Analysis of the raw spectral datasets showed specific changes linked to the different stages during unrestricted yeast growth, as well as specific changes linked to each of the four tested starvation conditions . Analysis of changes in concentrations of more than 40 metabolites by Multivariate Curve Resolution – Alternating Least Squares (MCR-ALS) showed the normal progression of key metabolites during lag, exponential and stationary unrestricted growth phases, while reflecting the metabolic blockage induced by the starvation conditions. In this case, different metabolic intermediates accumulated over time, allowing identification of the different metabolic pathways specifically affected by each gene disruption. This synergy between NMR metabolomics and molecular biology may have clear implications for both genetic diagnostics and drug development.Disruption of specific metabolic pathways constitutes the mode of action of many known toxicants and it is responsible for the adverse phenotypes associated to human genetic defects. Conversely, many industrial applications rely on metabolic alterations of diverse microorganisms, whereas many therapeutic drugs aim to selectively disrupt pathogens’ metabolism. In this work we analyzed metabolic changes induced by auxotrophic starvation conditions in yeast in a non-targeted approach, using one-dimensional proton Nuclear Magnetic Resonance spectroscopy ( Metabolomics aims to identify the specific cellular processes undergoing in biological organisms by the identification and quantitation of dozens to thousands metabolites with high-throughput techniques, by using a non-aprioristic approach2Saccharomyces cerevisiae is widely used in many biological fields, such as biotechnologyHIS3, LEU2, MET15 and URA3, also called genetic markers) is confronted with a medium devoid of one or more of the essential metabolites it can no longer synthesize . Reports of metabolic disruption in yeast have previously focused on the triggered proteins14Among the eukaryotic microorganisms, the yeast Conventional technologies for metabolomic analyses include Nuclear Magnetic Resonance (NMR)1H NMR to identify metabolic variations related to distinct genetic backgrounds1H NMR to the study of local disruptions of metabolic pathways, an approach that can be extrapolated to determine the specific triggers for other locally disrupted processes.A previous study has proven the capacity of 1H NMR datasetBy combining the information obtained from the previous metabolic profiling with advanced data analyses, distinct metabolic profiles can be obtained rather than only specific metabolic markers for each studied condition. Here we took advantage of the chemometric approach MCR-ALSLack of each one of different auxotrophic markers resulted in a reduction of cell growth, probably reflecting the depletion of the respective internal pools . In this1H NMR spectral dataset . Two components explained 61.6% of the total variability, most of it associated to metabolomic changes in yeast cultured in His-DM and Ura-DM , confirmed a significant interaction (p ≤ 0.018) between time and yeast medium, either for the complete dataset or when using partial datasets, including any of the drop-out media versus control samples, confirming the temporal metabolome variability associated to the different growth conditions , a second, less defined one, including metabolites accumulated in the lack of L-histidine (His-DM), and the last one including the remaining metabolites . Close iMaterials and Methods and t1–t4, associated to four metabolic profiles, m1–m4, were obtained from this analysis, with an explained data variance of 85.7%. t1–t4 temporal components for each experimental condition are presented in m1–m4 metabolic profiles associated to each temporal profile are represented in the heatmap of Estimated concentration changes from proton resonances were analyzed using MCR-ALS  to exponential and lag growth phases, respectively. Analysis of the metabolites associated to each of these two components revealed that m1 has strong contribution of L-methionine, L-leucine, fatty acids, uracil precursors (orotate and orotidine-5P), and AMP. On the other side, m2 shows strong contributions of amino acids and amino acid precursors , citrate and trehalose, among others , L-ornithine, L-proline and L-lactic acid to m4  were also accumulated in Ura-DM, suggesting that both purine and pyrimidine pools were affected due to the lack of uracil in the medium. N6-methyladenosine, which is the most common internal mRNA modification in eukaryotesStarvation-induced metabolomic changes can be interpreted under the point of view of the biochemical pathways interrupted by the corresponding gene disruptions . This an1H NMR analysis that limit its use for metabolomic studies. On one hand, it is assumed that in terms of sensitivity (limit of detection), NMR clearly lags behind chromatographic/MS-based methods. Second, the intrinsic complexity of the 1H NMR spectra due to overlapping makes very complicate to evaluate complex mixtures of a wide variety of molecules present at very different molar concentrations, such as in metabolite extracts. Although the sensitivity and the resolution aspect is an instrumental problem that can be tackled by many technical improvements , the dynamic range problemThere are two characteristics of 1H NMR spectral dataset, and MCR-ALS on the metabolite concentrations. With these three chemometric methods, the metabolic responses of yeast at four starving conditions have been characterized  may trigger very different responses in the yeast metabolome, or that yeast growth efficiency is not correlated to the metabolic variance. These conclusions can be easily deduced from time and yeast medium, confirmed by ASCA, indicates that the lack of auxotrophic markers alters the velocity and duration of the different yeast growth events.Chemometric analysis of the complete 1H NMR data allowed the characterization and evaluation of the physiological conditions of a cultured organism. Qualitative metabolite concentration changes can be extracted from the loading plots associated to PCA analysis, as shown elsewhereTherefore, either by using PCA or ASCA, the analysis of m1 and m2) as reflecting the alternation between the stationary and the exponential growth phases, induced by the presence of high concentrations of glucose in the medium and regulated by the PP2A/TOR signalling pathwaym2 in m1 in m2 in 32We interpret the metabolic changes observed in yeast under unrestricted conditions (components m3 and m4) can be easily interpreted as the primary metabolic response from depleting the missing metabolites (i.e. uracil in Ura-DM), consisting on the accumulation of the precursors generated at the metabolic steps immediately upstream them (i.e. EIGP to His3p and Orotidine-5P to Ura3p), , . It is iSaccharomyces cerevisiae. This includes population mixtures or non-model biological organisms in which conventional pathway analyses approaches (i.e. ‘fluxomics’) might be difficult to implement.It is important to note that the use of MCR-ALS for studying -omic data should be applicable to essentially any other biological sample aside of the model organism 1H NMR spectral profiles and when identified metabolites were individually analyzed, suggests different regulatory pathways activated as a response to the different amino acids. Both L-leucine and L-methionine starvation have been linked to G0/G1 arrest through the PP2A/TOR signaling pathway, a mechanism fully compatible with our observations at the metabolome levels34353637Perhaps the most streaking observation of the metabolome analysis was the radical differences between the effects of L-histidine starvation on one side and of L-leucine and L-methionine starvation on the other side. Irrespectively of the effects for the global growth, Leu-DM and Met-DM cultures showed minimal metabolome variations during the 24 h-incubation period , whereas His-DM cells’ metabolome steadily diverged from its initial composition upon time. This effect, observed both for the complete 1H NMR to analyze metabolome effects of enzymatic pathway disruptions without any previous hypothesis nor anticipation of the nature of the possible metabolic pathway blockage. Analysis of the complete 1H NMR spectral profiles allowed us to distinguish between those conditions blocking the entry into the cell cycle (Leu-DM and Met-DM) from those that allow the progression of at least some metabolic pathways , and this without the need of identifying the specific metabolic concentration changes. Identification of the altered metabolites under each starvation condition could in principle allow the identification of the affected metabolic pathway in all four cases, and pinpoint the disrupted enzymatic steps in at least two of them. We conclude that the proposed NMR metabolomics strategy can be useful for studying models of metabolomic disruption either with genetic defects or with enzymatic inhibitors in many biological systems, including the study of the molecular target of biocides or the metabolic response of malignant cells to antitumorals.In this work, we used a genetically well-known model system to test the power of Therefore, we consider that the synergy between NMR metabolomics and molecular biology can be very useful in genetic studies, such as transcriptomics, but may be also applicable in genetic diagnostics and drug development.S. cerevisiae BY4741  cells were pre-cultured in YPD  medium on an orbital shaker (150 rpm) at 30 °C overnight. All following cultures were cultured with these shaking and temperature conditions. 2 L of YNB Synthetic Complete medium , 5 g/L (NH4)2SO4) supplemented with the appropriated auxotrophic markers  were inoculated with 200 μl of the pre-culture sample and left at the same temperature and shaking conditions until the culture reached an optical density at 600 nm (OD600) of approximately 0.8–1. Pellets from these resulting cultures were collected by centrifuging the cultures, but not washed, at 2000 rpm for 3 min and 4 °C. Pellets were used right after for inoculating erlenmeyers containing either YSC medium (control) or drop-out media missing either L-leucine, L-histidine, uracil or L-methionine, up to a final OD600 of 0.4–0.5. Resulting cultures were grown at 30 °C and 150 rpm.2HPO4 100 mM pH 7.0 followed by a centrifugation at 4700 g for 3 min. Resulting pellets were stored at −80 °C and lyophilized. Cell density was calculated as OD600, and viable cell counted by plating culture dilutions in YPD agar plates  for each sample.100 ml aliquots of every culture were collected six times during one day . Samples were arrested with a cold shock in ice and cell were harvested by centrifugation at 4000 g for 3 min, discarding the supernatant. Cells were washed twice in NaMetabolites were extracted by following the protocol published in a previous work2DPO4 100 mM, pH 7.0) in D2O with DSS 0.2 mM as internal standard.Aqueous samples were dissolved in 700 μl of deuterated phosphate buffer . Spectral size range covered from −2 to 10 ppm. Receiver gain was fixed to 34. Also, 512 scans were used with a relaxation delay of 5 seconds. Spectral size contained 65 k data points, and the acquired size was made of 32 k complex data points.Spectra were preprocessed with MestreNova v.10.0 . Spectra preprocessing consisted in an exponential apodization of 0.5 Hz, a manual phasing and a baseline correction with Bernstein polynomial of 3rd order. After adjusting the reference to DSS, water (4.41–5.16 ppm), methanol (3.30–3.37 ppm), chloroform (7.64−7.69 ppm) and DSS (<0.8 ppm) regions were removed. Data points which chemical shifts were higher than 10.3 ppm were also removed. The final NMR dataset consisted on a data matrix of 90 spectra (rows) having 35,342 ppm values (columns) each one. This data matrix was stored in ASCII file format.1H NMR signals using a home-made 1H NMR spectra libraryBiocyc databaseMetabolite assignment was performed by a detailed targeted metabolite profiling analysis of the 1H NMR spectral matrix were performed using BATMAN R20Relative metabolite quantifications of the 1H NMR spectra from the previous preprocessing steps were imported to Matlab R2014a  and analysed with the PLS toolbox 7.8.0 . In order to eliminate sample size effects, 1H NMR spectra were normalized using the Probabilistic Quotient Normalization (PQN)Chemical shift corrections were performed using the icoshiftPCA was applied to the mean-centered PQN-normalized NMR spectral data matrix (dimensions of 90 × 34443 data points), using Cross-Validation with Venetian Blinds to find the most reliable number of components to be included in the models.time and medium in this study). In order to check the statistical significance of the effects of the investigated factors and of their possible interactions, a permutation test was performed47ASCA45In order to resolve the metabolic patterns that evolve over time, the Multivariate Curve Resolution by Alternating Least SquaresMCR-ALS is a chemometric method which decomposes a data matrix using the following bilinear model:X (size I × J) has the concentrations of the J metabolites obtained by integrating their corresponding proton resonances, in the I yeast samples, cultured in a particular medium during a particular time period. This matrix bilinear decomposition gives two factor matrices, MT and T, the matrix of metabolic profiles, MT (N × J), and the matrix of temporal profiles, T (I × N). Each metabolic profile in M shows its metabolite composition, whereas T shows the contribution of each individual metabolic profile in every sample at different collection times. N represents the number of components used in the decomposition generated in the MCR-ALS analysis. N can be initially estimated by using a singular value decomposition (SVD)E matrix (size I × J) contains the residual information not explained by the model using the N considered components. A more detailed description of this method can be found in In this particular case, the data matrix 2)The quality of the MCR-ALS model was measured evaluating the lack-of-fit parameter, which is expressed by the percent of explained variance .


Lactococcus lactis and aspartate-derived amino acid synthesis in Arabidopsis thaliana to generalised supply-demand analysis.Generalised supply-demand analysis is a conceptual framework that views metabolism as a molecular economy. Metabolic pathways are partitioned into so-called supply and demand blocks that produce and consume a particular intermediate metabolite. By studying the response of these reaction blocks to perturbations in the concentration of the linking metabolite, different regulatory routes of interaction between the metabolite and its supply and demand blocks can be identified and their contribution quantified. These responses are mediated not only through direct substrate/product interactions, but also through allosteric effects. Here we subject previously published kinetic models of pyruvate metabolism in + allow otherwise independent metabolic branches to communicate. This causes the flux of one ATP-producing reaction block to increase in response to an increasing ATP/ADP ratio, while an NADH-consuming block flux decreases in response to an increasing NADH/NAD + ratio for certain ratio value ranges.Multiple routes of regulation are brought about by different mechanisms in each model, leading to behavioural and regulatory patterns that are generally difficult to predict from simple inspection of the reaction networks depicting the models. In the pyruvate model the moiety-conserved cycles of ATP/ADP and NADH/NAD In the aspartate model, aspartate semialdehyde can inhibit its supply block directly or by increasing the concentration of two amino acids (Lys and Thr) that occur as intermediates in demand blocks and act as allosteric inhibitors of isoenzymes in the supply block. These different routes of interaction from aspartate semialdehyde are each seen to contribute differently to the regulation of the aspartate semialdehyde supply block.Indirect routes of regulation between a metabolic intermediate and a reaction block that either produces or consumes this intermediate can play a much larger regulatory role than routes mediated through direct interactions. These indirect routes of regulation can also result in counter-intuitive metabolic behaviour. Performing generalised supply-demand analysis on two previously published models demonstrated the utility of this method as an entry point in the analysis of metabolic behaviour and the potential for obtaining novel results from previously analysed models by using new approaches.The online version of this article (doi:10.1186/s12918-015-0236-1) contains supplementary material, which is available to authorized users. Mycoplasma genitalium [The primary concern of molecular biology is to identify and characterise the individual components of biological systems. By focussing on the component level, this approach has generated an enormous amount of knowledge, but at the expense of disregarding emergent phenomena that arise from the multitude of interactions between these components. One way of overcoming this limitation is to construct, and subsequently study, mathematical models of these biological systems. This technique has become increasingly common, with models describing systems ranging in complexity from metabolic subsystems to genome-scale reconstructions of metabolism , 2 beingnitalium . With moGeneralised supply-demand analysis (GSDA) is a conceptual framework that views metabolic pathways as a molecular economy . It is bThe simplest way that reaction blocks can interact is through the common intermediate that links them, which can serve as either substrate or product or allosteric effector of supply and demand enzymes. If the only interactions are via the linking metabolite the situation is easy to analyse. However, it is possible that reaction blocks also interact indirectly through allosteric effects of a metabolite in one reaction block on an enzyme in the other reaction block; such a situation is quite common and it is here that GSDA is particularly useful in that it dissects all the routes of communication between supply and demand, both direct and indirect.+ link supply and demand reaction blocks. These cycles are called moiety-conserved cycles because they interconvert different forms of a chemical subgroup or moiety, the total concentration of which remains constant. For example, in the ATP/ADP cycle the moiety is ADP, which is interconverted between its free and its phosphorylated form. When there is no de novo synthesis or degradation of the ADP-moiety during the time-scale of observation, the sum of ADP and ATP remains constant even while their individual concentrations change, and the cycle is therefore moiety-conserving. In supply-demand analyses of such cycles the relevant variable that links the supply and demand reaction blocks is not a single concentration but rather a concentration ratio such as ATP/ADP or NADH/NAD +. These cycles usually form metabolic hubs where many functionally distinct pathways are integrated; an analysis of the interplay between supply and demand around these cycles is crucial for our understanding of metabolic regulation.Another common situation is where cofactor cycles such as ATP–ADP or NADH–NAD +. We show that changes in the ratios of the different forms of a moiety can cause counter-intuitive responses in reaction block fluxes. The second is a model of aspartate-derived amino acid synthesis in Arabidopsis thaliana [In this paper we use GSDA to investigate the regulatory effects brought about by multiple routes of interaction between supply and demand reaction blocks. We have chosen to analyse models of two metabolic pathways that differ from each other in terms of their regulatory mechanisms. The first is a model of pyruvate metabolism in lactic acid bacteria  where muthaliana  in whichMetabolic control analysis (MCA) is a form of sensitivity analysis in which the control properties of a steady-state metabolic system are quantified in terms of the responses of the system fluxes and metabolite concentrations to perturbations in the rates of the reactions , 10. Becelasticity coefficient describes the sensitivity of a reaction rate towards a change in any entity x that can affect that rate directly, such as a substrate, product, modifier or enzyme parameter. It is therefore a property local to a particular reaction and is defined as the ratio of the relative change in the rate of reaction i, vi, to the relative change in x: An control coefficient describes the sensitivity of a steady-state system variable, such as flux or concentration, towards a change in a local reaction rate. This coefficient is a systemic property that depends not only on the properties of the perturbed reaction but also on those of the other reactions and the topology of the network structure of the entire pathway. The flux-control coefficient is defined as the ratio of the relative change in a flux, J, to the relative change in a reaction rate, vi: A vi.Concentration-control coefficients are defined similarly, the flux being replaced by a metabolite concentration. The use of a total derivative signifies that the entire system is allowed to relax to a new steady state after the perturbation in response coefficient differs from a control coefficient in that it is defined with respect to a change not in a local reaction rate but in a system parameter, such as enzyme concentration or the fixed concentration of metabolite external to the system. A flux-response coefficient is defined similarly to a control coefficient as the ratio of the relative change in a flux, J, to the relative change in parameter x: A Again, in a concentration-response coefficient metabolite concentration replaces flux.The so-called partitioned response (or combined-response) equation describes the relationship between these three coefficients: x is channelled through the reaction i directly affected by x: the effect of δx on vi is described by δvi then propagates through the system resulting in a change in flux described by x affects more than one reaction, the overall flux-response is given by The overall flux-response to a perturbation in parameter i that are influenced directly by x.for all reactions Generalised supply-demand analysis (GSDA) is an extension of metabolic supply-demand analysis . In GSDA11This approach can be used to determine which block has the most control over the system flux and which block determines the degree of homoeostasis of the linking intermediate by comparing the response coefficients (or gradients of the rate characteristics at steady-state) of the supply and demand blocks towards the intermediate. In the case where p) depends on the value of RpJdemand−RpJsupply; the larger this value the smaller the absolute value of the concentration-control coefficients of the supply and demand blocks on p, and the better its homoeostasis [as in Fig. 1eostasis , 15.GSDA can also be used to identify the different routes of interaction between an intermediate and a reaction block and to quantify the relative contribution of each of these routes to the total response. In Fig. 1According to the partitioned-response property Eq. , each pamentclass2pt{minim2, so that a change in P will be transmitted via reaction 3 in the demand block to S2, affecting its concentration, which, in turn, affects reaction 1. The overall effect  was used to perform the modelling experiments and metabolic control analysis and to generate the resulting rate characteristic plots. RateChar automatically performs supply-demand analysis and produces rate-characteristic plots for each metabolite in a metabolic model.The Python simulator for cellular systems (PySCeS)  togetherTo investigate the effects of multiple routes of regulation through moiety-conserved cycles we used a kinetic model of pyruvate metabolism in lactic acid bacteria. The model was originally constructed by Hoefnagel et al.  and retr+ conserved moieties were treated as outlined previously, with the symbols ϕA,ϕC and ϕN representing the metabolite ratios. The values of ϕA and ϕN were fixed and varied over the ranges shown in Table The members of the ATP/ADP, acetyl-CoA/CoA and NADH/NAD Arabidopsis was used to investigate the effects of multiple routes of regulation brought about by allosteric effectors and multiple isoenzymes. The model was originally constructed by Curien et al. [A kinetic model of aspartate-derived amino acid synthesis in n et al.  in BerkeFor this case study the focus was to identify and quantify the different routes of regulation of aspartate-semialdehyde (ASA) with its supply block for the wild type as well as for knockouts of AKI and AKII. ASA, lysine (Lys) and threonine (Thr) were fixed and varied over the ranges shown in Table The knockouts of AKI, AKII and both AKI and AKII were simulated by setting their respective enzyme concentrations to zero in the model.Code for both models is provided in PySCeS model descriptor language  and a lumped glycolysis pathway (reaction 1), and is consumed by ATPase (reaction 12). The supply and demand blocks for ϕA are named according to the numbering of these consuming and producing reactions, i.e., block 1 and block 5 are ϕA supply blocks, while block 12 is a ϕA demand block, with the fluxes of these blocks symbolised by J1, J5 and J12 respectively (this naming convention for reaction blocks and their corresponding fluxes is used throughout this paper).The first conserved moiety we shall investigate is ADP, due to its relatively small number of interactions in this pathway. The ‘metabolite’ ϕA on its supply and demand blocks. In steady-state all the reaction blocks respond as expected towards increasing ϕA, with decreases in J1 and J5 and an increase in J12. At ϕA values below 0.4, however, there was an increase in J5 in response to increasing product (ATP) and decreasing substrate (ADP) concentration. Considering that acetate kinase is not product-activated, this positive flux response was unexpected.The rate characteristic plot Fig. a shows tϕA was investigated using partial response coefficients  and pyruvate dehydrogenase (reaction 3), and consumed by lactate dehydrogenase (reaction 2), acetoin dehydrogenase (reaction 11), acetaldehyde dehydrogenase (reaction 6), alcohol dehydrogenase (reaction 7) and NADH oxidase (reaction 13). While block 6 and block 7 are separate demand blocks for ϕN, they are also linked by acetaldehyde and therefore their rates are equal at steady-state. In cases where the observed results for these blocks are identical we refer only to block 6 for the sake of brevity. Due to the numerous interactions of ϕN in this system, there is potential for complex flux response behaviour.While notable, the counter-intuitive response to J6 responds non-monotonically to changing ϕN , which is produced by aspartate-semialdehyde dehydrogenase (ASADH or reaction 5) and consumed by two separate metabolic branches. The first step of the branch that produces threonine (Thr), cysteine (Cys) and isoleucine (Ile) as end products is catalysed by two isoenzymes, homoserine dehydrogenase I and II . The first step in the branch that produces lysine (Lys) as an end product is catalysed by the isoenzymes dihydrodipicolinate synthase 1 and 2 . Thr and Lys inhibit the isoenzymes catalysing the first step of their respective branches, as well as two of the four aspartate kinase isoenzymes catalysing the first step in the pathway: Thr inhibits aspartate kinase I and II  and Lys inhibits aspartate kinase 1 and 2 . Demand blocks of ASA can be defined according to the four consuming enzymes, with fluxes J5  AKI, (2) AKII, and (3) both AKI and AKII. These knockouts, among others, were previously modelled by Curien et al. . Steady-Together, reactions 1 and 2 contribute only 12 % of the total flux of the pathway at the reference steady-state , rather than the direct route via the ATP-producing enzyme acetate kinase (v5). This included both the steady-state value of ATP/ADP and the ATP/ADP-range where J5 had a positive response. This is most probably an incomplete picture of regulation by ATP/ADP, as the inhibition by ATP and ADP of L. lactis enzymes such as lactate dehydrogenase, alcohol dehydrogenase and glyceraldehyde 3-phosphate dehydrogenase [The most striking result was that moiety ratios far from the steady-state caused unexpected flux responses in two reaction blocks: The ATP/ADP-producing flux he model , thereforogenase , 26 was + with reaction block 6 via acetaldehyde dehydrogenase (v6) mostly determined the behaviour of J6 at steady-state, the interaction via pyruvate dehydrogenase (v3) dominated at higher NADH/NAD +-values, thereby causing a decrease in J6. In spite of the limitations of this model, this corresponds well with the previously established role of redox balance in regulating pyruvate flux distribution, where low NADH/NAD +-values are associated with mixed-acid fermentation and higher values with homolactic fermentation [+ [J3) by inhibition of pyruvate dehydrogenase, and therefore also the ethanol flux (J6), in response to the increase in NADH/NAD + was indeed observed [J3 should lead to a reduction in J6, but in reality matters are not that simple. While J6 and J3 did decrease concomitantly at higher NADH/NAD +-values, there were also values for which J6 increased while J3 decreased. The observed J6-response towards NADH/NAD + was shown to be a combination of complementary and competing non-monotonic effects that varied in importance with the value of the moiety ratio, thereby highlighting the utility of a model analysis tool such as GSDA for providing quantitative explanations for observed system behaviour.We found that while the direct route of interaction of NADH/NAD entation –30. Whilation [+  was not observed –30. Due + has been shown to determine pyruvate flux distribution in other organisms, such as Saccharomyces cerevisiae [Escherichia coli [L. lactis [+ in energy metabolism, NAD + and NADP + also play roles ranging from antioxidation to telomere metabolism as discussed in a comprehensive review by Ying [+, its application could shed light on the specific regulatory role of NADH/NAD + in other pathways.Unsurprisingly, NADH/NAD revisiae  and Eschhia coli , 33, in . lactis . For the by Ying . While tArabidopsis thaliana. Here we focussed on the regulation of the ASA supply block by ASA itself. This reaction block was of special interest as its first step is catalysed by four AK isoenzymes, two of which are inhibited by Thr, and the other two inhibited by Lys. Each of these inhibitors is produced by a separate metabolic branch, with two isoenzymes catalysing the initial step of each ASA-consuming branch. These features enable ASA to communicate with its supply block via multiple routes.The second model investigated describes aspartate-derived amino acid synthesis in J5 by ASA to less than 50 % of the wild-type, shifting flux control from the demand block to, less optimally [Our results show that the majority of regulation of the ASA supply block did not occur via the interaction of ASA with its producing reaction, but rather by interaction with its demand blocks, which in turn affected the concentrations of the AK inhibitors Lys and Thr. One intuitively expects that regulation should occur via the shortest route, especially when taking into account the relatively high sensitivity of aspartate-semialdehyde dehydrogenase towards ASA at the steady-state in this system. The most unexpected result is the apparent importance of AKI and AKII in the ASA supply block regulation, in spite of their low contribution towards total flux. Previously, Curien et al.  analysedptimally , the supϕN=0.0012 due to the huge values of The source of the flux responses of both models was investigated by separating the partial response coefficients into their control and elasticity components. In this way the flux response coefficients could be classified as originating predominantly from a local (i.e. enzyme) property or from a system property. We broadly classified a control or elasticity coefficient as having a dominant contribution towards the response coefficient in two different ways: either (1) the magnitude of one coefficient outweighs the contribution of the other, or (2) one coefficient changes in value over a parameter range while the other remains relatively constant; the varying coefficient therefore determines the change in response coefficient. In certain cases we found that the elasticity coefficients dominated the flux response (e.g., the large values of J5 towards ASA is not due to product inhibition of ASADH, but rather due to upstream inhibition of the aspartate kinase isoenzymes by inhibitors downstream from ASA (Fig. The work presented here reiterates the fact that metabolic systems can exhibit complex behaviour that cannot be predicted from simple inspection of the reaction network. Even when the network structure is considered together with enzyme-kinetic properties, in some cases understanding does not emerge intuitively. Furthermore, as the size and complexity of a system increases, so too does the variety of possible behaviours. Examples are the instances of apparent substrate inhibition and product activation in the pyruvate model Figs. a and 6a,6ASA Fig. . The pheϕN at ϕN=0.0012 were due to these reactions being near equilibrium, a situation where for any reaction the thermodynamic term determines the value of its substrate and product elasticity coefficients. This observation was therefore only possible due to infinite elasticity coefficients being a very obvious and well-known sign of a reaction near equilibrium. To fully understand the pathways investigated here in terms of control patterns or in terms of the thermodynamics and kinetics of the pathway enzymes will require further analysis.It is possible to analyse regulation at a deeper level by analysing the control coefficients that form part of the partial response coefficients in term of so-called control patterns . A contrL. lactis is an important organism in the dairy industry where the desirable products of pyruvate metabolism, such as diacetyl and acetaldehyde, are not always produced in equally desirable quantities [L. lactis to increase these products is therefore an appealing prospect. While A. thaliana itself is not industrially important, it is used as a model organism for plant species in general. Here the modification of the aspartate-derived amino acid synthesis pathway to increase the production of the essential amino acids threonine and lysine could lead to the development of crops with increased nutritional value [Both pathways studied here have potential biotechnological and industrial applications. antities , 27, 29.al value , 40. Howby the intermediate itself becomes convoluted when these reaction blocks can also interact through other intermediates, and not only through the linking intermediate. Generalised supply-demand analysis is a framework that allows for the identification of regulatory features of a metabolic pathway, one of which is the quantitative relative contribution of multiple routes of regulation of supply or demand blocks by the intermediate that links them.The regulation of the supply and demand blocks of a specific intermediate + in multiple reactions caused counter-intuitive responses in the fluxes of their producing and consuming blocks, and a model of aspartate metabolism where aspartate-semialdehyde could communicate with its supply block via multiple branching routes that were enabled by allosteric affectors and isoenzymes. Our findings showed that indirect routes of interaction between an intermediate and a reaction block can play a more significant role than the direct route.Here we have demonstrated the use of generalised supply-demand analysis in disentangling various routes of regulation in a model of pyruvate metabolism where the involvement of the conserved moieties ATP/ADP and NADH/NAD We also demonstrated the utility of using a variety of analytic techniques in the further analysis of metabolic models. Both models provided novel results in spite of their having been studied by their original authors in the past , 12. FurThe original SBML versions of the models used in this paper can be found online in the BioModels Database  under th


Escherichia coli metabolic pathways have been modeled extensively at the enzymatic and genetic levels, but existing models cannot accurately reproduce experimental behaviors in a batch culture, due to the inadequate estimation of a specific cell growth rate and a large number of unmeasured parameters.A kinetic model provides insights into the dynamic response of biological systems and predicts how their complex metabolic and gene regulatory networks generate particular functions. Of many biological systems, E. coli in a batch culture, which includes the glycolytic pathway, tricarboxylic acid cycle, pentose phosphate pathway, Entner-Doudoroff pathway, anaplerotic pathway, glyoxylate shunt, oxidative phosphorylation, phosphotransferase system (Pts), non-Pts and metabolic gene regulations by four protein transcription factors: cAMP receptor, catabolite repressor/activator, pyruvate dehydrogenase complex repressor and isocitrate lyase regulator. The kinetic parameters were estimated by a constrained optimization method on a supercomputer. The model estimated a specific growth rate based on reaction kinetics and accurately reproduced the dynamics of wild-type E. coli and multiple genetic mutants in a batch culture.In this study, we developed a detailed kinetic model for the central carbon metabolism of This model overcame the intrinsic limitations of existing kinetic models in a batch culture, predicted the effects of multilayer regulations  on central carbon metabolism and proposed rationally designed fast-growing cells based on understandings of molecular processes.The online version of this article (doi:10.1186/s12934-016-0511-x) contains supplementary material, which is available to authorized users. Systems biology and synthetic biology aim to understand the mechanism by which a biochemical network yields dynamic behaviors in response to environmental stresses or genetic variations and to rationally design and engineer such networks –5. The bEscherichia coli has been extensively modeled [E. coli is widely used to produce useful materials in the industry and has been studied extensively as a model microbe; and (2) central carbon metabolism is the basis of the conserved phenomenon of life and the hub on which nearly all catabolic and biosynthetic processes are built.Hundreds of the kinetic models from microbes to mammals have been presented and construction of complete models is still underway, as shown in the BioModels database , 10 and  modeled  because E. coli to simulate the transient data obtained by the fast sampling system. Schmid et al. [trp operon gene expression with the metabolic network of central carbon metabolism to enhance the production of tryptophan. Experimental observations of intracellular metabolite concentrations under transient response conditions were used to estimate the kinetic parameters. Recently, Pontes Freitas Alberton et al. [Chassagnole et al.  developed et al.  construcn et al.  and Peskn et al.  built dyn et al.  integratE. coli central metabolism have been built. Since both metabolite concentrations and enzyme concentrations vary over time and with changing intracellular and extracellular conditions, the models must integrate gene regulatory networks and define cell growth functions that involve a number of reactions and gene expressions. Transcription factors (TFs), such as catabolite repressor/activator (Cra), cAMP receptor protein (Crp), anoxic redox control protein (ArcA), pyruvate dehydrogenase complex repressor (PdhR), fumarate nitrate reduction regulator (Fnr) and isocitrate lyase regulator (IclR), regulate the expression of central metabolic genes. Kadir et al. [In a batch culture, several kinetic models of r et al.  developer et al.  built a r et al.  integratr et al.  construcEstimation of specific growth rates is key to dynamic modeling in a batch culture. The Monod equation  and its E. coli in a batch culture to overcome intrinsic problems of the existing kinetic models. Our model accurately reproduced the dynamics of WT and multiple genetic mutants in a batch culture and estimated a specific growth rate based on molecular processes. The unknown values of kinetic parameters were estimated by a constrained optimization method on a supercomputer.In this study, we develop a kinetic model for the central carbon metabolism of E. coli, including the glycolytic pathway, TCA cycle, pentose phosphate pathway, Entner-Doudoroff (ED) pathway, anaplerotic pathway, glyoxylate shunt, oxidative phosphorylation, Pts and non-Pts. Four TFs  were employed to regulate metabolic gene expressions. The employed network map is shown in Fig. We developed a detailed kinetic model for the central carbon metabolism of pykF knockout mutant (∆pykF), pgi knockout mutant (∆pgi) and ppc knockout mutant (∆ppc) strains were compared with the experimental data on biomass and extracellular glucose and acetate concentrations in a batch culture  and their complexes for WT and three mutants to confirm their function Fig. . The conpykF and ∆pgi  and at the stationary phase  in a batch culture , probably because our model was built based on batch-culture data in which the specific growth rate is high. This suggested that our model is not still applicable to a low dilution rate. Note that there were no experimental data for the genetic mutants cultured at a high dilution rate.In , not onlE. coli mutant strains under aerobic [In this study, we used the experimental data of Shimizu’s group for model construction and validation. Metabolomics  and flux aerobic  and anae aerobic –30. Howe aerobic  should nkcat and Vmax) were simulated by a finite difference method [kMdh1_cat, kcatPpc_, k_catPfk, kFbp_cat) were identified as the critical factors responsible for cell growth. These results are reasonable, because glucose uptake  determines cell growth, the branching reactions  directly involve the metabolic flows of glycolysis and TCA cycle and irreversible enzymes are more responsible for reaction changes than reversible ones.To find critical parameters for cell growth of WT, the sensitivities of the cell concentration with respect to 38 kinetic parameters of enzyme activities  and allosteric reactions. It is difficult to directly measure those magnitudes in vivo. Only a few studies have estimated how allosteric regulations contribute to nditions , 33, sugThe synthesis ratios of virtual mutants lacking binding between a TF and metabolite are shown in Fig. crp [Although the virtual mutants would be difficult to implement in vivo, we can illustrate one experimental validation. The simulated results of the virtual mutant without a Crp-cAMP complex were consistent with the experimental data for ∆crp . The actAllosteric enzyme activity is modulated by binding of an effector metabolite to a site other than the enzyme’s active site. We constructed a virtual mutant that prevents binding of effector metabolites to each allosteric enzyme. For the allosteric enzymes of Pgi and Cs, their synthesis ratios were close to one (data not shown), suggesting that their allosteric regulations hardly function or are little effective under the employed condition. This observation does not rule out potential functions under other stress conditions. Figure Pfk activity is inhibited by PEP. Removal of this allosteric effect slightly increased the synthesis ratio of Pfk itself and its neighboring (Fbp and Pyk) reactions, TCA cycle  and glyoxylate shunt (Icl and Ms) Fig. a. Pyk acpgi and that of the glucose uptake for ∆ppc indicate that the models of ∆pgi and ∆ppc do not efficiently convert the consumed glucose into cell growth or ATP production. The model underestimated the TCA cycle fluxes for ∆pgi, or at a low dilution rate. They suggest that the model misses some mechanisms controlling the glucose uptake and TCA cycle under the suppressed growth.Despite extensive optimization of parameters, a small fraction of our simulated results is not well consistent with experimental data. Such discrepancies suggest biological complexity rather than mathematical difficulties in optimization. The inconsistency of the cell growth for ∆ppc, PEP was accumulated to increase the glucose uptake rate (the Pts4 reaction) and the TCA cycle fluxes were suppressed because ∆ppc does not supply OAA to the TCA cycle. OAA is a key metabolite that drives the TCA cycle. The growth of ∆ppc was determined by the balance between the increased glucose uptake by accumulated PEP and the reduced TCA cycle fluxes by lack of the anaplerotic reaction. The suppressed growth of ∆pgi was caused by the mechanism that the reduced PEP and AcCoA decrease the fluxes of the glucose uptake and TCA cycle, respectively. Since the TCA cycle is a main source of cofactors such as NADH and FADH2 necessary for oxidative phosphorylation-mediated ATP production, the kinetic model can adjust the flux of the TCA cycle to alter the cell growth rate or ATP production. Actually, ATP is used not only for cell growth but also for adaptation/stress responses that regulate metabolism against unusual genetic and environmental conditions, such as gene knockout and low dilution rate. Thus, TCA cycle regulations for ATP production are critically responsible for growth estimation.We focus on the TCA cycle and the glucose uptake. For ∆pgi and for WT at a low dilution rate. TCA cycle flux could be affected by the fluxes of the anaplerotic pathway at PEP, acetate production pathway at AcCoA and glyoxylate shunt at AcCoA and ICIT. In addition, the rates of such metabolic reactions are directly modulated by coenzyme concentrations. Thus, lack of coenzyme dynamics would cause inconsistencies with experimental data. Cofactor concentrations  vary with time, depending on growth phase and genetic conditions. To integrate the variations in the cofactor concentrations, we need to include all of the reactions with cofactors, but it is difficult at the moment because many of the reactions with cofactors are outside the central carbon metabolism. For (ii), the kinetic model does not consider a decrease in dissolved oxygen, which is consumed by oxidative phosphorylation to produce ATP from NADH and FADH2; however, in a real batch culture, dissolved oxygen would decrease with increasing cell growth. In the late growth phase, metabolic reactions involving such coenzymes would be affected by a shortage of dissolved oxygen. Considering the dynamics of dissolved oxygen would be effective in improving the prediction accuracy of the kinetic model.To improve our model, we suggest the following problems: (i) the dynamics of coenzymes, such as ATP, NADH and NADPH, are not considered, which alter energy and redox status; (ii) the dissolved oxygen concentration is not incorporated, which directly impacts ATP production; (iii) information on the interaction between central carbon metabolism and peripheral subnetworks such as amino acid, protein, lipid and nucleotide syntheses is lacking; (iv) some regulatory networks remain to be revealed. For (i), the flux of the TCA cycle, which directly relates to ATP production, was underestimated for ∆The proposed kinetic model is the first model to our knowledge that reproduces the dynamics of multiple genetically modified mutants under an aerobic condition in a batch culture. Our model has strong advantages over previous models: (i) It employs literature-based detailed kinetic equations with gene regulations to accurately reproduce experimental data for WT and multiple genetic mutants in a batch culture, while estimating a specific cell growth rate based on the ATP production mechanism. (ii) The values of many kinetic parameters were extensively estimated by a constrained optimization technique on a supercomputer. (iii) Our model predicts the effects of multilayer regulations  on central carbon metabolism and enables rational design of fast-growing cells.pykF, whereas it neither reproduced the dynamics of ∆pgi nor ∆ppc  has been studied to explore the optimal growth of E. coli –39. It sE. coli , a ratioThe hypotheses generated from the inconsistencies between the simulation and experimental results need to be tested carefully with further experiments and iterative modeling, providing information on bottlenecks of cellular systems. Extension of the model with greater accuracy and integration of simulation with measurements is a powerful methodology for rational improvement and design of metabolic and gene regulatory networks.E. coli central carbon metabolism will be built that includes both sugar (carbon source) uptake [In the near future, an extended kinetic model of an ) uptake  and ammo) uptake –43 and r) uptake , 44. HowE. coli, should be constructed to reproduce complex dynamics of a series of genetic mutants under different conditions, such as sugar starvation, nitrogen starvation, anaerobic conditions, osmotic pressure and a change in pH and combined with systematic experiments. The virtual E. coli is a “blueprint” unicellular organism that is advantageous because the overall central metabolic pathway structure is remarkably conserved. It provides a platform for understanding the design principles underlying molecular processes, rational design of useful material production and further modeling efforts of a variety of cells.The proposed kinetic model remains to be improved to adapt many genetic and environmental changes. A comprehensive dynamic model, called a virtual Escherichia coli metabolic pathways have been modeled extensively at the enzymatic and genetic levels, but existing models cannot accurately reproduce experimental behaviors in a batch culture, due to inadequate estimation of cell growth function based on its molecular processes and a large number of unmeasured parameters. We developed a detailed kinetic model for the central carbon metabolism of E. coli in a batch culture, which includes the glycolytic pathway, tricarboxylic acid cycle, pentose phosphate pathway, Entner-Doudoroff pathway, anaplerotic pathway, glyoxylate shunt, oxidative phosphorylation, Pts, non-Pts and metabolic gene regulations by four protein transcription factors. The kinetic parameter values were extensively estimated by a constrained optimization method on a supercomputer. The model estimated a specific growth rate based on reaction kinetics and accurately reproduced the dynamics of WT and multiple genetic mutants in a batch culture. This model overcame the intrinsic limitations of existing kinetic models, predicted the effects of multilayer regulations on central carbon metabolism and proposed rationally designed fast-growing cells based on understandings of molecular processes.We used the following kinetic model for a batch or continuous culture:D, is set to zero. X is the cell concentration in a reactor, x1 is the vector of 50 time-varying molecule  concentrations, x2 is the vector of ancillary variables including intracellular protein (TF and TF-metabolite complex) concentrations, y is the vector of extracellular substrate (glucose and acetate) concentrations, yfeed is the substrate concentration vector of the feed, p is the vector of 341 kinetic or constant parameters, μ is the specific growth rate, g is the function vector of specific substrate (glucose and acetate) uptake rates, f is the function vector of mass balance equations with respect to x1. The IclR concentration was set to a constant value. Details of the mass balance equations, reaction rates and ancillary variables are presented in Additional file The equations show the dynamics of a batch culture when the dilution rate, The visualization of the simulated results was performed using MATLAB R2014b on a personal computer .A specific cell growth rate was estimated based on its direct connecting to ATP production flux. The total ATP production flux is given by:P/O) and (P/O)′ indicate the Phosphate/Oxygen (P/O) ratios for NADH and FADH2, respectively under aerobic conditions. Assuming that a specific cell growth rate, µ, is linearly correlated with the specific ATP production rate [vATP is the specific ATP production flux computed by Eq.  as follows:The detailed rate equations for twelve precursor metabolites are shown in Additional file We estimated 351 model parameter values using limited amount of experimental data. Thus, most of parameter values are not identifiable. It is often costly and time-consuming to collect enough experimental data to identify all of those model parameters. This is a common situation in kinetic modeling. Instead, we developed a constrained optimization method to estimate parameter values by using limited experimental data and available measured parameter values. We assumed that in vitro measured values are close to in vivo values. The constrained optimization seeks reasonable parameter values, i.e., they are close to the in vitro measured values and allows the model to reproduce in vivo behaviors. This approach does not guarantee the estimated parameter values are ‘true’. However, at least, use of the estimated parameter values is the most realistic choice, considering the currently available experimental data. Details in parameter estimation are shown in Additional file 1, λ2 and λ3 were used for Class I, II and III, respectively. If the values of Class I parameters change drastically, large penalties are imposed (λ1 > λ2 > λ3 ≥ 0). Therefore, such parameter values are unlikely to survive to the end of the optimization process.The parameter estimation problem is formulated as a constrained optimization problem:tal data . We cateTo solve the constrained optimization problem, we employed genetic algorithms (GAs) with UNDX  as a croi is the time index and j is the index of independent parameters. In this analysis, we calculated X) with respect to 38 kinetic parameters of enzyme activities (kcat and Vmax). A perturbation coefficient of 0.01 was used.The finite difference method is used to simulate dynamic sensitivities . It is ar indicates high consistency. The p values are used for testing the hypothesis that the simulated and experimental fluxes are uncorrelated. .The Pearson’s correlation coefficient between the simulated fluxes and experimental data was calculated with p values. A high value of KCrp-cAMP, KCra-FBP and KPdhR-PYR 105-fold in the equations for Crp-cAMP, Cra-BP and PdhR-PYR, respectively  was cultured in the synthetic medium in a batch culture [pgi, ∆pykF) strains was conducted at 37 °C in a working volume of 1.2 L in a 2-L reactor equipped with pH, dissolved oxygen and temperature sensors. The air flow rate was maintained at 1 L/min and the pH was maintained at 7.0 by automatic addition of HCl or NaOH throughout cultivation. The same E. coli strain was cultured in the synthetic medium in a continuous culture [−1. Cultures were grown aerobically at 37 °C in a total working volume of 1 L, in a 2-L jar fermenter equipped with pH, dissolved oxygen concentration and temperature sensors and a turbidity meter. The air flow rate was kept at 1 L/min and pH was maintained at 7.0 by automatic addition of HCl or NaOH for the duration of the culture. Table  culture  where thThe kinetic model: the MATLAB version and the SBML version that consists of SBML (model) and SED-ML (simulation settings) files are freely available for non-commercial use according to the GNU Free Documentation License (GFDL) at:http://www.cadlive.jp/cadlive_main/Softwares/KineticModel/Ecolimetabolism.html.http://www.cadlive.jp/.MATLAB2007 or higher is required. Our project, named Computer-Aided Design Living System (CADLIVE) Project, is described at