Escherichia coli, is remarkably efficient, producing close to the maximum amount of biomass per unit of nutrient consumed. This observation raises the question of what regulatory mechanisms enable such efficiency. Here, we propose that simple product-feedback inhibition by itself is capable of leading to such optimality. We analyze several representative metabolic modules—starting from a linear pathway and advancing to a bidirectional pathway and metabolic cycle, and finally to integration of two different nutrient inputs. In each case, our mathematical analysis shows that product-feedback inhibition is not only homeostatic but also, with appropriate feedback connections, can minimize futile cycling and optimize fluxes. However, the effectiveness of simple product-feedback inhibition comes at the cost of high levels of some metabolite pools, potentially associated with toxicity and osmotic imbalance. These large metabolite pool sizes can be restricted if feedback inhibition is ultrasensitive. Indeed, the multi-layer regulation of metabolism by control of enzyme expression, enzyme covalent modification, and allostery is expected to result in such ultrasensitive feedbacks. To experimentally test whether the qualitative predictions from our analysis of feedback inhibition apply to metabolic modules beyond linear pathways, we examine the case of nitrogen assimilation in E. coli, which involves both nutrient integration and a metabolic cycle. We find that the feedback regulation scheme suggested by our mathematical analysis closely aligns with the actual regulation of the network and is sufficient to explain much of the dynamical behavior of relevant metabolite pool sizes in nutrient-switching experiments.Recent evidence suggests that the metabolism of some organisms, such as  E. coli, are extraordinarily efficient in producing biomass under a variety of different nutrient conditions. This observation raises the question of what physical mechanisms enable such efficiency. Here, we propose that simple product-feedback inhibition by itself is capable of leading to such optimality. Product-feedback inhibition is a metabolic regulatory scheme in which an end product inhibits the first dedicated step of the chain of reactions leading to its own synthesis. Our mathematical analysis of several representative metabolic modules suggests that simple feedback inhibition can indeed allow for optimal and efficient biomass production. However, the effectiveness of simple product-feedback inhibition comes at the cost of high levels of some metabolite pools, potentially associated with toxicity and osmotic imbalance. These large metabolite pools can be restricted if feedback inhibition is ultrasensitive. We find that the feedback regulation scheme suggested by our mathematical analysis closely aligns with the actual regulation of the nitrogen assimilation network in E. coli and is sufficient to explain much of the dynamical behavior of relevant metabolite pool sizes seen in experiments.Bacteria live in remarkably diverse environments and constantly adapt to changing nutrient conditions. Recent evidence suggests that some bacteria, such as  E. coli, maximize their growth rates per molecule of carbon source consumed et al, 2003 and Lee et al, 2006). Despite their predictive strength and wide applicability, FBA-based methods are limited; FBA assumes that fluxes are optimal (thereby assuming perfect regulation) but does not reveal how these optimal fluxes are achieved. This leaves open the question: how can cells achieve nearly optimal fluxes for efficient growth?Much is known about the metabolic reactions that lead to the production of biomass and energy in cells. However, understanding the logic of metabolic regulation has been challenging due to the network's scale and complexity. Flux-balance analysis (FBA), a constraint-based computational approach, has been used to show that some microorganisms, including Previously, some complex bio-molecular networks have been successfully analyzed and understood in terms of simple modules For regulation of these modules we invoke only product-feedback inhibition. Since its discovery in the late 1950's, product-feedback inhibition has become recognized as one of the cornerstones of metabolic regulation E. coli.To test our understanding of the physiological role of product-feedback inhibition, we compared our simple models to actual regulation of the glutamine-glutamate nitrogen assimilation cycle, including its integration with carbon metabolism. We find important similarities between the product-feedback inhibition scheme that we propose based on general principles and the actual regulatory mechanisms present in If, as we will argue, simple product-feedback inhibition is enough to achieve nearly optimal growth, why is real metabolic regulation so complex? Metabolic feedback regulation exists at various levels, such as, control of enzyme mRNA transcription To elucidate the main findings of our mathematical analysis, we first consider a minimal metabolic circuit  in whichTo go beyond FBA and explicitly consider the regulation of fluxes, we assume product-feedback inhibition acts on the input flux such thatIn our simple linear pathway model, the growth rate i.e. until the ability to produce metabolite Combining Eqs. 1 and 2  simple product-feedback inhibition is enough to approach the optimal flux-balance growth rate, and (2) metabolite-pool sizes are small when growth limiting but become large when not growth limiting. These large non-growth-limiting metabolite pools can be restricted by more complex ultrasensitive feedback regulation. We test the generality of these features for various metabolic modules drawn from real metabolism.Bidirectional pathways, such as glycolysis/gluconeogenesis, are used for switching between different nutrient sources, e.g. glucose (a 6-carbon unit) and lactate (a 3-carbon unit). At the heart of these bidirectional pathways are metabolites that are linked by two different enzymatic reactions (or pathways) of differing energetics due to different cofactor requirements, e.g. fructose-6-phosphate and fructose-1,6-bisphosphate, linked by phosphofructokinase in glycolysis and fructose-bisphosphatase in gluconeogenesis. Since these interconversions may allow cycling, limiting futile cycles between these metabolites is essential for achieving optimal growth.Here we consider a simple module of two interconverting metabolites shown in i.e. at least one of the interconversion fluxes is zero.Limited availability of interconversion enzymes is modeled by the constraint on the interconversion fluxes We compare two different regulatory schemes for this module. The simpler of the two schemes, minimal product-feedback inhibition (Min-FI) assumes feedbacks only on the input nutrient fluxes (the minimum number of feedbacks required to have a stable-steady state solution), while full product-feedback inhibition (Full-FI) assumes feedbacks on all the fluxes. Full-FI yields the following kinetic equations for the metabolite pools i.e. to avoid futile cycling while allowing adequate flux from non-growth-limiting metabolite pool to growth-limiting metabolite pool. To avoid futile cycling, the interconversion flux should preferentially flow from the non-growth limiting pool to the growth-limiting pool. This is achieved by choosing the Michaelis-Menten constant for each outgoing interconversion flux to be much larger than the growth-saturating substrate pool size, e.g. To achieve optimal growth, the feedback-inhibition constants are chosen according to the logic of flux-balance analysis, Numerical solutions for the steady-state growth rate and metabolite-pool sizes for the two alternative regulatory schemes are shown in Organisms metabolize some nutrients using metabolic cycles, e.g. the TCA cycle in carbon metabolism. A metabolic cycle is a wrapped linear pathway where the end product is essential for the first step of the pathway. Consequently, the import of nutrients is slowed or stopped if there is not enough end product available. Therefore, an adequate pool of the end product must always be maintained in order to achieve optimal growth. Here we analyze a module based on the two-intermediate glutamine-glutamate nitrogen-assimilation cycle. In this cycle, ammonium  to glutamate (E). The kinetic equations for the the Full-FI scheme areInterestingly, we find that neither of the two Min-FI schemes yield steady-state solutions that are stable in all of the three regimes: For the two-feedback Full-FI scheme, to maximize the growth rate in the ents see .The numerical solution of the kinetic equations for the Full-FI scheme  shows thE. coli, nitrogen in the form of ammonium  are used for both biomass and energy, optimal partitioning of the carbon flux is essential for optimal growth. Here, we consider a simple module that integerates carbon and nitrogen fluxes. In The metabolic module shown in nitrogen . The othDepending on the constraints on the input fluxes:  by  see . In Fig.i.e. the affinity of the reaction for its energy substrate (ATP) is assumed to be high. The auto-regulatory negative feedbacks in the regulation scheme ensure a stable steady state.Like previous modules, we assume product-feedback inhibition of all the input fluxes . This yii.e. the carbon-dependent nitrogen flux is turned on only after the carbon-independent nitrogen flux reaches its maximum. This is accomplished by choosing To achieve optimal growth, the feedback-inhibition constants are chosen according to the logic of flux-balance analysis, The kinetic equations (7) are readily solved numerically for the steady-state growth rate and metabolite-pool sizes . As for r larger . In contIn experiments, it has been shown that the ATP-independent GDH pathway is preferred under glucose-limited growth The results show that simple product-feedback inhibition is sufficient to achieve the optimal flux-balance growth rate in all regimes. As for the other modules considered, larger feedback-inhibition constants improve growth rate but result in large pools of non-growth-limiting metabolites. Increasing the Hill coefficients of the feedbacks restricts pool sizes and simultaneously reduces the growth-rate deficits.E. coli has been studied in great detail, perhaps more carefully than any other metabolic sub-network Regulation of nitrogen assimilation in i.e., the feedback is weak). However, given the large cellular pool size of glutamate  by glutamine (glnE). The steady-state metabolite pool sizes of the two strains are nearly identical before the nitrogen upshift; however, upon nitrogen upshift, the fold changes in both milation . These omilation . Furthermilation .Within our model, the WT strain is described by the module with all three feedbacks present , while tSome of the system's dynamics, in particular the overshoot of glutamine in the wild-type strain, are not captured by our simple feedback model. Generally, time-delay in the feedback may result in an overshoot in a feedback-inhibited system. This is consistent with the specific implementation of feedback by glutamine on GS: a cascade of covalent modification reactions which occur on the We also compared the growth rate response of the wild-type and feedback-defective strains to relief of nitrogen limitation. Consistent with experimental results, the simulations predicted a bigger increase in the growth rate in the WT strain than in the feedback-defective strain following nitrogen upshift . In the E. coli, the FBA-predicted optima agree remarkably well with experiments Understanding metabolism and its regulation have long been central goals of biochemistry. Recently, flux-balance analysis (FBA), a constraint-based computational approach, has been used to predict the optimal metabolic fluxes and growth rates of microorganisms in different environments. In several cases, in particular involving i.e. those with high Hill coefficients) can substantially restrict these pool sizes; the higher the Hill coefficient of the feedbacks, the smaller the increase in pool size required to achieve the same degree of inhibition. This suggests that the need for ultrasensitive mechanisms to control metabolite pool sizes may account for some of the complexity found in metabolic regulation in real cells at both the transcriptional and post-transcriptional levels.An important trade-off is that larger inhibition constants result in larger pool sizes of non-growth-limiting metabolites, which can be detrimental to growth. However, ultrasensitive feedback mechanisms  can be detrimental to a cell's growth at high enough concentrations. Metabolites at high concentration can interact nonspecifically with various enzymes and disrupt metabolic reactions Ultrasensitivity is a common feature of feedback inhibition. At the transcriptional level, multiple promoter binding sites along with other cooperative mechanisms like DNA looping yield ultrasensitive responses Our study of simple representative metabolic modules is an attempt to identify the design principles underlying the regulatory mechanisms that optimize metabolic function, such as biomass production The analyses were carried out using kinetic equations . The equations account for the concentration of each component in the metabolic modules and the steady-state solutions were numerically obtained using MATLAB. For details on the flux-balance analysis (FBA) see Text S1Additional information.(0.25 MB PDF)Click here for additional data file.


In the first approach, analytic equations have to be tediously derived for each organism, substrate or labelling pattern, while in the second approach, the global nature of an optimum solution is difficult to prove and comprehensive measurements of external fluxes to augment the 13C isotopomer data are typically needed.Metabolic fluxes provide invaluable insight on the integrated response of a cell to environmental stimuli or genetic modifications. Current computational methods for estimating the metabolic fluxes from 13C isotopomer measurement data. In the presented framework, equation systems constraining the fluxes are derived automatically from the model of the metabolism of an organism. The framework is designed to be applicable with all metabolic network topologies, 13C isotopomer measurement techniques, substrates and substrate labelling patterns.We present a novel analytic framework for estimating metabolic flux ratios in the cell from Bacillus subtilis and Saccharomyces cerevisiae we show that our framework is able to automatically produce the flux ratios discovered so far by the domain experts with tedious manual analysis. Furthermore, we show by in silico calculability analysis that our framework can rapidly produce flux ratio equations – as well as predict when the flux ratios are unobtainable by linear means – also for substrates not related to glucose.By analyzing nuclear magnetic resonance (NMR) and mass spectrometry (MS) measurement data obtained from the experiments on glucose with the model micro-organisms 13C metabolic flux analysis framework introduced in this article constitutes of flow and independence analysis of metabolic fragments and techniques for manipulating isotopomer measurements with vector space techniques. These methods facilitate efficient, analytic computation of the ratios between the fluxes of pathways that converge to a common junction metabolite. The framework can been seen as a generalization and formalization of existing tradition for computing metabolic flux ratios where equations constraining flux ratios are manually derived, usually without explicitly showing the formal proofs of the validity of the equations.The core of  From microorganisms to animals and plants, cells adjust their metabolic operations to fulfill the demand of energy and biosynthetic precursors. In nature this is a challenging task because substrate availability is typically limited and often changing in its composition. To ensure viability on a broad palette of chemically heterogeneous substrates, cells have developed intertwined enzymatic networks that also confer robustness against genetic mutations. Optimum redistribution of molecular fluxes in metabolism is achieved by multilevel regulation circuits. In recent years, experimental measurement of in vivo metabolic fluxes has attracted much attention. For example, in biotechnology metabolic fluxes are utilized to lead rational strain engineering, whereas systems biologists assess fluxes to unravel targets and mechanisms of metabolic regulation.Metabolic fluxes are often estimated using flux balance analysis (FBA) ,2. In FB13C labelled substrate, observe the fate of 13C atoms in the cell at isotopomeric steady state with mass spectrometry (MS) or nuclear magnetic resonance (NMR) measurements, and then infer the metabolic fluxes from the measurements. The rationale behind these 13C tracer experiment is that, often alternative pathways between metabolites in the network manipulate the carbon backbones of the metabolites differently, thus inducing different 13C labelling patterns to metabolites. Then, constraints to fluxes complementary to the basic stoichiometric constraints can be derived by measuring the relative abundances of different labelling patterns in the metabolites.A more direct method for experimental determination of the metabolic fluxes is to feed an organism with 13C labelling patterns, the isotopomer distributions, of some metabolites, usually protein bound amino acids in the network, and no isotopomer information at all for many intermediate metabolites of interest -glucose was used as a carbon source. Furthermore, an upper bound for a ratio of GA3P molecules that have visited transketolase reaction was obtained by manually simplifying the model of the metabolic network. Excluding pyruvate, we were able to compute the same ratios with [1-13C]-glucose as a carbon source.In comparison to eukaryotic a priori, but not in positionally labelled data, where the fractional enrichment of a fragment depends on the network topology and the fluxes. This kind of irregularities are in general caused by noise in fragments with low intensity or by coeluting analytes with overlapping fragment masses.) Again, differences between the flux ratios estimated by different methods can be explained by numerical instabilities and by differences in isotopomer information applied during the estimation. Variation in the estimated flux ratios between repeated experiments  was negligible.We compared the computed flux ratios to ones obtained with the software FiatFlux  that is B. subtilis with malate.One of the strengths of the presented framework is that it is able to automatically produce metabolic flux ratios also when other external labelled substrates than commonly used glucose are fed to organisms. To demonstrate this ability, we applied our framework to predict what flux information would be available, if we feed in silico calculability analysis  to examine which flux ratios are calculable in the best case from GC-MS measurements of amino acids, when B. subtilis is grown on [U-13C]-labelled malate. Interestingly, our fragment flow analysis revealed that – with the reaction reversibilites in the applied model – the isotopomer distributions of GA3P, PEP and pyruvate depend only on the isotopomer distribution of the fragment containing the first three carbons of oxaloacetate, but not on the relative fluxes producing these metabolites. Thus, isotopomer balances for GA3P, PEP and pyruvate reduce to mass balances and the ratios of fluxes producing these metabolites cannot be estimated. This somewhat surprising phenomenon is due the fact that the rearrangements of carbon chains occurring in PPP pathway will affect only to the carbon fragments that will be recycled in the upper metabolism but not the carbon fragments that can flow back GA3P, PEP and pyruvate from PPP .We applied the B. subtilis grown on [U-13C]-labelled malate agreed with the results of fragment flow analysis: constraints to the isotopomer distributions of fluxes entering to these metabolites were identical within the limits of measurement accuracy. On the other hand, our framework was able to estimate for example the TCA-cycle activity also when B. subtilis is grown on malate, just as predicted by the calculability analysis.Preliminary experiments with GC-MS data from 13C metabolic flux ratio analysis. At the heart of the framework lie the techniques for flow analysis of a metabolic network and for manipulating isotopomer measurements as linear subspaces. These techniques facilitate the efficient and analytic computation of the ratios between the fluxes producing the same junction metabolite. The framework can be seen as a generalization and formalization of existing analytic methods for computing metabolic flux ratios Our experiments with NMR and MS data show that the framework is able to provide relevant information about metabolic fluxes, even when only constraints to the isotopomer distributions of protein-bound amino acids are measured.in silico calculability analysis.Thanks to recent advancements in measurement technology improving the feasibility of mass isotopomer measurements of intermediate metabolites ,33, we eSecond, the manipulation of isotopomer measurements as linear subspaces offers a natural way for comparing measurements from different metabolites that contain overlapping information to detect inconsistencies in the measurements: it is enough to compare propagated isotopomer information in the fragments that belong to the same equivalence class. Third, as MS isotopomer measurement techniques have to be developed separately for different intermediate metabolites or metabolite classes, it will be very useful to select a small subset of intermediates that gives enough information about the interesting metabolic fluxes with least experimental effort. In future research, we want to tackle this problem by generalizing our earlier experimental planning method , to all 13C metabolic flux analysis only resorts to linear optimization techniques, it is not always able to provide as much information about the metabolic fluxes as the global isotopomer balancing frameworks utilizing more powerful, nonlinear optimization techniques  of fluxes, or a flux distribution.By 13C metabolic flux analysis presented in this article rests on the assumption that the metabolic network is in metabolic and isotopomeric steady state. In the metabolic steady state, metabolite balance, or mass balanceThe framework for Mi. Here, βi is the measured external in flow (βi < 0) or external out flow (βi > 0) of metabolite Mi. From balance equations (1) defined for every metabolite Mi we will obtain a metabolite balancing, or stoichiometric equation system.holds for each metabolite b of each metabolite Mi in the metabolic network the following isotopomer balance holds:In isotopomer steady state, for each isotopomer Mi while the latter can. However, using (2) is not in general admissible in practice: typically abundances PM(b) of isotopomers are not fully determined from the measurements, and we need to settle for some constraints to the distribution DM. A crucial building block of our framework is the representation of isotopomer measurements as systems of linear equations  and (2) bear a fundamental difference: the former cannot be used to estimate fluxes of alternative pathways producing ns (c.f. )sbh is the weight of isotopomer b in the h'th constraint, dh is a value derived from isotopomer measurements, and r is the total number of constraints. We call (3) isotopomer constraints. For a k carbon metabolite, 2k linearly independent isotopomer constraints – one for each isotopomer – are necessary and sufficient to constrain the isotopomer distribution DM to a point solution. A set of isotopomer constraints has a natural matrix representation SDM = d, where S = (sbh)b,h is a 2k by r matrix, where 1 ≤ r ≤ 2k is the number of isotopomer constraints  = 1 by definition always holds).where Mi as soon as we know the value of the same linear combination of isotopomer abundances for each subpool of Mi. We haveThe use of (3) follows from the simple observation that isotopomer balance (2) implies that each linear combination of isotopomers is balanced. Thus, we can write a new balance equation that constrains the fluxes producing sb that do not depend on j, i.e. they are the same for each subpool Mij. We call (4) a generalized isotopomer balance.where each 13C isotopes  and  and 13C s011,2 = s110,2 = s101,2 = 1, and sb,2 = 0 otherwise. Similarly, the coefficients sbk can be derived for all mass isotopomers +k, k = 0, ..., 3.which conforms to (3) by taking M|F of a three-carbon metabolite, containing the first and second carbon of M. The following equation holds for the mass isotopomer M|F(+1):Isotopomer data originating from Tandem MS, or MS-MS, falls into the same representation. Consider, for example, a fragment M, but the exact form of the equation depends on the mode of tandem MS. If the full scan mode is used, we obtainThe equation can be written in terms of the precursor M that have exactly one carbon among the first and second location contribute to the fragment mass isotopomer M|F(+1). On the other hand, in the daughter-ion scanning mode a single mass isotopomer, for example M(+2), is selected as the precursor. Then we obtainas all precursor molecules 13C atoms in total. We refer the reader to ) for approximately 1.5 residence times, so that about 78% of the biomass was uniformly labelled. 2D  COSY spectra of harvested and hydrolysed biomass were acquired for both aliphatic and aromatic resonances at 40°C on a Varian Inova 600 MHz NMR spectrometer. The software FCAL v.2.3.0 )  or a mixture of 0.6 g/L fully carbon labelled glucose ([U-13C])  and 2.4 g/L unlabeled glucose as the sole carbon source. Fourteen derivatized amino acids were analyzed for 13C labeling patterns with a series 8000GC combined with an MD800 mass spectrometer (Fisons instruments). More information about the details of the measurement procedure can be found from [In the second experiment und from  where idAR, JR and EU are the main contributors of the computational methods given in the article. AR implemented the methods and ran the experiments. PJ constructed the models of metabolic networks and contributed to the development of the computational methods. NZ and HM contributed the development of the computational methods. AR, JR, NZ and PJ wrote the manuscript. All authors have read and accepted the contents of the manuscript.S. cerevisiae in SBML formatModel of central carbon metabolism of . Additional file 1 contains the stoichiometric model of central carbon metabolism of S. cerevisiae used in the experiments of the article. The model is provided as a text file containing SBML compliant descriptions of metabolites and reactions in the model. Metabolites are identified by their KEGG LIGAND codes.Click here for fileIllustration of the model of central carbon metabolism of S. cerevisiae. Bidirectional reactions in PPP pathways are depicted as unidirectional for better readability.Click here for fileB. subtilis in SBML formatModel of central carbon metabolism of . Additional file 2 contains the stoichiometric model of central carbon metabolism of B. subtilis used in the experiments of the article. The model is provided as a text file containing SBML compliant descriptions of metabolites and reactions in the model. Metabolites are identified by their KEGG LIGAND codes.Click here for fileB. subtilisIllustration of the model of central carbon metabolism of . Bidirectional reactions in PPP pathways are depicted as unidirectional for better readability.Click here for file


Interactions between microbial species are sometimes mediated by the exchange of small molecules, secreted by one species and metabolized by another. Both one-way  and two-way  interactions may contribute to complex networks of interdependencies. Understanding these interactions constitutes an open challenge in microbial ecology, with applications ranging from the human microbiome to environmental sustainability. In parallel to natural communities, it is possible to explore interactions in artificial microbial ecosystems, e.g. pairs of genetically engineered mutualistic strains. Here we computationally generate artificial microbial ecosystems without re-engineering the microbes themselves, but rather by predicting their growth on appropriately designed media. We use genome-scale stoichiometric models of metabolism to identify media that can sustain growth for a pair of species, but fail to do so for one or both individual species, thereby inducing putative symbiotic interactions. We first tested our approach on two previously studied mutualistic pairs, and on a pair of highly curated model organisms, showing that our algorithms successfully recapitulate known interactions, robustly predict new ones, and provide novel insight on exchanged molecules. We then applied our method to all possible pairs of seven microbial species, and found that it is always possible to identify putative media that induce commensalism or mutualism. Our analysis also suggests that symbiotic interactions may arise more readily through environmental fluctuations than genetic modifications. We envision that our approach will help generate microbe-microbe interaction maps useful for understanding microbial consortia dynamics and evolution, and for exploring the full potential of natural metabolic pathways for metabolic engineering applications. Microbial metabolism affects biogeochemical cycles and human health. In most natural environments, multiple microbial species interact with each other, forming complex ecosystems whose properties are poorly understood. In an effort to understand inter-microbial interactions, and to explore new metabolic engineering avenues, researchers have started building artificial microbial ecosystems, e.g. pairs of genetically engineered strains that require each other for survival. Here we computationally explore the possibility of creating artificial microbial ecosystems without re-engineering the microbes themselves, but rather by manipulating the environment in which they grow. Specifically, using the framework of flux balance analysis, we predict environments in which either one or both microbes in a pair would not be able to grow without the other, inducing commensal (one-way) or mutualistic (two-way) interactions, respectively. Our algorithms can successfully recapitulate known inter-microbial interactions, and predict millions of new ones across any pair amongst different microbial species. Surprisingly, we find that it is always possible to identify conditions that induce mutualistic or commensal interactions between any two species. Hence, our method should help in mapping naturally occurring microbe-microbe interactions, and in engineering new ones through a novel, environment-driven branch of synthetic ecology. While several aspects of microbial metabolism can be fruitfully addressed by studying individual microbial species, many contemporary challenges, including environmental remediation and infectious diseases, require a massive effort towards understanding how microbes interact with each other. In fact, in nature, most microbes do not live in isolation, but rather exist as part of complex, dynamically changing, microbial consortia Metabolic interactions between pairs of microbial species could be thought of as unidirectional or bidirectional exchanges of small molecules, which may benefit one or both species . A commeIn parallel to experimental studies, the rise of genome-scale constraint-based models of metabolism has the potential to help address questions that cannot be easily addressed experimentally. Constraint-based models of metabolic networks represent an efficient framework for a quantitative understanding of microbial physiology Escherichia coli and Saccharomyces cerevisiae, and for all pairwise combinations of seven bacterial species: Escherichia coli, Helicobacter pylori, Salmonella typhimurium, Bacillus subtilis, Shewanella oneidensis, Methylobacterium extorquens, and Methanosarcina barkeri. In addition to providing an algorithmic platform for synthetic ecology exploration, we envisage that our approach will help mapping and understanding interactions that occur in natural microbial consortia.Here, we use constraint-based models to develop a new strategy for the study of metabolism-based symbiotic interactions in pairs of microbial species. While in most analyses of cross-feeding interactions the focus is on the properties of the organisms themselves, we take a different approach, asking whether, given two arbitrary organisms, it is possible to identify environmental conditions that induce a mutualistic or commensal interaction. We start by exploring known symbiotic pairs, to determine if available stoichiometric models seem to provide predictions that are in agreement with empirical observations. The algorithms we developed allow us not only to verify potential interactions, but also to produce lists of putatively exchanged metabolites. Then, we ask whether, given any two species whose stoichiometric models are available, it is possible to predict potential nutrient compositions that induce specific symbiotic behaviors, in particular commensalism and mutualism. Hence, taking advantage of the efficiency of constraint-based models, we explore the large space of possible media compositions, in search for nutrient combinations that sustain a co-culture of two species but do not support growth of each organism on its own. We apply our pipeline to the prediction of novel environments and interactions for a coculture of As a first step in our analysis we asked whether, using stoichiometric models, we could reproduce three metabolic interactions depicted in ade8 reaction might restore flux through the rest of the adenine biosynthesis pathway, based on the stoichiometric model We next asked whether the stoichiometric implementation of organism pairs could be used to generate predictions of the metabolites exchanged between the two species upon symbiotic growth. Towards this goal we developed an algorithm that allows us to predict what metabolites need to be exchanged between two species in order to survive under a given environmental condition . Our seaSo far, we have shown that joint stoichiometric models can be helpful in describing known cases of symbiotic interactions, providing novel testable predictions. This analysis, however, has been limited to a single medium composition. Can one generalize this approach, and try to identify a multitude of media that would impose mutualism or commensalism between any two species? To address this question, we developed an algorithm for the search of interaction-inducing media (SIM), aimed at finding a large number of minimal or near-minimal media that are predicted to induce interactions between two given microbial species see . As a prDesulfovibrio vulgaris and Methanococcus maripaludis , and detect specific patterns of interaction that can be reconciled, e.g., with the biochemistry of the syntrophic pair , and 16.8% are neutralism-inducing. In E. coli – S. cerevisiae pair. In particular, it can be seen that the interaction class predictions are highly robust with respect to individual perturbations that remove  they span wide spectra of function, environment and taxonomy; (ii) most of them have well characterized laboratory strains which could be used for future experimental testing; and (iii) they have publicly available stoichiometric models. While all stoichiometric models used here have undergone manual curation and some form of experimental validation, it is important to keep in mind that different models may have different levels of agreement with experimental observations. Thus, predicted interactions between arbitrary pairs should be evaluated in light of the expected fidelity of the corresponding individual stoichiometric models.It is in principle possible to extend our computation of interactions to any organism for which a stoichiometric reconstruction is available. Here we present a computation of all possible pair-wise interactions between seven bacteria of relevance to health (first three) or environmental (last four) applications, namely E.coli - S. typhimurium pair, to only one in the H. pylori - M. barkeri case. At a first glance, one can identify several trends in the patterns of predicted inter-species interactions. For example, E. coli is predicted to be able to interact with most organisms in a large number of different environments. These interactions appear to be dominated by commensalism, where E. coli acts as the provider. This may be due to a combination of E. coli's ability to survive on a variety of carbon sources and of its capacity to export a number of byproducts. In contrast, H. pylori, except for the interaction with E. coli, has very few interaction-inducing media and frequently acts as a recipient, possibly reflecting its near obligatory parasitic nature M. barkeri, which is predicted to interact with other species in a moderate number of environments, most of which induce commensal interactions that have M. barkeri as the recipient. In general, pairs of organisms appear to be dominated only by a few interaction classes. In addition, specific organisms tend to have an overall specific role in interactions with all species. For example, E. coli and B. subtilis are largely on the giving end of commensal interactions, while M. barkeri and H. pylori are mainly on the receiving end, and a sizable portion of M. extorquens and S. oneidensis interactions are mutualistic. Furthermore, some pairs display a large proportion of neutral interactions, i.e. can individually grow on a lot of common minimal media. This is most prominent for the E. coli and S. typhimurium pair, for which such an outcome may be expected, based on the fact that they tend to occupy a similar environmental niche. What might be less intuitive is that, for this same pair, we found also numerous environments that induce commensalism and mutualism.The results of this interaction analysis are summarized in the matrix of pie charts found in E. coli and the archaeon M. barkeri is explored in detail in S. cerevisiae and E. coli and two cases for the E. coli - H. pylori pair  will produce a major change in the medium, i.e. consumption of resources used for growth, and generation of novel byproducts. Thus, the combined effect of the microbes is highly synergistic relative to what is expected by observing the two microbes alone. This phenomenon is formally analogous to an extreme epistatic interaction between gene deletions, such as synthetic lethality Our results offer new insight on some evolutionary aspects of microbial ecosystems. Cryptic metabolic interactions may be the source of the unculturablity of many organisms. Since next-generation sequencing technologies can now produce the sequenced genomes of organisms we can not culture, it is possible to construct the metabolic network model for a species that has never been grown in a lab as pure culture. From this model one could infer what metabolites such organism would require from an interaction partner, paving the way for novel experimental testing. The mechanisms responsible for the evolutionary emergence of mutualistic interactions are an unresolved puzzle, though there is evidence that gene loss or horizontal gene transfer may drive some of these processes Another aspect that should be stressed is that many of the predicted symbiosis-inducing media may be theoretically feasible, but still not practically viable in a straightforward way, e.g. because the relevant metabolic pathways or necessary transporters may be down-regulated, allosterically inhibited or kinetically unfavorable. Such limitations, as well as potential limitations in metabolite transportability, might be overcome by implementing targeted (e.g. regulatory) mutations, or rounds of experimental evolution Finally, we envision that our proposed approach of a computationally driven synthetic ecology based on re-designing environments rather than organisms could have several applications. First of all, in analogy with synthetic biology, and as explored already with some artificial synthrophic species, the payback will be partially in terms of understanding interactions by building them. This may be seen as a first step towards building a stoichiometry-based microbial interactome, to help in the interpretation of metagenomic sequencing and microbial ecosystem data. Moreover, in terms of metabolic engineering, using the enzymatic potential of multiple interacting species can greatly expand the space of process optimization possibilities. Generating novel pathways by inducing interactions between different organisms rather than (or in addition to) genetically engineering the genomes of individual species has several benefits. First, one could use the metabolic potential of organisms that may be hard to genetically manipulate. Second, communities may be inherently more stable than individual modified species, in which specific mutations could potentially revert. We anticipate that methods like the ones we propose will be important in developing and analyzing synthetic communities of organisms. Our algorithms can be extended to simulate communities containing more than two organisms, predict gene knockouts that would give rise to mutualistic interactions and eventually entire consortia of microorganisms. Furthermore, the algorithms and methods we developed could be extended to study human health related problems. In addition to understanding interactions in the human microbiome, similar approaches could be used to ask how different cell types interact within a specific tissue and how a pathogen interacts metabolically with the host it infects.S) is used to encode all the information about the topology and mass balance in a metabolic network, including the complete set of enzymatic and transport reactions in the system. Transport reactions, inferred from genome annotations, specialized prediction tools or literature curation, include both protein-catalyzed transport, e.g. ATP-driven transport, or ion-coupled symport/antiport, as well as free diffusion of small molecules  through the cell boundaries. Element ijS represents the number of molecules of metabolite i participating in reaction j . The stoichiometric matrix S can be used as the starting point for efficiently generating predictions of metabolic rates −1·(hr)−1) at a genome scale, e.g. using flux balance analysis (FBA) Sv = 0. This assumption generates a large number of equality constraints that define the space of feasible metabolic states for the system. Further constraints  are imposed through inequalities of the type iLB and iUB constitute vectors of lower and upper bounds of reaction i respectively. These constraints will be later written concisely as http://www.gnu.org/software/glpk/) called from a Matlab shell through GLPKmex (http://glpkmex.sourceforge.net/).Our algorithms use the framework of stoichiometric constraint-based models of metabolic networks, which have been described in detail elsewhere The toy model is composed of two simple organism models . Each suD. vulgaris and M. maripaludis, as described in D. vulgaris produces H2, acetate and formate, all byproducts which M. maripaludis can utilize to grow and produce methane. Stolyar et al.http://synthetic-ecology.bu.edu/. Our flux balance models involve 108 reactions for D. vulgaris and 103 for M. maripaludis. It is important to mention that these specific stoichiometric reconstructions are not genome-scale (as opposed to the ones used subsequently in our work), and only account for carbon, nitrogen, sulfur and hydrogen atoms.We implemented a stoichiometric model for the methanogenic syntrophic pair constituted by Lys2, by setting the upper and lower flux bounds to zero. This modeled strain corresponds to the experimentally constructed Lys- strain, and is unable to grow on glucose minimal media without lysine as a supplement. Similarly, to model the Ade- biological strain we identified and disabled the reactions associated with Ade8 gene. This resulted in a model that required an adenine supplement to grow on a minimal medium. The strains in 2, and allow free use of ammonia, sulfate, phosphate and salts.To create the joint yeast model, we began with two copies of the newest yeast genome scale metabolic reconstruction iMM904 Escherichia coliBacillus subtilisHelicobacter pyloriSalmonella typhimuriumMethanosarcina barkeriShewanella oneidensis we used an early version of the recently published model Methylobacterium extorquens we used a genome scale extension of a previous reconstruction The genome scale metabolic models for 5 of the organisms used have been published and are publicly available  uses the following compartments , we define the following reactions :Our approach for generating multi-species model extends the multi-species model employed by Stolyar i Xi [ENV] < = >i Xi [ENV] < = > Xi [EX1]i Xi [EX1] + Y < = > Xi [CYT1] + Zi is transported in and out of the cell through several different transporters, in order to know whether there is a net influx or efflux of Xi we would have to add up all the transporter fluxes. In our formulation, this is achieved simply by looking at the shuttle reaction flux. In a single species model, this would have been easily achieved by observing the exchange flux, but the extra degrees of freedom entailed by the multi-species model requires this extra layer of description. In addition, this formulation makes it much easier to implement our search algorithm for exchanged metabolites (SEM), in which we want to minimize the number of exchanged metabolites irrespective of the number of transporters available for each metabolite. The other important aspect of this distinction between exchange and shuttle fluxes is that, in terms of constraints, we have independent control on what molecules are environmentally available versus what molecules we want to make available for individual species. While this feature has not been used in the current work, it may be useful in future developments. The proposed formulation could serve as a standard way of building ecosystem-level stoichiometric models.In previous formulations of joint models for different species or organelles (1 and 2)TM between all the metabolites that are potentially transportable in the first and in the second model (metabolite sets (1)TM and (2)TM respectively). Each interchangeable metabolite i in (1 and 2)TM is associated with two shuttle reactions i can then be expressed as the following constraint:L is a large number (“infinite”), and iθ is a binary variable which assumes a value of 1 if metabolite i is transported between the two species, and 0 otherwise.We have developed a mixed integer linear programming algorithm to identify a minimal set of possible exchanged metabolites between two organisms 1 and 2 that can grow simultaneously under a specified condition. Solving this problem requires imposing additional constraints to the regular mass balance and capacity constraints. First, since we require growth of both organisms, we fix the minimal growth rate of both organisms  that can substitute in the medium an initially available source for a given atom. In the current work we focus on identifying different sources for carbon, nitrogen, sulfur, and phosphate only. The analysis could be in principle extended to other atomic contributions, including cofactor metals, such as iron. The core function in SIM is recursive, and is best described, for a specific atom A, through the following pseudo-code  see also :<Initialize CM = MMInitialize PM = {All environmental metabolites}\CMFunction Find_Replacement { Temporary Medium (TM) = CM\{molecules that contain A} Replacement Sets (RS) = empty set of replacement metabolites.growth>0 on union  X = Find X∈PM such that V if ( X is not empty ) {  TM = union  Remove X from PM  RS = Find_Replacement  RS = [[X], RS ]; } return RS}http://synthetic-ecology.bu.edu/) takes into account the fact that it may not be possible for a single metabolite to substitute a previous one. In such case the function will continue searching for an additional metabolite that would allow nonzero growth. Hence, it may be the case that at a particular iteration, two molecules are compensating for the initially removed one. In the subsequent step, the algorithm will bifurcate, and try to remove each of these molecules individually.Note that the real algorithm , and recalculating the interaction-inducing media based on different choices of the initial carbon sources . Regardless of which initial medium was used, the same metabolites were identified as being viable carbon sources in the different trials. The identified media (i.e. combinations of the above metabolites) were almost identical (average 97.4% overlap±2%), regardless of the initial medium used.EXv} of exchange reactions (labeled as (1) in the section Multi-species stoichiometric models above). We then solve a minimization problem which uses, in addition to the usual FBA constraints: (i) a constraint on minimal growth rates, as described for SEM  of the M matrix, by implementing an average linkage hierarchical clustering using the Jaccard distance as a metric in Matlab. Alternate clustering methods gave equivalent results. Rows were clustered with the same method, but, for To cluster the metabolites of all the media identified in the syntrophic yeast pair , we compS. cerevisiae and E. coli pair, 1000 media were chosen for each interaction class at random. For each of these media the set of metabolites was perturbed and the pair retested for interaction class 100 times. This was done by selecting a carbon containing metabolite, and replacing it with another carbon containing metabolite at random . The transition probabilities fore each interaction class were then calculated as the mean fraction of times a given interaction class is transformed into another interaction class upon the perturbation  insults, we extended the perturbation analysis by randomly selecting and applying k random insertions or deletions 1000 times, and counting the number of times the interaction class change. The randomly added reactions were taken from the subset of KEGG reactions For the urbation . In ordeFigure S1Interaction-inducing media identified for the pair of yeast strains of (0.11 MB PDF)Click here for additional data file.Figure S2Results from the modeling of the syntrophic interaction between two S. cerevisiae strains engineered to be auxotrophic for adenine (Ade-) or lysine (Lys-) respectively.(0.09 MB PDF)Click here for additional data file.Figure S3Metabolite usage predicted for the pair of engineered yeast strains in media that induce commensal interactions.(0.18 MB PDF)Click here for additional data file.Figure S4Robustness of predicted interaction types upon gene deletions in the joint model for M. extorquens and M. barkeri.(0.10 MB PDF)Click here for additional data file.Figure S5Two examples depicting the details of environment-induced mutualistic interactions identified through the SIM algorithm for the  pair.(0.15 MB PDF)Click here for additional data file.Figure S6Interaction-inducing media identified for the S. cerevisiae - E. coli pair.(0.14 MB PDF)Click here for additional data file.Table S1Number of media that induce each possible class of interaction for every pair of microbes.(0.01 MB XLS)Click here for additional data file.Table S2List of metabolites composing the initial medium for applying the SIM algorithm to each pair of species.(0.02 MB XLS)Click here for additional data file.Table S3Possible inferences that one could make from comparing predicted outcomes of interactions during growth on different media with corresponding experimental results.(0.01 MB XLS)Click here for additional data file.Table S4Exchanged metabolites for two mutualism-inducing media for two different interacting pairs of organisms.(0.01 MB XLS)Click here for additional data file.Text S1Media ranking methods.(0.06 MB PDF)Click here for additional data file.


This is the first study that has been undertaken on the data-driven identification of a dynamic liver central carbon metabolism model and its application in the analysis of the distribution of metabolic control in hepatoma cells.The liver plays a major role in metabolism and performs a number of vital functions in the body. Therefore, the determination of hepatic metabolite dynamics and the analysis of the control of the respective biochemical pathways are of great pharmacological and medical importance. Extra- and intracellular time-series data from stimulus-response experiments are gaining in importance in the identification of in silico metabolite dynamics were in accordance with the experimental data. The central carbon metabolism of hepatomas was further analyzed with a particular focus on the control of metabolite concentrations and metabolic fluxes. It was observed that the enzyme glucose-6-phosphate dehydrogenase exerted substantial negative control over the glycolytic flux, whereas oxidative phosphorylation had a significant positive control. The control over the rate of NADPH consumption was found to be shared between the NADPH-demand itself (0.65) and the NADPH supply (0.38).Dynamic metabolite data were collected from HepG2 cells after they had been deprived of extracellular glucose. The concentration of 25 extra- and intracellular intermediates was quantified using HPLC, LC-MS-MS, and GC-MS. The Based on time-series data, a dynamic central carbon metabolism model was developed for the investigation of new and complex metabolic control patterns in hepatoma cells. The control patterns found support the hypotheses that the glucose-6-phosphate dehydrogenase and the Warburg effect are promising targets for tumor treatment. The systems-oriented identification of metabolite dynamics is a first step towards the genome-based assessment of potential risks posed by nutrients and drugs. Dynamic network models of the hepatic metabolism enable quantitative systems-level analyses of (i) detailed metabolic control patterns, (ii) metabolic implications in liver cancer, and (iii) metabolic processes such as detoxification. Moreover, systems-oriented analyses of the dynamics and control of the central carbon metabolism in the liver are an important step on the avenue towards the personalized prognosis of drug actions and/or long-term effects. This will eventually lead to a reduction in potential side effects and healthcare costs as well as enabling quick, rational decisions to be made in the course of expensive drug discovery processes. However, due to the limitations of wet and dry lab procedures ,2, modelSeveral metabolic functions and processes are constantly and concurrently maintained in the liver, which is a complex organ performing a plethora of vital functions . These fin vitro measurements or from intracellular metabolite time-series data. Teusink et al. reconstructed a dynamic model of yeast glycolysis based on in vitro kinetics; the authors observed substantial differences between model-predicted and experimentally determined in vivo metabolite levels [in vivo metabolite time-series data for the identification of intracellular enzyme kinetics [Escherichia coli [in vivo dynamics of glycolytic intermediates in Escherichia coli and showed the importance of growth rate-dependent metabolome analysis [Saccharomyces cerevisiae [Escherichia coli [Corynebacterium glutamicum [When building a dynamic model, the enzyme kinetics can either be deduced from non-physiological e levels . Therefokinetics ,22. Thiskinetics . Hofmannkinetics . Luo et hia coli . Schaub analysis . So far,revisiae . Enzyme revisiae . Chassaghia coli . Kresnowhia coli . Magnus utamicum .The analysis of metabolic control provides a mathematical framework for quantifying the responses of fluxes and intermediate concentrations to changes in internal and external parameters such as nutrient and drug concentrations at the systems level -31. ContThe objective of this study is to provide systems-level analyses of the dynamics and control of the central carbon metabolism in hepatoma cells. Transient extra- and intracellular intermediate concentrations were experimentally observed in HepG2 cells in a stimulus response experiment. The experimental data were then used to parameterize a dynamic network model of the hepatic central carbon metabolism. The reaction kinetics were approximated using canonical linlog kinetics. This approach yields a good approximation quality while only requiring the determination of comparatively few parameters ,38,39. SIn the present study, a stimulus response experiment was performed with HepG2 cells. After growing HepG2 cells on a glucose-containing medium, they were incubated with fresh medium for two hours and then exposed to a medium lacking glucose. Metabolite time-series data were determined and used to parameterize a dynamic network model of the central carbon metabolism. The model takes into account 49 reactions (including 5 transportation steps) that convert 45 balanced compounds (40 intracellular and 5 extracellular metabolites). The metabolic network is depicted in figure The following paragraphs will focus on the concordance of the model simulations with the experimental data and on the application of the model for quantifying and interpreting the distribution of metabolic control.In vivo and in silico data were normalized with respect to the estimated reference values. It is worth noting that the perturbation triggered significant changes in the metabolite levels, and these changes provided important information about the underlying network dynamics.A total of 25 metabolite time courses were experimentally determined, of which 5 corresponded to extracellular metabolites and 20 to intracellular metabolites. The experimental data and the corresponding model simulations are summarized in Figure After exchanging the glucose-containing culture medium with the glucose-free medium, the extracellular glucose level dropped drastically. The remaining extracellular glucose was consumed by the cells within a period of 120 min. The extracellular pyruvate and lactate levels also dropped considerably because of the medium exchange, but started to accumulate again. At the end of the experiment, i.e. after 180 min, the pyruvate values were even slightly higher than the estimated reference level. Lactate did not reach 50% of its reference value, which was the result of a decreasing lactate secretion rate. The initial efflux rate was twenty times higher for lactate than for pyruvate. This means that, in absolute terms, still more lactate than pyruvate was produced during the experiment. Extracellular alanine was consumed throughout the experiment, while extracellular serine accumulated. It is worth noting that besides the lack of glucose, the system was also perturbed as a result of the changes occurring in the extracellular pyruvate, lactate, alanine, and serine levels.m value, facilitates the diffusion of glucose into or out of the cells [In accordance with the extracellular glucose levels, the intracellular glucose pool also decreased steeply. HepG2 cells have high GLUT2 transporter activities . The GLUhe cells . It can In the first 10 min of the experiment, the model simulations showed decreasing ribose-5-phosphate and ribulose-5-phosphate levels, followed by an increase, and then another decrease. Some discrepancy between the initial experimental data points and the simulations was observed for both metabolites, which could be an indication of a damped oscillation with rather high amplitude.The first TCA cycle intermediate pools, i.e. citrate, cis-aconitate, and isocitrate, exhibited oscillatory dynamics. This was also found in the model simulations. It is interesting to note that three pairs of conjugate-complex eigenvalues were observed for the Jacobian matrix, which suggests that the system is capable of damped oscillations. The model simulations showed a non-oscillating decrease of fumarate and malate. There was some discrepancy between the simulated time courses for fumarate and malate and the experimentally observed concentrations after 30 min. However, the corresponding standard deviations were large.The time courses of the experimentally determined cofactors NAD, ATP, and NADP only deviated slightly from their initial values. This means that despite the substantial changes in the metabolite levels in the central carbon metabolism, the homeostatic regulatory machinery of the hepatoma cells only allowed for small changes among the highly linked cofactors: ATP decreased slightly but remained at above 80% of its reference concentration, the NAD level increased only marginally, NADP increased a little more, reaching 143% of its initial value. In contrast to these observations, distinct cofactor dynamics have been observed in similar stimulus response experiments in prokaryotes and yeast ,21,26.The experimentally determined reference intermediate levels are provided as supplementary data  was found to have substantial negative control over the formation of glycerol (r26).Lactate dehydrogenase r18) had a substantial positive control over the glycolytic fluxes. Ainscow and Brand reported positive control of lactate production on glycolysis in primary hepatocytes isolated from fed rats  had a su.The pyruvate dehydrogenase complex (r36) and the pyruvate secretion step r38) had a negative control over the glycolytic flux. For pyruvate oxidation, Ainscow and Brand also observed a negative control over glycolysis in rat hepatocytes [ had a neAinscow and Brand observed a negative control for oxidative phosphorylation over the glycolytic flux in primary rat hepatocytes (flux control coefficient of -0.26) . This waThe control of the pentose-phosphate pathway  depends to a great extent on the demand for reduction equivalents (r22) and the glucose-6-phosphate dehydrogenase enzyme (r10). This means that flux control coefficients of 0.63 and 0.41 of the individual fluxes in the pentose-phosphate shunt were observed for NADPH consumption (r22) and the glucose-6-phosphate dehydrogenase enzyme (r10), respectively. Kather et al. also reported that the glucose-6-phosphate dehydrogenase and the NADPH/NADP ratio control the pentose-phosphate pathway of isolated fat-cells . Sabate in vivo metabolite dynamics, Vaseghi et al. concluded that in Saccharomyces cerevisiae the pentose-phosphate pathway acts as a functional unit that is controlled by the demand for biosynthesis and is modulated by the energy state of the cell [The predominant control of the pentose-phosphate pathway by the glucose-6-phosphate dehydrogenase (r10) and the demand for reduction equivalents (r22) is also interesting with respect to the discussion of modular structures in metabolic networks. Using dynamic modeling and experimental observations of the cell . In accothe cell . In thisAinscow and Brand applied top-down methods to elucidate metabolic control patterns in isolated rat hepatocytes. They included only one common reaction block for pyruvate transport, TCA cycle, and five-sixths of the respiratory chain ,32. ThusReaction r42 describes the exchange of alpha-ketoglutarate with the biomass. In the dynamic network model, the rate of r42 depends only on the level of its product alpha-ketoglutarate. The corresponding elasticity coefficient was determined to -0.5. This means that changes in the level of alpha-ketoglutarate are directly mirrored in changes in the flux through the r42 reaction, and, thus, r42 was found to be strongly influenced by several enzymes.Figure NADPH consumption (r22) was mainly controlled by itself (0.65). However, it is important to note that it is not only the demand of NADPH alone that affects the NADPH consumption flux, but also the supply of NADPH (0.38). This means that an increase in NADPH production yields an increase in NADPH consumption, i.e. a stimulation of biosynthetic reactions. Put differently, the dependence of NADPH demand on NADPH supply provides further evidence for the hypothesis that tumor growth is limited by NADPH production.Numerous papers have dealt with the control of oxidative phosphorylation in isolated rat liver cells ,34,59. TThe steady state NADPH level was found to be very sensitive to two reactions - the glucose-6-phosphate dehydrogenase (r10) and the consumption of reduction equivalents (r22) . In both cases, the glycolytic enzymes  had a positive, albeit low, control over the cofactors. As expected, the glucose-6-phosphate dehydrogenase enzyme (r10) had a negative control over both intermediates, i.e. control coefficients of -0.06 for ATP and -0.27 for NADH, respectively. In contrast, the r12 (phosphogluconate dehydrogenase), r14 (ribulose-phosphate 3-epimerase), and r16  enzymes in the pentose-phosphate pathway had a positive control over the NADH and ATP levels. A major characteristic of cancer cells, including the hepatoma cells analyzed in this study, is the secretion of lactate under aerobic conditions . The aerPartial internal response coefficients quantify system responses to changes in the concentration of intermediates ,60,61. AThis study dealt with the quantitative assessment of the dynamics and control of the central carbon metabolism in hepatoma cells. Metabolite time-series data analyzed in a stimulus response experiment revealed substantial changes in the concentrations of intermediates, and were used for identifying network dynamics. Control analysis was applied in order to break down the internal control structure of the central carbon metabolism in hepatoma cells. In comparison to previous top-down approaches, this study enabled the more detailed analysis of the underlying control patterns. Rather than describing how sub-systems interact with each other, the control distribution approach used quantifies the influences the individual enzymes have on each other. It was possible to unravel many different interactions: Glucose-6-phosphate dehydrogenase had a substantial negative control over the glycolytic flux. Partial flux control coefficients were determined in order to assess the importance of the individual interactions in mediating changes in the flux through the glucose-6-phosphate isomerase enzyme ,60,61. Iin vivo metabolite time-series measurements from primary human cells. Moreover, compartmentalization was not accounted for in the dynamic network model. Thus, control principles affected by compartmentalization might differ to some extent from the results obtained in this work, e.g. cytosolic intermediates may have less effects on mitochondrial enzymes and vice versa.Similarly, glucose-6-phosphate dehydrogenase negatively controls the end of the TCA cycle. The negative control is mainly mediated by an increased NADPH/NADP ratio. The subsequent reaction steps in the TCA cycle are negatively controlled by elevated product levels. The concept of partial flux control proved to be essential for unraveling these control structures. It should be noted that the detailed control structures unraveled in this work had been mainly compared with hepatic control principles obtained from applying top-down approaches in rat hepatocytes ,32. To fPartial internal response coefficients were determined in order to investigate the reaction steps that are most relevant in counteracting an increase in intermediates in order to return to the steady state ,62.  IntIt is envisaged that in the near future, it will be possible to predict the effects of nutrients in the liver at the inter-individual level by coupling metabolic network models to gene regulation and by integrating individual transcriptome and proteome data. Moreover, systems-oriented analyses of hepatic responses to xenobiotics might enable the personalized prognosis of drug actions and/or their persistency.® Number HB-8065™) were incubated at 37°C in 6-well-plates in 5% CO2 atmosphere. The cells were cultured in alanyl-glutamine-free William's medium E  that was supplemented with penicillin (100 U/mL), streptomycin (100 mg/mL), and Gibco™ Insulin-Transferrin-Selenium (100X) supplement . No fetal calf serum was added to the medium. The 6-well plates were shaken at 20 rpm throughout the experiment . The number of cells was determined with a Neubauer counting chamber. The intracellular flux map corresponding to this experimental setup was determined previously [HepG2 cells  and (ii) solvent B . The following gradient programs were implemented: 100% buffer A from 0 min to 3.5 min, increase to 100% B until 43.5 min, remaining at 100% B until 51 min, decrease to 100% A until 56 min and remaining at 100% A until 66 min.Nucleotide analysis was performed by reversed phase ion pair high performance liquid chromatography. The HPLC system  consisted of an Agilent 1200 series autosampler, an Agilent 1200 series Binary Pump SL, an Agilent 1200 series thermostatted column compartment, and an Agilent 1200 series diode array detector set at 260 and 340 nm. The nucleotides were separated and quantified on an RP-C-18 column that was combined with a guard column  at a flow rate of 1 ml/min. The mobile phases were (i) buffer A . The model comprises glycolysis (EMP), the pentose-phosphate pathway (PPP), and the tricarboxylic acid (TCA) cycle. In the cataplerotic section, the malic enzyme, which decarboxylates malate to pyruvate, is taken into account. Reduced NADH is regenerated in the lactate dehydrogenase and oxidative phosphorylation reactions. P/O ratios of 2.5 and 1.5 were assumed for NADH and succinate, respectively [A metabolic network model was reconstructed for the identification of hepatic metabolite dynamics. The model was based on a previously published isotopomer model used for the estimation of intracellular fluxes from transient ing data . The modectively . No consectively ; i.e. liectively . Based oectively , the metectively  and inclectively . Furtherectively .The following set of metabolite mass balances was set up to describe the time-dependent behavior of the metabolic system presented above:N denotes the stoichiometric matrix and r the rate vector. (c0) is a square diagonal matrix with reference concentrations on its main diagonal; ® Core2™ Quad CPU, 2.66 GHz, 4 GB RAM).The ordinary differential equations (ODEs) were reformulated as differential algebraic equations (DAEs) to improve both the performance and stability of the numerical integrations, i.e. the conservation relations were solved algebraically. The DAE system was simulated with the linearly implicit differential algebraic solver LIMEX . On averin vivo kinetics and metabolic redesign [Canonical linear-logarithmic (linlog) kinetics were applied for approximating the reaction rates in equation (1) -72. The redesign . Linlog redesign ,38,39. Iredesign . The matredesign (2)J0 is the reference steady state flux distribution, i is a vector of ones. ij that describe the local effect of an infinitesimal change in concentration j on the rate of reaction i, i.e.in which Assuming constant enzyme levels, equation (2) can be reduced toJ0 and c0, and the corresponding kinetic parameters, i.e. J0 was estimated from transient 13C-labeling data [c0 and Parameterizing the kinetic model requires the specification of a reference steady state, i.e. ing data ,7. In thAt the outset of a simulation run, all intracellular metabolite levels in silico model simulations and in vivo measurement data: The variance-weighted sum of squared residuals χ2 between experimentally observed and simulated metabolite data, cm and cs, was minimized according towhere m is a diagonal matrix containing the measurement variances. An evolution strategy was applied for parameter fine-tuning that included a self adapting mutation operator [in which Σoperator ,75. To eNo confidence limits were calculated for the estimated parameters. For parameter estimation, however, a multi-start optimization approach was taken and the distribution of control was consistently determined from the parameters estimated and, thus, was considered to be reliable. It is worth noting that in an exploratory study, Nikerel et al. investigated the identification of kinetic parameters in a dynamic model based on linlog kinetics, and found that the underlying control structures were inherently robust against non-identifiable elasticities . MoreoveJ given byIn this study, the local stability of the biochemical system was investigated by analyzing the eigenvalues of its Jacobian matrix NR and L are the reduced stoichiometric matrix and link matrix, respectively [where ectively . A steadA metabolic control analysis was carried out to assess systemic steady state properties. In this context, the concentration control coefficient Similarly, flux control coefficient By applying the summation and connectivity theorems, the concentration and flux control coefficients can be calculated from the estimated elasticities and steady state concentrations (10)andThe control that one enzyme exerts over another is mediated by changes in the levels of intermediates. Enzymatic reaction rates respond to changes in substrate, product, and effector levels. The concept of a partial flux control coefficient allows the quantification of the fractions of the flux change in relation to changes occurring in individual intermediates ,60,61. PThe individual summands ticities  and partticities . Howeverticities . TherefoA stable system that operates at steady state will counteract changes in intermediate levels and eventually return to its original steady state . Elevatedy state ,62, i.e.According to the connectivity theorem the sum of the partial internal response coefficients for each intermediate is -1. For a given enzyme j and metabolite i, the internal response coefficient r itself . GraphicPPP: pentose-phosphate pathway; TCA: tricarboxylic acid; EMP: Embden-Meyerhof-Parnas; VLDL: very-low-density lipoproteins; HPLC: high performance liquid chromatography; GC-MS: gas chromatography-mass spectrometry; LC-MS-MS: liquid chromatography-mass spectrometry-mass spectrometry; ODE: ordinary differential equation; DAE: differential algebraic equation; ROS: reactive oxygen species; GLC: glucose; G6P: glucose-6-phosphate; G1P: glucose-1-phosphate; F6P: fructose-6-phosphate; F16P: fructose-1,6-bisphosphate; DHAP: dihydroxyacetone phosphate; GAP: glyceraldehyde 3-phosphate; 13PG: 1,3-bisphospho-glycerate; G3P: 3-phosphoglycerate; G2P: 2-phosphoglycerate; PEP: phosphoenolpyruvate; PYR: pyruvate; SER: serine; LAC: lactate; ALA: alanine; GL6P: 6-phospho-glucono-1,5-lactone; 6PG: 6-phospho-gluconate; RIBU5P: ribulose 5-phosphate; RIBO5P: ribose 5-phosphate; XYL5P: xylulose 5-phosphate; S7P: sedoheptulose 7-phosphate; E4P: erythrose 4-phosphate; ACCOA: acetyl-CoA; CIT: citrate; CISAC: cis-aconitate; ISOCIT: isocitrate; AKG: alpha-ketoglutarate; SUCCOA: succinyl-CoA; SUC: succinate; FUM: fumarate; MAL: malate; OAC: oxaloacetate; ATP: adenosintriphosphate; ADP: adenosindiphosphate; AMP: adenosinmonophosphate; NADP(H): nicotinamide adenine dinucleotide phosphate; NAD(H): nicotinamide adenine dinucleotide; r1: glucokinase; r2: glucose-6-phosphate isomerase; r3: phosphofructokinase; r4: fructose-bisphosphate aldolase; r5: triose-phosphate isomerase; r6: glyceraldehyde-3-phosphate dehydrogenase; r7: phosphoglycerate kinase; r8: phosphoglycerate mutase; r9: pyruvate kinase; r10: glucose-6-phosphate dehydrogenase; r11: 6-phosphogluconolactonase; r12: phosphogluconate dehydrogenase; r13: ribose-5-phosphate isomerase; r14: ribulose-phosphate 3-epimerase; r15: transketolase; r16: transketolase; r17: phosphopyruvate hydratase; r18: lactate dehydrogenase; r19: adenosinetriphosphatase; r20: alanine transaminase; r21: phosphoglucomutase; r22: NADPH consumption; r23: glycogen synthesis; r24: transaldolase; r25: adenylate kinase; r26: glycerol formation; r27: nucleotide synthesis; r28: serine synthesis; r29: citrate synthase; r30: aconitate hydratase; r31: aconitate hydratase; r32: isocitrate dehydrogenase; r33: succinate-CoA ligase; r34: fumarate hydratase; r35: malate dehydrogenase; r36: pyruvate dehydrogenase complex; r37: alpha-ketoglutarate dehydrogenase complex; r38: pyruvate synthesis; r39: valine leucine isoleucine metabolism; r40: succinate dehydrogenase; r41: oxidative phosphorylation; r42: alpha-ketoglutarate synthesis; r43: malic enzyme; r44: glutamate dehydrogenase; r45: lactate transport; r46: pyruvate transport; r47: glucose transport (GLUT2); r48: alanine transport; r49: serine transport;a was involved in the design and execution of the perturbation experiment, he also performed the model identification and systems-level analyses, conceived the study, and drafted the manuscript. UH contributed to the design of the experimental setup, coordinated the chemical analyses and participated in the design of the study. MR and KMb conceived the study and contributed to its design. KMb coordinated the experimental design, model set-up and analysis, and co-drafted the manuscript. All authors read and approved the final manuscript.KMReference extracellular and intracellular metabolite levels. The subscripts 'ex' and 'in' denote extracellular and intracellular metabolites, respectively. Intracellular and extracellular values are given in mmol/lcv and mmol/lwell.Click here for fileFlux control coefficientsClick here for fileConcentration control coefficientsClick here for filePartial internal response coefficients. According to the connectivity theorem, the sum of the partial internal response coefficients for each intermediate is -1. Perturbations in moiety-conserved sets cannot be counteracted in order to reach the previous steady state, which is the reason why no partial response coefficients are listed for ATP, ADP, AMP, NADP, NADPH, NAD, and NADH.Click here for fileElasticity matrix. The scaled elasticities are based on metabolite time-series data. Only non-zero entries are shown. The subscript 'ex' denotes extracellular metabolites.Click here for file