactate limited chemostat (D = 0.095 hS. oneidensis MR-1 chemostat cultures were grown at different dilution rates and the lactate consumption rates (mmol/(g AFDW•h)) were measured. The growth and non-growth rate dependent ATP requirements were calculated by the metabolic model using this data as described previously To estimate growth- and non-growth rate dependent ATP requirements (mmol ATP/(g AFDW•h)), a series of A constraint-based model was developed based on the metabolic reconstruction for MR-1. These models include three types of constraints, the first is a steady-state mass balance constraint, where the production rate minus the consumption rate for each metabolite must equal zero. These steady-state mass balance constraints can be represented as:In most cases the linear system of equations is underdetermined so there are multiple flux distributions that satisfy the imposed the constraints. FBA uses optimization to identify flux distributions that maximize or minimize a given objective function i+H+→ATP+H2O) and its flux is constrained to be positive; this ensures that a futile cycle must take on non-zero fluxes to hydrolyze the ATP that is produced by ATPS. FVA using these constraints can be used to identify all reactions that can participate in futile cycles. To find individual futile cycles, a mixed-integer linear programming problem was formulated (Eq. 3–8) to minimize the number of reactions included in the cycle (Eq. 3), where n is the total number of reactions in the network. If the flux through the reaction is non-zero the corresponding value of the decision variable, jy, must be one (Eq. 5). The fluxes and decision variables must satisfy the mass balance (Eq. 4), thermodynamic, enzyme capacity constraints (Eq. 5), and positive ATPS flux constraint  in constraint-based models of metabolism. All exchange fluxes are constrained to be zero so that no metabolites can enter or exit the system. To find futile cycles an artificial ATP synthesis (ATPS) reaction is added Click here for additional data file.Table S2Reactions and GPR associations in iSO783.(0.28 MB XLS)Click here for additional data file.Table S3Metabolites and their abbreviations used in iSO783.(0.15 MB XLS)Click here for additional data file.Table S4Reactions used in the smallest 130 futile cycles.(0.02 MB XLS)Click here for additional data file.Table S5The 33 model predicted carbon sources.(0.02 MB XLS)Click here for additional data file.Table S6Bacterial strains and plasmids used for this study.(0.04 MB DOC)Click here for additional data file.Table S7Primers used in this study.(0.06 MB DOC)Click here for additional data file.Text S1Summary of additional experimental results.(0.06 MB DOC)Click here for additional data file.Text S2Supplemental experimental methods.(0.05 MB DOC)Click here for additional data file.Text S3Methods for cycle calculations.(0.13 MB DOC)Click here for additional data file.Figure S1S. oneidensis MR-1 wild-type (filled circles), and selected deletion mutants. Panel A: ΔSO3855 (open triangle) and ΔSO4118 (open diamond). Panel B: ΔSO4606 (open circle) and (filled triangle) double mutant ΔSO4606/SO2363. Cells were cultivated in 100-well plates in Bioscreen C; each well  received 100 µl of M1 medium supplemented with 20 mM D,L-lactate.Growth dynamics of (0.10 MB PDF)Click here for additional data file.Figure S2S. oneidensis MR-1 ΔSO3471 mutants on lactate (45 mM) in M1 medium and organic acids concentration dynamics. Cells were added in the beginning to make final optical density 0.08 at 600 nm. Crimp-sealed serum bottles were used for cultivation.Growth of (0.03 MB PDF)Click here for additional data file.Figure S3S. oneidensis MR-1 ΔSO3471 biomass on lactate (45 mM) in M1 medium. Biomass accumulation was expressed as optical density at 600 mn. Crimpsealed serum bottles were used for cultivation.Influence of glycine (A) and threonine (B) additions on maximal accumulation of (0.12 MB PDF)Click here for additional data file.Figure S4S. oneidensis MR-1 wild-type and selected deletion mutants. Wild-type (filled circle) and ΔSO0781 (open circle) deletion mutant were grown on lactate (18 mM) or acetate (45 mM) in M1 medium supplemented with NH4Cl or glycine (10 mM) as the sole source of nitrogen. Crimp-sealed serum bottles were used for cultivation, starting OD600 values were 0.01 (A and B) and 0.003 (C).Growth dynamics of (0.08 MB PDF)Click here for additional data file.Figure S5S. oneidensis MR-1. The network was constructed based on genome annotation.Metabolic network for interconversion of C1-compounds and biosynthesis/degradation of relevant amino acids in (0.10 MB PDF)Click here for additional data file.Figure S6S. oneidensis MR-1 wild-type (A) and ΔSO3471 mutant (B) in M1 medium supplemented with different compounds as sole sources of carbon and energy. Crimp-sealed serum bottles were used for cultivation, and starting OD600 value was 0.015 for all experiments.Growth of (0.13 MB PDF)Click here for additional data file.Figure S7S. oneidensis ΔSO0424 cells in M1 medium supplemented with 18 mM D,L-lactate. 70 ml serum bottles containing 15 ml of medium were used. Periodically 0.7–0.8 ml samples were withdrawn to measure OD600 and organic acids in 0.22 µm filtrates of culture.Aerobic growth of (0.07 MB PDF)Click here for additional data file.


All three models, however, lack a detailed description of lipid metabolism and thus are unable to be used as integrated scaffolds for gaining insights into lipid metabolism from multilevel omic measurement technologies (e.g. genome-wide mRNA levels). To overcome this limitation, we reconstructed a new version of the Saccharomyces cerevisiae genome-scale model, iIN800 that includes a more rigorous and detailed description of lipid metabolism.Up to now, there have been three published versions of a yeast genome-scale metabolic model: in silico single gene deletions by iIN800 were consistent with experimental data. In addition, 13C-labeling experiments validated the new biomass equations and calculated intracellular fluxes. To demonstrate the applicability of iIN800, we show that the model can be used as a scaffold to reveal the regulatory importance of lipid metabolism precursors and intermediates that would have been missed in previous models from transcriptome datasets.The reconstructed metabolic model comprises 1446 reactions and 1013 metabolites. Beyond incorporating new reactions involved in lipid metabolism, we also present new biomass equations that improve the predictive power of flux balance analysis simulations. Predictions of both growth capability and large scale iIN800 as a network scaffold is shown to be a valuable tool for elucidating the behavior of complex metabolic networks, particularly for identifying regulatory targets in lipid metabolism that can be used for industrial applications or for understanding lipid disease states.Performing integrated analyses using  Saccharomyces cerevisiae is widely used for production of many different commercial compounds such as food, feed, beverages and pharmaceuticals [The yeast euticals . It alsoeuticals ,3. Aftereuticals , about 4euticals . This haeuticals -7.Several human diseases  are associated with disorders in lipid metabolism -10. The Previous work has shown that genome-scale metabolic models provide an excellent scaffold for integrating data into single, coherent models . The caliFF708, iND750 and iLL672, have been published. All three models, however, lack a detailed description of the lipid metabolism. The first model, iFF708 [iFF708 shows good predictions of many different cellular functions [iND750 [iND750 is fully compartmentalized, consisting of 1498 reactions linked to 750 ORFs. The model was validated by a large-scale gene deletion study and metabolic phenotypes [iND750 contains more reactions and metabolites in lipid metabolism than iFF708, but still lacks a comprehensive description of lipid metabolism. The third published model is iLL672, which is derived from iFF708 and comprises 1038 reactions. Several dead-end reactions of iFF708 were eliminated leading to an improved accuracy of the single gene deletion prediction [13C-labeling experiments to study the robustness of different yeast mutants [So far, three yeast genome-scale metabolic models, , iFF708 , consistunctions  and geneunctions . However [iND750 . iND750 enotypes  and was enotypes . iND750 ediction . However mutants .iFF708 as a template for building a model based on recent literature that contains new reactions in lipid metabolism and transport relative to all previous models. The new model named iIN800 includes 92 additional ORFs and provides a more detailed structure of lipid metabolism, tRNA synthesis and transport processes than previous models. The biomass composition, which is very important for flux balance analysis and predicting lethality, was also recalculated and improved. iIN800 was validated with large-scale gene deletion data and growth simulation predictions. Simulated intracellular fluxes were also supported by 13C-labeling flux experimental data. Finally, we show that the transcriptome data of yeast cultivated under various growth conditions can be integrated with iIN800 to identify lipid related Reporter Metabolites. We anticipate that iIN800 will be useful as a scaffold for integrating multilevel omic data and that this new model will have a significant impact in the emerging field of lipidomics.Here our objective was to expand the genome-scale metabolic model of yeast to include a detailed description of lipid metabolism for use as a scaffold to integrate omics data. We used iND750 and the smaller scope of iLL672, the metabolic model iFF708 was selected as a template for the development of the model iIN800. Pathway and reaction databases (e.g. KEGG), online resources (e.g. SGD), and literature were used to expand iFF708, with particular focus on lipid metabolism. iIN800 contains 340 total reactions in lipid metabolism, more than at least 143 reactions greater than previous models  , β-ketoacyl-ACP reductase, β-dehydroxyacyl-ACP dehydratase and enoyl-ACP reductase. In the cytosol, these enzymes are encoded by the multifunctional FAS1 and FAS2. In the mitochondria, however, fatty acid synthesis is carried out by the products encoded by CEM1, OAR1, HTD2 and ETR1. These ORFs were missing from previous models, which prevented simulation of mitochondrial fatty acid synthesis. Fatty acid elongation, which leads to the production of long-chain fatty acids, was not included in iFF708, but was also updated in iIN800. Including fatty acid elongation resulted in the addition of four major biochemical reaction steps: condensing enzyme, 3-ketoacyl-CoA reductase, enoyl-CoA dehydratase and enoyl-CoA reductase [ELO1, ELO2, ELO3, IFA38 and TSC13. While the gene encoding enoyl-CoA dehydratase has not been identified in S. cerevisiae, the reaction was inferred due to the identification of long chain fatty acids in yeast.To compare metabolic characteristics of the different s) Table . Fatty aeductase . These rFAT1, encoding an enzyme for long-chain fatty acid activation was missing in iFF708 and iLL672. The genes SPS19, ECI1 and DCI1 are also now included in iIN800. As a result, iIN800 can simulate the oxidation of unsaturated fatty acids.β-oxidation is the process where fatty acids, after becoming activated in the form of acyl-CoAs, are broken down to make acetyl-CoA, and ultimately energy. iIN800 according to a recently reported model [iFF708. Sphingolipid synthesis is the only sub-category in iIN800 with a significantly lower reaction tally than iND750. This is because iND750 incorporated both C24:0 and C26:0 as very long-chain fatty acids (the back bone of sphingolipids) to produce ceramides. Because the amount of very long chain fatty acids in S. cerevisiae is so low relative to other fatty acid species  [iIN800 treats very long chain fatty acids as a single metabolite. As a result, fewer reactions are present in sphingolipid synthesis.Sphingolipid synthesis reactions were added to ed model , resultiiIN800. However, esterification of sterols and degradation of lipids, which were not included in all other previous models, are present in iIN800 .In summary, iIN800 was to address the concern that the biomass composition of S. cerevisiae changes under different growth conditions. For example, during growth on excess glucose the carbohydrate content increases and during growth on excess ammonium the protein content increases.The biomass equation is crucial for using genome-scale models to simulate growth using flux balance analysis (FBA). Therefore, an important consideration in the development of iIN800 towards changes in the macro-molecular composition, we performed constraint-based simulations by varying the protein, RNA, carbohydrate and lipid content of the biomass in physiological relevant ranges based on previous experimental reports [To assess the sensitivity of flux simulations using  reports -29, fromIn summary, the sensitivity analysis shows that the biomass composition can significantly impact predictions made with genome-scale metabolic models to varying degrees based on different growth conditions. We therefore present new biomass equations to be used under C-limited and N-limited growth conditions, respectively. These compositions result from previous studies and our own measurements of lipids and fatty acids across multiple N-limited and C-limited growth conditions (data not shown). Using a separate biomass composition for N-limited cultures has not been proposed previously. The N-limited biomass equation is therefore new. Relative to previous C-limited biomass compositions, the most dramatic changes in our here proposed biomass equation is with respect to the lipids and fatty acids Table . While oIn silico genome-scale models are most generally used to predict various phenotypes. These include growth rates and extracellular secretion rates of metabolite products, as well as uptake rates of nutrients. In addition, models can be employed to explore active route(s) in metabolic pathways under certain growth conditions as illustrated for a genome-scale metabolic model of E. coli [S. cerevisiae genome-scale metabolic models [ E. coli -32 as wec models .iIN800, we first investigated the model's ability to simulate aerobic and anaerobic growth in glucose- or ammonium-limited conditions. Several published chemostat datasets were used as experimental references. As shown in Figure To validate 13C-flux analysis data to further confirm the computed intracellular fluxes. Specifically, fluxes in the central carbon metabolism at two different growth conditions were both measured by 13C-labeling experiments and calculated by FBA using iIN800. The model validation is shown in Figure Since the new biomass equations would be expected to impact the overall flux distributions, we used iIN800, we investigated the ability of the model to predict for growth viability due to a single gene deletion. In silico deletion phenotype predictions were examined for the new model with cells grown in both minimal media with a sole carbon source  and with rich media (YPD). iIN800 was assessed for its ability to make correct predictions based on experimental data [in silico single gene deletion predictions are given in Table iIN800, derived from 3392 total predictions, was 89.36%, with 95.50% sensitivity and 38.69% selectivity. The evaluation of the mean of a confusion matrix as the geometric mean of iIN800 equals 60.79%. The performance of the iIN800 model has improved by ~2% and ~7% in terms of overall prediction rate compared with the models iFF708 and iND750, respectively. We believe that the improvement is mainly due to upgrades in the biomass equation, which is consistent with results from Kuepfer et al. demonstrating that more accurate biomass compositions lead to improved lethality predictions [To verify further tal data ,34. A sudictions . The faldictions ,19iIN800 and iFF708 were used to calculate Reporter Metabolites. Multiple sets of transcriptome data were used for analysis. Lists of the top thirty most significant Reporter Metabolites for several perturbations are compared between iIN800 and iFF708 in Table iIN800 are marked in bold.Genome-scale metabolic models have shown promise for identifying Reporter Metabolites, defined as metabolites whose neighboring genes in a bipartite metabolic graph are most significantly affected and respond as a group to genetic or environmental perturbations . Such aniIN800 that would have been missed if iFF708 was used as the scaffold  were identified. These genes were then used to search for highly regulated subnetworks within a protein-protein and protein-DNA interaction network. By applying a p-value threshold of 0.01 to filter for genes with significant gene expression, we inferred a regulatory network controlling the expression of lipid metabolism genes associated to the Reporter Metabolites , OAF1 (β-oxidation), and INO1 and INO4 (phospholipid synthesis), among others. Previously reported genome-scale models are not capable of being used as scaffolds for implicating the conditional response of these lipid metabolism regulators because they lack a detailed description of lipid metabolism.Without the expanded model, the importance of cellular regulation stemming from lipid metabolism would be missed in analyses where metabolic topology is used for integrating data. As an illustration, we integrated results from our Reporter Metabolite analysis with known protein-protein and protein-DNA interaction networks to infer regulatory structure. First, genes associated to Reporter Metabolites in lipid metabolism unique to s Figure . StrikinS. cerevisiae genome-scale metabolic model. In this work, we focused on improving the formulation of lipid metabolism relative to previously published S. cerevisiae genome-scale metabolic models. Validating the model and new biomass equations, the constraint-based simulation of iIN800 showed accurate predictions of cellular growth and is also consistent with 13C-labeling experiments. Furthermore, in silico gene essentialness predictions were found to be in high agreement with in vivo results. Finally, we show that iIN800, being more complete, is a better network scaffold for integration of multilevel omics data.Genome-scale metabolic models have emerged as a valuable tool in the post-genomic era for illustrating whole-cell functions based on the complete network of biochemical reactions. An iterative reconstruction process is required to achieve a comprehensive iIN800 is positioned to have a broader impact than previously described yeast models. Its capability of predictions were consistent with a number of experimental data both quantitatively (growth rate) and qualitatively . Moreover, the new model is positioned to be used for studying the regulation and role of lipid metabolism during different growth conditions. With the high degree of homology in lipid metabolism between yeast and humans and emergence of lipidomics, this is expected to allow for new insights into the connection between lipid metabolism and overall cellular function for industrial and medical applications.In conclusion, by incorporating a more complete description of lipid metabolism, S. cerevisiae genome-scale metabolic model was done by expanding iFF708 [S. cerevisiae, such as SGD [iFF708, called iIN800, was visualized by Adobe Illustrator software (Adobe Systems), and then converted to EPS format (Adobe Systems) format which is downloadable as Additional file iIN800 is provided as Additional file Reconstruction of the g iFF708 . The addh as SGD , MIPS [4h as SGD  and YPD h as SGD , were alh as SGD , ExPASy h as SGD , and Reah as SGD , were usiIN800 was used for construction of a stoichiometric matrix S (m × n). In the stoichiometric matrix, m = 1013, which is the number of metabolites, and n = 1446, which is the number of metabolic reactions. With an assumption of steady state for all metabolite pools, a linear equation constraining the fluxes in the metabolic network is obtained [The reaction set in obtained ,47:v is a vector that contains all the fluxes in the model. Equation (1) has a large number of degrees of freedom, i.e. it is an underdetermined problem, and linear programming was employed to solve the equation system by maximizing an objective function Z , an approach generally referred to as flux balance analysis (FBA) [Here is (FBA) ,47. The Maximize:Subject to:α and β are lower and upper bounds of fluxes respectively, ω is a weight vector indicating an amount of desired metabolites for biomass synthesis. For irreversible fluxes semi-positive infinite boundary was applied as 0 ≤ v ≤ ∞, and fully infinite boundaries was applied as -∞ ≤ v ≤ ∞ for reversible fluxes. The problem was solved by using the commercial linear programming software package LINDO . The calculated intracellular fluxes were overlaid on the visualized genome-scale map as described previously by the ReMapper software .where -1. The calculations were performed as described previously [The biomass composition was re-calculated in order to improve the prediction of the model during growth at different nutrition-limitations, i.e. carbon- and nitrogen-limited growth condition. The contents of macro-molecules were extracted from the thesis of Schulze  who measeviously . The caleviously . Deoxyrieviously . Lipid ciIN800 were evaluated by using FBA and linear programming to simulate the biomass flux representing the in silico growth rate, which were derived by maximizing the biomass production. Data from various carbon-limited and nitrogen-limited chemostat experiments performed at either aerobic or anaerobic growth condition were taken from the literature for comparisons , which was the objective function, was changed depending on the growth conditions evaluated according to the data provide in Table The metabolic capabilities of iIN800 was evaluated by eliminating the reaction(s) corresponding to each gene in the model from the stoichiometric matrix S and then simulating growth of the mutant by FBA. The in silico gene essentialities were simulated for growth on rich- and minimal-medium. For minimal media, different carbon sources , ammonium, sulphate and phosphate were evaluated. For rich media, the uptake fluxes of amino acids, purines and pyrimidines were added as additional constraints as previously described [in silico simulations were compared to experimental data available in the MIPS and SGD databases and from competitive growth assays [iIN800 to predict gene essentiality was evaluated based on the criteria defined as follows:The impact of individual gene deletions on cell growth of escribed . The in h assays  as well h assays . The powwhere TP = true positive, TN = true negative, FP = false positive, FN = false negative. Positive and negative values referred to viable and lethal phenotype, respectively.Published microarray data were retrieved from Gene Expression Omnibus (GEO) . The CELBriefly, we describe the Reporter Metabolite calculations. The genome-scale model was converted to a bipartite undirected graph. In this graph each metabolite node has as neighbors the enzymes catalyzing the formation and consumption of the metabolite. The transcriptome data were mapped on the enzyme nodes using the significant values of gene expression. The normal commutative distribution was used to convert the p-values to a Z-score for further calculations. To identify an importance of metabolites in the metabolic network of the particular experimental conditions, the reporter algorithm was applied as described earlier .The interactome network was initially constructed with data obtained from YPD , ChIP-ch13-labeling flux experiments, helped curate the model and contributed to manuscript writing. AM, CT, KL and SC contributed to the manuscript preparations, JN and SB participated in the concept and design of the study. All authors read and approved the final manuscript.IN designed the study, performed the metabolic reconstruction and validation, and contributed to manuscript writing. MCJ carried out the CAdditional ORFs. List if additional ORFs and their references containing in iIN800.Click here for fileLipid metabolism reactions and comparison. Comparison of lipid metabolism reactions of all S. cerevisiae genome-scale models.Click here for fileGrowth simulation results. Growth simulations and comparison with experimental measurements.Click here for fileAerobic Flux distribution. Visualization of flux distribution of aerobic growth mapping on Figure Click here for fileAnaerobic Flux distribution. Visualization of flux distribution of anaerobic growth mapping on Figure Click here for fileHigh resolution file of Figure S. cerevisiae metabolic map is provided as EPS format.Click here for fileiIN800 model. List of all participated reactions in iIN800 model.Click here for file


Simulations show that activation of ATP-coupled load reactions plus glucose oxidation is brought about by an increase of only two different conductances: a [Ca2+] dependent increase of cytosolic load conductances, and an increase of phosphofructokinase conductance by [AMP], which in turn becomes increased through [ADP] generation by those load reactions. In ventricular myocytes, this feedback mechanism is sufficient to increase cellular power output and O2 consumption several fold, without any appreciable impairment of energetic parameters. Glucose oxidation proceeds near maximal power output, since transformed input and output conductances are nearly equal, yielding an efficiency of about 0.5. This conductance matching is fulfilled also by glucose oxidation of β-cells. But, as a price for the metabolic mechanism of glucose recognition, β-cells have only a limited capability to increase their power output.A new formalism to describe metabolic fluxes as well as membrane transport processes was developed. The new flux equations are comparable to other phenomenological laws. Michaelis-Menten like expressions, as well as flux equations of nonequilibrium thermodynamics, can be regarded as special cases of these new equations. For metabolic network modeling, variable conductances and driving forces are required to enable pathway control and to allow a rapid response to perturbations. When applied to oxidative phosphorylation, results of simulations show that whole oxidative phosphorylation cannot be described as a two-flux-system according to nonequilibrium thermodynamics, although all coupled reactions  In recent years mathematical modeling of metabolic pathways became increasingly important as a helpful tool for a deeper understanding of biochemical reaction networks in cellular metabolism and energetics. Besides older kinetic approaches, several new models were developed, whose flux equations contain driving forces, primarily to eliminate possible inconsistencies with the Second Law of Thermodynamics –9. In twIn this study, the phenomenological character of equations is underlined, especially in relation to the realities of living cells. Equations are based on the concept of entropy production  and asso2 consumption, energetic parameters of working hearts like the cytosolic ATP concentration ([ATP]c) are not appreciably lowered under these conditions ) is mandatory to activate insulin secretion. This increase of substrate concentration is not only needed as a stimulus ,30, but Both markedly different cell types use the same reactions of glucose metabolism, but with an appreciably different ability to gain free energy from these metabolic pathways. The solution of this problem may elucidate the control mechanism by which the flow of free energy of glucose oxidation becomes available for increased power outputIn previous articles  a neA (J/mol) denotes the affinity or driving force of a given reaction. It is defined as A = −dG/dξ (G = Gibbs free energy (J/mol), ξ = extent of reaction (mol)). A is not constant, but depends on the mass action quotient of variable nonequilibrium activities (≈concentrations). L (μM/ms × mol/J) denotes the conductance of that reaction. It is treated here as a variable, which can be varied by concentrations of metabolites, cofactors, and inorganic ions like Ca2+ (c’s).J is given byWhen applied to membrane transport reactions, flux orG’s denote conductances (in pS), Δμ̃ and Δμ (both in mV) are the electro-chemical and chemical potential differences, respectively, of the transported substance. α represents a conversion factor converting electric current I into flux J (see Section 3).respectively. Both T = absolute temperature (K), V = system volume (L), diS/dt = entropy produced during time interval dt). For T = const., an equivalent form of this equation is given by constant). For k = 1 k > 1, (3a) changes to Hill’s Equation c induced forced oscillations (see Section 2.3.2). At high A’s (panels A and B), flux oscillations are brought about mainly by activation factors, whereas at near zero driving forces, flux oscillations follow the oscillations of respective A’s about zero. The Second Law of Thermodynamics demands that the reaction rate of a spontaneously proceeding reaction goes against zero continuously. The oscillations about zero (c).In out zero  do not vL’s respectively, a metabolic pathway composed of n in series enzyme-catalyzed reactions may be regarded. If, e.g., Li is increased by a factor f at constant L’s, the pathway flux J expectedly would be increased by a factor f′ < f. Then, according to Ohm’s law, the fractional increase of J is equal to the fractional increases of all n − 1 affinities at the n − 1 remaining conductances. Only the fractional change of Ai at Li  must be different from all others. It is given by ΔA/A0 = (ΔJ/J0 − (f − 1))/f.To demonstrate the different behavior between pathway fluxes composed of constant and variable n − 1 fractional changes of affinities are not equal as is to be expected for constant conductances. This fact is associated with a remarkably different quality. Pathway fluxes containing variable conductances, after a given perturbation, can reach a new steady state much more rapidly than those having constant conductances. This is verified with a simple simulation . Under variable conditions a new steady state is reached already after 3.0 min (see L’s the new steady state develops only after 160 min (not shown).The above conditions of constant conductances are equivalent to a simple electric network, but are probably not compatible with a metabolic pathway. Since, under these latter conditions, variable enzyme activities determine conductances and thus might be responsible for a quite different behavior. The  min see , whereasA’s to yield LEnzmax × Aconst = VEnzmax =const. ), under the same conditions are unable to produce a new steady state. Obviously, in addition to variable conductances, the inclusion of variable driving forces in pathway fluxes is indispensible for the toleration of non-infinitesimal changes of conductances as they occur in living cells, for instance during activation of glucose metabolism, to increase power output.In this context, it seems worth mentioning that Michaelis-Menten type formulations of pathway flux  has to be transformed to yield the same magnitude as the flux of the first part. Since a given Φ can be expressed by any other reliable product of J and A, and consequently also by a product containing a J of desired magnitude, e.g., JGK (which is a measure of glucose utilization), an altered affinity has to be determined in such a way that Φ remains unchanged. This transformed affinity is given byThis latter fact has to be taken into account, when and the associated transformed conductance byM values and other modeling parameters may suffice to fulfill reliability requirements.Such transformed values have to be used, when the steady state pathway flux of a metabolic network containing one or several fluxes of different magnitude is to be determined. To develop a simulation of a metabolic network like coupled glucose oxidation, it is not necessary to know all parameters exactly. If glucose utilization and/or oxygen consumption are known from experiments, conductances can be adjusted for a maximal power output. Affinities of single reactions often are given or may be estimated from Gibbs energies of formation [Alb]. With known stoichiometric coefficients the simulation must yield correct results also with respect to thermodynamic constraints, even if the steepness of flux equations is not precisely met. This means that the use of adjusted constants like KCExJ, which is defined asIn Metabolic Control Analysis (MCA) several dimensionless coefficients are defined, to quantify metabolic control at steady state . One of Ex = one particular enzyme concentration of a metabolic pathway of several reaction steps in series; ΔJx = change of pathway flux produced by a perturbation ΔEx/Ex = f − 1). According to MCA, the sum of flux control coefficients (f − 1) → 0.(red]) is fixed . As a source and sink, glucose ([Glu]) and pyruvate ([Pyr]) concentrations  are both held constant. The new steady states are produced by multiplying successively respective maximal conductances by the same factor f. In all cases a new steady state can be obtained, in which all individual fluxes of the pathway have changed by the same degree, including that with the imposed change. In addition, affinities and intermediates have changed, but to a different extent in each case. From the newly adjusted pathway fluxes J, the initial flux J0, and the imposed f, all flux control coefficients can be calculated. For f = 1.01 this yields CGKJ = 0.1258, CAldJ = 0.0021, CTiJ = 0.00037, CGJ = 0.0068, and CWJ = 0.8623, yielding To demonstrate changes of a pathway flux after a small perturbation, a simulation of GLY is used, in which the reduced nicotinamide adenine dinucleotide concentration (c, and Ca2+ pumps by [Ca2+]c, so that pump fluxes slow down when substrate concentrations become sufficiently lowered.In principle, to avoid static head production, coupled reactions are controlled in addition to parallel leak fluxes by their own substrates. For instance, Na-K pumps are kinetically controlled by c is absent.To prove Stucki’s hypothesis of conductance matching, a simulation of OP fuelled by pyruvate was developed , as well as between J2 and X1 . From this linear behavior Stucki concluded that for a given qov , X1 may be the only variable of this two-flux-system, and that all other parameters, i.e., X2, L11, and L12 are constant and can be derived from experimental results ) might become limiting as in β-cells (see below). Because [Glu] activation of hexokinase is saturated at resting concentrations ([Glu] = 4.0 mM), its conductance cannot vary which makes it more difficult if not impossible to develop a new steady state after a perturbation. This can be avoided by introducing a feedback inhibition of hexokinase by the concentration of glucose-6-phosphate ([G6P]), which in simulations can be expressed by the concentration of fructose-6-phosphate ([F6P]), since both intermediates are virtually at equilibrium through the phosphoglucose isomerase reaction (A2). Such a feedback can also avoid an extreme increase of [G6P] and [F6P]. So [F6P] appears as an additional variable in simulations of glucose oxidation in VMs. As a consequence, and in contrast to β-cell simulations, the PFK reaction is incorporated as an individual reaction step  into the glycolytic reaction sequence of VMs. It is activated by [F6P] and in addition by [AMP]c, and is inhibited by [ATP]c. Also the pyruvate kinase (PK) reaction, which is part of several contracted in series reactions, is inhibited in VMs by [ATP]c (A3).Hexokinase of heart muscle has a very low KCJ = 1.0. When conductances are changed successively, CJ does not reach 1.0. A pronounced change can already be obtained by changing simultaneously merely two conductances, that of JW , and that of JPFK . For f = 2.0, ∑CEnzJ under these conditions reaches a value of 0.8725. Interestingly, this value can be appreciably increased further to 0.9757 by including the indirect uncoupling flux JPL. In contrast, when all remaining conductances of these pathways are increased simultaneously by f = 2, this yields a ∑CEnzJ value of 0.0112 only. It seems noteworthy that also a direct uncoupling can appreciably augment ∑CEnzJ. For instance, increasing conductances of only [Ca2+]c dependent load reactions by f = 1.1, yields a ∑CEnzJ of 0.248. When under the same conditions the ATP synthase reaction is slightly uncoupled (λsp = λsh = 0.01), a ∑CEnzJ of 2.77 is obtained. This large increase of the sum of control coefficients by uncoupling is brought about by an appreciable increase of A⃗tot , and dehydrogenases of the citric acid cycle  is virtually without effect on power output and O2 consumption in present simulations, because respective conductances (LPDHmax and LCACmax) are adjusted to rather high values.The above results of control analysis show that increasing only two conductances may be sufficient to appreciably increase pathway flux and thus, also power output. A simultaneous increase of all maximal conductances is not necessary; the variability of conductances obviously is able to produce the demanded increase of whole pathway flux. Moreover, also fluxes through 2+]m activation becomes indispensable at an increasing power output [2+]m [JSY) by [Ca2+]m cannot increase power output, but reduces dissipation of free energy of this reaction. Beside these latter effects of [Ca2+]m, mitochondrial Ca2+ fluxes may be needed to synchronize free energy flows of several mitochondria during contraction cycles. Otherwise an optimal interplay of all involved reactions might not be guaranteed.In real VMs, these conductances might be appreciably lower, so that a m . In pres2+ transport by SERCA pumps are activated by an increase of [Ca2+]c. This in turn leads to an increase of ATPc consumption with a concomitant elevation of [ADP]c and [Pi]c. Because the adenylate kinase (AK) reaction is near equilibrium, this means that also [AMP]c must increase and PFK becomes activated, with the result that all pathway fluxes associated with glucose oxidation become activated too. So activation of ATPc utilization is followed by an appropriately adjusted ATPc delivery. In this way load reactions not only deliver useful work, but concomitantly generate [AMP]c, which quasi as a third messenger activates ATPc production, so that a drastic decrease of [ATP]c and associated AATPc may be prevented, even under conditions of a markedly increased power output. Present simulations demonstrate that the increase of only [Ca2+]c dependent load conductances and [AMP]c dependent LPFK is needed, to switch from low to a high power output.In the present simulation as well as in real VMs, important load reactions like muscular contraction or Ca2 consumption of working hearts shows linear dependence on mechanical power output over a wide range of delivered power c dependent change of τm. From NET it is clear that increasing Aτ must reduce the resultant force Acoup, so that the associated flux must be reduced too. This does not only decrease velocity of contraction, but also increases efficiency of this reaction.Oed power –25. SuchPWτ,= −ΦWτ= −JWτAWτ, JO2 depends linearly on this variable. Only at very high [Ca2+]c’s, O2 consumption begins to be larger than would be expected from linearity. Panel B shows that JO2 depends linearly on [ADP]c and [AMP]c. These results of simulations, however, do not support the conclusion that O2 consumption may be activated by [ADP]c at the level of ATP/ADP exchange of mitochondria. Even a tenfold increase of this flux conductance (LAEmax) could not further increase O2 consumption, which underlines above mentioned results of MCA. With permeabilized cardiomyocytes it could be shown c were operative also in coupled glucose oxidation of real VMs, an activation of whole pathway flux is absolutely necessary to deliver free energy under conditions of an increased consumption of free energy. Since it is not stored sufficiently in glucose metabolism itself including OP, it must be delivered by other stores, that is, mainly from the extracellular space in the case of VMs. So the controlled flow of free energy through the whole metabolic pathway is necessary to satisfy changing free energy demands. As is demonstrated with simulations, the most effective points of control are given by [Ca2+]c dependent load reactions and PFK. The flow of information from load to delivery is brought about by the feedback via AK of [AMP]c on PFK.But even if the above mentioned activation effects of [ADP]Δcφ), which in turn trigger periodic Ca2+ release from and accumulation into the sarcoplasmic reticulum (SR). The oscillating [Ca2+]c then may initiate—beside other activations—periodic contraction and relaxation of myofibrils. Thus, such [Ca2+]c oscillations are not generated by an intrinsic oscillator, but rather are forced by rhythmic depolarizations of Δcφ It seems justified, therefore, to simulate rhythmic behavior by simple sinusoidal oscillations of [Ca2+]c (A18). 2+]c oscillations. The arithmetic means of such oscillations deviate slightly from steady state results. For instance, when results of 2+]c = 0.18 μM JO2 and PWτ are 0.121 μM/ms and 3.273 J/Ls, respectively, in the absence of oscillations. In the presence of forced oscillations, respective means are 0.122 μM/ms and 3.432 J/Ls. Values at 0.72 μM [Ca2+]c are 0.570 μM/ms and 96.45 J/Ls, and 0.553 μM/ms and 95.18 J/Ls, respectively. Therefore, it seems justified to conclude that deductions made with respect to steady state are valid also under conditions of forced oscillations.Up till now all results were related to steady state conditions, intrinsic oscillations do not occur under these conditions and forced oscillations were excluded. VMs in heart tissue, however, contract rhythmically at various frequencies and variable pressure developments. These oscillating contractions are known to be induced by rhythmic depolarizations of the membrane potential  would be inappropriate to show that power output of coupled glucose oxidation is near maximal. The problem of non-reliable overall parameters can be circumvented, however, if transformed conductances were taken into account.Li matches the conductance of the outer circuit, Le. A battery can be regarded as a coupled two-flux-system, in which a chemical reaction with affinity A2 is coupled to an electrical potential difference, Δφ = −U, with affinity A1. Coupled glucose oxidation, when transformed to equal flux velocities, can be regarded analogously: the input force is given by A⃗ov, while the coupled output force is given by −A⃗ATPc. Both forces and conductances L⃗i and L⃗e can be obtained from respective dissipation functions as described above. In analogy to a simple electric circuit consisting of a battery whose poles are connected by an electrical resistance (Re = 1/Le) with an attached load, L⃗i is related to the whole pathway of glucose oxidation including coupled ATPc production, and Le to ATPc utilizing reactions, i.e., all cytosolic ATPases. As in an electric circuit, only the electrical resistance (Re) of an energy converter is involved with power maximation. In energy metabolism it is therefore only that part of L⃗W, which is associated with ATP splitting. That is, the flux through AATPc (JWp) is the relevant flux, and Le therefore has to be derived from the input dissipation function ΦWp, and not from total dissipation function ΦW = ΦWld + ΦWp. It is given byIt is well known in electrical engineering that power output of a battery becomes maximal when the internal conductance L⃗i is given byc, i.e., power output, is identical to the input dissipation function of the load reactionDelivery of free energy from coupled glucose oxidation in the form of ATPI = electrical current, and E = electromotive force), the respective flux is given byAnalogous to andPower output can be expressed then asor with L⃗i and A⃗ov were both constant, then ΦW p would be a function of Λ alone with a maximum at Λ = 1.0, or at L⃗e = L⃗iIf Λ is given byWith Λ = 1, yields η = 0.5.and GLY, A14) with constant conductances  and, in addition, with a feed back by [AMP]c on PFK leads however to entirely different results, when Λ is increased by an increase of [Ca2+]c . Only one point at Λ = 0.82 ([Ca2+]c = 0.18 μM) fulfils Equation (13g), all other values for ΦWp, and especially those found for higher [Ca2+]c’s are markedly elevated above that curve, but are all at nearly the same value of Λ , near a value of 0.5 (0.56)  . InteresΦWp must always fulfill the associated hypothetical power curve calculated each time for a given pair of values L⃗i; and A⃗ov. These curves are hypothetical insofar as especially L⃗i  is not constant at varying L⃗e. That is, only one single point of the curve related to a given particular condition is of significance.The respective points of Λ from 1.0 can be obtained by uncoupling OP. Λ’s. Both conductances, L⃗e as well as L⃗i, are increased by uncoupling OP, but L⃗e to a much higher degree, so that Λ increases and thus efficiency decreases. Λ’s, power output points are close to their hypothetical respective power curve. Comparison of these uncoupled values with those obtained for coupled conditions shows that larger losses of useful power obviously can be prevented. This power preservation is associated, however, with a marked reduction in efficiency  and adenylate kinase (AK), respectively.In VMs there are three well known pathways of [ATP]c and to shuttle it between mitochondria and cytosolic locations of high ATP usage like actomyosin ATPases in the myofilament lattice c production through the action of the PCr system counteracts PFK activation. Therefore, delivery of free energy may depend also on this reaction.It is widely accepted that the primary tasks of the phosphocreatine (PCr) system is to buffer [ATP] lattice ,49. In ac replenishment and power output. In the absence of [AMP]c activation of PFK and without PCr buffering, an increase of [Ca2+]c from 0.18 to only 0.32 μM is sufficient to increase [ADP]c from 80.8 μM to 4.24 mM (an increase of O2 consumption and ΦWp is abolished under these conditions). When PCr buffering can occur in the absence of [AMP]c activation, [ADP]c elevation is less pronounced (to 2.88 mM). On the other hand, under conditions of activation, an increase of [ADP]c is markedly abolished (to 110.14 μM). Additional PCr buffering then is virtually without effect (108.75 μM).While PCr shuttling is not included in simulations, AK and CK catalyzed reactions are present in all simulations of complete glucose oxidation. So, simulations without activation of PFK may show to what extent this activation may contribute to [ATP]4−] and [ADP3−]c c leads to Perhaps the most important task of the PCr system may be to function as a shuttle for [ATP[ADP3−]c , for theand2− is recycled, whereas PCr2− and Cr are consumed and produced, respectively. In the intermembrane compartment similar reactions occur, but with opposite directions. From the adenine nucleotide exchange reaction (JAE) at the inner membrane, ATP4− is delivered to the intermembrane space (‘im’), and ADP3− is transported into the matrix. Both are recycled by the PCr reaction in this compartment,In the filament compartment MgATP4−]im and [ADP3−]im cannot be equilibrated rapidly with the cytosol. The associated affinity, AATPim, may be high, so that here the PCrim reaction is forced into the direction shown in reaction (R1d). In contrast, in the environment of ATPases, AATPf may be lower, whereby here the PCrf reaction may be forced into the reverse direction ((R1a)). At both locations the PCr system may be near equilibrium, but because of different AATP’s, at different respective mass action ratios in both compartments. Two opposed concentration gradients, one of [PCr2−] and one of [Cr] are produced, driving diffusion of PCr2− from mitochondria to myofilaments, and Cr from myofilaments to mitochondria. The crossing of the outer mitochondrial membrane and the myofilament/cytosol interface by PCr2− occurs via electroneutral exchange against HPO42−. In the myofilament compartment, one H+ from H2PO4− restores one consumed proton by the PCr reaction. A third concentration gradient formed by [HPO42−] drives diffusion of this ion from myofilaments to mitochondria. In the intermembrane space, HPO42− takes up one H+ produced here from the reversed PCr reaction and finally enters as H2PO4− ion H/Pi symport at the inner membrane.Because of the limited permeability of the VDAC pore for adenine nucleotides,  oscillations occurred with such high peak values of about 10% as was found by Honda et al. . ACPK oscillates now again around zero. When power output switches back to lower values, the reverse processes lead to a re-increase of AATPc until respective ATPc rates match. The PCr reaction again oscillates around zero driving force, but now at a re-increased [PCr]. Supposedly, it is not necessary that concentrations of the PCr system must be changed during a contraction cycle to allow formation of sufficiently steep gradients. As mentioned above, this might be brought about by compartmentalization of AATPc.During repetitive contraction cycles oscillations of respective flows can be expected . It is qa et al. , as this2−] and [Cr] may be produced preferably at interfaces of mitochondria/cytosol and myofibrils/cytosol, respectively. For the maintenance of flows, it is necessary that compartments of high and low AATP are in close proximity, because otherwise gradients could be destroyed by soluble CK of the cytosol which may be present also in this compartment at high activity. Such structural prerequisites obviously are realized in VMs, in which mitochondria surround myofibrils and the sarcolemma in a highly ordered way.Gradients of [PCr2+]c and [ATP]c dependent like other load reactions of the cytosol. The sequence of events, however, leading to an activating increase of [Ca2+]c in β-cells is remarkably different from activation of VMs. In contrast to this latter cell type, an increase of [Ca2+]c in the β-cell is induced intracellularly by an increase of pathway fluxes of coupled glucose oxidation and associated decrease of [ADP]c (increase of AATPc). The lowered [ADP]c in turn closes ATP-sensitive K+ channels (KATP), leading to a depolarization of Δc φ and an influx of Ca2+ from the extracellular space through opened (by depolarization) voltagegated Ca2+ channels (CaV) into the cytosol [2+]c increase can certainly only be realized by oscillations. A low [ADP]c and an elevated [Ca2+]c cannot coexist over a longer period, because an increased [Ca2+]c would activate cytosolic load reactions including insulin exocytosis, which in turn leads to a re-increase of [ADP]c, a repolarization of Δcφ via opening of KATP channels, and a re-closure of CaV channels. A metastable state must be generated, which is characterized by oscillations with a phase shift between the two variables [Ca2+]c and [ADP]c c ,10. Thatc, but through activation of glucokinase by cytosolic [Glu]. Glucokinase has a much higher KM value than hexokinase from heart muscle and, therefore, is not saturated at resting (4.0–5.0 mM) [Glu]s. So, an increase of [Glu] from resting levels (4.0 mM) to 10.0 mM, although without an effect in VMs, activates glucose metabolism in β-cells. An increase of [Ca2+]c and [AMP]c is not needed for this kind of activation. The increase of [Glu] acts as a stimulus for insulin secretion, whereas the glucokinase reaction, beside its function as a hexokinase in GLY, constitutes in addition the recognition mechanism for this special stimulus.The initiation of an increased glucose metabolism, in contrast to VMs, does not proceed via activation of PFK by [AMP]c as a variable, so that certain flexibility also for β-cell simulations may be ensured. This is the main difference  between simulations of whole coupled glucose oxidation of VMs and β-cells. In these latter cells the concentration of total adenine nucleotide concentrations is, however, much lower than in VMs. In β-cells, especially [ATP]c is much lower . The responsiveness of PFK and PK to the inhibitory action of [ATP]c, therefore, may be drastically lowered in β-cells, even if in this cell type the same isoenzymes as in VMs were expressed. That is, the functional characteristics of these enzymes might be markedly changed simply by a lowering of [ATP]c.Glucokinase of β-cells is known to be not inhibited like hexokinase by G6P]. In simulations of glucose metabolism of VMs, the inhibition by the latter variable is needed to make this first reaction step more flexible for the adjustment of a steady state. Because [Glu] is not a variable but a fixed parameter, flexibility of the first step of GLY in β-cells has been introduced by contracting the first three reactions of GLY, including the PFK reaction to one single step  causes a reduction of power output (0.18 μM [Ca2+]c) in these cells of about 43 %, and an increase of [ADP]c from 260 to 3153 μM. At higher [Ca2+]c’s, these effects are even more pronounced.The above described mode of glucose recognition has its price, however. Compared with VMs, delivery of free energy in β-cells via coupled glucose oxidation is drastically cut back through the limited capability of GK to respond on [Glu] activation. Power output at 4.0 mM [Glu] can be increased only up to a  of 10.0 mM β-cells are less susceptible to cell damage, but insulin release can be seriously jeopardized by a relative weak uncoupling. Under activated conditions at very low values of c in β-cells would be markedly increased. Furthermore, because it seems plausible to suggest that mitochondria of other cell types like muscle cells might not differ in this respect, a tight coupling of inner mitochondrial membranes can be expected.From this behavior of β-cells, a fundamental conclusion with respect to the degree of coupling of mitochondrial inner membrane reactions can be reached: especially ATP synthase must be tightly coupled, because otherwise [ADP]tot] does not exceed 1.0 mM. At higher concentrations normal oscillations of Δ cφ and [Ca2+]c cannot be elicited anymore, whereby insulin release becomes markedly reduced. In the absence of PCr shuttling, normal functioning of stimulus-secretion coupling nevertheless may be possible, since the oscillatory frequency of activated β-cells is very low compared to rhythmic contractions of VMs, so that diffusional restrictions for adenine nucleotides cannot impair power output.As is already described above, the PCr system shuttles ATP free energy between mitochondria and ATPases. It is questionable, however, if this system of facilitated transport may be operative in β-cells, because the buffering effect of the PCr system might interfere with the oscillatory machinery of stimulus-secretion coupling. Δ cφ are omitted in present simulations. In addition, also most of SR reactions are excluded, only Ca2+ pumping of the sarco/endoplasmatic reticulum Ca2+ ATPase (SERCA) as an ATP consuming reaction is included in simulations. [Ca2+]c therefore appears in calculations not as a variable but as an adjustable parameter.For a treatment of coupled glucose oxidation as an integral part of cellular energetics, cell membrane and SR reactions are of secondary importance. Therefore, to simplify expressions, all reactions of the cell membrane and α values have to be adapted for VMs. Data from Aliev et al.  and [Mg2+] dependent ATP hydrolysis and mitochondrial transport reactions are taken from reference c and [Mg2+]m are set for both cell types to 0.8 mM. Constants for the AK and CK reaction (A10 and A11), respectively, are taken from Golding et al. c dependent load reactions and at PFK. For maximal power output respective conductances of in—and output fluxes must be similar in magnitude. This conductance matching is sufficiently fulfilled over a wide range of useful power generation. It may represent the basic mechanism of energy metabolism to ensure a high cellular power output under conditions of a sufficient supply of substrate and oxygen. Moreover, it may be regarded as a necessary prerequisite for the development of so-called fight or flight behavior, as it can be observed in higher vertebrates as well in more primitive forms.In simulations of coupled glucose oxidation, a drastic increase of free energy flow to increase power output can be achieved only at two points, at [CaIn β-cells, the GK enzyme is limiting the metabolic rate of coupled glucose oxidation, whereby the metabolic mechanism of glucose recognition is made possible. Obviously, only a few changes in the first reaction steps of glucose metabolism are sufficient to produce that remarkably large difference of power output between VMs and β-cells. On the other hand, both cell types differ enormously not only in size and geometry, but also in their markedly different degrees of structural organization. This strongly indicates that a task such as high power output may be guaranteed only if, in addition to adequately controlled pathways, that appropriate structural realities also exist. Only in this way, conductance matching for a maximal power output can be realized.