The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions. Metabolic network is the outmost layer of cellular activity from the genome. The genome of a cell is a comprehensive and condensed information base, defining a boundary for the biochemical capacity of the cell. The processing of genetic information passes through several layers of fabrication and regulation before reaching their end products. This is from information to the function, from genotype to phenotype. Metabolic enzymes count for a significant percentage of the end products of genes, and their activity sets the physiology of the cell. Since metabolic network activity is the major representative of cell functionality, it is of great importance to gain as much knowledge as possible on the active metabolic network at a specific cellular state.Systems-based approach to molecular biology has contributed to an increased knowledge of metabolic pathways for an increasing number of organisms, and led to almost complete metabolic networks for a number of major organisms, from yeast to human. Such static networks are available in a condition-independent manner through web-based databases such as KEGG or MetaCyc  to be determined. Under the assumption of steady state, the concentration of each intracellular metabolite is not going to change with time, meaning the sum of rate of reactions producing that metabolite is equivalent to the sum of rate of reactions consuming that metabolite . This is represented mathematically as follows:Given a genome-scale reaction network, the aim is to find the active reaction network at a specific condition or for a specific cell type in a multicellular organism Box . The corBox 1(i)a priori database information on the reactions.At the lowest level of information, we want to know what the structure of the network is, representing it with an undirected  graph in which each node stands for a metabolite and each edge stands for a biochemical transformation. Alternative to the retrieval from the metabolic reaction databases, the structure of the network – both directed and undirected – can also be estimated to some extent by analyzing and reverse engineering the metabolome data without the use of (ii)At a higher level, the information on the stoichiometry of reactions can be incorporated, leading to a directed stoichiometric biochemical network.(iii)Having the stoichiometric structure of the network, we can characterize the metabolic state in more detail by quantifying the metabolic fluxes. In most cases, rather than a unique flux distribution, constraints are set on flux values to shrink the solution space. Such modeling approaches are known as Constraint-Based Modeling. This level of understanding the active metabolic network (structure + flux distribution) has been the area of focus in the research community for more than a decade. In most cases, the information provided at this level has been satisfactory for engineering research to design more efficient cell factories, and also, recently, for medical research to distinguish significant differences between healthy and disease states.(iv)There are, however, certain limitations at the above level although it provides a network activity structure weighted with fluxes. The dynamic behavior of the system cannot be captured, and the predictability power of such models is hampered mainly because they are not considering the role of regulatory mechanisms in controlling the rate of biochemical reactions. In some cases, the regulation of reaction rates plays such a dominant role that it would be hard to make any prediction by just considering the flux-based network activity structure. Here come the kinetic models into the picture, which take enzymatic regulations and metabolite concentrations into account for a dynamic and better prediction of network structure.Our understanding of an active metabolic network can be sorted into several stages of information.The experimental approach is based on stable-isotope (mostly 13C carbon) labeling of the major carbon source, and then tracing the propagation of the labeled carbon atoms down to protein-bound amino acids at isotopic steady state by using mass spectrometry or NMR spectroscopy . Instead of the prediction of flux distributions, these methods, however, may significantly help in the discovery of active metabolic networks in context/tissue-specific cells and in the conditions where a relevant objective function cannot be hypothesized.The rate of an enzymatic reaction inside the cell is a function of several different factors, such as the concentration of substrates, products, and regulators of the enzyme and also the amount of available active enzyme for that reaction. Among these factors, the concentration of active enzymes can be related to the activity of genes through layers of transcription, translation, and post-translational modifications. Transcriptome data are much more accessible and comprehensive compared to the other omics data. Several different research groups have developed different strategies to incorporate transcriptome data into constraint-based models. The idea behind this is that the amount of mRNAs (gene activities) may be correlated with the concentration of active enzymes, and hence this can be utilized to provide additional constraints on metabolic fluxes. At the bottom line, if an enzyme coding gene is not transcribed at steady state, the corresponding reaction should be inactive at that steady state, if there is no other enzyme catalyzing that reaction. This idea was first used by Akesson et al. to set the flux values to zero for those reactions whose corresponding genes were expressed at low levels   to become capable of catalyzing the reactions. This is one of the main reasons behind inconsistency between protein levels and reaction rates. On the other hand, the turn over number  of one enzyme may differ by several orders of magnitude from the turn over number of another enzyme Hoppe, . It meanOne approach to find more specific and physiologically relevant flux distributions is to provide additional constraints by specifying the directionality of reversible reactions. This can be done by taking Gibbs free energies of metabolites into consideration. The Gibbs free energy change of a reversible biochemical transformation (one reaction or a series of reactions) determines the direction of that transformation and its departure from reversibility. The earlier studies assumed standard conditions , and did not explicitly consider metabolite concentrations in the calculation of Gibbs energy changes of reactions due to the scarcity of metabolome data  a better flux distribution can be found thanks to the metabolome-based constraint provided by Eq. One reconciliation approach will be the integrative use of flux-balance equation Eq.  and rearAn approach getting popular to construct genome-scale kinetic models is ensemble modeling. This modeling approach constructs kinetic models from an ensemble of models, and filters the inconsistent models out by using the results of perturbation experiments (Tran et al., In summary, both bottom-up and top-down discovery of metabolic networks have come a long way in the last 20 years, providing the scientific community with a number of computational methods, as reviewed in this review. Considering the improvements that are being experienced both on the coverage and precision of metabolome data, the coming decade will witness an exponential increase in the number of metabolome datasets, similar to what was experienced with transcriptome data in the last decade. This review aimed at drawing attention to this point, as ways to reconcile the two major metabolic network discovery approaches will gain increasing importance.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.


Here, we deal with homeostatic balance phenomena from a metabolic point of view and we present a new computational model merging three single-cell models, already available from our research group: the first model reproduced the metabolic behaviour of a hepatocyte, the second one represented an endothelial cell, and the third one described an adipocyte. Multiple interconnections were created among these three models in order to mimic the main physiological interactions that are known for the examined cell phenotypes. The ultimate aim was to recreate the accomplishment of the homeostatic balance as it was observed for an in vitro connected three-culture system concerning glucose and lipid metabolism in the presence of the medium flow. The whole model was based on a modular approach and on a set of nonlinear differential equations implemented in Simulink, applying Michaelis-Menten kinetic laws and some energy balance considerations to the studied metabolic pathways. Our in silico model was then validated against experimental datasets coming from literature about the cited in vitro model. The agreement between simulated and experimental results was good and the behaviour of the connected culture system was reproduced through an adequate parameter evaluation. The developed model may help other researchers to investigate further about integrated metabolism and the regulation mechanisms underlying the physiological homeostasis.The biochemistry of a system made up of three kinds of cell is virtually impossible to work out without the use of  This fact, in turn, has forced a review of the concept of a cell as a mere collection of components to be treated separately Systems biology applies quantitative, mechanistic modelling to study genetic networks, signal transduction pathways and metabolic networks with the aim to yield a more global, in-depth and integrated understanding of biological systems. From a systems biology perspective, for example, all living organisms share a notable feature, which is afforded by the interconnection and co-execution of different functionalities: a high level of robustness against external and internal perturbations in silico biology”. The introduction of computational methods and instruments to complement the traditional experimental ones accelerates the generation of new hypotheses, and the research validation cycle in silico analyses are validated by experimenters, and the results are used to update the computational model exploited, thus involving various scientific fields System level understanding of complex processes is common in engineering disciplines and relies heavily on mathematical models, informatics and methods from systems theory. The biological field is indeed facing an increased use of mathematical models and computer simulations; therefore, this approach is often referred to as “In silico biology also offers many advantages over in vivo and in vitro experiments: quick predictions of phenomena of interest, a great reduction of production costs, no ethical problems , and relating them to the systems theory language, our group developed HEMETβ  Literature offers many attempts to model and simulate molecular processes, ranging from genetic regulatory networks to metabolic pathways, and presents several software packages, such as MIST In vivo, many physiological and pathophysiological processes involve a great network of signalling molecules, through which cells belonging to different tissues can communicate and cooperate in spite of physical distance in vitro or in silico models are needed to gain insight into these complex systems and to counteract pathological states with effective therapies. In a simplified model of energy substrate metabolism in the visceral region, three main tissues have to be considered as the first basic elements to reproduce: hepatic, adipose and endothelial tissues in vitro model of this three-tissue system already exists concerning the glucose and lipid metabolism, the aminoacidic degradation and the main synthetic functions in vitro human visceral region to study cross-talking phenomena and their effect on metabolic regulation. They showed this culture system to be suitable for baseline studies with cell monocultures in vivo glucose and lipid metabolism and of homeostatic mechanisms.More simple in silico model as a coexistence and functional integration of the three different metabolic profiles considered, attempting to recreate the homeostatic balance observed in vitro. At first, each cell type was modelled as a standalone entity, with its own proliferation rate and specific metabolic pathways. The standalone models were then “connected” by modelling molecular interactions among them through metabolite uptake/release phenomena, and different kinds of cellular connections, thus generating a 3-way  model. Then, the model was validated against available experimental data coming from literature datasets about the dynamic in vitro model described above. Available data concerned only extracellular species in the culture medium besides measurements of cell population growth.In this paper, we introduce a new computational multi-scale model that merge the previous three single-cell models  with adequate interconnections, relating metabolic regulation to molecular biochemical mechanisms. We aimed to reproduce the metabolic behaviour of three distinct cell culture systems only connected by the medium fluid flow (dynamic 3-way connected cell culture system): we conceived the final et al.Our model implements metabolic networks using nonlinear differential equations and systems theory approach, and linking biochemical pathways only to enzymatic reactions and metabolite inter-change. The presented model was created following the basic structure and design principles of previously developed models like HEMETβ in vitro model Chemical stimuli  and physical ones  were integrated in quantitative terms to the complex metabolic interconnected blocks chains. The modular layout, also in agreement with the corresponding −1) are the Michaelis-Menten constant and the maximum catalysis rate of enzyme, respectively.As hinted before, the basic blocks derived from Michaelis-Menten kinetic model for irreversible enzymatic reactions:−1) and −1) are the maximum catalysis rate that can be reached in direct and inverse reaction, respectively. IfFor reversible reactions, the Michaelis-Menten equation we referred to is:Competitive enzymatic inhibition was introduced in the model by In general, metabolic pathways involve reactions with multiple substrates and/or products and other equations have to be defined. Supposing to deal with an in vivo and existing biochemical data usually originate from different experimental settings, cell types and state of cells.In this model, the maximum rates in direct and inverse reactions are supposed equal (in accordance with their similar order of magnitude) and these parameters include correction factors to count other non-instantaneous processes, such as gene expression, that slow down global processes in vivo and/or in vitro, as we did developing CREPE In accordance with systems theory approach, it is possible to reproduce entire metabolic pathways as series of ODEs , in which metabolite concentrations are state variables and 2) and with excess substrates concentration, hence considering cell culture proliferation, nutrient uptake glycolysis, pentose phosphate pathway, degradation of proteins, urea production, glycogen, fatty acid and albumin syntheses, whereas excluding the other metabolic pathways, such as β-oxidation. ENMET mimics the same principal metabolic pathways, with the exclusion of glycogen and albumin synthesis and the addition of shear stress generation, nitric oxide production and endothelin-1 secretion, connecting mechanical stimuli responses  to other biochemical reactions. ADMET includes the following metabolic pathways: glucose and aminoacid uptake, glycolysis, pentose phosphate pathway, Krebs cycle, aminoacid degradation, fatty acid and triglyceride synthesis, lipolysis, and the energy function. In particular, this model mimics the behaviour of a human white fat cell that responds to various compositions of the culture medium, with glycerol and free fatty acid release, which are the main indicators of fat cell activity. In the present work, we focused our attention on the integration of metabolism for the three different cell phenotypes and we dealt with these metabolic pathways: a suitable revision of cell culture proliferation models, the maintenance of glycemic balance, the uptake or release processes for specific metabolites, the triglyceride/free fatty acid cycle and glyceroneogenesis. These topics are individually discussed below. The additions regarding detailed carbohydrate metabolism and other metabolic aspects were necessary to describe interactions among different cell types. To take a couple of examples: we had to implement anabolic pathways, such as gluconeogenesis, to account for a glucose release process; similarly, we had to introduce glycerol metabolism pathway to validate our model against experimental glycerol concentration data. Novelties and improvements introduced with regard to the model presented are described in details in the following sections. S1, S2 and S3 Tables).Here is a synthesis of the main metabolic pathways already reproduced in the previous three different virtual cells. HEMETβ model describes the hepatic cell metabolism in standard conditions  to test hypotheses and estimate parameter values.−1) and the negative term relating to Numerical data about hepatocytes derived from the study −1 and Estimated mean coefficient values were used for the implementation phase: Data about endothelial cells proliferation came from the study Adipocytes were similarly treated: experiments considered in the subsequent validation phase involved only mature adipocytes, while culture conditions and the duration of experiments did not allow cells to differentiate, as well explained and confirmed by cell counting tests in the work For endothelial cells and adipocytes, cell proliferation model was described by the following equation:et al. did not report numerical data about cell growth, but they affirmed that cell counting tests were performed demonstrating that the dynamic flux did not influence the examined cell proliferation processes.These simple equations about cell proliferation may clash with the detailed enzymatic step introduced in the model (see below), but we choose not to take into account other aspects, e.g. turn over of different metabolites, in order to make our final model less complex. We instead focused our modelling efforts on metabolic pathways. The main organs taking part in energy metabolism differ in their specific enzyme content: each one is specialized for storing, using or producing different kinds of energy substrates such as triglycerides (TGs), proteins or glycogen. Because glucose and fatty acids are alternative substrates, sometimes competing, many interactions among metabolic pathways involve them For example, one of the main roles of the liver is the maintenance of glycemic levels: this organ is able to perceive a fasted state and then enhance glucose synthesis and its exportation to other tissues. In co-cultures described in The transportation of molecules through the cell membrane bilayer is of paramount importance for the organism vitality The liver is one of the main regulators of metabolite flux, removing metabolites from blood or releasing them in it. In particular, fatty acid uptake phenomena in hepatocytes have been intensely investigated, for example Kinetic studies, employing almost-physiological conditions, have shown that FFA uptake rates can best be interpreted as the combination of a saturable component and a linear non-saturable one 3H]-oleate uptake assays. As shown in in silico model.In this work, in order to simplify fatty acid transport modelling, only a saturable kinetic was chosen with the mediation of a single kind of protein, CD36, for all three cell phenotypes involved. Kinetic parameters for long-chain fatty acids were studied for adipocytes, hepatocytes 2/s) and the membrane thickness 14C]-labelled solute assays and radioactivity measurements. In this work, we assumed a diffusive process thoroughly mediated by aquaglyceroporins to mimic glycerol transport in hepatic and adipose tissues. Permeability coefficients for AQP7 In our body, adipocytes are one of the major sources of glycerol, which is in turn one of the main substrates of hepatic gluconeogenesis During fasting in all mammals, triglyceride stored in adipose tissue is hydrolysed by a hormone-sensitive lipase to produce free fatty acids and glycerol. Glycerol is exported to the liver, whereas in the adipose tissue there is a considerable re-esterification of FFA depending on intracellular glycerol-3-phosphate concentration. The triglyceride/fatty acid cycle includes local intracellular recycling, within the adipose tissue, and extracellular or systemic recycling, through the formation of TGs in the liver. Intracellular recycling appears to represent almost 20–30% of the total, whereas non-adipose tissue recycling (primarily hepatic) accounts for 50% of re-esterification of fatty acids in healthy adults after an overnight fast The liver can readily use the glycerol as a source of glycerol-3-phosphate thanks to a considerable glycerol kinase activity. In adipose tissue, instead, there is a special pathway for the generation of glycerol-3-phosphate from precursors other than glucose: it is termed glyceroneogenesis and it is an abbreviated version of gluconeogenesis. Indeed, the tissue contains both pyruvate carboxylase and the cytosolic form of phosphoenolpyruvate carboxykinase. Therefore, any variation in adipocyte glucose uptake and in glyceroneogenesis flux, notably affects triglyceride/fatty acid cycle in these cells In order to reproduce hepatic cell behaviour with regard to metabolic homeostasis, we introduced the following aspects in the model: gluconeogenesis, glycogenolysis, glycerol metabolism, FFA and TG syntheses, glucose uptake and release, fatty acid uptake, triglyceride release and glycerol uptake.Gluconeogenesis is the generation of glucose from non-carbohydrate carbon substrates such as pyruvate. In this work, only two substrates of that kind were considered: aminoacids and adipose glycerol. This way proceeds in opposite direction with respect to glycolysis and three specific enzymes counteract glycolytic irreversible kinetic steps, whereas the other seven gluconeogenic reactions are catalysed by the remaining glycolytic enzymes. The gluconeogenic enzymes introduced are pyruvate carboxylase , phosphoenolpyruvate carboxykinase  and fructose-1,6-bisphosphatase .in vitro) and α-1,6-glycosidase . The result is the production of glucose and glucose-6-phosphate.Glycogenolysis involves mobilization and degradation of glycogen stores to produce directly available energy substrates and implies the breakage of As discussed above, glycerol uptake was modelled through the first Fick's law as a pore mediated (AQP9) diffusive process. Once in the hepatocyte, glycerol can become a gluconeogenic substrate through the combined action of glycerol kinase  and of phosphate glycerol dehydrogenase . The ATP-dependent phosphorilation catalyzed by glycerol kinase gives glycerol-3-phosphate, which can also become a substrate for TG synthesis.Fatty acid transport instead was treated with a saturation kinetic through transmembrane protein CD36. FFA and TG syntheses were then modelled following the kinetic approach reported in The hepatic metabolic pathways implemented are summarized in In order to reproduce endothelial cell behaviour with regard to metabolic homeostasis, we considered the following metabolic pathways: gluconeogenesis, FFA and TG syntheses, lipolytic action of lipoprotein lipase, glucose uptake and release, fatty acid uptake.On the inner surface of capillaries, circulating TGs can be hydrolyzed to form glycerol and FFA thanks to the action of the extracellular enzyme lipoprotein lipase . The neighbouring cells can reabsorb energy products. This metabolic aspect is involved only in the 3-way connection scheme, where hepatic TGs act as enzymatic substrate. In regards to fatty acid release, we referred to data reported in study All the other pathways were implemented as described above for the hepatocyte. The endothelial cell metabolism implemented is summarized in In order to reproduce adipocyte behaviour with regard to metabolic homeostasis, we dealt with the subsequent pathways: glyceroneogenesis, glucose uptake and release, fatty acid uptake and release, intracellular re-esterification of fatty acids, glycerol release.For the glyceroneogenesis, we exploited enzymatic blocks already implemented in the available adipocyte model: pyruvate carboxilase, phosphoenolpyruvate carboxykinase (now reversible), and glycerol-3-phosphate dehydrogenase. The adipose intracellular component of the previously described triglyceride/fatty acid cycle accounts for about 25% of the re-esterification of the total TGs produced by the cells themselves. As done for the hepatocyte, glycerol release was modelled as a pore mediated (AQP7) diffusive process for glycerol coming from TG hydrolysis.The whole adipocyte metabolism implemented is summarized in As we will see later, a key point of the validation phase is the comparison between simulated metabolite concentrations and the measured ones for glucose, fatty acids and glycerol. For each metabolite in the culture medium, a corresponding extracellular integrator was implemented in the model. Initial condition values were specified basing upon available experimental data in vitro cell systems in dynamic conditions: single-cell simulations, which were compared with baseline monoculture studies carried out in the presence of the medium flow, and simulations for a three-cell in silico model, which were compared with results from the 3-way connected culture system, were examined.At first, in this work, single-cell simulations were compared with baseline monoculture experiments focusing on static conditions. Then, two kinds of configuration were studied to investigate about the metabolic homeostasis of the same As the configuration changed, from single-cell model to three-cell model, so did state equations for metabolites of interest . Extracellular metabolite concentrations for the 3-way connected system were described through the following three state equations:S2 Table). All the values used for new kinetic enzyme parameters are listed in where ,  The validation phase was based upon three studies The duration of all their experiments was equal to 48 h, so we assumed that one simulation time unit was equivalent to 4 h and each simulation lasted 12 time units. We used ode 23 s (stiff/Mod.Rosenbrock) as numerical integration method. The cell simulators did not take into account any change of the culture medium.Extracellular concentration data were available from the three works for four different sampling times  and for glucose, fatty acid and glycerol concentrations. We extracted their numerical values exploiting tables or graphical analysis of plots reported. Extracted values were expressed as means with respective standard deviation and they were often affected by an unmodifiable large deviation Escherichia coli and Saccharomyces cerevisiae. In our model, intracellular metabolite concentrations were modelled through corresponding integrator blocks: given the lack of precise data, we hypothesised that cells were empty at the beginning of the simulations and we therefore set the initial condition value to zero for each intracellular integrator.Currently, as for intracellular metabolite concentration, quantitation of all the metabolites in a cellular system in a given state at a given point in time is impossible, because of the lack of simple automated analytical strategies that can effect this in a reproducible and robust way. The main challenges are the chemical complexity and heterogeneity of metabolites, the dynamic range of the measuring technique, the throughput of the measurements, and the extraction protocols 3 hepatocytes and 200 mg of adipose tissue (about 300•103 cells) were cultivated in static wells or inserted in modular bioreactor chambers (MCmB 2.0) with extremely low shear stress for cell cultures. 80•103 endothelial cells were seeded in static conditions or transferred to a laminar flow chamber for dynamic tests.First of all, we validated single-cell models against data from baseline studies in silico models.Proliferation data were not available from the same work for a comparison with simulated data. We implemented the proliferation models discussed above. Then, according to what is affirmed in in silico aiming to reproduce the difference between the presence (dynamic conditions) and absence (static conditions) of the culture medium flow (S1(A) and S1(B) Figures). For each case tested, a different set of initialization values was associated to that variable: the sets consisted of heuristically estimated correction factors that were applied to enzyme kinetic parameters (S1(C) Figure). The function of the correction factors was to modify selectively kinetic parameters according to different culture conditions and to reproduce the main features of metabolic profiles experimentally observed. The identification of correction factors to apply allowed us to make hypotheses about the differential activation of metabolic pathways in the culture conditions considered.As far as metabolic profiles are concerned, a new pop-up variable to select was introduced In silico, we obtained the same behaviour through an adequate regulation of kinetic parameters for both glucose and fatty acid uptake processes. In vitro, hepatocytes showed glycerol uptake over time, principally in dynamic conditions S2(A) and S2(B) Figures).For hepatocyte monocultures, we obtained a general and good agreement between experimental and simulated behaviours in the static as well in the dynamic situation and The endothelial cell simulator included shear stress parameters in dynamic conditions. As far as glucose and fatty acid metabolism was concerned, the model was able to reproduce the mean experimental behaviour observed In silico, we indeed regulated glucose metabolism parameters. Fatty acid release was present in both static and dynamic experimental conditions S3(A) and S3(B) Figures). Once again, the implementation of aquaglyceroporin-mediated glycerol transport improved the results. It was not possible to enhance glycerol release further due to the general consistency of the model. As already seen for endothelial cells, zero initial condition for intracellular glycerol integrator was a drawback for the model itself.For adipocytes, the simulation results had a fair agreement with experimental data, principally in dynamic conditions. In the adipocyte culture, glucose concentration was stable in static conditions whereas there was a net glucose uptake in the dynamic ones, probably due to the effect of the culture medium flow in silico model was subsequently validated involving the examined three cell phenotypes at the same time. We referred to experimental data reported in in vitro culture system aiming to reproduce the metabolic homeostasis of the visceral region. This system involved hepatocytes, endothelial cells and adipocytes: 250·103 hepatocytes and 50·103 adipocytes were inserted in modular bioreactor chambers (MCmB 2.0) with extremely low shear stress for cell cultures, whereas 25·103 endothelial cells were transferred to a laminar flow chamber for dynamic tests. The chambers were connected together through the culture medium flow.The in silico model, we set the values of enzymatic parameters at the same values used for monoculture simulations in dynamic conditions, even if a small reduction of fatty acid metabolism for adipocytes was necessary in order to maintain the consistency of the model.At first, in the three-cell Experimental data showed the presence of a homeostatic regulation mechanism: changes in glucose concentration were negligible, with hepatic tissue preserving normal glucose levels Corresponding simulation results differed from experimental observations, showing only a cumulative glucose uptake with respect to dynamic monocultures, a complete removal of free fatty acids in the medium in contrast to a small release from endothelial and adipose cultures, and a net glycerol decrease in the medium as it is typical of the hepatic population. It was evident that the hepatic population played a leading role in the shaping of the overall metabolic profile. Moreover, the zero-initial conditions for intracellular integrators had a large effect on it  of the pop-up variable created to distinguish the static (A) from the dynamic (B) culture conditions for cell monocultures. It is followed by a screenshot (C) of a Matlab file (.m) showing the association of the pop-up variable value to a set of initialization values for enzymatic parameters.(TIF)Click here for additional data file.S2 FigureMeasured  and simulated glycerol trends in the culture medium for hepatic monocultures. Upper figure refers to static conditions, the other one describes dynamic conditions. Solid line represents the simulated data, while circles (for the static case) and squares (for the dynamic case) represent the corresponding experimental data. Measured values are expressed as means ± standard deviation for experiments run at least in triplicate: numerical values are reported in (TIF)Click here for additional data file.S3 FigureMeasured  and simulated glycerol trends in the culture medium for adipose monocultures. Upper figure refers to static conditions, the other one describes dynamic conditions. Solid line represents the simulated data, while circles (for the static case) and squares (for the dynamic case) represent the corresponding experimental data. Measured values are expressed as means ± standard deviation for experiments run at least in triplicate: numerical values are reported in (TIF)Click here for additional data file.S1 TableThe full list of all enzymes and consumption terms used in the modelling with their corresponding equations. In reaction kinetics (both in equilibrium and non-equlibrium conditions), oxidated-form cofactors  are considered in saturation, then they not play an active role on the regulation of catalysis rates. It is a good approximation, in fact they are in large quantity in cells. Enzymatic parameters: (DOCX)Click here for additional data file.S2 TableThe full list of state equations used in the modelling.(DOCX)Click here for additional data file.S3 TableThe full list of stoichiometric equations used in the modelling for aminoacid degradation.(DOCX)Click here for additional data file.


Mass spectrometry-based metabolome profiling became the method of choice in systems biology approaches and aims to enhance biological understanding of complex biological systems. Genomics, transcriptomics, and proteomics are well established technologies and are commonly used by many scientists. In comparison, metabolomics is an emerging field and has not reached such high-throughput, routine and coverage than other omics technologies. Nevertheless, substantial improvements were achieved during the last years. Integrated data derived from multi-omics approaches will provide a deeper understanding of entire biological systems. Metabolome profiling is mainly hampered by its diversity, variation of metabolite concentration by several orders of magnitude and biological data interpretation. Thus, multiple approaches are required to cover most of the metabolites. No software tool is capable of comprehensively translating all the data into a biologically meaningful context yet. In this review, we discuss the advantages of metabolome profiling and main obstacles limiting progress in systems biology. Metabolomics offers a framework for analyzing individuals with a specific phenotype at a molecular level in cell biology, personalized medicine, and systems biology ,2,3. MetSystems biology is a novel subject in the field of life science, which aims to understand biological systems as a whole entity, under a variety of conditions . The avaMetabolites are regarded as the final response of a biological system to environmental changes or gene regulations and, thus, an aberrant metabolism can be linked to disease severity and phenotypes. The metabolome is, thereby, the most predictive of phenotype ,4. MetabMetabolomics and systems biology-driven studies have a great potential for hypotheses generation and dissection of signaling networks in an unbiased or untargeted fashion . The maiIn this review, we will focus on the advantages and challenges in metabolome profiling for systems biological approaches and cover various techniques and their limitations with a special spotlight on real-time metabolome profiling as a very promising new strategy.Typically, a sample preparation protocol contains a solvent extraction step, ultrafiltration, solid-phase extraction and, optionally, a chemical derivatization step . The optDerivatization methods apply reagents, which chemically modify and transform a specific target structure. Thus, derivatization is one of the most effective method to improve the detection characteristics of metabolites in GC- or LC-MS, binding to LC columns, or to stabilize compounds. For example, formaldehyde can be used to label the amine groups through reductive amination. Silylation is a common derivatization reagent in GC-MS, as it transfers a wide range of functional groups, even though some products are not very stable .By derivatization, a sensitivity gain by several orders of magnitude can be achieved. The drawbacks are that an additional derivatization step is introduced and not all metabolites can be derivatized by only one reagent. Furthermore, the mass spectra are different in terms of parent and fragment masses from their endogenous counterparts. Thus, databases for endogenous compounds cannot be applied for reference matching and derivatization-specific databases are rare or have to be built from scratch.A combination of derivatization and internal standards (ISs), named isotope-coded derivatization (ICD), is a good alternative for relative quantification, in order to improve analytical precision, . The13C, 15N or deuterium)-labeled counterparts of compounds of interest. The ISs have the same chemical behavior as their endogenous counterparts, do not show drastic chromatographic isotope effects, and have the same retention time. The application of ISs is widespread, but one drawback is that they are not 100% labeled. Thus, an additional and indistinguishable unlabeled peak of typically 1%–2% intensity, depending on the impurity ratio may occur in the mass spectrum. Therefore, the amount of introduced ISs should be reduced to a minimum in order to avoid these interferences. Furthermore, isotopically-labeled ISs are not practical for large profiling approaches, since they are expensive and not available for the majority of compounds or it is impossible like for de novo identifications. To circumvent this bottleneck, only a few ISs, matching to similar compound groups, are selected. Ionization suppression or enhancement is matrix-specific and shows fluctuations over the elution time. This is not always properly reflected by only using a few ISs.In mass spectrometry, ISs are the method of choice for absolute or relative quantification, calibration curves, recovery rate determination, or to correct for matrix effects. Typically, ISs are isotopically -MS and liquid chromatography (LC)-MS, as well as nuclear magnetic resonance (NMR) spectroscopy .NMR is generally accepted as the gold standard in metabolite structural elucidation, due to its high selectivity, analytical reproducibility, non-destructive nature, and simplicity of sample preparation. However, it suffers from relatively low sensitivity compared to MS .Mass spectrometry-based approaches for metabolic profiling have the advantages of a high sensitivity and selectivity, as well as high throughput and depth of coverage . GC-MS hDue to its high sensitivity and wide range of molecules that can be analyzed, the usage of LC-MS has expanded rapidly over the past ten years ,29.E. coli extract [Bingol and colleagues introduced a strategy, which combines direct infusion MS with NMR (SUMMIT MS/NMR) for the identification of unknown metabolites in complex mixtures . First,  extract . This ap extract . Thus, i extract ,37.The metabolome is a collection of compounds with diverse physicochemical properties; no single retention mechanism is adequate to resolve complex sample mixtures that vary widely in their polarity, charge, and stability . UsuallyReversed-phase liquid chromatography (RPLC) is extensively used, because of its reproducible and predictable retention times, wide applicability to various classes of metabolites, and mobile phase compatibility for direct coupling to electrospray ionization mass spectrometry (ESI-MS) . The majThe combined use of HILIC and RPLC is an optimal method to increase metabolome coverage, because it is ideal for retaining extremely polar and lipophilic compounds . The maiTo overcome these problems, Haggarty and colleagues applied a method where a sample is injected onto both, RP and HILIC columns in tandem in a single injection . To solvThis tandem column approach was already successfully applied with quadrupole, time of flight (TOF), and orbitrap mass analyzers ,41,42,43de novo analyte identification, where no prior knowledge about compounds is necessary. In contrast, targeted metabolomics aims to detect a priori selected analytes, on the basis of known parent and fragment masses, with a method termed multiple reaction monitoring (MRM). Once optimized for every transition, the MRM approach has the advantage of selective and sensitive measurement of the selected analytes in complex samples. The specificity is achieved by fragmenting the analyte and by monitoring both parent and one [Experimental approaches can be classified into non-targeted and targeted metabolomics. Non-targeted metabolomics approaches are widely used for  and one ,46,47,48 and one ,51,52,53Savolainen and colleagues developed a GC-MS method using a high scan speed , which combines targeted and non-targeted metabolomics into one single accurate, reproducible, and reliable method . This meDirect sample injection on high-resolution mass spectrometers is an effective way to maximize analytical throughput, since sampling, sample preparation, and measurements are time-intensive and difficult to automate ,55. The E. coli extracts [Fuhrer and colleagues established a robust platform for high-throughput, accurate mass, and non-targeted metabolome profiling of extracts . This meextracts .Link and colleagues went a step further and performed real-time metabolome profiling by direct injection of living bacteria, yeast, and mammalian cells into a Q-TOF MS in order to reveal metabolic switches between starvation and growth . They de13C tracers, such as the main substrates for mammalian cell culture, glucose and glutamine, can be used [In vivo fluxes are calculated by mathematical models that describe the label propagation from isotopic patterns and extracellular transport rates [The original method of metabolic flux analysis (MFA) studies systems at a metabolic steady state, by determining metabolite transport rates within and out of tissues, cells, or their sub-compartments, which are then balanced in reaction networks to provide estimates of intracellular fluxes . The lim be used . Labeled be used . In vivort rates .Isotope labeled-MFA of co-cultures can be performed, in order to determine inter-species metabolite exchange and population dynamics. This method simplifies experimental and analytical procedures for co-culture flux analysis, improves accuracy, and allows flux elucidation in systems where physical separation of cells or proteins is difficult .Recently, we applied an isotope based flux analysis in order to determine the enzymatic activity of mutated pyrroline-5-carboxylate synthase (P5CS), a protein of the mitochondrial proline cycle. The mutation causes an autosomal-dominant form of cutis laxa with progeroid features. The flux analysis revealed that mutated cells had a reduced P5CS enzymatic activity leading to a delayed proline accumulation .The advantage of fluxomics is that the turnover of virtually any metabolite can be studied by isotope labeling. New pathways or disease-causing genes can be elucidated, a perfect method for specific tasks. Systems biological approaches are mainly hampered by the complexity of the entire system, as most pathways are not straightly leading from A to B, introducing a bias and are, hence, difficult to compute.Mass spectrometry imaging (MSI) is a spatially-resolved label-free technique, which can directly identify and map the spatial distribution and abundance of known or unknown molecular species in tissues . MetabolLimited by the absence of a comprehensive MSI method, normalization, and sample preparation techniques suitable for all metabolite classes, we can barely talk about a systems-wide approach, which covers the metabolome. Derivatization enables increased detection of metabolites that are hard to ionize, but may cause analyte suppression or delocalization . Neverthin silico prediction, and usually contain MS/MS data in order to facilitate metabolite identification. The most established repositories for biological compounds are METLIN, featuring 242,000 entries, 14,000 with high-resolution MS/MS data [Metabolite databases are repositories of metabolite information, based on experimental confirmation or /MS data , the Hum/MS data , and Mas/MS data .in silico-generated compound databases are available as well, such as MINE, containing over 571,000 compounds [in silico databases can give rise to too many false-positive identifications just by chance. Based on our experience, databases contain several erroneous entries. Especially, the MS spectra are sometimes of poor quality, they are recorded by different groups with different MS instrumentations, and the provided instrument settings are sometimes very scarce.Several ompounds , MyCompoompounds . MatchinAll data derived from metabolome profiling studies should be made publically available in according depository databases. Thus, full transparency is guaranteed and datasets can be reused for future identification, quantification, secondary analysis, or systems biology approaches. Data storage, maintenance, and harmonization are critical points, since abandoned or broken depositories would cause a significant loss of knowledge. Currently, just a few metabolomics-specific depositories, such as MetaboLights  and PMR Due to the complexity and chemical diversity of the metabolome with metabolite concentrations spread over a wide range of magnitudes, identification is still a challenge. In addition to the variety of instruments and their different operation and acquisition methods, even more programs exist for data processing, typically for a specific class of data. For example, different instrument settings used in LC-MS, such as collision energy, resolution, targeted, non-targeted, and fragmentation methods, such as CID (collision induced dissociation), HCD (higher energy collision dissociation), ETD (electron-transfer dissociation), and PQD (pulsed-Q dissociation) ,78,79,80One of the best, but time consuming, options is to create an instrument specific MRM method for a set of preselected metabolites. The advantage of using up to three MRMs and their MRM ion ratios, which are stable properties between transitions  for robuDue to its complex nature, non-targeted metabolomics has to be linked to advanced chemometric techniques, to reduce the data complexity into a smaller set of manageable signals . Analytiin silico target identification methods, including chemical similarity database searches, are used, such as CSNAP  [As target identification is one of the most critical steps, ulldown) . Severalulldown) . The iniulldown) .At this point, a large knowledge gap exists in the translation from changes in metabolite concentration in body fluids to organ biochemistry and (molecular) physiological interpretation . ExistinWhat does it actually mean, if metabolite X from a distinct pathway is found to be decreased? On one hand, downstream enzymes could have an increased activity or, on the other hand, the enzyme producing metabolite X could have a decreased activity; both can lead to a decreased level of metabolite X. Enzyme activities can be influenced by their specific product by steric inhibition/feedback-inhibition or activation, and thereby guarantee a balanced homeostasis in the cell. This strategy avoids large metabolic changes with a potential negative effect for the cell.Many metabolites play a role in several pathways and are the product or substrate of many different enzymes or processes. Thus, it is a challenge to pinpoint an altered metabolite to a specific pathway or enzyme. Nevertheless, the pathway information may already give the correct answer, or at least a hint, for a biological question. Changes in metabolite abundances can be mapped to specific pathways, thereby providing mechanistic information of the process under study. Data derived from metabolic profiling can be complemented by genome, proteome, clinical, and environmental data, which supports the discovery of potential biomarkers that would not have been identified with targeted studies alone .www.metaboanalyst.ca), permits a comprehensive metabolomic data analysis, visualization and interpretation, including complex statistical calculations [Metabolome profiles have the advantage to detect unknown compounds (shotgun) and alterations on a global scale (shotgun and targeted). As many metabolites usually originate from several different processes, specific methods have to be used for validation, like a knockdown of the according enzyme or isotope-labeled MFA. Many bioinformatics tools are continuously created to address several important questions in the metabolomic field, like interpreting profiling data. MetaboAnalyst (ulations . Metabolulations . Integraulations  is a tooBiomarker discovery is driven by applying new instrumentation, protocols, and software tools, in order to find novel and specific key metabolic features, which are characteristic for specific pathological conditions, diseases, or cancer. Surprisingly, the clinical breakthrough is still out of sight. Nevertheless, metabolomic key features indicative for diseases such as depression , schizopThis can be accomplished the best by an integrative approach taking many omics subdisciplines into account . Thus, aThe metabolome, lying closest to the phenotype and the most predictive of phenotype, is of emerging interest for systems biologists. Metabolomics has a long lasting importance in the field of biomarker detection and, finally, for drug treatments. No universal instrument or method exists yet, which is capable of measuring the entire metabolome at once. Currently, we are still in the status of metabolomic profiling, intensive parallelization of different approaches and methods are transforming metabolomic profiling steadily into metabolome profiling. For a holistic view, integration of genome, transcriptome, proteome, and/or metabolome datasets can significantly enhance the insight into biological questions and molecular interactions between these disciplines. The integration of different molecular profiling data into a comprehensive entity is still challenging, especially in the bioinformatics area. Knowledge about the function of metabolites and, specifically, their multiple biological interactions are still missing. Thus, interpretation of results has to be handled with care. Our review highlights the advantages of metabolome profiles for systems biology approaches, as well as the current pitfalls, such as data interpretation and translation of results into a biologically-useful meaning.


Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (The online version of this article (doi:10.1007/s11538-014-9960-8) contains supplementary material, which is available to authorized users. Comprehensive methods using high-throughput analytical instruments have made it possible to simultaneously measure cellular metabolite concentrations (or their relative quantities referenced by peak intensities or heights) Fiehn . Using tThe simplification of mathematical modeling using power-law representations, such as saturable and synergistic (S)-system or generalized mass action (GMA)-system representations in the framework of biochemical systems theory (BST) Savageau , probablSeveral methods that use time-series data of metabolite concentrations to estimate the kinetic parameters of the S-system equations have been proposed Chou . For exaThe present study, therefore, proposes a simple method for constructing a mathematical model in an S-system equation model, in which the number of parameters to be estimated is decreased significantly in a special case, and the probable behaviors of unmeasurable metabolite concentrations can also be predicted. A mathematical model is constructed in non-dimensionalized S-system equation form, and the number of unknown rate constants for influxes and effluxes is reduced using the constraints derived from a network structure. Kinetic orders are fixed at a value of 0.5 or The evolution of intracellular metabolite concentrations, mentclass2pt{minimSavageau , b. OnceWhen the system has a steady state, Eq.  can be tConsider a metabolic reaction network with a linear structure consisting of the metabolites Let us consider a metabolic reaction network where metabolites mentclass2pt{minimIt is not easy to determine all the kinetic parameters experimentally in a relatively large-scale system. As the first step of the performance evaluation of the PENDISC method, therefore, the present work assigns an average value of 0.5 or The transient behaviors of metabolite concentrations in a network system are mainly governed by the structure of a network. For example, in a linear structure where the metabolites are lined up, variations in the metabolite concentrations are propagated in downstream direction. The magnitudes of these concentration values and the times, at which an increase or decrease in the concentration is reversed, are strongly controlled by the reaction kinetics. In such variations, the rate constants are responsible not only for the magnitudes of metabolite concentrations at each time point but also for shifting reaction curves in the direction of the time axis. On the other hand, the kinetic orders are closely associated with the shapes of the reaction curves, rather than their shift. Thus, the rate constants given in this estimation play an important role in compensating for the differences in the calculated values generated as a result of setting the kinetic orders at 0.5 or For parameter estimation in a relatively large-scale metabolic reaction system, it is very important to reduce the number of unknown parameters as much as possible. This will enhance the rate of convergence, decrease the number of parameter values grouped together, and reduce the estimation time. In an S-system model consisting of Consider the S-system equations derived from the linear network, as shown in Fig. S1 (Supplementary Information 3). The equations and initial values are given in Supplementary Information 1.Consider the S-system equations derived from the network structure with a branched metabolic pathway, as shown in Fig. in vitro reconstitution in the model plant A. thaliana. The performance of the PENDISC method is investigated by considering the time-series data obtained from in silico calculations as experimental data. The equations and initial values are given in Supplementary Information 1.The aspartate-derived amino acid biosynthetic pathway in plants is controlled by several feedback inhibitions and activations, and forms a relatively complicated network structure Fig. . The matThe calculations are performed using a g++ compiler running on Ubuntu Linux 12.04 with Intel(R) Core(TM) i7 CPU 870@2.93 GHz. The Levenberg–Marquardt method is applied to the parameter estimation using a C program adopted from the literature . Data points were removed one by one from the 11 time-series data for all metabolites , and parameters were repeatedly estimated using the remaining 10 time-series data. The results indicated that this method can estimate parameters successfully. Among these removal operations, the performance of the PENDISC method decreased most when the data at Finally, to verify whether this method with fixed kinetic orders is practically applicable, the predictive simulations were performed using the constructed mathematical model. The concentrations of The branched metabolic pathway model with inhibition and activation Fig.  was usedThe final values of the mentclass2pt{minimAny analytical method cannot measure every metabolite concentration in a pathway network. It is, therefore, important to test whether the PENDISC method is applicable to a case where there are some unmeasurable metabolite concentrations in the network.Consider a case where mentclass2pt{minimThe converged values of When a value of the same order of magnitude as the initial values  of other dimensionless metabolite concentrations was assigned to Measured metabolite concentrations usually contain biological variations and analytical errors. The effect of noise on the probability of convergence was investigated using the branched metabolic pathway model with inhibition and activation Fig. . Twenty-We further consider case where metabolite concentrations contain biological variations and analytical errors, and some of the metabolite concentrations are unmeasurable in the branched metabolic pathway model with inhibition and activation. Twenty-one time-series data with random noise of up to The results indicate that the PENDISC method has high potential for handling both noisy and unmeasurable metabolite concentration data. The method does not require us to use true parameter values in the first step of parameter estimation and provides calculated results close to the behavior of the time-series data of metabolite concentrations, which will allow us to estimate better parameter values and then construct a useful mathematical model to analyze metabolic reaction systems.l-aspartyl-4-phosphate concentration, The aspartate-derived amino acid biosynthesis illustrated in Fig. entclass1pt{minimal-aspartyl-4-phosphate Below is the link to the electronic supplementary material.


A mathematical model consisting of a microbe’s entire metabolic map can be rapidly determined from whole-genome sequencing and annotating the genomic material encoded in its DNA. Flux-balance analysis (FBA), a linear programming technique that uses metabolic models to predict the phenotypic responses imposed by environmental elements and factors, is the leading method to simulate and manipulate cellular growth in silico. However, the process of creating an accurate model to use in FBA consists of a series of steps involving a multitude of connections between bioinformatics databases, enzyme resources, and metabolic pathways. We present the methodology and procedure to obtain a metabolic model using PyFBA, an extensible Python-based open-source software package aimed to provide a platform where functional annotations are used to build metabolic models . Backed by the Model SEED biochemistry database, PyFBA contains methods to reconstruct a microbe’s metabolic map, run FBA upon different media conditions, and gap-fill its metabolism. The extensibility of PyFBA facilitates novel techniques in creating accurate genome-scale metabolic models.Microbiological studies are increasingly relying on  The metabolic summary of a genome was limited to a few tables of higher metabolic categories. Genome-scale metabolic networks have the potential to completely change our perspective of microbial genomics and of the meaning inferred from a genome sequence , ATP production, or any other output of the system, the system of equations representing the cell must produce a solution that results in flux through that single equation that represents the objective function; the optimization is typically to maximize the amount of flux through that equation. In modeling bacterial cells there are almost always more reactions than there are compounds (whose concentrations are unknown) that describe the system. For example, the Citrobacter model we recently published recently contains 1,399 reactions (columns) and 1,301 compounds (rows) , described elsewhere in this special issue have become the enotypes . The reas (rows) . Therefos (rows) .1, and IBM ILOG CPLEX Optimization Studio  , the comn Studio  is not tn Studio . There an Studio , KBase , GenBank files, GFF files, or RAST genome directories.The list of functional roles in a genome can be downloaded from the RAST website in several different formats: for example, from the After identifying the protein encoding genes present in the organism, and assigning functions to those proteins, the enzyme complexes that are created by those proteins must be characterized. EC numbers  are mostFigure 1). For example, the functional role “Phosphoenolpyruvate-protein phosphotransferase of PTS system (EC 2.7.3.9)” encoded by the ptsI gene in Escherichia coli is involved in several different complexes each associated with the import of a different sugar ; the Ubiquinol-cytochrome C complex requires ten different functional roles each encoded by a separate gene ; and the role “Alkaline phosphatase (EC 3.1.3.1)” encoded by the phoA gene in E. coli is in a complex by itself . The first step in identifying the reactions that are encoded by a genome is therefore to convert the functional roles associated with the proteins identified in the genome to enzyme complexes that are functional in the cell. Comparably, each reaction in a cell can require one or more complexes, while each complex can be involved in one or more reactions, thus creating another many-to-many relationship. For example, the complex created by alkaline phosphatase is responsible for many dephosphorylation reactions  while the dodecomeric glutamine synthetase catalyzes a single reaction .Enzyme complexes can be formed by one or several functional roles, and each functional role can be involved in one or more complexes, illustrating a many-to-many relationship  and reactions or pathways can be obtained from several public resources, such as EXPASY2 , the KEG2 . The stoichiometric matrix provides the first level of constraint on the metabolic system — it contains only those reactions and their associated metabolites present within the network, defining the feasible space of phenotypes the system can express. The cells of the matrix represent the relationship between each of the compounds and each of the reactions in the network; thus, a reaction that is not included in the stoichiometric matrix is not included in the model. All phenotypes recognized in the cell must be included in the stoichiometric matrix for an accurate metabolic model.A genome-scale metabolic model starts with a list of reaction equations, compounds, and compartments, and for the mathematical solution we convert that to a Citrobacter model discussed earlier  included in the Citrobacter model. The cells that contain a zero have been left blank for visual purposes.To construct the stoichiometric matrix, all of the compounds used in all the reactions are stored in the rows of a matrix. All the reactions used in the model are stored in the columns of the matrix, and the individual cells contain the stoichiometry of each compound in each reaction, with negative values indicating that the compound is consumed in the reaction; zero indicating that the compound is not involved in the reaction; and positive values indicating that the compound is produced by the reaction. Most of the values in the stoichiometric matrix are zero because most of the compounds are not involved in many reactions. The dimensions of the matrix are the number of compounds and the number of reactions; thus for the  earlier  the matrCitrobacter model includes 175 compounds in the extracellular compartment.Compounds in the stoichiometric matrix are also denoted by the compartment in which they are located to differentiate which compounds are required inside the cell from those required outside the cell. The location also provides a convenient mechanism to constrain the model based on which compounds are in the media and which can be transported (see below). Bacterial models typically use just two compartments: intra- or extra-cellular, while models of Eukaryotes often include other compartments, such as the mitochondria or chloroplast . For theFigure 2 and provided in the supplementary table as a tab-separated text file . An example stoichiometric matrix is shown in The media in which the organism is growing defines another constraint imposed upon the metabolic model. Encoding defined media is straightforward, and recipes for almost all media [including complex media such as lysogeny broth (LB) media] are available online. The only difficulty is to ensure correlation between the compound names used in the media formulation and the compound names used in the metabolic reactions. One approach to overcome that obstacle, used, for example, by the Model SEED, is to use a separate database of compounds with unique IDs. By default, of course, the media components have an extracellular location, and the presence of transporters is required to move them into the cell; another constraint imposed on the genome-scale metabolic model. Historically, identification of transporter proteins is challenging because they are largely homologous to each other and only differ by their substrate specificity . LatitudThe linear programming solution to the genome-scale metabolic model requires that compounds are taken up from the outside , and also that some compounds are secreted from the cell (waste products). Moreover, each compound in the stoichiometric matrix must be balanced for a solution to the problem. Therefore, a set of unconstrained reactions are generated that consume all external compounds in the model, but do not do anything with those compounds . These reactions also provide the media compounds as if from nowhere (in practice this is akin to the media compounds diffusing toward the cell as they are consumed). These reactions are sometimes called drain flux reactions or external reactions, and in PyFBA they are called uptake and secretion reactions. Since the set of uptake and secretion reactions is dependent on the external compounds produced by the model and the external compounds present in the media, it is generally calculated for each model upon creation.reaction bounds that limit the flux through that reaction. In most cases, the reaction bound also assigns the directionality of the reaction. As shown in Figure 2A, the direction of reaction r1 is set from left to right. This is controlled by setting the lower bound of reaction 1r to zero , thus preventing reaction 1r from producing compounds A and D by the linear solver. Furthermore, an alternative approach to designating the directionality of a reaction is to limit the flux through the reaction by negating the coefficients in the equations. The limits are conventionally positive if a reaction proceeds from left to right; negative if a reaction proceeds from right to left; and positive and negative if a reaction is bidirectional. The reactions bounds are applied to the linear solver before the stoichiometric matrix is solved.In solving linear equations of underdetermined systems, a defined solution space has to be provided that limits the parameters applied to each of the reactions. It is highly unlikely that one, or a few, reactions would have extremely high fluxes through them while the other reactions in the cell have moderate or low fluxes. Therefore, each reaction in the stoichiometric matrix is controlled by a set of Figure 3). The benefit in this method instead of completely removing the uptake/secretion reaction from the stoichiometric matrix is oxygen produced by intracellular reactions could still be secreted from the cell while still preventing oxygen uptake from the environment.The media formulation (described above) is typically encoded as a list of compounds that are present in the media, and this is used to determine the reaction bounds of the reactions that transport these compounds into the cell. As we noted, there are a series of uptake and secretion reactions that mimic the diffusion of a media compound toward the cell, and the diffusion of a waste product away from the cell. By setting the bounds of these reactions appropriately, we can control the growth conditions of the cell. If the reaction bounds for diffusion of media components toward the cell are set to allow production of those components and if they are required for growth, they can be consumed. Similarly, the reaction bounds are set to only allow consumption of waste products so that they are removed from the media at the same rate that they are created. The reaction bounds can be manipulated to mimic gene knockouts and environmental changes. For example, simulating an anaerobic environment is accomplished by removing the model’s input oxygen capability by setting the bound to zero , and thus overall (with the exception of compounds that are taken up or secreted) the concentration of the compounds sums to 0. This is the steady state mass balance that allows FBA to perform without any kinetic information, and also acts as another constraint on the system. To ensure that the compound consumption is equal to production, the compound bounds are set so that the concentration of the compound can not be greater or less than zero.A central tenet of FBA is the assumption that the change in each compound concentration is equal or balanced , however, with different outcomes represented by alternate equations it may be more suitable to minimize the flux through that equation. The biomass equation reaction is typically added as the first or last row in the stoichiometric matrix.A single reaction is designated as the objective function and is included in the stoichiometric matrix. This is usually the biomass reaction  added to the stoichiometric matrix, the system can be solved by linear programming. The solvers return the value of the flux through the reaction designated as the objective function, with a value above one generally indicating growth, and a value approaching zero indicating no growth .gap-filling. The gap-filling step of building the model is the point where most of the erroneous assertions about the metabolism of an organism are made. A selection of reactions has to be added to the metabolic network derived from the genome annotations, and the selection is often made with little supporting evidence. Consequently, there are many different approaches for identifying the reactions missing from a model, including identifying missing reactions from expression information  can be used to prune unnecessary reactions in the model.Citrobacter a gap-filling approach may be to identify all functional roles annotated in all other Citrobacter genomes and the likelihood that the functional role should also be in this Citrobacter genome . Reactions can be suggested for addition to the model based on those annotations and their likelihoods. In addition to suggesting new reactions to the model, the PyFBA gap-filling approach is extensible with new approaches as they are developed.PyFBA includes several different modules for gap-filling, sequentially suggesting reactions to add to the model. For example, there is a set of 109 predefined reactions that are present in every model tested to date and that can be added to gap-fill any model. If an organism is known to grow on a particular media, reactions are also identified to be added to the model that transport the media components into the cell. As noted elsewhere, the identification of transport reactions from genome sequences is problematic, and therefore using phenotype data ensures accurate representation of the biology of the organism in the model. Reactions are identified that connect to orphan compounds – compounds that are only associated with a single reaction in the network. If the orphan compounds are consumed they either need to be produced by another reaction or transported into the cell by a transport reaction. If the orphan compounds are produced in the model they either need to be secreted as waste (via a transport reaction) or consumed in another reaction. A gap-filling approach is also included in PyFBA that analyzes the presence of all the subsystems in the reaction network, and proposes reactions that complete the subsystems in the model. A general framework is also available that accepts tuples of annotations from other genome(s) and the probability that those annotations are associated with the current model and proposes reactions based on those annotations. For example, when building a model of O(log n) complexity (where n is the number of reactions that are proposed to be added) as it is based on binary search, however, under the worst conditions the algorithm will approach O(n) complexity as all the reactions in the model have to be tested.There are many different approaches that can be used to suggest reactions to be added to models, but most approaches will suggest many more reactions to add than are actually needed for growth. Therefore, excess reactions, that are not absolutely essential for growth, should be trimmed from those suggestions. PyFBA includes a recursive algorithm to reduce a set of proposed reactions from the initial proposal to just those reactions that are absolutely required for growth. Under the best conditions, this algorithm provides O(n) complexity (where n is the number of reactions in the model) as each reaction is tested one at a time. It is also worth noting that another method previously developed to identify network redundancy and insubstantial reactions, but is not yet implemented in PyFBA, is flux-variability analysis  are added using the two methods PyFBA.fba.reaction_bounds and PyFBA.fba.compound_bounds. Finally, the stoichiometric matrix is solved using the linear programming solver.Starting with a genome annotated in RAST, download the annotations as a spreadsheet from the RAST job overview page. This provides a file that can be opened in any office suite of software and contains information about all of the genes identified in the genome, including the location of the protein encoding gene , and most importantly, the function of the protein. We connect the functional roles in the Figure 4 illustrates the typical workflow for PyFBA alongside the key module functions used at each step.Gap-filling is available in PyFBA using the PyFBA.gapfill modules. As described above, these modules provide several different mechanisms for gap-filling as well as methods to bisect the reactions proposed to be added to your model for growth. 7 (Supplementary Material Citrobacter model discussed previously (8 (Supplementary Material We have created an iPython Notebookeviously . A seconGenome-scale metabolic modeling extends the usefulness of the base microbial genome annotation by identifying the biochemistry that is actually happening in the cell. The conversion of functional roles to reactions highlights our understanding of the cellular metabolism, while the gaps that remain and need filling before the model “grows” highlight areas where we have less detailed understanding of the biochemistry. PyFBA is a novel Python based implementation of flux balance analysis that can be easily extended and modified to provide new metabolic modeling capabilities.Gap-filling chooses reactions to add to the model in order to generate growth, and with a database of over 30,000 reactions from which to choose there are many solutions that could result in growth of the model. Therefore, in order to be meaningful, FBA approaches must be constrained using real biological and physicochemical constraints determined from experimentation. Whole genome sequencing and bioinformatics analyses rapidly identify metabolic genes for building draft genome-scale metabolic models . Genome-Identifying reactions during gap-filling inadvertently leads to an opportunity to improve genomic annotations. Regions where DNA sequences were not assigned a function due to types of problems with the annotation step, such as the sequence lacking known homology to another organism, can be connected to the gap-filled reactions from PyFBA. This positive feedback has not been efficiently captured by previous software but could provide current databases a means for improving their annotations, narrowing the search space of functional roles the genetic material may be associated with. Future endeavors in model reconciliation will support associations between gap-filled reactions and unannotated genome content.There are several limitations to the previous versions of genome-scale metabolic modeling that the new iterations of these models overcome. For example, most models lack an integration of regulatory processes in the networks — if a gene is present it is assumed to be expressed and functional. Recent models include transcription factors and gene expression information alongside traditional models . AnotherDC worked on PyFBA development, algorithm design, prepared and wrote manuscript, created figures, and data analysis. JE provided SEED biochemistry resources and discussion. CH provided SEED resources and discussion. RO provided RAST consultation. TO provided algorithm design discussion. RE worked on PyFBA development, algorithm design, wrote manuscript, data analysis, code testing, and code distribution.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.