Cellular metabolism assembles in a structurally highly conserved, but functionally dynamic system, known as the metabolic network. This network involves highly active, enzyme-catalyzed metabolic pathways that provide the building blocks for cell growth. In parallel, however, chemical reactivity of metabolites and unspecific enzyme function give rise to a number of side products that are not part of canonical metabolic pathways. It is increasingly acknowledged that these molecules are important for the evolution of metabolism, affect metabolic efficiency, and that they play a potential role in human disease—age-related disorders and cancer in particular. In this review we discuss the impact of oxidative and other cellular stressors on the formation of metabolic side products, which originate as a consequence of: (i) chemical reactivity or modification of regular metabolites; (ii) through modifications in substrate specificity of damaged enzymes; and (iii) through altered metabolic flux that protects cells in stress conditions. In particular, oxidative and heat stress conditions are causative of metabolite and enzymatic damage and thus promote the non-canonical metabolic activity of the cells through an increased repertoire of side products. On the basis of selected examples, we discuss the consequences of non-canonical metabolic reactivity on evolution, function and repair of the metabolic network. During its lifespan, a cell is exposed to many hazards and changes in the environment. These include varying pH and temperature, osmotic imbalances, radiation, drought, starvation, contact with deleterious or toxic chemicals, or biotic interactions with other species. These stress situations can manifest as an acute pulse, or be sustained over time, and can affect cellular functioning and ultimately impair cell growth, replicative capabilities, and/or promote aging. Stress-induced damage to biological macromolecules such as DNA, proteins and membrane components has been intensively studied and characterized ,2,3,4. H2O2), superoxide anion (O2−), or hydroxyl radical (•HO). Non-enzymatic chemical reactivity plays a crucial role in this scenario, as for example in the context of the Fe(II)-catalyzed Fenton reaction, that converts H2O2 into •HO [One of the most important causes of metabolic damage is unspecific oxidation. Basal levels of oxidizing molecules arise constantly from normal cellular processes involving redox reactions or in the mitochondrial or photosynthetic electron transport chains . Normal into •HO . Superoxinto •HO ,14,15. Tinto •HO ,17,  and methionine are the most prone to oxidation . When thnd aging ,29.2O2 [Biological systems exploit this property of metabolites and use them as scavengers for ROS. This applies not only to methionine and cysteine, but also to pyruvate, α-tocopherol, ascorbic acid, or other amino acids ,30,31,322O2 .In analogy to DNA and protein repair, cells have developed a series of control mechanisms to cope with the oxidized/chemically damaged metabolites, summarized by the term “metabolite repair”  or “metaS-sulfoxide and the R-sulfoxide residues, respectively, predominantly within a protein context [RMsr) is only present in prokaryotes [R-sulfoxide. Interestingly, MsrC exhibits no sequence homology with MsrA and MsrB, indicating independent evolutionary origin of these functionally overlapping proteins. In higher plants, where no specific MsrC-like activity exists, the repair function on free methionine-R-sulfoxide is efficiently covered by a subtype of MsrB proteins  [An illustrative example for specific oxidative stress-related repair concerns methionine. Repair of oxidized methionine does occur when the amino acid is in its free form as well as when it is part of a protein ,44 Figu. Three e context . MsrC  , evidencication) ,47,49,50ication) , cancer ication) , drug inication) , or aginication) . Evidencication) .Metabolism comprises a large diversity of molecules. The spectrum of possible combinatorial reactions and modifications on metabolites extends to a huge space of chemical reactions. Some modifications occur however more frequent than others. For instance, nucleotide metabolism is by its nature composed of many metabolites possessing high structural similarities. A range of abnormal nucleotides is generated as a consequence of spontaneous oxidation . Others R and S hydrated forms of NAD(P)H display high structural similarity with the cofactors but are non-functional and inhibit various dehydrogenase reactions [S enantiomeric derivative back to NAD(P)H [R and S hydrated forms, an enzyme that appears fused to the dehydratase in some species such as Escherichia coli. Interestingly, in higher plants [Another quantitatively highly relevant case concerns chemical modification of enzymatic coenzymes, such as NADH or FADH. Hydration of NADH or NADPH is common, occurring either non-enzymatically  or as a eactions . An ADP/ NAD(P)H . Its actr plants ,67 and ar plants  both genA second aspect of the susceptibility of metabolism concerns non-enzymatic reactions that occur as part of normal metabolism or through non-specific chemical reactivity but that contribute to canonical metabolic pathways ,70. SuchNon-enzymatic reactions are dependent on the chemical environment , and must therefore be particularly sensitive to stress conditions. This is well illustrated for the case of non-enzymatic protein acylation: A number of essential, endogenous thioester metabolites, such as acetyl-CoA or succinyl-CoA, can unspecifically cross-acylate protein lysines ,73. ProtE. coli’s resistance to a high number of compounds is mediated by the outer-membrane pore-forming protein TolC [E. coli tolC mutants show lower fitness phenotypes in certain stress conditions [While specific repair mechanisms might have evolved for non-canonical metabolites which are produced in higher quantities or present strong cytotoxic effects, it is reasonable to assume that not all metabolic side products possess specific clearance mechanisms. This becomes illustrative, as the number of potential chemical reaction products from non-enzymatic reactivity exceeds the number of enzymes encoded in a typical genome by several orders of magnitude. A broad range of metabolites, including especially those for which no specific cleaning enzyme exists ,76,77, mein TolC . This trein TolC ,83. Therein TolC : E. colinditions , accumulnditions , and ovenditions . Similarnditions .A third important aspect of metabolism during stress conditions does not concern the direct chemical modification of metabolites, but affects them indirectly by altering enzyme function. Upon damage, several enzymes decrease in substrate specificity and simultaneously increase in promiscuity. When enzymes are modified, novel subsidiary activities and interactions can arise concomitantly from the altered proteins, enabling additional metabolic reactions, some of potential physiological significance ,88. It iMost enzymes accept multiple substrates and possess affinities for a wider range of compounds, a phenomenon referred to as substrate promiscuity A  and isocitrate dehydrogenase (IDH1 and IDH2). MDH typically catalyzes the interconversion between malate and oxaloacetate, but possesses certain affinity towards α-ketoglutarate. Despite the much higher affinity for the canonical substrate, high intracellular levels of α-ketoglutarate promote that MDH also produces lutarate . Deleter product . An anallutarate . This nolutarate . These maciduria , a genetaciduria  and mutae repair .Importantly, such secondary activities of enzymes are often latent in normal growth conditions, but can become relevant in response to environmental changes or stresses  and some other enzymes that are canonically iron-dependent, actually accept both iron Fe(II) and manganese Mn(II) as cofactor ,101. As et al. [in vivo protective role of Met-misincorporation for cell survival and growth under ROS stress.Despite being an energetic burden to the cell, promiscuity and multi-substrate specificity is an integral biological property in metabolic networks, and is essential as it is necessary for the evolution of metabolism . In someet al.  demonstret al.  reveals Saccharomyces cerevisiae [The antioxidant function of Met residues might be also the cause of AUA codon reassignment in mitochondria, from isoleucine (Ile) to Met, which is widespread in vertebrates and also occurs in several invertebrates with a highly aerobic metabolism (like insects) and in some unicellular eukaryotes, including revisiae . With threvisiae .Candida albicans [Candida interactions with the host microenvironment. In particular, experimental evidence shows that adherence capacities improve while recognition by the hosts immune system decreases [Candida virulence.Another case in which ambiguous tRNA acylation has been proven beneficial is that of the fungus albicans   for different metabolites may change according to conditions [2O2 to assure rapid inactivation when levels of this metabolite rise [Enzyme activities are tunable and the degree of affinity and/or efficiency . Increaite rise  and pyruite rise ,125 are ite rise . In thisite rise , so thatTPO1 [2O2 being a product of polyamine oxidation [2O2 upon induction by a spermine analogue [Another oxidant-induced change in metabolic flux distribution is connected to the polyamine metabolites spermine, spermidine and putrescine. These polycations are implicated in a multitude of cellular functions, including the stress response . TreatmeTPO1 . Yeast cTPO1 . In thisxidation . Studiesanalogue . Overexpanalogue ,133.et al. [Carbonell et al.  implies et al. ,136. Theet al. . Intereset al. . Recentlet al. .Also metabolite repair—potentially in the form of much more rudimentary mechanisms—might date back to the very early stages of evolution and could already have been important for the development of metabolism during the origin of life , as firsWith the advent of systems biology and analytical techniques that allow analyzing multiple cellular metabolites in parallel, it has become clear that metabolism is constituted by a highly dynamic network. In this short review, we discuss examples that reveal the impact of stress conditions on metabolites, metabolic reactions and metabolic flux. Non-enzymatic reactions, chemical reactivity between metabolites, and enzyme promiscuity are inevitable consequence of the chemical properties of essential metabolites, and mechanistic and structural constraints of the participating enzymes. In stress conditions, these factors play synergetic roles in the propagation of errors and damage within metabolism, but also form the basis to reconfigure metabolism so that cells can adapt to changing or stress-inducing environments ,140.Metabolism in stress situations appears to be mainly affected by: (i) direct chemical modification of metabolites; or (ii) damage on enzymes that change their substrate specificity and/or catalytic activity. Temporary blockage of metabolic pathways translates as changes in the metabolic flux distribution. Although stress situations appear to be deleterious in the first instance, they have been exploited by evolution to extend the metabolic network, and to develop dynamic response mechanism to cope with changes in the environment. This includes either the use of promiscuous metabolites in signaling, so that repair and damage responses are initiated and function as stress sensors ,27,141,


The fermentation of glucose using microbial mixed cultures is of great interest given its potential to convert wastes into valuable products at low cost, however, the difficulties associated with the control of the process still pose important challenges for its industrial implementation. A deeper understanding of the fermentation process involving metabolic and biochemical principles is very necessary to overcome these difficulties. In this work a novel metabolic energy based model is presented that accurately predicts for the first time the experimentally observed changes in product spectrum with pH. The model predicts the observed shift towards formate production at high pH, accompanied with ethanol and acetate production. Acetate (accompanied with a more reduced product) and butyrate are predicted main products at low pH. The production of propionate between pH 6 and 8 is also predicted. These results are mechanistically explained for the first time considering the impact that variable proton motive potential and active transport energy costs have in terms of energy harvest over different products yielding. The model results, in line with numerous reported experiments, validate the mechanistic and bioenergetics hypotheses that fermentative mixed cultures products yielding appears to be controlled by the principle of maximum energy harvest and the necessity of balancing the redox equivalents in absence of external electron acceptors. Carbohydrates anaerobic fermentation towards volatile fatty acids (VFAs) has an increased interest due to its potential to provide building blocks from wastes towards a plethora of diverse valuable products. These chemical building blocks and complex biofuels , 2 or biFermentations are environments with low energy available where microorganisms behave as highly efficient energy scavengers –22. MixePrevious modelling efforts in literature have attempted to describe product formation in MCF under different pH but have only partly succeeded or simply fell short –27. SincEnergy-based modelling approaches have been proposed to mechanistically describe the impact of environmental conditions on MCF catabolic activities by means of bioenergetics , 39. TheIn this work, the model developed is applied to the understand of the pH role as operational variable into the product spectrum and this is targeted referring to the most complete experimental work done by Temudo et al. 2007 , previouThe main goal of the model is to mechanistically describe the product spectrum shifts and trends experimentally observed in the mixed culture fermentation as function of the environmental conditions fixed in a continuous stirred tank reactor  and extra—cellular volume domains, including pH and full ionic speciation are modelled and simulated dynamically  methods for large metabolic networks , do typiFeasible reaction intermediate intracellular metabolites concentrations can be assumed to have to fall between a maximum of 10 mM and a minimum of 1 μM  for physBy conducting a thermodynamic assessment of the metabolic network presented in The metabolism of a microbial cell can be described as a system organized in an energy harvesting catabolism coupled to an energy consuming anabolism and maintenance . Cells cThe reversible nature of the ATP—synthase mechanism , allows H+) is commonly defined as energy liberated when a proton enters in the cytoplasm [in − Δψout, with the inner membrane surface considered negative. Δψ has been reported near to a constant value depending on the microorganism and growth conditions [H+ variations are solely considered due to variations on the external pH [Proton motive force /(red)), due to its more negative reduction potential, is the only electron carrier considered capable to direct H2 production [2  strongly rule out direct H2 production from this carrier under cytoplasmic conditions [NAD(H) has a less negative reductive potential than ferredoxin and although in previous models NAD(H) was considered an electron carrier capable of direct Hoduction , both exoduction  and theroduction , 32 (ΔG0nditions . NAD(H) nditions .2) is the third electron carrier considered in the model and it is associated to the highly exergonic metabolic reactions because of its less negative reduction potential. FAD reduction can be coupled to energy harvest by proton translocation [2) electron carrier plays the role of an intermediate facilitating the coupling of a highly energetic metabolic reaction with the generation of proton motive force described with the oxidation of NADH following the mechanism presented in Eqs  isd in Eqs .Met.A +2 instead of one proton translocation in these highly energetic reactions, this was not considered due to the experimental observed 1:1 stoichiometry of H2 respect to pyruvate oxidation [Although Seedorf et al. 2008  also sugxidation . The sam2 associated to a proton translocation mediating the reduction of acetaldehyde to ethanol. This has not been reported but it has been found as a necessary mechanism to ensure the prediction of the observed high yield of ethanol production. In the ethanol pathway, the reduction of acetaldehyde to ethanol is typically exergonic . However, reduction of ferredoxin by acetaldehyde has been reported [2 involved is proposed as possible in the ethanol pathway at conditions of low ΔμH+.In the network of xergonic , but thereported , 62 thuse−/molCx·h transferred in the glycolysis [Smax = 0.75 molGlu/molCx·h is based on 4 electrons transferred in the glycolysis [+ reduced per mol of glucose). No accumulation of intermediate metabolites is considered and a constant concentration of 7.5 mM assumed for intracellular pyruvate [Kinetic differences in metabolic reaction rates are expected to be not highly significant due to the nature of the system. The overall process rate is assumed controlled by the glucose uptake rate and glycolysis, which being highly exergonic, is never limited by thermodynamics. Therefore highly general and similar kinetic parameters are assumed across the board for all metabolic routes as they did not impact the predicted product spectrum trends during on our preliminary assessment (not shown). The overall process rate is modelled assuming one general maximum corresponding to 3 molycolysis . Any kinycolysis   is not described and only products transport is modelled with distinction between uncharged species (free diffusion) and charged (active transport).Passive transport is modelled considering that the lipid bilayer membrane controls only the cross of charged species but does not act as a barrier for small uncharged species. These species are assumed as freely diffusing through the membrane with no energy coupling or control from the cell homeostasis. A major difficulty arises from the largely unknown diffusion coefficients of all species through a cell membrane. If these values are accepted to be within the same order of magnitude, the main differences in diffusion rates come due to differences in the partition coefficients  i.e. ac.Active transport of charged and/or large molecules that are not freely diffusing through the cell membrane is coupled to metabolic energy exchange which is known to be performed by a diversity of transport proteins (ports) allowing only specific molecules to cross . For thei is the solute charge.Any changes in membrane potential associated to the transport of charged species are compensated by the needed proton translocation coupled to ATP hydrolysis. In this way the cell is capable of the maintenance of its homeostasis and membrane potential. The potential associated to a solute transport across the membrane is calculated by All charged products considered in the fermentation model are negatively charged and their transport outside the cytoplasm leads to a decrease in the potential of the membrane  needed for transport fuelling (−) or harvested from transport energy surplus (+) are calculated as proposed in the well-known recycling model , Eq (7) Anabolism and decay processes are modelled trough two overall mass balanced reactions. Anabolism (from glucose) is modelled limited by substrate and energy availability that comes from catabolism –68. To aCx·h [A ratio of (ADP·Pi)/ATP concentrations is considered maintained constant at ΔG of −50 kJ/mol for ATP hydrolysis to preserve the cell homeostasis . Part ofCx·h  plus theCx·h  (Sectioni) to maximize ATP yielding in catabolism  and formate production (through ferredoxin or direct pyruvate oxidation) are equivalent and no evidence suggests that extracellular pH could have an impact on them [2 + H2 to formate at high pH , leads to electrons allocation in reductive fermentation steps. The need for this complete electron balance fully accounted for in the model, is a main constraint during the maximization of ATP production and appears to be in line with the experimental observations.Fermentation with acetate as only product has not been experimentally reported being its production always accompanied by other more reduced products yielding . The maiAt low pH, butyrate and acetate are predicted as major products as well as experimentally reported Figs  and 8 wiBased on the metabolic network in H+ is modelled as only depending on external pH, when it is low, ΔpH increases and more energy is needed to translocate one proton across the cell (ΔμH+ increases). In ethanol pathway, the energy available during FADH2—mediated acetaldehyde reduction is not as high as that in crotonyl—CoA reduction (part of the butyrate pathway) or that in fumarate or in acryl—CoA reductions (part of the propionate pathways)  which elevates the capacity of energy harvest by this pathway making together with acetate yielding, its production competitive comparatively to yield butyrate or acetate plus propionate. This comes together with the higher energy available for acidic components transport at high pH, and makes the ethanol production more favourable than propionate in terms of energy yield as formate, which is the strongest acid, is produced in ethanol pathway  permits one proton translocation  and could affect the model prediction capacity in some cases.+ recovery impacting the electron balances and possibly involving other electron carriers not considered could have significant roles [Alternative additional mechanisms of NADH/NADnt roles .1.8O0.5N0.2).The impact of anabolism and decay on the NADH balance has not been included and only the oxidation or reduction present in catabolism  by modification of the upper parts of the metabolic network. The model application to the study of more complex substrates  is however thought to be more troublesome due to the number of additional factors that could deviate from the model assumptions . Experimentally, when using complex substrates, the control of the products spectrum is difficult, however, mechanistic insights on their fermentation, such as those obtained through in this study with glucose, do contribute towards the overall understanding and accelerate the industrial application of these bioprocesses towards valuable products recovery from wastes. Extensions of the metabolic network to address additional or more complex substrates are not expected to pose major impacts on computational times to solve the model as the already long simulation times required are mainly caused by short integration time steps due to the stiffness of specific variables.The proposed model provides insights into energetically based mechanisms of the trends and shifts observed on the product spectrum in glucose fermentations; the model has some limitations and areas for further development to be considered including:2/H2 and formate production.The model developed, based on the optimization of the ATP production under a detailed metabolic network and with a full account of the electron balances and membrane transport energetics is, to our knowledge, the first mechanistic model succeeding in the prediction of observed shifts in major fermentation products with external pH, including the shift between COThe breakthrough improvement respect to previous models is attributed to the more comprehensive account for the different electron carriers and their roles, a more complete metabolic reaction network and a detailed modelling of the energetics of solutes transport across the cell membrane. Additional value comes from the minimum parameter fitting needed and the fact that all results obtained are mechanistically related.Under this approach, mixed culture fermentations, known to take place under strong energy limitation, are treated as networks that optimize the energy harvest rate of the overall mixed microbial population. The model focuses on first principles and on the energetic constrains imposed by the environment and avoids other specific physiological and ecological mechanisms. The results obtained under this modelling approach strongly support the hypothesis that mixed culture microbial ecosystems can be described as highly efficient energy harvesters in which, independently from the microbial community composition, the conditions of maximum energy harvest rate are achieved in the long term.S1 File(PDF)Click here for additional data file.S2 File(PDF)Click here for additional data file.


Altered cellular energy metabolism is a hallmark of many diseases, one notable example being cancer. Here, we focus on the identification of the transition from healthy to abnormal metabolic states. To do this, we study the dynamics of energy production in a cell. Due to the thermodynamic openness of a living cell, the inability to instantaneously match fluctuating supply and demand in energy metabolism results in nonautonomous time-varying oscillatory dynamics. However, such oscillatory dynamics is often neglected and treated as stochastic. Based on experimental evidence of metabolic oscillations, we show that changes in metabolic state can be described robustly by alterations in the chronotaxicity of the corresponding metabolic oscillations, i.e. the ability of an oscillator to resist external perturbations. We also present a method for the identification of chronotaxicity, applicable to general oscillatory signals and, importantly, apply this to real experimental data. Evidence of chronotaxicity was found in glycolytic oscillations in real yeast cells, verifying that chronotaxicity could be used to study transitions between metabolic states. Cellular energy metabolism encompasses many processes, ultimately resulting in the production of adenosine triphosphate (ATP), the fuel continuously used by cells for many essential functions, such as maintenance of ionic balance across the plasma membrane, signalling, and protein synthesis. Every day, we turnover the equivalent of our body weight in ATP234678967811The hypothesis that such a robust characteristic exists is based on a number of experimental observations of common patterns in metabolic dynamics which are distinctive in different metabolic states, suggesting that we may be able to identify a transition from a healthy or altered states by observing the properties of the dynamics of cellular metabolism.ψm). Although the oscillatory nature of energy metabolism is now more often appreciated31516171819202122β cells3ψm were observed, and it was concluded that these were probably entraining the whole metabolic network of the cell29First of all we focus on the oscillatory and time-dependent nature of the dynamics of energy metabolism. Indeed, the energy produced by a cell continuously fluctuates due to rate constants involved in the production and use of energy. Recently developed experimental techniques for the observation of energy metabolism313Energy production via different metabolic processes is tightly regulated. Each metabolic state of the cell will be characterised by different pathways of ATP production. This will result in clear differences between healthy and altered states, arising from the cell switching between glycolytic and mitochondrial ATP production as a primary source of energy. A widely observed example of this is the metabolic switch to glycolysis for an increased proportion of energy production in cancer cells, even in the presence of oxygen. This is known as the Warburg effect31Metabolic oscillations observed in glycolysis and in the mitochondria are coupled and can influence each other depending on the state of the cell20212735et al.S. cerevisiae) cells, we investigated the chronotaxic properties of glycolytic oscillations. Yeast cells have been shown to have metabolic similarities with cancer cellsIt was previously shown that chronotaxicity can be identified in a single time seriesHere, we demonstrate that glycolytic oscillations in real yeast cells show clear signs of chronotaxicity. Based on this, we propose chronotaxicity as a robust characteristic whose alterations signify changes in energy metabolism, facilitating identification of altered states in the cell. A theoretical model of different metabolic states is developed and the interplay between glycolytic and mitochondrial involvement in ATP production within a cell is investigated. We also consider how metabolic oscillations may be driven by factors such as substrate availability.The model shows how the temporal evolution of different states of cellular energy metabolism could be described based on changes in the robustness to external perturbations, or chronotaxicity. This provides a potential method of observing metabolic switches in real cells and investigating possible links to carcinogenesis.et al.38et al.Glycolysis in yeast cells is one of the most widely studied and well characterised biological oscillators. It was previously thought that glycolytic oscillations only arose as a result of synchronization between yeast cells, but recently Gustavsson α for the 16 included cells was 0.768, which characterises oscillations as chronotaxic. An example analysis on a real yeast cell can be seen in 29NADH data obtained by Gustavsson and co-authorsBased on experimental observations of sustained oscillations, and the evidence of chronotaxicity highlighted in yeast cells, we now consider the chronotaxicity of cellular energy metabolism in healthy and ‘altered’ states, and how this information could be used to observe transitions between these states over time. We consider chronotaxicity during the metabolic transition of a single cell from a state in which aerobic respiration provides the majority of ATP, to one where the cell is increasingly reliant on glycolysis. We consider the former as a healthy state, and the latter as an undesirable state for most cells. An upregulation of glycolysis may be observed temporarily in intermittent hypoxia, or consistently in cancer or yeast cells. Whilst a sign of stress in hypoxic cells, normal yeast cells actually demonstrate a preference for a glycolytic metabolism, displaying many similar metabolic features to cancer cells39Firstly, we discuss the important features of cellular energy metabolism relevant to the model see . ATP proIn the model which follows, we identify glycolytic and mitochondrial oscillators, and simplify the metabolic pathways and interactions between oscillators to only include features which are necessary to capture chronotaxicity, which can describe subtle changes in dynamics due to the change in the interactions between metabolic oscillators.β cells433et al. demonstrated that the frequency of glycolytic oscillations is directly affected by sugar transportOscillations in glycolysis have long been observed in many types of cells, including yeastin vivo was further exploredet al. investigated the effects on oscillatory glycolysis of stochastic, periodic, and steady sources of substrateThe effects of the inevitable fluctuations in the availability of glucose in vivo, we consider glycolysis as a single oscillator, the glycolytic oscillator (GO), which may be influenced by external glucose levels.Based on the observed oscillations in glycolysis, and the inevitable time-variability of glucose availability ψm oscillationsMitochondrial oscillations have been associated with cycles of oxidation and reduction of the intracellular NADH pool and extramitochondrial factors. In cases of oxidative stress or substrate deprivation in cardiac myocytes, the inner mitochondrial membrane potential may destabilise, causing depolarization and oscillation141314ψm as a measure of mitochondrial metabolic activity, we combine the Krebs cycle and OXPHOS, both of which occur in the mitochondria, into a single metabolic oscillator, the mitochondrial oscillator (MO), which may be driven internally or by the extramitochondrial factors such as the plasma membrane potential or Ca2+As is effectively assumed when observing Δψm. They also demonstrated the indirect influence of mitochondrial ATP production on glycolysis even in this state, via sensing of the ATP/ADP ratio, i.e. the lower this ratio, the harder glycolysis has to work. This link is provided by the reversal of the inhibition of PFK in the glycolytic oscillatorInteractions between mitochondrial and glycolytic oscillations have been experimentally demonstrated under metabolic stress in cardiac myocytesinteractions between these oscillators (MO and GO) which would change in a transition to an altered metabolic state. Therefore, our model provides sufficient detail to capture this transition, by considering only these interactions  could be provided by any inner structure of the oscillator, i.e. we assume that due to finite reaction times and interactions within structural elements of the oscillator the stable time-dependent point attractor could appear. Importantly, the oscillations observed by Gustavsson et al.In the second configuration, the chronotaxicity could be created due to the changes in chronotaxicity, i.e. alterations in the stability of metabolic oscillations in different states.Hereafter we do not distinguish between these two configurations, and consider the external resources glucose and oxygen as the drivers which directly or indirectly define chronotaxicity of the GO and MO, independent of the exact mechanism by which this occurs. Our focus will be on the MO). The end products of glycolysis which are relevant to the model are glycolytic ATP (ATPGO) and NADH. The MO is regulated by the availability of substrates. Here, we consider the availability of NADH as the primary influence on the mitochondrial oscillator  and oxygen (O), respectively. The inputs to the GO are considered to be glucose and mitochondrial ATP  is white Gaussian noise. Considering that the GO and MO are continuously interacting, as discussed above, they are represented as bidirectionally coupled oscillators, with coupling strengths ε1 and ε2 which may vary to represent different metabolic states. The inhibitory nature of the influence of ATPMO production on ATPGO production is represented by a repulsive coupling ε1, whilst the excitatory nature of glycolytic oscillations on mitochondrial oscillations is represented by an attractive coupling ε2. The external influences on the GO and MO are represented as unidirectionally coupled drivers, with coupling strengths ε3 and ε4 for O and G respectively, which may also vary.where The chronotaxic dynamics of this model was tested numerically. The system (1) was integrated with varying parameters. Numerically, for an oscillator to be chronotaxic, it was required that the observed oscillator was synchronized to one of the unidirectionally coupled drivers G or O. Using this test, 7 different types of dynamics were revealed, the most relevant 5 regions shown in GO or ATPMO to determine their chronotaxicity. To demonstrate this, phase fluctuation analysis was applied to the generated dynamics of GO and MO using parameters from each region shown in In real data, utilising chronotaxicity as the defining parameter of the system is superior to the consideration of synchronization alone, as it can be identified experimentally from any single time series, whereas synchronization requires measurements of all interacting oscillators. Therefore, in this case, it would be sufficient to have measurements of only ATPet al.48The applicability of the model is tested on the data of NADH recorded by Gustavsson et al.In the experiments by Gustavsson ε1 = 0, ε2 = 0, ε3 = 0, ε4 = 0.25, σ = 0.2) state using the instantaneous frequency extracted from the real experimental data. To make the system chronotaxic, the extracted frequency was used as the driver ωG of the glycolytic oscillator. This provided a chronotaxic oscillator with the same oscillation frequency as the experimental data, allowing the DFA exponent α to be compared between cases  as calculated using the Wilcoxon ranksum test. This shows that our model, although simple, incorporates enough features to allow the calculation of the presented characteristic, chronotaxicity, and that evidence of this characteristic appears to be present in yeast glycolytic dynamics. This verifies the applicability of our model to the glycolytic oscillator. Further investigation is required into the mitochondrial oscillator, and other metabolic states.The distributions of exponents did not significantly differ between those calculated in the cells and those calculated in the simulated chronotaxic system 3435The class of chronotaxic systems identifies oscillatory dynamical systems with dynamics ordered in time  is a vector of coordinates which fully determines the state of a system at a given moment of time in phase space x ∈ Rm. Alternatively, chronotaxic systems can be described by drive and response systems, as followswhere xA(t) (see p (xA(t) can be viewed as a uniformly hyperbolic trajectoryxA(t) can only contract in an unperturbed chronotaxic system. For more details and for relations between chronotaxic and other dynamical systems see ref. [The main defining feature of chronotaxic systems is a time-dependent steady state of point attractor A(t) see  which ex)  does not change its sign. In the case of a particular choice ε(t) > 0, the time-dependent steady state where x is chronotaxic due to the influence from the driver p, chronotaxicity will change when the external influence from p changes. This makes chronotaxicity a perfect candidate for investigation in the study of metabolic oscillators under changing driving influences.Taking into account that the dynamical system φA*, from the continuous wavelet transformOne of main advantages of chronotaxicity is that it can be identified experimentally from a single time series, whereas otherwise the identification of drive-response relationship would require measurements of the driver as well as the response system. To identify chronotaxicity in a time series, a method named phase fluctuation analysis (PFA) was recently developeds,t) is the mother wavelet which is time-shifted according to t and scaled according to the parameter s. The oscillation can then be traced in WT. The instantaneous frequency of the oscillation at each time point can be estimated using either the synchrosqueezed wavelet transformφA*.where Ψ for the scale equal to n is then defined by the following equation,To estimate Yn(t) is the integrated and detrended time series of length N. The self-similarity parameter is given by the gradient of the line of the plot of logF(n) against logn. The self-similarity parameter α for Δφ for uncorrelated Gaussian noise (as expected in chronotaxic systems) gives a value of 0.5; in contrast, for integrated white Gaussian noise (as expected in non-chronotaxic systems) the parameter α returns a value of 1.5. In n was chosen to be equal to 2 cycles of oscillations, and the largest length n was chosen to be equal to 15 cycles of oscillations. where In order to reliably test for chronotaxicity, it should be noted that the time series should be sufficiently long, i.e. contain at least 30 cycles of oscillation (may vary depending on the characteristics of the data), be evenly sampled, and have a sampling frequency which is high enough to capture the dynamics at the frequency of interestHow to cite this article: Lancaster, G. et al. Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states. Sci. Rep. 6, 29584; doi: 10.1038/srep29584 (2016).


We address this challenge in the newly expanded version of a software tool for the analysis of biological networks, VisANT 5.0. We focus in particular on facilitating the visual exploration of metabolic interaction between microbes in a community, e.g. as predicted by COMETS , a dynamic stoichiometric modeling framework. Using VisANT’s unique metagraph implementation, we show how one can use VisANT 5.0 to explore different time-dependent ecosystem-level metabolic networks. In particular, we analyze the metabolic interaction network between two bacteria previously shown to display an obligate cross-feeding interdependency. In addition, we illustrate how a putative minimal gut microbiome community could be represented in our framework, making it possible to highlight interactions across multiple coexisting species. We envisage that the “symbiotic layout” of VisANT can be employed as a general tool for the analysis of metabolism in complex microbial communities as well as heterogeneous human tissues. VisANT is freely available at:  PLOS Computational Biology Software paper.This is a Metabolism comprises a complex network of biochemical reactions that guarantee a supply of energy and building blocks to every living cell. More broadly, however, metabolism can be viewed as a multicellular or ecosystem-level phenomenon, encompassing not only the biochemical transformations occurring within each cell, but also the exchange of molecules across different cells or organisms. Indeed, most microbial life takes place in complex multi-species microbial communities whose dynamics is highly dependent on metabolite-mediated microbe-microbe and microbe-environment interactions. Through such interactions, soil and ocean communities participate in the global cycling of oxygen, carbon and nitrogen ,2, whileThe opportunity to scale genome-level models to simulate complex communities poses new analysis and visualization challenges. One major challenge is the implementation of hierarchical representations of these systems and the outcomes of model simulations. Ideally, all the details of intracellular networks would be maintained, but at the same time researchers would be able to zoom out to obtain an ecosystem-level view of the whole community, with a major emphasis on the network of metabolites exchanged between species. A number of tools have been developed for analyzing and/or visualizing metabolic network and fluxes –27, withHere we present an approach that addresses the challenge of extracting data from genome-scale models, and visualizing the ensuing ecosystem-level network, with numerous potential applications to the study of the human microbiome and other microbial communities. Our approach was developed within release 5.0 of VisANT, a workbench for the integrative analysis of biological networks. In comparison to other tools –27, VisANew features in VisANT 5.0 are aimed at facilitating the visual exploration of metabolite exchange and competition between microbes in a community. The main features of VisANT 5.0 that make this possible are: 1) Metagraph-based multi-model visualization, where each metabolic network model is encapsulated by an expandable metanode. 2) New layout algorithms and color schemes to classify metabolites as mediating different types of interactions between organisms (e.g. cross-feeding or competition); 3) Dynamic flux visualization to capture the time-dependent network variation and flux distribution, with the capability to export the changes as animated GIF files; 4) Comparison of the flux distribution of the community-level network under different conditions; 5) Exploratory navigation of reactions and metabolites; 6) Query of enzymes to facilitate the integration of signaling networks, regulatory networks, and expression data. 7) Capacity to edit metabolic networks, through navigation of built-in hierarchy of Enzyme Commission (EC) nomenclature.VisANT is a widely used tool for the building and analysis of biological networks. Initially focused on the interaction network between bio-molecules in its first release , VisANT As shown in Working with your own data, at Page 5  that preserves all the information for users to start a new analysis exactly from the point at which the network was saved. Networks can be exported as tab-delimited edge-lists, and saved as images or high-resolution SVG files. While in the current work we describe in detail only analyses performed using COMETS output files, the capacity of VisANT to represent community-level networks from other sources (e.g. SBML files generated from Model SEED ) is detat Page 5 .VisANT 5.0 uses a standard bipartite graph representation of metabolic reactions, in which two types of nodes, metabolites and reactions, are connected through directed edges to visualize the product-substrate structure . FurtherFunctions associated with built-in Enzyme Nomenclature at Page 14, One of VisANT’s main goals is to assist network analysis by integrating biological knowledge from different sources or layers of complexity. In this release of VisANT, we add integration of KEGG reaction and compound databases and the Enzyme Commission (EC) hierarchy. These new features not only provide easy exploration of the functional classification of enzymes, but also support the creation of reaction nodes with convenient drag & drop operations from the Hierarchy Explorer (left side of VisANT) to the main network panel  metabolite. The huge size of the multi-organism metabolic networks poses a great visualization challenge. We focused mainly on the development of functions that would help interpret the metabolic exchange (syntrophy) or the competition for common resources between cells/organisms. Metabolic network sizes may vary widely, based on the specific setup and biological questions being asked. The metabolic model of E. coli , when reAn example of a two-species microbial consortium is shown in Rescale Selected Edges Logarithmically in page 10 for more details  is proportional to the intensity of the flux. The user can however choose to map the fluxes onto edge thicknesses logarithmically, to enhance visibility of fluxes that span multiple orders of magnitude , with no limit to the number of states compared. When performing a comparative visualization, each edge is divided into several segments with different colors representing the flux of corresponding conditions (or locations), and the thickness of each segment is proportional to the amount of flux. Alternatively, for the comparison between two states, it is possible to scale the thickness of each arrow to reflect the difference between the fluxes under the two different conditions/locations. An example case study for the comparative analysis is available in E. coli and a S. enterica strains previously designed and evolved to form an obligate syntrophic consortium [E. coli strain had been genetically modified such that it cannot synthesize methionine. S. enterica cannot use lactose as a carbon source. In the evolved consortium, the two organisms can survive on lactose only in the presence of each other, by exchanging methionine and a carbon source (likely acetate) respectively. This consortium has been studied experimentally and simulated computationally in previous work [In the first case study , we examnsortium ,44. The ous work . We used−5 and removed highly connected cofactors , NADP(H)). The final VisANT VisML file representing this network is available as Supplementary File 1.To investigate COMETS data for this consortium using VisANT, a user can open a COMETS Manifest file under the “Symbiosis” menu. The user can select a particular point, or visualize the metabolic activity of the whole system, averaged over the different spatial locations. VisANT will process the model and flux files designated by the COMETS Manifest file, and automatically provide a multi-species layout. By default the network is initially displayed with no overlaid flux values. The layout consists of two metanodes, representing the two organisms. In our case, flux information was additionally loaded (as specified by the Manifest file), and can be viewed by advancing the slider at the top of the screen. In the default symbiotic layout, only exchange reactions are initially displayed. Additional reactions/metabolites can be displayed by double clicking on nodes whose connectivity is considered of interest. In order to facilitate the interpretation of the results, one can remove low intensity fluxes (by setting a weight cutoff threshold) and hide highly connected metabolites (listed in a file specified by the Manifest file). These operations should be followed by a recalculation of the symbiotic layout. For this case study, we set the lower weight cutoff threshold for rescaled fluxes to 10E. coli, which in turn secretes the acetate usable by S. enterica. Curiously, at the particular time point analyzed, the exchange of galactose  also seems significant, and constitutes a novel testable prediction. Using VisANT’s ability to trace metabolites through the network, we can see that galactose is produced in E. coli, as a necessary consequence of lactose breakdown through β-galactosidase. While the glucose produced by this reaction proceeds through glycolysis, the galactose is predicted to be secreted, and utilized by S. enterica.As seen in http://kbase.us/) [For this second case study , we intease.us/) , convert−4). This time we get the six model metanodes in a circle, surrounding all metabolites that interact with more than one model  other carbon sources seem dominant. For example, in H. pylori, the model predicts a significant uptake of proline, which has been reported to be important for H. pylori gut colonization[L. acidophilus and utilized by C. difficile and E. coli. In turn, C. difficile is predicted to utilize formate, which E. coli secretes as a by-product. This seems plausible since C. difficile is known to have a formate dehydrogenase enzyme [B. longum and utilized by C. difficile and E. coli. Some evidence for this type of activity by B. longum has recently been presented in the literature [The community-level network of human intestine-associated bacteria displayed in onization. An intee enzyme . Anotherterature . The dethttp://visant.bu.edu and COMETS at http://comets.bu.edu.VisANT 5.0, in conjunction with COMETS dFBA simulations of microbial consortia, was able to corroborate results from a well-studied syntrophic exchange, and to provide nontrivial insight into possible metabolite-mediated interactions in a putative complex multi-organism community. As long as our future understanding of gene functions catches up with our capacity to sequence genomes and build models , similarS1 Table(XLSX)Click here for additional data file.S1 Dataset(ZIP)Click here for additional data file.S2 Dataset(ZIP)Click here for additional data file.S1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S3 Fig(DOCX)Click here for additional data file.S1 Text(PDF)Click here for additional data file.S2 Text(PDF)Click here for additional data file.S1 Video(MP4)Click here for additional data file.


Enzymes shape cellular metabolism, are regulated, fast, and for most cases specific. Enzymes do not however prevent the parallel occurrence of non-enzymatic reactions. Non-enzymatic reactions were important for the evolution of metabolic pathways, but are retained as part of the modern metabolic network. They divide into unspecific chemical reactivity and specific reactions that occur either exclusively non-enzymatically as part of the metabolic network, or in parallel to existing enzyme functions. Non-enzymatic reactions resemble catalytic mechanisms as found in all major enzyme classes and occur spontaneously, small molecule  catalyzed or light-induced. The frequent occurrence of non-enzymatic reactions impacts on stability and metabolic network structure, and has thus to be considered in the context of metabolic disease, network modeling, biotechnology and drug design. Current Opinion in Biotechnology 2015, 34:153–161Systems biologyThis review comes from a themed issue on Sarah Maria Fendt and Costas D MaranasEdited by Issue and the EditorialFor a complete overview see the Available online 22nd January 2015http://dx.doi.org/10.1016/j.copbio.2014.12.020http://creativecommons.org/licenses/by/4.0/).0958-1669/© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (The metabolic network originates from a low number (or one) of ancestral forms, and all living organisms share core reaction sequences and structural properties in their metabolic networks . GlycolyIt is important to emphasize that the same thermodynamic principles apply for non-enzymatic and enzymatic reactions, and every enzymatic reaction can occur in principle also non-enzymatically •. Non-enThe presence of enzymes does not prevent non-enzymatic reactions to occur across the metabolic landscape. On the basis of their principal mode of action, we divide non-enzymatic reactions into three classes b: Class 3 where a precursor is transported to the skin, to be converted by UV light to previtamin D3 [3 biosynthesis, in which previtamin D3 undergoes spontaneous isomerization forming vitamin D3 [Other non-enzymatic reactions are highly specific and are integral part of the metabolic network. Class II reactions occur purely non-enzymatically. A well-known example is the maturation of vitamin Dtamin D3 •. Most Ctamin D3 •.(i)Oxidoreductases: catalase (2O2) is formed as a (by-)product in various redox reactions. In combination with Fenton chemistry, H2O2 can react into superoxide and damage proteins, RNA, DNA and lipids [2O2 into water and oxygen [catalase . Hydroged lipids . Catalasd oxygen . A simild oxygen , 21. Desd oxygen , 23), an(ii)Transferases: glutathione-S-transferases (GST) (es (GST) . GSTs co(iii)Hydrolases: 6-Phosphogluconolactonase (6PGL) (l-ascorbate biosynthesis) [e (6PGL) . 6PGL isnthesis)  and hydrnthesis) , epoxidenthesis)  and liponthesis)  possess (iv)Lyases: ergothioneine and tetrahydrobiopterin (BH4) (in (BH4) . Ergothi(v)Isomerases: glycolysis, PPP and isomerization in vitamin D biosynthesis (ynthesis . Non-enz(vi)Ligases: tRNA loading and hydrolysis . Examples include the spontaneous transamination of glyoxylic acid and amino acids , the iso(i)Limited catalyst availability: metal ions and minerals may qualify as excellent catalysts, but often are not readily available. Molybdenum for instance is low concentrated in most ecosystems, while Fe(II) became limited during earth history [ history . Enzymat history .(ii)Substrate specificity: enzyme folds can achieve substantial substrate specificity and differentiate similar molecules, for instance glucose-6-phosphate from fructose-6-phosphate [hosphate . This alhosphate .(iii)Negative catalysis: enzymes can function to prevent side reactions, a concept termed negative catalysis [d-2-hydroxyglutarate in cancer (IDH1 and IDH2), or in d-2-hydroglutaric aciduria (IDH2) [atalysis . Negativa (IDH2) , 47•, ana (IDH2) .(iv)Regulation of metabolism: surviving starvation and stress situations as well as development of multicellular organisms requires regulation of metabolism. Non-enzymatic catalysts are however not readily tunable. Enzymes instead allow multiple levels of control, including allosteric regulation, cooperativity, post-translational modifications and genetic/transcriptional regulation [gulation , 49••.Small-molecule compounds are excellent catalysts in order to accelerate chemical reactions. However, in biological systems other important constraints apply in parallel, and explain the success of enzymes :(i)LimitIn vitro regarded as a perfect enzyme solely limited by diffusion rate [in vivo competitively inhibited by molecules with high structural similarity to its substrates, as for example phosphoenol pyruvate (PEP) [The dominance of enzymes impressively demonstrates their benefits for living organisms. Nonetheless, also enzymatic catalysis creates limitations. First, enzymatic structures can be highly temperature sensitive, a reason for the low thermo-tolerance of most species. Secondly, enzymatic catalysis is costly, as protein biosynthesis is one of the most energy-consuming cellular processes . Third, ion rate , it is ite (PEP) . Some ente (PEP) .Metabolic modeling has become popular in biotechnology, for instance helping to understand function and behavior of metabolic systems in constraint-based flux balance analyses (FBA) •. LimiteAlso unspecific Class I reactions have a strong influence on the metabolic network, especially when cells are exposed to increased temperature and stress conditions. Exploring their system wide impact is — due to their unspecific nature and the formation of various non-enzymatic metabolic products — a difficult task. Class I reactions require sophisticated metabolite repair strategies , that caIn this respect, it is worth mentioning the possible non-enzymatic contribution to metabolic transport processes. Non-enzymatic transport is often referred to as ‘membrane leakage’, a term which however falls short of taking into account that specific physical properties of metabolite and membrane composition determine the probability of a molecule to membrane diffuse. Metabolites can be attracted to specific physico-chemical environments resulting in their accumulation, causing spontaneous spatial segregation, hydrophilic–lipophilic phase separation, and membrane adsorption . A well Metabolism offers a plethora of targets for developing the next generation of pharmaceuticals to treat cancer and neurodegenerative disorders , 65. NonNon-enzymatic reactions occur frequently within the metabolic network. We distinguish reactions with low substrate specificity (Class I) from specific reactions that occur exclusively non-enzymatically (Class II), and reactions that occur analogous to the six principal enzyme categories (Class III). Providing a template for the evolutionary selection of metabolic enzymes, non-enzymatic reactions did form the basis for the evolution of metabolism. They have however never been depleted from the chemical environment of the cell, and occur within or in parallel to exiting enzyme function. Non-enzymatic reactions should thus not be regarded as cumbersome side effects, but as integral part of the metabolic network. As such, they play a role in human metabolic disease, and have to be considered in genome-scale reconstructions of metabolic networks, in particular in extremophiles, when designing biotechnological models, and further, when selecting enzymes for drug targeting and considering the side-effects of drugs. Non-enzymatic reactions are thus central for understanding fundamental problems in biology and play an essential role in cellular metabolism, human health, and ageing.• of special interest•• of outstanding interestPapers of particular interest, published within the period of review, have been highlighted as:


Rhodococcus jostii RHA1 growing on different substrates is capable of accumulating simultaneously three types of carbon storage compounds: glycogen, polyhydroxyalkanoates (PHA), and triacylglycerols (TAG). Under nitrogen-limited (N-limited) condition, the level of storage increases as is commonly observed for other bacteria. The proportion of each storage compound changes with substrate, but it remains unclear what modelling approach should be adopted to predict the relative composition of the mixture of the storage compounds. We analyzed the growth of R. jostii RHA1 under N-limited conditions using a genome-scale metabolic modelling approach to determine which global metabolic objective function could be used for the prediction.R. jostii RHA1 model (iMT1174) produced during this study contains 1,243 balanced metabolites, 1,935 unique reactions, and 1,174 open reading frames (ORFs).The 13C-labelling experiments of amino acids further supported the application of the environmental MOMA principle in the context of changing environment. Finally, it was found that the quantitative predictions of the storage mixture during N-limited storage accumulation were fairly sensitive to the biomass composition, as expected.Seven objective functions used with flux balance analysis (FBA) were compared for their capacity to predict the mixture of storage compounds accumulated after the sudden onset of N-limitation. Predictive abilities were determined using a Bayesian approach. Experimental data on storage accumulation mixture  were obtained for batch cultures grown on glucose or acetate. The best FBA simulation results were obtained using a novel objective function for the N-limited condition which combined the maximization of the storage fluxes and the minimization of metabolic adjustments (MOMA) with the preceding non-limited conditions . The FBA solutions for the non-limited growth conditions were simply constrained by the objective function of growth rate maximization. Measurement of central metabolic fluxes by R. jostii RHA1 cultures suggested that the intracellular reaction flux profile immediately after the onset of N-limited condition are impacted by the values of the same fluxes during the period of non-limited growth. PHA turned out to be the main storage pool of the mixture in R. jostii RHA1.The genome-scale metabolic model analysis of The online version of this article (doi:10.1186/s12918-015-0190-y) contains supplementary material, which is available to authorized users. Rhodococcus jostii RHA1 (RHA1) was isolated from lindane-contaminated soil and is best known for its superior ability to biodegrade polychlorinated biphenyls (PCBs) [Rhodococci are widely spread in many habitats such as soil, fresh water, seawater, and activated sludge wastewater treatment systems –4. Theirs (PCBs) . The gens (PCBs) . It holdR. jostii RHA1 also contains many genes for the metabolism of various storage compounds including polyphosphate (polyP), glycogen, wax esters (WE), triacylglycerols (TAG), and polyhydroxyalkanoates (PHA) [R. jostii RHA1 accumulates these various storage compounds at the same time, but in different proportions [To face rapidly changing environmental conditions in its natural habitat, the genome of es (PHA) . It was portions . It remaportions , the expR. jostii RHA1  was reconstructed in silico. For this reconstruction, storage compounds were defined independently of the biomass composition as pseudo-secretory by-products; that is, although storage compounds are not secreted, they are set so that they are secreted by the metabolic model for analysis of the storage metabolism. This model definition allows the study of the variation of storage metabolism.To investigate how to predict the accumulation of storage compounds during nutrient-limited conditions with regard to the consumption of carbon substrate, the genome-scale metabolic network of Genome-scale metabolic models are typically underdetermined  because the number of metabolites  are lower than the number of reaction fluxes (variables). Consequently, they can be analyzed by means of linear programming to find an optimal metabolic flux profile as defined by a linear objective function (optimization criterion). Therefore, these objective functions are central to the prediction exercise. In the context of the current study, here are the two main questions we aim to answer. (1) Is there an objective function that enables us to predict the proportions of storage compound(s) and their associated metabolic fluxes observed under N-limited condition? (2) What are some of the main factors influencing the proportions of the storage compounds accumulated?Several objective functions have been defined and examined in the past to study a large number of metabolic situations , 13, herminimization of the metabolic adjustment between the N-limited and non-limited conditions ,minimization of the metabolic fluxes  ,minimization of ATP production rate (minATP) ,maximization of ATP production rate (maxATP) ,minimization of the production rate of redox potential (minNADH) ,maximization of the total storage fluxes in the N-limited condition (maxStorage),maximization of the total storage fluxes in conjunction with environmental MOMA .In the current study, maximization of the growth rate (and yield) was adopted as the main objective function for the growth of RHA1 during non-limited growth condition. However, the difficulties arise for the N-limited storage accumulation because the synthesis of new biomass does not occur. Thus, novel objective functions needed to be examined, and seven objective functions were evaluated.When environmental MOMA was used for which the non-limited and N-limited culture phases interact, the implementation of these objective functions consisted in developing an optimization algorithm by first maximizing the growth rate under non-limited conditions, and then searching the solution space thus delimited using the above mentioned objective functions.13C-labelling experiments to characterize fluxes during the non-limited growth phase were conducted to determine how much the reaction fluxes during the non-limited growth phases constrained the N-limited metabolic model solution compared to simply measuring the fluxes of storage compounds accumulated during the N-limited culture phase.The performance of the objective functions in predicting the accumulation of the mixture of storage compounds on two different carbon sources (glucose and acetate) under N-limited conditions were compared with our experimental observations using a Bayesian approach. Finally, in silico metabolic network of R. jostii RHA1 (iMT1174) contains 1,243 balanced (intracellular) compounds, 1,935 unique reactions, and 1,174 ORFs  in order to make the model most useful for the research community interested in R. jostii RHA1. Mono-, di-, tri-, and tetra-chlorobiphenyl were added in iMT1174 metabolic model; reactions A000540 – A00104 show all the enzymatic steps that were associated with PCB degradation; the genes involved in degradation of these PCBs were bphA, bphB, bphC, and bphD [The reconstructed and bphD , 18–20.TR. jostii RHA1 is detailed in Additional file R. jostii RHA1 are detailed in Additional file R. jostii RHA1 are detailed in Additional file iMT1174 model is the higher frequency NAD, NADH, and oxygen in reactions than the energy-associated metabolites, which is different than with most published bacterial genome-scale metabolic models. This is because of the large number of oxygenase and oxidoreductase reactions involved in xenobiotics degradation pathways and included in the current iMT1174 model.Seven storage compounds were defined independently of the biomass composition as extracellular compounds connected to 11 fictional transport reactions to study the variation of storage compound accumulation namely: glycogen, α,α-trehalose, PHB, PHV, TAG, WE, and the non-carbon-based polyP. As these compounds were observed experimentally or detailed genomic investigation revealed the presence of specific genes , pathwayThe conversion rates of various storage compounds when glucose and acetate were used as the sole carbon and energy sources during non-limited and N-limited conditions were experimentally measured. Initial ammonium concentrations in the N-limited cultures were adjusted such that the N-source was 10 times lower than that in the non-limited cultures; the nitrogen sources in the N-limited cultures were exhausted at a time equivalent to the mid-exponential phase of the non-limited cultures. Oxygen uptake rate (OUR) time profiles of RHA1 in culture media containing glucose or acetate and either non-limiting or limiting concentrations of ammonium demonstrated a clear change in the respiration behaviour of the culture when the nitrogen source was exhausted Fig. . Samples4+, PO43−, glycogen, PHB, TAG. Additionally, the consumption rate of O2 was also monitored over time. Using these data, conversion rates were calculated. Considering the elemental and COD balances, the conversion rates were reconciled  and their statistical consistency checked  [R. jostii RHA1 consumed acetate faster than glucose, and the specific substrate uptake rate during the N-limited phase was less than 14 % of the one in the non-limited phase , NH errors) . The meaiMT1174) and comparing seven objective functions. To do so, a list of unique reactions was generated by eliminating the redundancy in the network due to the large number of isoenzymes ) was found to be very sensitive to the non-growth associated maintenance energy (NGAM) for most of the objective functions examined as was expected  predicted the accumulation of a mixture of storage compounds Fig. .Fig. 5MeFor the objective functions that simulated a single storage compound accumulation, only the maxStorage objective function simulated PHA accumulation when the culture contained glucose and acetate as C-source Fig. . The othUsing a Bayesian-based objective function discrimination method , all theR. jostii RHA1 when faced with sudden nutrient-limited condition. Based on our results, it appears that the cells maintain the reaction flux profiles under carbon-excess/nutrient-limited conditions somewhat similar to the one developed during the non-limited growth conditions while maximizing their storage accumulation. This seems logical from a global regulation perspective as this solution would simply follow the regulatory program for growth and diverting the excess carbon found locally in the biochemical network to the closest storage compound. It would also maximize the responsiveness of the organism, while minimizing the protein turnover that would be necessary to adapt to the new conditions.The simulation results presented here could be understood as possible outcomes of global regulatory principles applied by R. jostii RHA1 used in our model by the E. coli biomass of the iJR904 [iAF1260 [iMT1174, iJR904, and iAF1260. The most probable objective function  was used for these simulations.The previous section concluded that the metabolic fluxes developed during the non-limited growth determined the fluxes during the N-limited storage accumulation period. Consequently, changing the biomass composition could affect the relative composition of the predicted mixture of storage compounds. This hypothesis was tested by substituting the biomass of e iJR904  and iAF1[iAF1260  metaboliE. coli biomass of the iJR904 model with both carbon substrates led to an increase in the proportion of PHA within the storage compounds accumulated by 11.9 % on glucose and 21.6 % on acetate, while the proportions of TAG and glycogen both decreased  to elucidate the metabolic behaviour of the R. jostii RHA1 cell  was built, and used in flux balance analysis with different objective functions to predict the fluxes of storage compounds during a period of N-limitation following a period of balanced maximal growth. Among the seven objective functions examined, the objective function maximization of storage in the N-limited condition combined with environmental MOMA was able to reproduce best the storage accumulation fluxes observed experimentally for glucose and acetate as C-source. To further understand the constraints imposed by the environmental MOMA objective function, the possible variability of fluxes through 19 central metabolic reactions during N-limited storage-accumulating conditions were compared to fluxes through the same reactions during non-limited growth obtained by 13C-MFA. The comparison showed how the environmental MOMA could constrain the reaction fluxes in the N-limited conditions. Altogether, the data presented in herein suggest that for R. jostii RHA1 during N-limited storage accumulating conditions the storage production to efficiently save the C-source, while the reaction fluxes remain somewhat similar to the profile in the immediately preceding period when its growth was not limited. Finally, the analysis demonstrates the applicability of the MOMA objective function to analyze rapid changes in successive different environmental conditions such as non-limited growth followed by N-limited storage-accumulating substrate consumption.R. jostii RHA1, the list of genes in its annotated genome sequence was converted to a list of associated balanced biochemical reactions, which form the basic framework of the model. Subsequently, the model was analyzed in light of literature data to determine if some reactions may have been missing from the list of annotated genes. The reactions were added along with transport reactions to make a physiologically meaningful cellular model. In the case of RHA1, although annotated, several degradation pathways of various xenobiotics were missing from the Kyoto Encyclopaedia of Genes and Genomes (KEGG) ) to values comparable to those of the experimental data. Finally, the growth-associated maintenance energy (GAM) was set to 30 mmol-ATP/g-DW according to the literature data [As the first step in reconstructing the cellular metabolic network of ase used ) and thease used , 27 to aase used , 28, TAGase used , 29, 30,atabases , 32. Theure data .S) with rows and columns corresponding to the metabolites and reactions, respectively, in order to be quantified by means of the FBA technique.Additional file X is the (m × 1) vector of the concentrations of the balanced metabolites , v denotes the (n × 1) vector of the entire metabolic fluxes, and S stands for the m × n stoichiometric matrix; note that in the case of the iMT1174 model with the unique reactions, the dimension of the stoichiometric matrix is 1243 × 1935.The gene-protein-reaction (GPR) association, along with the stoichiometric matrix, is a qualitative representation of the cellular network. The metabolic model of RHA1 was studied quantitatively by setting up a series of mass balances around each intracellular metabolite that can be expressed in matrix notation as: S.v = 0. This assumption is plausible due to the fast equilibration of intracellular metabolite pools  compared to the time-scale of genetic regulation (minutes) [The model was basically solved by assuming that the cellular network is at steady-state, which simplifies the previous equation to minutes)  and due minutes) –35. Consminutes) .iMT1174 metabolic network. Seven objective functions were implemented namely: 1) minimization of the metabolic adjustment between non-limited growth and N-limited storage accumulation , 2) minimization of the metabolic fluxes  [The goal of the study was to examine objective functions for the quantitative prediction of the accumulation rates of storage compounds during conditions of nitrogen-limitation and carbon-excess using the nFluxes) , 4) maxinFluxes) , 5) mininFluxes) , 6) maxiThe Language of Technical Computing MATLAB environment . The model was balanced for elemental mass and charges and a number of reactions were considered irreversible , but the enzymatic capacity of reactions remained unbounded. The substrate uptake rate (in the non-limited and N-limited conditions), phosphorus and ammonium uptake rates in the non-limited condition were constrained according to our experimental observations. N-limited conditions were then simulated by reducing to zero the uptake flux of NH3 into the cellular network.We solved the linear programming problem using the COBRA toolbox  within TR. jostii RHA1 in batch; labelled and unlabelled glucose and acetate were employed as the sole carbon sources. The labelling tests were performed using a μ-24 bioreactor (Applikon Biotechnology), while the unlabelled batch tests were accomplished with a respirometer model AER-200 .To validate the model we performed two different sets of culture conditions namely: N- and non-limited conditions of R. jostii strain RHA1 was cultivated aerobically at 28 °C and pH 7 in mineral salts medium (MSM) according to Schlegel et al. [4Cl (1.00 g/L), KH2PO4 (1.50 g/L), Na2HPO4.12H2O (9 g/L), FeNH4-Citrate (1.20 mg/L), MgSO4.7H2O (0.20 g/L), CaCl2 (0.02 g/L), Hoagland solution (2.00 mL/L), and carbon source (10 g-COD/L). Glucose and sodium acetate were used as the sole carbon sources. Cells were harvested during mid-exponential (non-limited condition) and end-exponential (both non- and N-limited conditions), and late stationary phases (N-limited condition), centrifuged and stored at −80 °C for further analyses. To generate nitrogen-limiting conditions, the concentration of ammonium chloride in MSM was reduced to 0.1 g/L such that the nitrogen source was exhausted before the carbon source.l et al. . The MSMTotal and volatile suspended solids (TSS/VSS) were measured according to the standard method 2540 D/2540 E ; chemica2SO4; 1 μL Trinonadecanoin  was used as internal standard for quantification [Cellular TAG was measured by gas chromatography (GC) according to  with somfication . Methanofication . The orgR. jostii RHA1 culture, which was cultivated aerobically at 28 °C and pH 7 in MSM, was transferred (0.5 mL) into 5-mL cells of the μ-24 bioreactor (Applikon Biotechnology); these reactor cells had already been filled with 4.5 mL of fresh MSM supplemented with labelled carbon sources including 1-13C-Acetate and 2-13C-Acetate Sodium salt, and 1-13C-Glucose as the sole carbon sources; and then, cells were harvested during the exponential growth phase. It should be noted that the culture condition was at the non-limited growth condition .Fresh 27-myristic acid), the samples were mixed by vortex and sonication for several times, each time taking 10–20 s. Furthermore, the samples were centrifuged at 15000 rpm for 10 min at room temperature. The samples were transferred into GC-MS vials and cooked at 70 °C for 30 min in a hot block. 70 μL of N-tert-butyldimethylsilyl-N-methyltrifluoroacetamide (TBDMS) was added into the vials and cooked at 70 °C for 1 h in a hot block to derivatize the samples. GC-MS analyses were performed with an Agilent 5975C mass selective detector coupled to a 7890A gas chromatograph  fitted with a 7693 autosampler and a DB-5MS+DG capillary column (30 m plus 10 m Duraguard®), diameter 0.25 mm, film thickness 0.25 mm . The GC temperature program started with a 1 min hold at 60 °C followed by a 10 °C/min ramp to 300 °C. Bake-out was at 320 °C for 10 min. The injector and interface to the MS were held at 285 °C. The helium carrier flow rate was held constant at 1.5 mL/min (or a flow rate such that the TBDMS derivative of the D27-myristic acid has a retention time of 18 min). When operated in full scan mode, the scan range was 50–700 Da. 1 μL of the sample was injected in splitless mode.Proteinogenic amino acids of the biomass were analyzed using gas chromatography mass spectrometry (GC-MS) technique according to Nanchen et al. with some modifications . The bio13C-metabolic flux analysis (13C-MFA). The model represents the central metabolism which includes glycolysis and gluconeogenesis, Entner-Doudoroff pathway, tricarboxylic acid (TCA) cycle, pentose phosphate pathway, anaplerotic carboxylation and decarboxylation, storage metabolic reactions, amino acid biosynthetic reactions, and anabolic routes into biomass. Additional file R. jostii RHA1 for which 13C-MFA was implemented. We used the openFLUX software application under MATLAB environment  to solve for the fluxes [R. jostii RHA1 together with mass isotopomer distribution data of the labelled amino acids that were produced using the iMS2Flux software [We aim at estimating the reactions involved in central metabolism in the non-limited condition using e fluxes . The appsoftware  were useR. jostii RHA1 and their respective standard errors in the non-limited condition were calculated according to [Weighted average of 100 solutions of central metabolic fluxes of rding to . Theses All the supporting data are included in the following additional files.


Plasmodium falciparum undergoes a complex life cycle, including an intraerythrocytic developmental cycle, during which it is metabolically dependent on the infected human red blood cell (RBC). To describe whole cell metabolic activity within both P. falciparum and RBCs during the asexual reproduction phase of the intraerythrocytic developmental cycle, we developed an integrated host-parasite metabolic modeling framework driven by time-dependent gene expression data.The malarial parasite 1) stage-specific production of biomass components and their precursors in the parasite and 2) metabolite concentration changes in the medium of P. falciparum-infected RBC cultures. The model allowed us to explore time- and strain-dependent P. falciparum metabolism and hypothesize how host cell metabolism alters in response to malarial infection. Specifically, the metabolic analysis showed that uninfected RBCs that coexist with infected cells in the same culture decrease their production of 2,3-bisphosphoglycerate, an oxygen-carrying regulator, reducing the ability of hemoglobin in these cells to release oxygen. Furthermore, in response to parasite-induced oxidative stress, infected RBCs downgraded their glycolytic flux by using the pentose phosphate pathway and secreting ribulose-5-phosphate. This mechanism links individually observed experimental phenomena, such as glycolytic inhibition and ribulose-5-phosphate secretion, to the oxidative stress response.We validated the model by reproducing the experimentally determined per se, alterations in gene expression levels caused by regulatory mechanisms are manifested in the model as altered metabolic states. This provides the model the capability to capture complex multicellular host-pathogen metabolic interactions of the infected RBC culture. The system-level analysis revealed complex relationships such as how the parasite can reduce oxygen release in uninfected cells in the presence of infected RBCs as well as the role of different metabolic pathways involved in the oxidative stress response of infected RBCs.Although the metabolic model does not incorporate regulatory mechanisms The online version of this article (doi:10.1186/s12918-016-0291-2) contains supplementary material, which is available to authorized users. Plasmodium falciparum, the most virulent causative agent of malaria, engages in with its host environment  and pyruvate kinase [PYK]) in RBCs that are cocultured with infected RBCs but are not infected themselves, to decrease glucose utilization in the uninfected RBCs  represents the total RBC concentration in the culture, which was equal to 0.11 · 1012 RBCs/l based on a hematocrit of 1 % [vτi,cEX and vτi,iEX by solving Eqs. where (mmol/l) , τ indict of 1 % . The coet of 1 % . We obtaP. falciparum [P. falciparum and RBCs at each hour during the IDC. We used the modeling framework shown in Fig. P. falciparum strains , including the fluxes for biomass production and metabolite uptake/secretion.By combining the metabolic network of the malarial parasite lciparum , the netlciparum , and thelciparum , 19  the available experimental data for the HB3 strain [2) model results for the HB3, 3D7, and Dd2 strains. The comparison with the experimental data for the HB3 strain using the integrated model closely followed the agreement seen in the previously published data based on the standalone model  synthesis during the IDC with 3 strain , 30 and rvations , 30. Ther of 0.52–0.68 and r2 of 0.27–0.46) between time-series fluxes in each pair of strains. The high correlation is a reflection of the similarly highly conserved nature of the time-series gene expression data among strains, when extracellular and plasma membrane-associated genes were excluded [r2 of 0.38–0.58 . Table excluded . Indeed,Falciparum is not completely understood, the capacity to withstand polyamine depletion has been explored for anti-malarial drug development [Figure elopment , 34. Thu12 RBC) at 28 h post infection. On the contrary, the reactions in the tricarboxylic acid (TCA) cycle all exhibited similar time-dependent flux profiles among the strains  was produced from glycolysis and other metabolic pathways and consumed by non-glycolytic metabolism and non-metabolic activity in a time- and strain-dependent manner. These processes exhibited a qualitative overall similarity, but with strain-specific differences. In particular, Fig. P. falciparum metabolic network. The interpretation of the resultant metabolite changes rely on two main underlying assumptions, i.e., a correlation between mRNA and enzyme levels and limited non-transcriptional-based regulatory processes of metabolism. These assumptions are largely borne out by the observed general agreement with experimental data, but can also lead to non-biological model predictions, e.g., DNA production levels can continue into the ring stage from the schizont stage because of a lack of explicit cell-cycle regulation in the model. The correlation between mRNA levels and enzyme levels propagates high-frequency variations in mRNA levels to enzyme levels and, hence, variable metabolite levels. In reality, the transcriptional and translational machinery in the cell may not be able to respond quickly enough to these variations. We examined this latter point with respect to the biomass metabolites in more detail in Additional file The modeling framework relies on gene expression data to drive parasite IDC metabolism using constrained stoichiometry defined by the Although we did not identify any major qualitative metabolic differences during the IDC between the strains for the RBC culture condition examined here, the cross-species comparison showed potentially important strain differences. Thus, despite the expected high correlation among gene transcription between the strains, there was a significantly higher impact of these differences on the metabolic level.per se. To validate the modeled metabolic activity of the host cells, we compared time-course extracellular metabolite concentrations profiles predicted by our model to those derived from the experimentally measured extracellular metabolite data of a P. falciparum 3D7-infected RBC culture [−4 mM (pantothenate) to 101 mM (glucose). Figure Compared with our previous work using a standalone model , the adv culture   secretion into the medium closely matched the experimental data, with the bulk of the pyridoxine uptake and thiamine secretion coming from the uninfected RBCs. In the infected culture, thiamine was secreted, but to a lesser extent than in the uninfected culture.Consistent with the experimental data there was a small choline secretion in the uninfected control condition , and a cThe model correctly predicted uptake of pantothenate, whereas the comparison of the predicted uptake of riboflavin (a required metabolite ) was obsP. falciparum metabolic network component continuously synthesizing protein by metabolizing amino acids from the host hemoglobin, transporting the excess to the RBC, and, ultimately, to the medium [Figure e medium . The mode medium , asparage medium , and forIn summary, the coupled host-pathogen metabolic network model showed a general good agreement with the available experimental data, and the bulk of the important metabolic processes and pathways showed quantitative agreements. Given the depth and sophistication of the model construct, we next examined how the infecting pathogen influences and manipulates host-cell metabolism in the cultured media.P. falciparum-infected RBC culture, uninfected RBCs have been observed to decrease their glucose consumption, lactate production, and activity of two glycolytic enzymes (PFK and PYK) [Besides functioning as an exclusive energy source , the glyand PYK) . To undeFigure P. falciparum might affect the glycolytic metabolism of uninfected RBCs by impairing their oxygen-releasing capabilities.The predicted loss of oxygen-releasing capability of cocultured RBCs might be another mechanism that contributes to the hypoxic effects of malarial anemia. While one of the known mechanisms of malarial anemia is the sequestration by the spleen of infected and morphologically abnormal RBCs, it is still unclear of how the malarial parasite influences uninfected RBCs . Other tP. falciparum [Importantly, the glycolytic pathways showed differential temporal activation among infected and cocultured RBCs. Figure lciparum   the inhibition of the host glycolysis by the malaria parasite [2) the parasite-exacerbated oxidative stress faced by RBCs [3) the ribulose-5-phosphate secretion induced by P. falciparum infection [4) the malarial resistance for G6PD-deficient patients [The coupled host-pathogen model simulation provided a comprehensive metabolic description of how infected RBCs respond to the parasite-generated oxidative stress. Given the increase in stress, infected host cells inhibited PFK and PYK see Fig. , two enzparasite , 2) the  by RBCs , 3) the nfection , and 4) patients  into a sP. falciparum is complex, with two different hosts and multiple stages within each host. During the human blood stage, the asexual reproductive phase during the IDC takes place in infected RBCs, resulting in the familiar malarial symptoms of the disease. A key aspect of the host-pathogen interaction during the IDC is the heavy nutritional requirements faced by the rapidly dividing parasite. The host cell provides the environment and most nutrients necessary for the metabolism of the parasite, while at the same time, the parasite alters the metabolic activity of the host cell [P. falciparum metabolic network models have not captured these host-parasite metabolic interactions, although these models have correctly described the metabolism and growth phenotypes of the parasite during the IDC [P. falciparum and human RBCs and using time course-dependent gene expression of the parasite during the IDC to drive the modeled metabolism.The life cycle of ost cell , 7, 8. P the IDC , 12, 15.P. falciparum [r2 reduced by 20–30 %), indicating a quantitative less consistency in exactly how the metabolic program was executed during the IDC. We noted consistent strain-dependent differences among certain metabolites, e.g., NAD, FAD, protoheme, and polyamines, whereas others, such as 10-formyltetrahydrofolate, coenzyme-A, and thiamine-diphosphate, do not show strain-dependent differences. Differences in onset and peak ATP-production levels also differed noticeably among the three strains. Because the model provides the theoretical framework for describing metabolism, it requires condition-specific gene expression data to instantiate a particular condition. Thus, strain differences might become more important under different physiological stress or drug treatment conditions [Given the hourly gene expression data for three strains  of lciparum , 19, we nditions .The integrated host-pathogen metabolic model included the ability to describe separate populations of infected and uninfected RBCs in the same culture, allowing us to investigate the detailed and complex metabolic responses of the host. However, the underlying mechanisms by which the parasite regulates and affects cellular host processes, including both metabolic and non-metabolic are not always known. Here, we have taken an approach to directly implement such host-pathogen interactions by explicitly manipulating particular fluxes and modeling the downstream metabolic effects in our modeling framework.Given the established glycolytic inhibition of uninfected RBCs under malarial infection , we predP. falciparum used the glycolysis pathway of infected RBCs to drive the metabolic flux from glucose to the pentose phosphate pathway. This process reduced parasite-induced reactive oxygen species and generated ribulose-5-phosphate as the final metabolic product, which was ultimately secreted to the environment. These predictions highlighted the importance of the G6PD enzyme in this process and provided a rationale for the observed malarial resistance of G6PD-deficient patients. To our knowledge, this is first description that links the oxidative stress response to a number of individual observations on parasite-induced metabolic changes in RBCs  as wellhibition .Anopheles mosquitos and humans. In humans, the blood stage of the disease is associated with the debilitating clinical symptoms of malaria. These symptoms are linked to the parasite undergoing synchronized asexual reproduction in RBCs, during which one parent cell multiplies into 16–32 daughter cells in ~48 h. Here, we developed a genome-scale, gene-expression-driven integrated host-pathogen metabolic network model that can capture and describe systemic changes in metabolism of the replicating malaria parasite P. falciparum as well as for infected and cocultured uninfected human RBCs. Although the modeling framework does not explicitly incorporate regulatory mechanisms, changes in the tightly controlled gene expression program of the parasite are sufficient to drive metabolic alterations in the modeling framework. This allowed us to predict not only strain-specific metabolic programs of P. falciparum during the reproductive cycle but also to examine parasite modulation of host metabolism in surrounding RBCs. Our system-level analysis suggested a primary metabolic similarity between the three studied strains, but also pointed to specific difference in metabolite production levels. Furthermore, our analysis revealed complex relationships such as how the parasite reduces oxygen-releasing capability of uninfected cells in the presence of infected RBCs as well as the role of different metabolic pathways involved in the oxidative stress response of infected RBCs.During its life cycle, the malaria parasite sequentially progresses through multiple stages in female P. falciparum-infected RBCs; LDH, lactate dehydrogenase; MNPf, metabolic network of P. falciparum; MNRBC, metabolic network of RBC; NAD, nicotinamide adenine dinucleotide; NADPH, nicotinamide adenine dinucleotide phosphate; NIC, number of internal compartments; NM, number of metabolites; NR, number of reactions; nRBC, normal RBCs; PFK, phosphofructokinase; PGI, glucose-6-phosphate isomerase; PGK, phosphoglycerate kinase; PGM, phosphoglycerate mutase; PYK, pyruvate kinase; RBC, red blood cell; RPMI, Roswell Park Memorial Institute; RU5Pt, the transport of ribulose 5-phosphate from iRBCs into the medium; TPI, triose-phosphate isomerasecRBC, cocultured uninfected RBCs; DPGase, diphosphoglycerate phosphatase; DPGM, diphosphoglycero mutase; ENO, enolase; FAD, flavin adenine dinucleotide; FBA, fructose bisphosphate aldolase; G6PD, glucose 6-phosphate dehydrogenase; GAPD, glyceraldehyde-3-phosphate dehydrogenase; GSH, reduced glutathione; GSHox, the GSH-based oxidative stress alleviation; GSSG, oxidized glutathione; HEX, hexokinase; IDC, intraerythrocytic developmental cycle; iRBC,