Escherichia coli central metabolism that links growth to environment. Metabolic control analyses confirm that the control is widely distributed across the network and highlight strong interconnections between all the pathways. Exploration of the model solution space reveals that several robust properties emerge from metabolic regulation, from the molecular level  to the overall cellular physiology , while allowing a large degree of flexibility at most individual metabolic steps. These properties have important physiological implications for E. coli and significantly expand the self-regulating capacities of its metabolism.The metabolism of microorganisms is regulated through two main mechanisms: changes of enzyme capacities as a consequence of gene expression modulation  and changes of enzyme activities through metabolite-enzyme interactions. An increasing body of evidence indicates that hierarchical control is insufficient to explain metabolic behaviors, but the system-wide impact of metabolic regulation remains largely uncharacterized. To clarify its role, we developed and validated a detailed kinetic model of  Escherichia coli, a model organism in Systems and Synthetic biology. Model simulations indicate that kinetic considerations of metabolism alone can explain data from hundreds of experiments, without needing to invoke regulation of gene expression. In particular, metabolic regulation is sufficient to coordinate carbon utilization, redox and energy production, and growth, while maintaining local flexibility at individual metabolic steps. These findings indicate that the self-regulating capacities of E. coli metabolism are far more significant than previously expected, and improve our understanding on how cells work.Metabolism is a fundamental biochemical process that enables cells to operate and grow by converting nutrients into ‘building blocks’ and energy. Metabolism happens through the work of enzymes, which are encoded by genes. Thus, genes and their regulation are often thought of controlling metabolism, somewhat at the top of a hierarchical control system. However, an increasing body of evidence indicates that metabolism plays an active role in the control of its own operation via a dense network of metabolite-enzyme interactions. The system-wide role of metabolic regulation is hard to dissect and so far remains largely uncharacterized. To better understand its role, we constructed a detailed kinetic model of the carbon and energy metabolism of the bacterium  Metabolism is a fundamental biochemical process that converts nutrients into energy and biomass precursors, thus enabling cells to maintain their structures, grow, and respond to their environment. While the topology of metabolic networks is fairly well known, understanding how metabolic behaviours emerge from the dynamic interactions of their molecular components remains one of the main challenges faced by systems biology and is crucial for the development of synthetic biology .i.e. the metabolic fluxes, represents the ultimate output of several regulatory mechanisms. Metabolic fluxes are functions of enzyme activities and of the concentrations of reactants, products, and other effectors. While the enzyme activities are the ultimate outcome of gene expression through the hierarchy of transcriptional, post-transcriptional, translational and post-translational regulatory mechanisms, the reactant and effector concentrations are directly regulated at the metabolic level by enzyme activities themselves. Hierarchical regulation, and in particular transcriptional regulation, has attracted much attention because of mature experimental methods, but also because of early examples of flux increase with enzyme induction [13C-flux analyses revealed that flux distributions in Saccharomyces cerevisiae and Escherichia coli are incredibly robust to the deletion of global transcriptional regulators [The operation of metabolic networks, nduction , 3. Thesgulators , 5. Integulators –9. Theree.g. Mycoplasma genitalium [Mathematical frameworks such as metabolic control analysis , 11 werenitalium , but unfE. coli, which constitutes the backbone of its metabolism by providing macromolecular precursors, reducing equivalents, and energy for growth and maintenance. While previous studies typically focused on the role of particular regulatory interactions, we attempt to determine whether more global and generic properties arise from the interplay of the many regulatory interactions that compose metabolic regulation. To accomplish this, a kinetic model of E. coli central carbon and energy metabolism was developed and validated against a large set of existing experimental data. This model includes more mechanistic details than previous ones, and the impact of metabolic regulation on this system was analyzed using local and global methods.In this study, we aim at investigating the role of metabolic regulation on the central metabolic network of Escherichia coli cultivated on glucose under aerobic conditions , glycolysis and gluconeogenesis (EMP), pentose phosphate (PPP) and Entner-Doudoroff (EDP) pathways, anaplerotic reactions (AR), tricarboxylic acid cycle (TCA), glyoxylate shunt (GS), acetate metabolism (AC), nucleotide interconversion reactions (NC) and oxidative phosphorylation (OP). A reaction was also included to account for the consumption of metabolic precursors, reducing equivalents, and energy, and thus linking metabolism to cell proliferation. To account for metabolic regulation, a total of 255 metabolite-enzyme interactions  were included in the model, amongst which 34 are long-range regulatory interactions .The kinetic model developed in this study represents the central metabolism of nditions . This moE. coli metabolism were used as scaffolds to construct this model [2)) and simulate energy and redox metabolism. Previous models accounted for the consumption of metabolic precursors for growth in a decoupled way. This may be enough from the point of view of mass balance, but results in artifacts if used for an understanding of dynamics and regulation. In contrast the present model includes a single reaction to model growth, which ensures that the building blocks are consumed in stoichiometric proportions fixed by the cell composition, and not independently from each other. The rate of this reaction is a function of the intracellular concentrations of all the building blocks. This represents a significant improvement by satisfying the following growth rate properties: i) it monotonically increases with the availability of each building block, ii) it is asymptotically independent of each pool above a saturating concentration, and iii) it approaches zero if any pool approaches zero [Previously published kinetic models of is model , 31, 32.hes zero . These phes zero .E. coli cultivated under carbon limitation, a condition frequently experienced by this bacterium in laboratories, in industrial bioprocesses, and likely in its natural environment. To the extent possible, values of the biochemical parameters were taken from experimental determinations available in the literature. Parameters not available in the literature were estimated to reproduce steady-state and time-course experimental data obtained from a unique E. coli strain (the model strain K-12 MG1655) grown under a unique reference condition  [the model was not forced to reproduce them, providing an important validation of the model. Detailed information on the construction and validation of the model is given in the Methods section and Supporting Information  , 34–37. 2 > 20%) –40. Whilormation . The modormation  formatteE. coli central metabolism in the reference state (see above) were investigated under the metabolic control analysis framework [e.g. through change in the enzyme concentration E), on each flux (J) and each metabolite concentration (M). Since each metabolic step affects all fluxes and concentrations to some extent, we calculate a metric of its overall control on fluxes and concentrations as the L2 norm of all its flux- and concentration-control coefficients  action of signal transduction and gene expression, which is not represented in this model; if it were its effect would thus be overlaid (likely with a delay) on the direct effect displayed in our model. Reactions that were identified by previous models as exerting a strong flux control under similar environmental conditions, such as the glucose phosphotransferase reactions or phosphofructokinase [bo oxidase , glucose-6-phosphate dehydrogenase , glyceraldehyde-3-phosphate dehydrogenase , citrate synthase  and the anabolic machinery  are the ones with the largest share. A similar situation was observed for the control of concentrations, which is widely distributed across the network, and with the environment as the strongest control. In fact, a significant correlation  can be observed between the overall flux- and concentration-control exerted by each step ,ach step , indicatach step .Further analysis confirmed the wide distribution of flux control across all the enzymes, with 97% of the individual control coefficients between -0.3 and 0.3 . These oDespite the low control exerted by enzymes over fluxes and concentrations at the network level, a detailed analysis of flux control coefficients reveals generic regulatory patterns between most of the pathways . A genere.g. between the TCA cycle and the glyoxylate shunt or between the pentose phosphate and Entner-Doudoroff pathways. It is important to note that the fraction of flux diverted to each branch does not depend only on the local enzyme kinetics, contrary to what is sometimes suggested [For example, the control of the partition of carbon through competing pathways is shared between enzymes of each pathway. The glycolytic phosphofructokinase (PFK) exerts a  negative control on the PPP and ED fluxes  controls fluxes through the TCA cycle . The solution space of each model was explored using a random sampling approach: 600,000 flux distributions were uniformly sampled from the solution space using the stoichiometric model, and steady-states were simulated for 600,000 sets of random enzyme levels using the kinetic model. For each set, enzyme levels (i.e. Vmax) were sampled from a log uniform distribution  to ensure each order of magnitude to be sampled in similar proportions. It is important to mention that cells do not express enzymes levels according to the distribution generated, therefore the distribution of the variables is not expected to provide any information on the probability for a cell to reach a specific state in vivo [To get a broader picture of the role of metabolic regulation on the coordination of  in vivo . Rather,We first investigated the relationship between supply (glucose uptake) and demand (growth), which provides information on the allocation of resources by the metabolic network . Direct E. coli growing on glucose. Importantly, these data were not used for parameter estimation, thereby they constitute an independent validation and provide a robust assessment of the predictive ability of the model. These experimental observations correspond to the region of the solution space less frequently sampled using the stoichiometric model, but they closely match the region sampled by the kinetic model (E. coli is closer to the metabolic model that is regulated by metabolite-enzyme interactions (the kinetic model) than it is to a metabolic model that would be regulated by gene expression alone (the stoichiometric model). Hence, metabolic regulation alone, without needing to invoke coordinated expression of genes, seems to be sufficient to explain the emergence of a coupling between anabolic (growth) and catabolic (glucose uptake) fluxes, and thereby appears to be a major determinant of the overall cellular physiology by ensuring an efficient and robust allocation of nutrients towards growth.To evaluate this prediction quantitatively, we gathered from the literature experimental data obtained from 254 growth experiments carried out under similar environmental conditions (glucose as sole carbon source in aerobic conditions) , 53–67 . These dic model . This meE. coli were calculated for each steady-state reached by the kinetic model, namely: growth and glucose uptake rates, ATP, NADH and NADPH production rates, sum of all intracellular fluxes, sum of all intracellular metabolite concentrations and cost of enzymes , reflecting the important role of oxidative phosphorylation in energy production under aerobic conditions.A systematic positive correlation was predicted between some anabolic and catabolic fluxes and yields: glucose uptake rate, growth rate, NADPH production rate, biomass yield and NADPH yield (with ρ > 0.85), indicating a considerable degree of coordination in the metabolic operation. These variables are negatively correlated with the energetic (ATP and NADH) yields (ρ < -0.85), which is consistent with the fact that the single carbon source, glucose, is used by two competing metabolic processes: energy production and biomass synthesis, reflected in an increase in Yper se. The outcome of predictive analyses based on this assumption (such as the minimization of the sum of fluxes in FBA according to the hypothesis that cells minimize their enzyme levels) should therefore be interpreted with caution.The low correlation coefficient between the sum of fluxes and the cost of enzymes (ρ = 0.11) indicates that the sum of fluxes cannot be considered as a proxy for enzyme investment O2_uptake, vGlc_uptake, vNADH_production, vATP_production, with ρ > 0.84), and the relative contribution of this pathway negatively correlated with anabolic rates and yields  and positively correlated with energy yields (ρ > 0.90 for ATP and NADH yields). Thus, the partition of carbon between energy production (ATP and NADPH) and growth (via the synthesis of many anabolic precursors) is predicted to be realized primarily at the level of the TCA cycle and appears to be largely controlled at the metabolic level.In general, systemic variables correlated poorly with relative and absolute fluxes from most of the pathways. This is interesting as it shows that while there is coordination between several processes, there is nevertheless a significant degree of flexibility in the intracellular flux distribution. A notable exception was observed for the TCA cycle: its absolute flux is positively correlated with catabolic and energy fluxes  were collected from the literature –65, 67 . These dic model . The resin vivo in both prokaryotic (E. coli) and eukaryotic (S. cerevisiae) microorganisms [E. coli and S. cerevisiae are highly conserved, the present results may explain why similar properties are observed in both microorganisms, though this hypothesis requires further investigation.Interestingly, additional couplings predicted by the model were recently observed rganisms : betweenE. coli central metabolism, its boundaries were determined with and without considering metabolic regulation by using the kinetic and the stoichiometric models, respectively. Unexpectedly, the boundaries were similar for both models . InE. coli, which provides building blocks, cofactors, and energy for growth and maintenance. We developed, to our knowledge, the first detailed kinetic model of this system that links metabolism to environment and cell proliferation through intracellular metabolites levels. This model, validated by 778 independent flux data from some 266 experiments, allowed the identification of several properties which emerge from metabolic regulation and explain many experimental observations of E. coli’s physiology. The intrinsic, self-regulating capacities of E. coli central metabolism appear to be far more significant than previously expected. The results presented here imply that gene regulation is not required to explain these properties.In this study, we investigated the contribution of metabolic regulation on the operation of the central metabolism of E. coli metabolism, and likely not to the metabolism of other organisms. Its persistence in the literature is a major handicap to understanding metabolism. In fact, the central metabolism is not even self-contained in terms of control due to a large portion of control being exerted by the environment, making E. coli responsive to environmental changes. One of the most striking examples of this phenomenon is manifested in growth controlling most fluxes but being controlled virtually by glucose availability alone. The low control exerted by single enzymes on the system makes the metabolic operation of E. coli robust to fluctuations of enzyme levels that may arise from noise in gene expression or other factors. Moreover, the majority of control resides not within but outside the controlled pathways. The dense, yet highly organized, interactions between pathways allow a rapid and coordinated response of the entire system to perturbations.Metabolic control analysis showed that the flux and concentration control exerted by single enzymes is low and largely distributed across the network, confirming again the insights of Kacser and Burns . This siE. coli, as was previously believed [E. coli strains and mutants are confined to a small region of the solution space, this is not due to kinetic constraints as it is possible to simulate other behaviors simply by changing parameter values. This apparent paradox can be resolved, of course, if the action of natural selection had favored these behaviors.Exploration of the solution space indicated that metabolic regulation does not significantly restrict the metabolic capabilities of believed , 69. WhiE. coli metabolism [E. coli metabolism displays remarkably robust yet simple emergent properties, and these properties have major implications on its overall cellular physiology, e.g. by preventing unnecessary osmotic stress, maintaining the coordination between key processes, and optimizing the allocation of resources towards particular functions such as growth.The systematic mapping of the relationships between various systemic variables revealed that metabolic regulation is sufficient to explain the emergence of several functional couplings, which are independent from gene regulation (since they are conserved when enzyme levels are changed randomly by orders of magnitude) and cannot be explained by stoichiometric constraints. An important finding is that metabolic regulation alone may be responsible for the coordination of major catabolic, energetic and anabolic processes at the cellular level to optimize growth. Metabolic regulation thus appears to be sufficient to maintain multi-dimensional optimality of tabolism . DespiteE. coli central metabolism reflect the evolutionary selection that has been exerted on the ensemble of enzymes  to realize a network with these properties. Since central metabolism is essential in most organisms and is highly conserved across the three domains of life, it is tempting to speculate that metabolic regulation is responsible for the very similar operation principles observed in different organisms [The self-regulating capabilities of rganisms .E. coli, but it is in addition to the properties observed here, since these can operate without it. For instance, the robustness of the flux partition to the deletion of global transcriptional regulators was interpreted as a low control of this partition at the hierarchical level [Of course we do not suggest that hierarchical regulation does not play an important role in the metabolic operation of al level , and oural level , 75, 88.Escherichia coli K-12 MG1655 , two reactions were included to represent the continuous glucose inflow into the environment and acetate wash out .The model contains three compartments: the environment and the two cellular compartments: periplasm and cytoplasm. The periplasmic volume is set to be 20% of the total cell volume . Since tBiological systems are open systems, three exchange reactions were therefore included to enable the transport of extracellular glucose (XCH_GLC), acetate (XCH_ACE) and phosphate (XCH_P) between the environment and the periplasm. Their rate was modelled as a saturable, porin-facilitated diffusion process through the outer membrane , using aDetailed description of the glucose phosphotransferase system was taken from . ReactioE. coli uses oxidative phosphorylation to produce ATP. The main components of this pathway are two NADH dehydrogenases (reactions NDHI and NDHII), the succinate dehydrogenase complex (reactions SDH and SQR), the cytochrome bo oxidase (CYTBO) and the ATP synthase (ATP_SYN) [+ from cytoplasm to periplasm, with an H+/e- ratio of 2 [2. Further transfer of electrons from FADH2 to Q (reaction SQR) occurs via the three other proteins. CYTBO couples the two-electron oxidation of ubiquinol (QH2) with the four-electron reduction of molecular oxygen to water. This enzyme also functions as a proton pump, with an H+/e- ratio of 2 [+/ATP ratio of 4 [+ pumps (NDHI and CYTBO) and ATP synthase on pH gradient across the membrane was considered using the relation proposed by [In aerobic conditions, ATP_SYN) . NDHI antio of 2 . SQR is tio of 2 . The protio of 4 . Oxidatiposed by . The rati) non-growth associated processes which consume ATP are lumped in the reaction ATP_NGAM, ii) adenylate kinase (reaction ADK), which catalyzes the reversible conversion of AMP and ATP into two molecules of ADP, iii) adenylate cyclase (CYA), which catalyzes the synthesis of cAMP from ATP, and iv) cAMP phosphodiesterase (DOS), which hydrolyses cAMP into AMP. The reversible reduction of NADP by NADH is catalyzed by two transhydrogenases [Several processes strongly impact the balance of ATP/ADP/AMP/cAMP pools and had to be considered to fit the experimental data: ogenases  lumped iSi, the rate of this reaction was modeled using the following equation:An overall pseudo-reaction was defined to describe cellular growth in terms of all the required metabolic precursors, with stoichiometric coefficients taken from the biomass function of iAF1260 . Assumine.g. Michaelis constants of the biomass function), or for which biochemical measurements are generally not representative of intracellular conditions (e.g. Vmax) were estimated to reproduce in the best possible way 276 experimental data obtained from E. coli K-12 MG1655 grown on glucose, under aerobic condition, at a dilution rate of 0.1 h-1. These data were steady state fluxes and metabolite concentrations [p is the parameter vector, f is the objective function which evaluates the deviation between the simulated and measured data, g(p) is the constraint function, and c is the constraint vector. The objective function f was defined as the sum of squared weighted errors:xi is the experimental value of the data point i, with experimental standard deviation σi, and yi(p) is the corresponding simulated value. Constraints were defined on estimated parameters  to ensure they are kept within a biologically reasonable range. The objective function was minimized with the Particle Swarm Optimization algorithm [Values of 56% of the parameters  were directly taken from the literature. Parameters not available in the literature, which do not have a real biochemical estimate  after converting the model into Fortran. All the scripts are provided in Supporting Information . Absolute and relative error tolerances were set to 10−8 and 10−6, respectively.Steady-states were calculated using the J and metabolite M in response to a fractional change in the rate of the step E coefficients, were calculated as follows:Scaled flux (ECJ) and concentration (ECC) controls exerted on the system by the step E were calculated as the L2-norm of all its control coefficients:The overall flux . For each set, enzyme levels were sampled over two orders of magnitude  from a log uniform distribution, which ensures each order of magnitude to be sampled in similar proportions.A total of 600,000 flux distributions were uniformly sampled within the solution space of a stoichiometric version of the kinetic model, using the Cobra Toolbox (v2.0.5) and Matlab 2013. In parallel, the cor function of R stats package) and mutual information (mutinformation function of infotheo R package v1.2.0).For each steady state, the following variables were calculated: growth rate, glucose and oxygen uptake rates, ATP, NADH and NADPH production rates and yields, sum of fluxes, cost of enzymes, biomass yield, total intracellular metabolites pool, ATP production rate and enzyme cost per sum of fluxes, and sum of fluxes per glucose consumed. Enzyme cost, defined as the total amount of amino acids present in central metabolic enzymes, was calculated by summing for each reaction the product of enzyme concentration by the number of amino acids in the corresponding enzyme, similarly to , 86. EnzE. coli K-12 strains  were grown in different conditions  . We independently validated these model predictions based on a test set of experimentally observed phenotypes that were not used during model construction. We collected from the literature a total of 778 intracellular and extracellular flux data from some 266 experiments where several wild-type and mutant emostat)  [5, 27, E. coli growing on glucose. Glucose uptake, catabolism, energy and redox production and growth were predicted to be strongly coupled despite large, random changes of gene expression. All the experimental data support the model-driven hypothesis that metabolic regulation is sufficient to maintain the tight coordination between these key metabolic processes.The good agreement between simulated and experimental validation data Figs –6 indicaS1 Table(XLSX)Click here for additional data file.S1 Text(PDF)Click here for additional data file.S1 Model(ZIP)Click here for additional data file.S1 Dataset(XLSX)Click here for additional data file.S2 Dataset(XLSX)Click here for additional data file.S1 Code(ZIP)Click here for additional data file.


Plants produce a diverse repertoire of specialized metabolites that have multiple roles throughout their life cycle. Some of these metabolites are essential components of the aroma and flavor of flowers and fruits. Unfortunately, attempts to increase the yield and prolong the shelf life of crops have generally been associated with reduced levels of volatile specialized metabolites and hence with decreased aroma and flavor. Thus, there is a need for the development of new varieties that will retain their desired traits while gaining enhanced scent and flavor. Metabolic engineering holds great promise as a tool for improving the profile of emitted volatiles of domesticated crops. This mini review discusses recent attempts to utilize metabolic engineering of the phenylpropanoid and its primary precursor pathway to enhance the aroma and flavor of flowers and fruits. These volatile metabolites can attract pollinators and seed dispersals, stimulate or suppress signaling cascades and protect against harsh environmental conditions, herbivores or pathogens [Plants synthesize a diverse repertoire of specialized metabolites that play important roles in various aspects of plant life such as growth, development, reproduction, defense and environmental responses ,2. Volatathogens ,4,5. Theathogens ,7,8. Theathogens ,9,10.Throughout the years, crop-breeding schemes were largely focused on attaining traits such as rapid growth, high yields and long post-harvesting shelf life. Less attention was devoted to maintaining or improving desirable aroma and flavor, partially because growers are generally paid for yield rather then for taste or aroma. Furthermore, aroma and flavor are complex traits controlled by multiple genes, and unlike yield or shelf life, are difficult to screen for. Hence, modern breeding schemes often lead to domesticated crops that produce less volatile metabolites, resulting in the loss of some of their desired aroma and flavor ,9. In reArabidopsis Production Of Anthocyanin Pigment1 (PAP1) transcription factor into rose flowers resulted in increased levels of phenylpropanoid-derived color and scent compounds, as well as higher levels of terpenoid scent compounds. Olfactory assays revealed that the enhanced levels of scent volatiles could be identified by both bees and humans [Several attempts have been made to improve the aroma and flavor of flowers and fruits by metabolic engineering of AAA-derived pathways . One d humans . Howeverd humans ,18,19 ord humans . Furtherd humans .A different approach, taken by our lab in the last few years, is to augment the amount of the primary metabolites—the AAAs—in an effort to increase the carbon flux towards the metabolic synthesis of specialized metabolites. This approach can be used to study the regulatory interactions between pathways of primary and specialized metabolism associated with the AAAs, to identify bottlenecks in the biosynthetic pathways and to look at cross regulation between different pathway branches. Moreover, elucidation of the secondary metabolites produced by various plant species, particularly crop plants, is hindered by the fact that many of these metabolites accumulate to very low steady state levels that are below detection threshold. Enhancing the production, and hence the levels of AAA-derived specialized metabolites in transgenic lines, can serve as a valuable tool for the detection of these low abundance compounds.Arabidopsis thaliana [AroG gene (AroG*), encoding a feedback-insensitive DAHPS , condenses these two products to form 3-deoxy-di-arabino-heptulosonate 7-phosphate (DAHP). DAHP is then directed via the shikimate and the AAAs biosynthesis pathways to form AAA, with chorismate serving as an intermediate metabolite . Thus, tthaliana ,23, and thaliana  and a tothaliana ,26. Recethaliana . One hetve DAHPS . As DAHPolecules . These colecules . Similarabolites . The traabolites . In a grenhanced . Taken tPheA gene (PheA*), encoding a feedback-insensitive bi-functional chorismate mutase/prephenate dehydratase gene. The PheA gene converts chorismate via prephentate into phenylpyruvate, directing the carbon flux to the phenylpyruvate branch of the AAAs pathway leading to phenylalanine synthesis (PheA* was expected to direct the flux more specifically towards phenylalanine and the specialized metabolites that are derived from it [PheA* gene in Arabidopsis seedlings resulted in increased levels of phenylalanine [PheA* overexpressing lines had increased levels of several specialized metabolites derived from phenylalanine and tyrosine, but reduced levels of several specialized metabolites derived from tryptophan. Though the mechanistic reason for these changes is still unclear, these results imply regulatory cross-interactions between the flux of AAA biosynthesis from chorismate and their metabolism into various specialized metabolites [PheA* in tomato fruits led only to minor changes in the levels of the AAAs or any of the identified volatile metabolites [AroG* and the PheA* genes had a metabolic profile that was predominantly impacted by the expression of the AroG* gene. However, the aroma attributes of the tomato fruits expressing both genes were unique and different from those of the lines expressing a single gene, suggesting a contribution of the PheA* gene to the overall metabolic profile [Arabidopsis transcription factor AtMYB12 in tomato fruits [Arabidopsis. Expression of AtMYB12 in tomato fruits induced the expression of genes encoding enzymes of flavonol and hydroxycinnamic ester biosynthesis, resulting in exceptionally high levels of phenylpropanoids, specifically flavonols and caffeoyl qunic acids [A second bacterial gene heterologously expressed in transgenic plants is a mutated ynthesis . Thus, e from it . Expresslalanine . Intriguabolites . In contabolites , and tom profile . Taken to fruits . AtMYB12ic acids . Interesic acids . It was In conclusion, the use of metabolic engineering can provide new information on the regulation of the channeling of primary metabolism to specialized metabolism, the cross-interaction of different metabolic pathways and the repertoire of specialized secondary metabolites in different plant species. In turn, gaining information on the various secondary metabolites and the metabolic pathways involving their production can contribute to the development of knowledge-based breeding strategies. Furthermore, metabolic engineering opens a new venue to stimulate the production of specialized metabolites and to enhance the quality of various plant organs. In particular, it can overcome the general negative correlation between flavor and aroma and long shelf life in different crops, an issue that has so far been difficult to solve by classical breeding.


Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes. As one of the key inventions in evolution, oxygenic photosynthesis has transformed life on Earth and dominates the Earth’s primary productivity today . Electrons, derived from water, are provided to the electron transport chain (ETC) and molecular oxygen is released as the byproduct of photosynthesis.Survival and growth of (most) cyanobacteria begins with the absorption of photons facilitated by large light-harvesting antennae, the phycobilisomes, and chlorophyll The ETC consists of a number of large protein complexes, mostly located in the thylakoid membrane. Electrons are transferred along the ETC, ultimately resulting in the regeneration of adenosine triphosphate (ATP) and reduced nicotinamide adenine dinucleotide phosphate (NADPH) as energy carrier and reductant, respectively. The functioning of the photosystems and the ETC are complex biophysical processes and objects of intense research. The respective processes are characterized by fast time scales and transitions between a large number of possible states. While a number of detailed computational models of these processes are available, often with a focus on photosystem II, the respective models typically do not describe regeneration of ATP and NADPH, and hence are not straightforwardly connected to other cellular functions.2). Cyanobacteria possess mechanisms to concentrate inorganic carbon in the vicinity of the CO2-fixing enzyme, the ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO), making use of bacterial microcompartments known as carboxysomes. Compared to the light reactions, the relevant time scales of the so-called dark reactions are significantly slower. Modeling of CO2-concentrating mechanisms (CCMs) typically involves consideration of diffusion and spatial structure.The ATP and NADPH regenerated by the photosynthetic light reactions play a crucial role for almost all other cellular processes. Beyond their role as energy donor and reductant, they also serve as important signaling compounds to convey information about the intracellular state. Regenerated ATP and NADPH are utilized to assimilate atmospheric carbon dioxide .While current kinetic models of metabolism rarely involve more than a few dozen compounds, cellular metabolism is increasingly analyzed using large-scale metabolic reconstructions and constraint-based computational methods. Metabolic network reconstructions are based upon the predicted gene content deduced from genomic DNA and aim to provide an unbiased and comprehensive account of all interconversions of small molecules inside a single cell or a compartment. Unlike kinetic models, metabolic reconstructions only make use of the stoichiometric properties of the respective interconversions, and manually curated reconstructions have been reported for a number of cyanobacteria , Photosystem I (PSI), and ATP synthase (ATPase). See Figure In most cyanobacteria, light harvesting is facilitated by large antenna complexes, the phycobilisomes. Phycobilisomes are attached to the cytoplasmic surface of the thylakoid membrane  or cytochrome-c (cyt-c). At PSI, electrons are transferred to ferredoxin and eventually to NAPDH using light-induced excitation of the PSI reaction center . Alternatively, electrons from the excited PSI state can be transferred back to PQ and Cytb6f , details of CET are still under debate and insufficiently understood. Photosynthetic electron flow results in a protein gradient across the thylakoid membrane that drives regeneration of ATP by the ATPase.PSII splits water and reduces the plastoquinone (PQ) pool. The latter mediates the transport of electrons from PSII to Cytb6f complex, and PC (or cyt-c) as soluble electron carrier are involved in respiratory as well as photosynthetic electron transport. While photosynthesis exclusively takes place in the thylakoid membrane, a rudimentary respiratory chain is also present in the plasma membrane  curve of cyanobacteria and microalgae. Early models were derived by Crill , Megard Beyond overall bulk models of photosynthesis, there is a significant history of biophysical models to understand oxygen evolution and chlorophyll fluorescence transients, often with a focus on PSII, as well as to understand specific properties, such as energy distribution in the photosynthetic apparatus , assimilation of CO2 by RuBisCO, and the subsequent synthesis of cellular building blocks mediated by a network of metabolic reactions. Computational concepts used to describe cyanobacterial metabolism have been discussed previously  genome of Synechococcus elongatus PCC 7942 may correspond to a shift of metabolic regulatory strategies from transcriptional control in latter toward post-transcriptional control in the former . Rate equations are derived from enzyme kinetic mechanisms, and implemented using  non-linear Michaelis–Menten type functions. The rate equations consider allosteric regulations, as well as other post-translational mechanisms, as far as such interactions are known. The light reactions are typically highly simplified. In the model of Pettersson and Ryde-Pettersson  and its +) as dynamic variables that allow coupling to the ETC. In this respect, first steps have been made for plant metabolism. The models of Laisk et al.  and redox state , as signaling compounds  to facilitate the uptake and acquisition of inorganic carbon. CCMs allow cyanobacteria to raise the local concentration of CO2 in the vicinity of the carboxylating enzyme RuBisCO, and thereby overcome the comparatively low affinity of RuBisCO for CO2 and depress the competitive oxygenation reaction (photorespiration). Cyanobacterial CCMs typically make use of dedicated microcompartments, the carboxysomes, that separate the assimilation of CO2 by RuBisCO from the rest of the cell. The CCMs of cyanobacteria relies on a number of components. The respective mechanisms are reasonably well understood  and is computationally feasible also for networks consisting of several thousands of reactions. The strength of stoichiometric models and constraint-based analysis are questions such as the following: What is the maximal growth yield for a given light or carbon input? Which set of enzymes is essential for the synthesis of certain biomass components? How many distinct biochemical paths exist for the synthesis of certain biomass components and how do these pathways differ with respect to cellular energy expenditure and cofactor utilization? Due to the specific computational methodology, however, a direct integration of large-scale stoichiometric models into kinetic models of metabolism remains challenging. Various extensions toward incorporating dynamics have been proposed .In addition to the biochemistry of metabolism, phototrophic growth is highly dependent on regulatory networks to coordinate growth and to relay environmental information. To this end, of particular relevance is the cyanobacterial circadian clock—discovered in the late 1980s and unique among prokaryotes  and Table in vivo) for selected models of the cyanobacterial circadian clock.The KaiC phosphorylation rhythm has widely been studied in systems biology, and hence, a variety of mathematical models have been put forward. The first models were rather minimal to explain how sustained oscillations in phosphorylation of KaiC occur, including no intermediate steps of phosphorylation, introducing feedbacks on KaiC phosphorylation or assuming hypothetical states of KaiA, KaiB, and KaiC  to the 24-h period of the environment and to transmit temporal information to downstream processes resulting in circadian rhythms in cellular physiology. Clock input cues involve the cellular ATP/ADP ratio, which has a direct effect on the core clock by modulating the KaiCs kinase activity  and RpaA (regulator of phycobilisome association A)  and therefore require careful balance between different electron transport pathways and alternative electron “valves”. CCMs use energy and have implications for the efficiency of carbon assimilation. The cellular ATP/ADP ratio and the oxidized PQ pool relays information to the circadian clock, which affects transcriptional output and hence metabolic activity. Metabolism itself depends on cellular energy and redox potential—and must be appropriately coordinated to synthesize the right metabolites at the right time. The availability of ribosomes and amino acids, which are itself products of metabolism, affects the rates of translation of new proteins—which must be coordinated to account for damage, stability, and turnover times of proteins. In particular, the components of PSII complexes themselves are dependent on environmental conditions due to photodamage caused by ROS  periods of darkness (Hood et al., Mycoplasma genitalium—based on a subdivision of cell functionality into modules (Karr et al., Overall, there is increasing interest in whole-cell models to understand cellular trade-offs and functions in the context of a living cells. The construction of integrative computational models to predict phenotype from genotype has gained momentum with a first whole-cell model of the life cycle of the human pathogen Distinct from other approaches to whole-cell models, however, we argue that it is unlikely that a single universal model—a model that spans all scales from intracellular to intercellular to properties of ecosystems—will fulfill all requirements needed to describe cellular growth. Rather, we envision a modular approach. Depending on the research question, different temporal and spatial scales must be considered. The task is then to derive an appropriate representation of cellular processes that accounts for the spatial and temporal scales involved. The derived submodels should be consistent with more fine-grained representation and their construction must be informed by knowledge how processes interact and which trade-offs are relevant for a specific research question. We note that, besides the biological challenges, such a strategy also entails major computational challenges. As yet, the annotation of computational models is often poor. That is, the biochemical identity of model variables is not defined in a computer-readable format, and hence, merging of models typically requires extensive manual curation (Krause et al., e-cyanobacterium.org (Klement et al., Notwithstanding these challenges in computational methodology, we expect a growing library of models related to cyanobacterial growth that can inform and guide research how phototrophic organisms, such as cyanobacteria, adapt to complex environments. These models must increasingly adhere to common standards and should be made available on open platforms, such as the BioModels database (Li et al., SW and RS conducted the research and wrote the article. Both authors approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Plasmodium falciparum, and its thermodynamics-based flux analysis (TFA). Using previous absolute concentration data of the intraerythrocytic parasite, we applied TFA to iPfa and predicted up to 63 essential genes and 26 essential pairs of genes. Of the 63 genes, 35 have been experimentally validated and reported in the literature, and 28 have not been experimentally tested and include previously hypothesized or novel predictions of essential metabolic capabilities. Without metabolomics data, four of the genes would have been incorrectly predicted to be non-essential. TFA also indicated that substrate channeling should exist in two metabolic pathways to ensure the thermodynamic feasibility of the flux. Finally, analysis of the metabolic capabilities of P. falciparum led to the identification of both the minimal nutritional requirements and the genes that can become indispensable upon substrate inaccessibility. This model provides novel insight into the metabolic needs and capabilities of the malaria parasite and highlights metabolites and pathways that should be measured and characterized to identify potential thermodynamic bottlenecks and substrate channeling. The hypotheses presented seek to guide experimental studies to facilitate a better understanding of the parasite metabolism and the identification of targets for more efficient intervention.Novel antimalarial therapies are urgently needed for the fight against drug-resistant parasites. The metabolism of malaria parasites in infected cells is an attractive source of drug targets but is rather complex. Computational methods can handle this complexity and allow integrative analyses of cell metabolism. In this study, we present a genome-scale metabolic model (iPfa) of the deadliest malaria parasite,  Plasmodium falciparum, and its thermodynamics-based flux analysis (TFA). Our results support and extend the available experimental evidence on the essential genes and nutritional requirements of this organism. Besides, we identify metabolites that give rise to thermodynamic bottlenecks and suggest substrate channeling. Overall, these results provide novel insight into the metabolism of P. falciparum and may guide experimental studies to develop a better characterization of the parasite metabolism and the identification of antimalarial drug targets.Almost half of the world population is at risk of infection by malaria parasites. The rise in drug-resistant parasites requires better understanding and targeting of their metabolism. In this study, we present a genome-scale metabolic reconstruction (iPfa) of the deadliest malaria parasite,  Plasmodium species capable of infecting humans, P. falciparum is responsible for most malaria-related deaths. The current increase in parasites with resistance to most of the clinically used antimalarial drugs, including artemisinin, renders the treatment of this disease more challenging [Malaria remains a major global health care concern, with almost half of the world population at risk of infection that ultimately results in over half a million deaths each year . Of the llenging . The devllenging , 3) thatP. falciparum, iTH366 [P. falciparum metabolism that updates, among other important features, the functional annotation of the genome, the localization of the enzymes and the definition of the available substrates according to the currently existing data.Genome-scale metabolic models (GEMs) represent an invaluable platform for the integrative analysis of cell metabolism . Current, iTH366  and Plas, iTH366  or in th, iTH366 . HoweverThe standard approach for analyzing different phenotypes using GEMs is flux balance analysis (FBA) , 10. FBAThermodynamic bottlenecks arise when alternative metabolic pathways are thermodynamically impeded although, based on network topology, they could have theoretically served a metabolic function. Unfavorable thermodynamics imposed by bulk-phase metabolite concentrations can be circumvented with substrate channeling. Substrate channeling involves the coupling of two or more reactions, and the common intermediate is transferred from the first enzyme to the second without escaping into the bulk phase. Such process has a major effect on the thermodynamics and kinetics of the involved catalytic functions and might determine specific responses to regulatory mechanisms. Techniques such as isotope dilution or enrichment, competing reaction or enzyme buffering have been traditionally used to detect and characterize substrate channeling for an enzyme pair or larger metabolon . Such meP. falciparum that can reveal potential targets in its metabolism for efficient intervention. We also seek to identify metabolites whose intracellular concentrations give rise to thermodynamic bottlenecks and pathways where substrate channeling may exist. These analyses can guide metabolomics and biochemical studies on the metabolism of the parasite. For this purpose, we developed a GEM of P. falciparum (iPfa) and performed thermodynamically consistent studies using TFA and integrating the metabolite concentration ranges previously measured in intraerythrocytic P. falciparum [P. falciparum.The primary goal of this study is to provide new insight into the essential metabolic capabilities and the nutritional requirements of lciparum –22. We pP. falciparum metabolism to reconstruct iPfa. A detailed description of the steps followed for the reconstruction process is provided in the We combined semi-automated approaches with a manual curation process based on the available literature on Plasmodium species  to the parasite’s cytosol, and 155 transports between intracellular compartments . Due to tability . These an orphan .The metabolic enzymes included in iPfa are distributed in six classes according to the E.C. identifiers. The majority of the metabolic enzymes in iPfa are transferases (43%), followed by oxidoreductases (24%), ligases (12%), hydrolases (12%), lyases (7%) and isomerases (2%) . RegardiP. falciparum metabolism. For example, based on recent findings [Toxoplasma gondii, ToxoNet1 [P. falciparum, iPfa is capable of growing on an in silico rich medium composed of 236 substrates that allow less restrictive conditions in the analyses. iPfa includes 245 common genes with iTH366 and 80 additional genes. Regarding metabolic tasks, iPfa accounts for 73 biomass building blocks of which 40 are common with iTH366 [P. falciparum. A detailed comparison of iPfa with the previous reconstructions iTH366 [The GEM iPfa presents an unbiased bottom-up reconstruction and an updated database of findings , the pyrfindings , PlasmoNfindings  and theifindings , 8 .We used iPfa to study single and double gene essentiality n silico . To undeP. falciparum, whereas the remaining 24 genes have not been examined empirically, to our knowledge. We grouped the 24 non-validated genes in two classes: the first class is composed of 14 genes that participate in metabolic pathways where other genes have been experimentally defined as essential, and the second class contains 10 genes that are associated with functions or pathways where other genes have not been reported as indispensable. Therefore, we could not hypothesize the latter class of genes to be essential based on previous context-dependent information. For example, the MEP/DOXP pathway in the apicoplast is essential in P. falciparum for the production of isopentenyl diphosphate and isoprenoid derivatives [We first performed essentiality studies without accounting for thermodynamic constraints and identified 55 genes that are essential for growth . The genivatives . There aivatives –33, whilrG’) and allows the integration of metabolomics data . We applied two different approaches within the TFA framework. In the first approach, we allowed the concentration of every intracellular metabolite to vary between 1 μM and 50 mM. Besides, the concentration of extracellular metabolites  varied between 0.01 μM and 100 mM. Such concentration limits are similar to the physiological ranges used in previous TFA studies [Next, we performed essentiality analysis using TFA, which includes information about the Gibbs free energy of reaction  with antimalarial inhibitors . DespiteP. falciparum trophozoites [In the second approach within the TFA framework, we integrated ten available metabolomics data sets, i.e., absolute concentrations measured in mature hozoites –22  were allowed to vary from 0.1 fM to 500 mM . While increasing the upper limit of the concentration range did not impact the essentiality of the three genes, decreasing the lower bound was critical for their essential function .KM, provides a measure of the substrate concentration required for effective catalysis to occur. The KM of the enzymes usually varies between 10−1 and 10−7 M. The KM values found in the literature indicate that metabolite concentrations of 1 fM are not physiologically relevant, which further supports the essential function of the P. falciparum genes predicted with TFA and generic concentration ranges.When the intracellular concentrations were decreased and allowed to vary between 0.01 μM and 50 mM, the gene encoding a serine palmitoyl transferase (E.C. 2.3.1.50) was incorrectly predicted as non-essential . The esscell / mol/Lcell based on the absolute minimum and maximum experimentally measured concentrations [We next sought the bottleneck metabolites and the associated reactions in iPfa whose directionalities were constrained and led to the essential function of the genes . The analysis of bottleneck metabolites suggests that AMP and ATP constitute a single minimal set of metabolites that is responsible for rendering three genes essential . The thrtrations –22  from ethanolamine through the Kennedy pathway . The botP. falciparum involved in the Kennedy pathway are expressed in the blood stages [Plasmodium berghei [TFA with metabolomics data rendered the Kennedy pathway thermodynamically infeasible. However, the genes of d stages , and evi berghei , which f berghei . When weP. falciparum, depend on the availability of a broad array of metabolites provided by the host cell and its surroundings. To characterize the nutritional requirements of P. falciparum, we followed and extended the approach previously applied to the related pathogen T. gondii to study the in silico minimal medium (IMM) [Obligate intracellular parasites, such as um (IMM) .in silico rich medium composed of 236 substrates . This result demonstrated that the non-appearance of two substrates in the same IMM is a necessary but not sufficient condition to define the substrate substitutability.backbone moieties) among the non-constitutive substrates, which allowed us to cluster the 36 non-constitutive substrates of the IMM  enzymes [Orotate is an intermediate metabolite in the canonical and highly conserved biosynthetic pathway of UMP, a common precursor of pyrimidine nucleotides. TFA of iPfa suggested that the biosynthetic pathway of pyrimidines is thermodynamically infeasible and hence the orotate backbone moiety, provided by orotate and (S)-dihydroorotate, needs to be taken up. However, the biosynthetic pathway of UMP, which involves six enzymes, is known to be functional  and esseimidines , 52. We  enzymes . Previou enzymes  and comp enzymes  studies  enzymes . The pre enzymes .P. falciparum, we evaluated single gene essentiality in iPfa for each of the alternative IMMs (in silico rich medium (less restrictive condition)   remainedndition) , and thendition) .P. falciparum and performed thermodynamics-based flux analysis to study the essential metabolic capabilities and the nutritional requirements of the parasite. Besides, we identified thermodynamic bottlenecks and hypothesized substrate channeling in the metabolic pathways. The results from this work, which have been compared with available experimental evidence, demonstrate that iPfa and its TFA can be used to fill in the knowledge gaps regarding the critical aspects of P. falciparum metabolism.In this work, we reconstructed a GEM for The highest accuracy score (59%) in the prediction of essential genes for growth was obtained using TFA with metabolomics data. Such approach revealed up to 63 lethal genes and 26 synthetic lethal pairs in iPfa . ExistinP. falciparum.The analysis of metabolic tasks identifies the effect of the gene knockouts on the parasite’s growth and suggests that the disruption of the 63 essential genes impair the production of up to 30 biomass precursors . When thP. falciparum a thermodynamic dependency between the production of phospholipids, phosphorylated nucleotides, and sugar nucleotides through the concentrations of the bottleneck metabolites. The knowledge of metabolic subsystems that are thermodynamically dependent can be used to design drugs that synergistically target these parts of the metabolism and prevent their metabolic regulation and rise of drug-resistant parasites.We identify eighteen bottleneck metabolites in iPfa, whose intracellular concentrations determine the directionality of a set of reactions and render eight genes essential . The botP. falciparum [P. falciparum requires the experimental characterization of the enzymatic mechanisms using techniques such as isotope dilution [Through the analysis of thermodynamic bottlenecks, we identify two thermodynamically infeasible pathways, i.e. the Kennedy and the pyrimidine biosynthesis pathway, that are functional in lciparum . The prelciparum , 54, 56.lciparum , 16. Thedilution .P. falciparum. The IMM analysis suggests that P. falciparum requires at least 23 substrates for growth and 13 of them are indispensable . These constraints in iPfa accounted for the intracellular conditions, like the pH, the membrane potential and the intracellular concentration ranges of the metabolites  , 61, 62,abolites . TFA furP. falciparum trophozoite-infected red blood cells [We created a thermodynamically curated version of iPfa where we allowed the concentration of every intracellular metabolite to vary between 1 μM and 50 mM, which is the physiological range used in similar TFA studies , 13. Theod cells  and one od cells . The remod cells . The phyod cells –22, in wod cells –22.cell. The concentration ranges are integrated within TFA and constrain the allowable ΔrG’ range of the reactions in which the metabolites participate and with it the flux ranges of the neighboring reactions. We integrated the metabolomics data sets one-by-one and simultaneously to study the number of bidirectional reactions and the predictions of essential genes. The essential genes varied among data sets, and the data set measured with LC-MS [We translated the reported values and measurement errors into ranges of concentration expressed in mol/Lth LC-MS  and the in silico growth reducing phenotypes. No additional filtering was applied to identify essential genes and pairs of genes.This analysis allowed the identification of the metabolic tasks or biomass building blocks that could not be performed or produced, respectively, upon knockout of the essential genes. The analysis involved two steps: first, the essential genes for biomass growth were identified following standard procedures . Second,P. falciparum (in vitro) available in the literature. Information for other Plasmodium spp. was also used for comparison. An accuracy score was calculated as (TP+TN)/(TP+TN+FP+FN), where TP (true positive) and TN (true negative) define predictions that correctly simulate growth and non-growth, respectively, based on the available experimental data. While FP  and FN  describe predictions that incorrectly simulate growth and non-growth, respectively. The accuracy score served to evaluate the prediction of essential genes. For the predictions with TFA and metabolomics data integrated, an accuracy score of 59% is obtained based on the data available for P. falciparum in the literature (references reported in P. berghei in the blood stages (PlasmoGEM data) [The genes predicted as essential in iPfa with FBA and TFA were compared with experimental information available in the literature. We used primarily experimental data for EM data) , 58. Thesimilarity between the essential enzymes in iPfa and the human proteome when there exists at least one matching protein in non-redundant human proteome (txid9606) with the standard protein BLAST settings in the bioinformatics software blastp version 2.6.0+ [We further tested whether the enzymes predicted as essential in iPfa are similar to any human protein. We define n 2.6.0+ : cutoff n 2.6.0+ .ΔrG’ and tested the gene essentiality of the three genes. These are the three genes that were further identified as essential with TFA using the generic concentration ranges (1 μM—50 mM) with reference to the FBA prediction (We reduced the lower bound ten orders of magnitudes (minimum intracellular concentration of 0.1 fM) and increased the upper bound ten fold (maximum intracellular concentration of 500 mM). We then recalculated the feasible range of ediction . The minThis study identified the metabolites responsible for the thermodynamic bottlenecks, which determined the directionality of a set of reactions and allowed the identification of eight genes as essential . iPfa waΔrG’) is a measure of its thermodynamic potential and based on the second law of thermodynamics, defines the thermodynamically feasible direction under which the reaction can operate, defined as reaction directionality [ΔrG’ accounts for the standard Gibbs free energy of a reaction (ΔrG0’), which was calculated using the group contribution method (GCM) [ΔrG0’ and the metabolite concentrations is expressed within TFA in the form of ranges that ultimately define the feasible range of ΔrG’ associated with each reaction. The range of ΔrG’ was known with Thermodynamic Variability Analysis (TVA) [ΔrG’ is negative, then we define the reaction to be unidirectional in the forward direction. When the range of ΔrG’ is positive and negative, then we define the reaction as bidirectional.The Gibbs free energy of a reaction  , 62, andis (TVA) , which fis (TVA) . We appl1 and E2) was simulated within the TFA framework. The reactions R1 and R2 catalyzed by E1 and E2 were lumped to define an overall reaction (L = R1+R2). The overall reaction eliminates the common intermediates and recycled metabolites since they are produced in the first reaction R1 and consumed in the second reaction R2 and vice versa, respectively. For example, if R1 involves the transformation A + B → I + C and R2 is defined as I + D → P + B, the final lumped or overall reaction L is defined as A + D → P + C. The overall reaction L does not involve the intermediate metabolite I and the recycled metabolite B. It is important to note that reactions R1 and R2 should be first defined in the direction that satisfies mass balances and allows flux through the pathway of study. Then the lumped reaction can be formed. For a pathway of study that contains reactions R1 and R2 the starting and product metabolites are usually A and P, respectively. Then, the reactions R1 and R2 should be defined as A + B → I + C and I + D → P + B. Other definitions, such as A + B → I + C and P + B → I + D, do not satisfy mass balances. In this study, the reactions of the pyrimidine biosynthesis pathway and the Kennedy pathway were defined to allow production of UMP and PE, respectively. The overall reaction was then allowed to be bidirectional. Thermodynamic properties were calculated for the overall reactions and TFA and Thermodynamic Variability Analysis (TVA) [ΔrG’ obtained from TVA.The presence of substrate channeling between two enzymes (Eis (TVA)  were perThe IMM analysis was performed following the strategy defined before . Here, Tin silico medium of 52 metabolites identified in the IMM. Second, we tested that under such conditions, the inclusion of each substrate of the group individually allowed simulated growth in iPfa. This analysis was also performed in the rich medium of 236 substrates to validate the groups of substrates that contained the three backbone moieties .This study was performed on the substrates of iPfa to validate their ability to substitute for each other and support growth. Groups of substrates were created based on the IMM analysis. Substrates were grouped if they never appeared in the same IMM and presented a common molecular substructure or backbone moiety. We validated these groups in two steps. First, we tested that iPfa could not grow when all substrates in a group were removed from the The tools and methods used are described in more detail in S1 Methods(PDF)Click here for additional data file.S1 Table1Gap-filling reactions are defined with their R-5 digit identifier as obtained from the KEGG database. Transport reactions are marked with T_. Cellular compartments are defined with the reaction name: _r, endoplasmic reticulum; _c, cytosol; _m, mitochondrion; _a, apicoplast. Note that the same gap-filling reaction can be suggested for more than one metabolic task.(XLSX)Click here for additional data file.S2 Table1Genes predicted as essential for iPfa growth in the in silico rich medium  essential; (gr) growth reducing; (ne) non-essential. 3Impact of the gene knockout on the metabolic tasks of iPfa is explainable based on the annotated function of the gene. 4This gene is involved in an essential pathway and is thus presumed to be essential. 5None of the reactions associated with this gene is single essential; the gene is essential when two or more associated reactions are knocked out. 6We define similarity between the essential enzymes in iPfa and the human proteome when there exists at least one matching protein in non-redundant human proteome (txid9606) with the standard protein BLAST settings in the bioinformatics software blastp version 2.6.0+ [n 2.6.0+ : cutoff n 2.6.0+ .(XLSX)Click here for additional data file.S3 Table1Pairs of genes predicted as essential for iPfa growth with TFA and the MS data  in the in silico rich medium Click here for additional data file.S4 Table1Reaction I.D. in iPfa. Cellular compartments are defined after “_” in the reaction I.D.: (_c) cytosol, (_m) mitochondrion, (_r) endoplasmic reticulum, (_e) extracellular. Transport reactions are marked with T_. 2Values of the standard Gibbs free energy of reaction (ΔG0') calculated with the group contribution method (GCM), as explained in the ΔG0' does not determine the reaction directionality. 3Reaction directionalities determined with Thermodynamic Variability Analysis (TVA). 4The reactions R02057_r, R01468_r, R02038_r, and T_c_to_r_C00189 are unidirectional (forwards) using TVA and generic concentration ranges, or blocked using TVA and metabolomics data (see data see .(XLSX)Click here for additional data file.S5 Table1Genes predicted as essential for iPfa growth with TFA and the MS data  in the (XLSX)Click here for additional data file.S6 Table1Gene IDs were obtained from PlasmoDB. 2K-ID or Orthology groups were obtained from the KEGG database. 3The E-value denotes the goodness of the annotation to the assigned metabolic function. The annotation process is described in detail in (XLSX)Click here for additional data file.S7 Table1Localizations from the ApiLoc database. Intracellular compartments are defined by letters, such as c, cytosol; m, mitochondrion; a, apicoplast; er, endoplasmic reticulum; fv, food vacuole; e, extracellular space/parasitophorous vacuole; n, nucleus; ag, Golgi apparatus.(XLSX)Click here for additional data file.S1 DatasetΔrG’ was calculated in both approaches. The reactions in iPfa were ranked based on two ranking criteria: the number of reactions impacted by each metabolite (sheet S1 A and sheet S1 C in S1 Dataset), and the global RoU (sheet S1 B and sheet S1 D in S1 Dataset) as defined in the ΔrG’ is higher than 0.1%.The concentration range of each metabolite was integrated separately in iPfa following two approaches. In the first approach, the concentration of the metabolite was integrated at-a-time in all compartments of iPfa where the metabolite appears (sheet S1 A and sheet S1 B in S1 Dataset). In the second approach, the concentration of the metabolite was integrated separately in each compartment of iPfa where the metabolite appears (sheet S1 C and sheet S1 D in S1 Dataset). The RoU in the (XLSX)Click here for additional data file.


E. coli and S. cerevisiae with available experimental concentrations were utilized to develop a SVM model of the negative logarithm of the concentration (-logC). In this statistic model, in addition to common descriptors of molecular properties, two special types of descriptors including metabolic network topologic descriptors and metabolic pathway descriptors were included. All 1997 descriptors were finally reduced into 14 by variable selections including genetic algorithm (GA). The model was evaluated through internal validations by 10-fold and leave-one-out (LOO) cross-validation, as well as external validations by predicting -logC values of the test set. The developed SVM model is robust and has a strong predictive potential . An effective tool could be provided by this analysis for the large-batch prediction of the intracellular concentrations of the micro-organisms’ metabolites.With the rapid growth of micro-organism metabolic networks, acquiring the intracellular concentration of microorganisms’ metabolites accurately in large-batch is critical to the development of metabolic engineering and synthetic biology. Complementary to the experimental methods, computational methods were used as effective assessing tools for the studies of intracellular concentrations of metabolites. In this study, the dataset of 130 metabolites from  There are a large amount of experimental methods for identifying both metabolite concentrations and flux direction with the rapid development of high-throughput LC-MS technology and other analytical technologies. However, as the intracellular concentration of most metabolites is quite low (at the level of micro-mole), it is difficult to determine them by current precise analytical instruments2, especially in mass determination. It is still a huge challenge for experimental measurements in microenvironment, especially in microorganism cells. On the other hand, to enrich the intracellular metabolites is still quite difficult and may decrease the accuracy of measurement. Recently, there are an increasing number of computational and mathematical models for simulations of the cellular metabolism in metabolic engineering and synthetic biology6, which require the metabolites’ concentrations as basic parameters. In addition, metabolite concentration can also be used as a criterion for antibacterial discovery7, which further increases the demand for concentration determination.Metabolic engineering has been widely used to raise the outputs of many significant small chemicals in different industrial and daily products, such as food, beverages, medicine and even enzymes. No matter these molecules are natural or synthesized, in order to increase the metabolic flux of the target molecules9. Commonly, based on the second law of thermodynamics, establishing a theoretical model requires quantitative information like metabolite concentration or metabolic fluxes, which are always interrelated. According to thermodynamics laws, a chemical reaction follows the Van’t Hoff equation as below  method to predict intracellular metabolite concentration, but the NET method needs Gibbs free energy of the metabolic reaction as the prior condition, which greatly limits its application scope because of the difficulty in Gibbs free energy measurement10. Hamilton et al. developed a method named thermodynamics-based metabolic flux analysis (TMFA), which is the developed from the general flux balance analysis and thermodynamic constraints analysis11. The TMFA method can predict an approximate range of metabolite concentrations based on relatively few information, which is more suitable for qualitative analysis rather than accurately quantitative analysis.However, few theoretical methods have been developed by far for prediction of the intracellular concentrations. As well known, absolute metabolite concentration is a bridge to a quantitative understanding of cellular metabolism, as concentrations affect both the free energies and rates of metabolic reactionsEquation ,1\documeet al. with combination of bioinformatics and cheminformatics8. It is possible to develop theoretical methods for predicting the intracellular concentration. Bar-Even et al. found that the hydrophobicity and charge of metabolites has great influence on the intracellular concentration of metabolites, and initially established a rough linear model for metabolites concentration prediction based on physical and chemical properties for the first time12. In the following researches, Zhu et al. found that there is a certain correlation between biological phenotype and metabolic network topology, in addition to physical and chemical properties, based on which a support vector machine model was established to predict the intracellular metabolite concentrations8. However, while the squared cross-validation correlation coefficients (Q2) of this model reached 0.59 in the internal validation in E. coli, it had no external validation with independent test set.At the same time, prediction of metabolites’ concentrations was also attempted by statistical methods. With the rapid development in microorganism metabolic network, the relationship between metabolic network and chemical reactions was explored after reconstructing metabolic network. Since most biological metabolites are small molecules and metabolic processes are basically chemical reactions, to some extent, the metabolic network organization has chemical basis, which was discussed by Zhu 12, less biological information was employed to predict metabolite concentrations. In this paper, in addition to molecular descriptors of structural and physicochemical properties, topological parameters in organism specific metabolic network and a novel type of parameters describing the involvement of a metabolite in specific pathways were utilized to improve the predictive performance, with discussion on their biological meaning. All these variables were applied to variable selection using genetic algorithm (GA)15 and an additional optimization procedure. Incorporated with the support vector machine algorithm20, the variable set was iteratively optimized to build the final prediction model21 which has the best performance in internal validation. The final model was then applied to the external validation in the test set, which was randomly selected from a dataset containing the experimental concentrations of 130 metabolites from two kinds of microorganisms, 93 metabolites from E. coli9 and 37 metabolites from S. cerevisiae22.In addition to molecular properties, it might be helpful to utilize information of metabolites’ biological functions in the concentration prediction, since the functions are generally affected by the biological characters like the intracellular concentrations. However, in the earlier studies2) between computational and experimental values is increasing. Until in the fifth round, when the number of selected variables m is lowered to 14, the best performances are obtained both in 10-fold cross-validation with RMSE = 0.741, Q2 = 0.55 and in LOO method with RMSE = 0.730, Q2 = 0.57. In the next three rounds, the performances of the models are not improved, but drop a little bit. And in the ninth round, the dramatic increase in RMSE to 0.853 and decrease in Q2 to 0.41 in 10-fold cross-validation, as well as to 0.828 and 0.45 in LOO respectively, convinced us to stop further attempts.After a preprocessing, the variable selection is performed on 1669 variables step by step, including three rounds of GA selection and a further optimization procedure. The results are evaluated by both 10-fold cross-validation and leave-one-out (LOO) validation, as shown in Table Generally the variables’ number is fewer in a model, the model quality is much better. However, taking into account the number of training set samples, 91 is much bigger than the number of variables, 14, finally 14 descriptors are picked out as the variable set for the final SVM model described below. Detailed information about the 14 variables is shown in Table In Table et al.8 or Bar-Even et al.12.As we can see from Tables 8, in addition to the parameter Degree, this optimal variable set contains a metabolic network topology variable named as Clustering-Coefficient, which represents the density of the network around the specific nodes. In graph theory, Clustering-Coefficient reflects the tendency of nodes to cluster together. If one node is connected with n other nodes, Clustering-Coefficient is the ratio of the number of edges between n nodes and the maximum number of potential maximum edges . In both figures, the average metabolite concentrations are positively correlated with the average Clustering-Coefficient of the group of metabolites. Combining with the correlation coefficients in Table As in Fig. The third type of variable is metabolic pathway variable. As in Table 24, although not strictly linear. This positive correlation was shown in Fig. 2 as high as 0.838, suggesting that metabolites more polar and thus more water-soluble may have higher intercellular concentrations. Therefore, the metabolite concentration could be predicted by chemical basis, at least partially.The reason why the pathway variables of these five non-core pathways are retained in the final model might be explained by the deviation of the concentrations and polarities of the 14 metabolites in these pathways from the average level. In microbe metabolic pathways, the concentration and the polarity of the metabolites are two key points. In intracellular micro-environment, the concentration and polarity of the metabolites are generally positively correlatede of the 14 metabolites in E. coli and S. cerevisiae are 2.77 and 2.32, respectively, much smaller than the overall average value as 3.57 of all the 130 metabolites in both organisms. It means that these 14 metabolites may have a lower polarity, but a higher concentration. This is a good example that the positive correlation between polarity and concentration of metabolites may vary in certain pathways of metabolites, such as the 14 metabolites in the five pathways of MPF descriptor. Therefore, this MPF descriptor can provide a contribution to complement the concentration prediction as an important variable.In Table 25 based on 91 samples in training set, and then it was tested by the independent test set containing 39 samples. The confidence interval of 20 randomized trials is: R2 = 0.75 ± 0.02, RMSE = 0.746 ± 0.020, Q2 = 0.54 ± 0.05; R2p = 0.56 ± 0.05, RMSEp = 0.744 ± 0.041, Q2p = 0.53 ± 0.05. The performance of the model is evaluated by randomly choosing one result as in Table Q2 = 0.55 and RMSE = 0.74 in the 10-fold cross-validation and Q2 = 0.57, RMSE = 0.730 in the LOO cross-validation, which both suggest a good stability. Moreover, in the external validation by the independent test set, the predicted vs experimental –logC values have Q2p = 0.58, R2p = 0.586, RMSE = 0.702, which also proved the good reliability of this model. In order to further demonstrate the robustness of the model, the variance of prediction error in the LOO cross-validation and the independent test was calculated as 0.53 and 0.52, respectively. Compared with previous studies, our model was further testified by external validations and showed good reliability.The prediction model of metabolite concentration employing 14 descriptors was built by SVM regressionBacillus subtilis26, which did not exist in our training set, were used to test the generalization ability in other micro-organisms, getting a good result of RMSE = 0.71. However, this data set comes from a different experimental protocol that may lead to some systematic error in the concentration prediction.In addition, 11 metabolites from The plot of the predicted vs. experimental –logC values is shown in Fig. The distribution of prediction errors is shown in Figure 27, which was shown as Williams plot in Fig. h* of 3 × 14/91 = 0.46. From Fig. In this paper, leverage method was used to define the application domain of the prediction model28. Therefore, if the prediction error of –logC is less than 1, it may be accepted in predicting intracellular metabolite concentration. In the earlier study by Zhu and his coworkers8, the model has sample size n = 80, R2 = 0.683, Q2 = 0.59, RMSE = 0.729, as in Table 2 = 0.740, Q2 = 0.57, RMSE = 0.730. Furthermore, our model was validated by predicting an independent test set containing 39 metabolites, and resulted in R2p = 0.586, Q2p = 0.58, RMSEp = 0.702.According to the results shown above, based on GA variable selection, 14 variables were picked out to build the final prediction model. The metabolite concentrations oscillate during different phases of life. For example, during the life cycle of a yeast cell the amplitude of metabolite oscillation is usually within 10-fold, with a median of 2.4-foldE. coli and S. cerevisiae. In order to evaluate the possible influence from same metabolites in both training and test sets, we reconstructed the models with a non-overlap strategy that the same molecules from E. coli and S. cerevisiae were divided both into the training set, or both into the test set, so as to prevent possible similarity between the training set and the test set. As shown in the Table When randomly separated the metabolites into the training sets and test sets, there may be some overlaps of metabolites in both E. coli, so their model may only fit well for this species. When the 130 compounds in the data sets including both E. coli and S. cerevisiae were put into one model together using Zhu’s modeling method, the Q2 of the reconstructed model could only achieve 0.46 in training set and 0.44 in test set, both less than 0.50. Our SVM model results in Q2 as 0.57 for the training set and 0.58 for predicting the test set, that is, greater power in fitness and reduced predictive error.In addition, compared with Zhu’s model, our model has a strong advantage in generalizability to different organisms. It is well known that the distributions of metabolite concentrations in different species are quite different, so they are difficult to be completely determined by the degree of metabolic networks only. Zhu’s model was only based on the dataset of Obviously, the performance of Zhu’s model could be explained well mainly by one network topological parameter, Degree. Beside Degree, Clustering-Coefficient is another important topological variable, which represents the density of metabolic reactions around the specific metabolites. In our predictive model, Clustering-Coefficient was found to also give some effective information of the differences between the distributions of metabolites’ concentrations in different organisms, and may help to improve the performance of the predictive model.30. Therefore, as shown in Fig. Furthermore, in this paper metabolic pathway variables were employed to predict metabolite concentration and to explain the complex relationship between the intracellular metabolite concentrations and molecular physicochemical properties. In the evolution, energy metabolism, synthesis and decomposition pathways are most critical. The metabolites in these core pathways generally have higher polarity to reach relative higher concentrations in the hydrophilic environment of plasma. However, some other intracellular metabolic pathways involving different hydrophilic environment, such as signal transduction pathways and the pathways of degradation of harmful substances in the environment, are also important for organisms to adjust the metabolism to external environment. In these non-core pathways, metabolites still need a relatively high concentration to maintain their biological function, despite their lower polarity. For example, in signal transduction, metabolites need lower polarity to pass through the phospholipid bilayerThe procedure to develop the models between the metabolite intracellular concentrations and the descriptors includes data collection, metabolic network reconstruction, descriptor calculations, variable selections, model development and validation, and test on application domain, as shown in Fig. 32. In the network reconstruction, the metabolic network was automatically reconstructed based on the reactant pairs from KEGG reaction database33, which were screened by two criteria. Firstly, reactant pairs which did not appear in the metabolic pathway of the organism should be deleted. Secondly, reactant pairs containing metabolites with unspecified residues were deleted32. In the reconstructed metabolic network, each node represents a metabolite while each edge represents a substrate-product relation, which was introduced in details by Ma et al.32. The reconstructed metabolic network of E. coli was consisted of 1002 nodes (metabolites) and 1424 undirectional edges (substrate-product relations), while the one of S. cerevisiae was consisted of 2563 nodes (metabolites) and 3123 undirectional edges (substrate-product relations).Metabolic network of organisms was reconstructed by Python-2.7 scripts35. And 1850 molecular descriptors were calculated by E-DRAGON38. These molecular descriptors involve different categories including topological, geometrical, electrostatic and other physicochemical molecular properties of the metabolites.The metabolic network topology parameters were calculated by Network Analyzer Plugin in Cytoscape-3.3.0E. coli and S. cerevisiae in the KEGG pathway database33. If one metabolite presents in one of these metabolic pathways, its variable for this pathway is defined as 1, otherwise it is recorded as 0. After removing pathway variables that have the same values for almost all metabolites in our dataset described below, the remaining variable set consists of 81 pathway variables which are subject to further variable selection as below. The metabolic pathway variables remaining after variable selection were used to define a new variable, named as MPF (Metabolite Pathways’ Feature) descriptor. If one metabolite participated in any one reaction among the metabolic pathways corresponding to the selected pathway variables, the MPF descriptor of this compound was defined as 1, otherwise it is defined as 0.Pathway variables were chosen as another type of descriptors work to describe the involvement of the metabolites in specific metabolic pathways. There are 116 pathways in 39. Due to the absence of some type of atoms in all the metabolites of our dataset, some molecular descriptors’ values might be zero or a constant for all molecules, and these descriptors were abandoned. Then the descriptors with a standard deviation of <0.001 should also be abandoned because of too little statistical meaning. After the preprocessing procedures, 1669 descriptors were retained from the 1977 descriptors.Variable selection was performed prior to the construction of the predictive model in order to eliminate redundant variables and pick out the optimal ones40. The confidence intervals of model results are calculated with 20 times.The 130 metabolites are randomly separated into a training set of 91 samples and a test set of 39 samples13 is used for variable selection for the training set. Three rounds of selections by GA were executed. In each round of variable selections, the population size of each generation is 100, the maximum generation is 100, and the mutation rate is 0.01, and the optimization objective is RMSE 41 is applied to filter out irrelevant variables from the 70 descriptors for the training set. In this method, one descriptor which had been deleted from the original 1669 descriptor set was added back into the 70-variables set to construct a new (70 + 1)-variables set, or one descriptor was deleted from these 70 descriptors to obtain a new (70 − 1)-variables set. When one descriptor was added to or deleted from the variable set, the effect of the change was evaluated according to the RMSE  and the optimal set of descriptors for the 91 samples in the training set was developed by the support vector machine (SVM) regression method, using the kernlab package in RQ2)  and RMSE (RMSEp) are employed to evaluate the predictive power of the model.The model developed from the training set was then externally validate by predicting the –logC values of the 39 metabolites in the test set. And in addition, 11 metabolites from 47, hi (Equation X is the n × k matrix of k variable values for n training set metabolites, and xi is the ith row vector of X. The superscript “T” refers to the matrix/vector transpose. The control leverage h* is set as 3k/n.The Williams plot for the SVM model is defined by leverageEquation , to illu2 and RMSE values by the GA variable selection procedures. These descriptors were significant in construction of a SVM regression model, based on a data set of 130 metabolites of the E. coli and S. cerevisiae, which was randomly separated into a training set of 91 samples and a test set of 39 samples. The results of internal LOO and 10-fold cross-validation indicated that the model is robust, while the external validations on the test set showed good prediction powers. Therefore, this SVM model might be useful for prediction of the intracellular metabolites concentration with a well-defined application domain when experimental values are difficult to be acquired.Combining chemical descriptors, topological parameters and metabolic pathways descriptors, a machine learning model can be constructed to predict the metabolite concentration with relative reliability. 14 optimal descriptors are effectively derived from a great amount of DRAGON descriptors and metabolic pathways descriptors according to QSupplementary information