Pseudomonas and Azotobacter, and these organisms may represent an alternative alginate source in the future. The current work describes an attempt to rationally develop a biological system tuned for very high levels of alginate production, based on a fundamental understanding of the system through metabolic modeling supported by transcriptomics studies and carefully controlled fermentations.Alginate is an industrially important polysaccharide, currently produced commercially by harvesting of marine brown sea-weeds. The polymer is also synthesized as an exo-polysaccharide by bacteria belonging to the genera Pseudomonas fluorescens was studied in a genomics perspective, using an alginate over-producing strain carrying a mutation in the anti-sigma factor gene mucA. Cells were cultivated in chemostats under nitrogen limitation on fructose or glycerol as carbon sources, and cell mass, growth rate, sugar uptake, alginate and CO2 production were monitored. In addition a genome scale metabolic model was constructed and samples were collected for transcriptome analyses. The analyses show that polymer production operates in a close to optimal way with respect to stoichiometric utilization of the carbon source and that the cells increase the uptake of carbon source to compensate for the additional needs following from alginate synthesis. The transcriptome studies show that in the presence of the mucA mutation, the alg operon is upregulated together with genes involved in energy generation, genes on both sides of the succinate node of the TCA cycle and genes encoding ribosomal and other translation-related proteins. Strains expressing a functional MucA protein  synthesize cellular biomass in an inefficient way, apparently due to a cycle that involves oxidation of NADPH without ATP production. The results of this study indicate that the most efficient way of using a mucA mutant as a cell factory for alginate production would be to use non-growing conditions and nitrogen deprivation.Alginate biosynthesis in The insights gained in this study should be very useful for a future efficient production of microbial alginates. Pseudomonas is a genus of Gram-negative bacteria with features that have made them interesting to a wide community of researchers for a long time. Pseudomonas spp. range from important human pathogens (P. aeruginosa), via biocontrol agents and plant commensals useful in agriculture (P. fluorescens) to one of the most widely used “cell factories” for production of high-value-added products in industrial biotechnology (P. putida), and the genus is characterized by a great metabolic versatility.Pseudomonas are also notable and well-studied in their capability to form biofilms  [A more recent development in the quest for (semi-)automation of the reconstruction process is the RAVEN Toolbox software suite [Agren bmitted]  that intP. fluorescens SBW25 genome  and ATP synthase) and one  generates GTP from ATP for consumption in alginate biosynthesis. It thus seems that all the top ranking enzymes suggested to be transcriptionally regulated can be linked directly to the uptake and conversion of the carbon source into alginate when the organism is grown on glycerol. This is in contrast to the situation on fructose as described above, and it could indicate that although only a few biochemical steps are different between the pathways leading to alginate from fructose and glycerol, respectively, the organism seems to regulate the metabolism surrounding the alginate biosynthetic precursors and cofactors quite differently on the two carbon sources. This could be of relevance if metabolic engineering of the alginate biosynthesis were to be pursued.When the wild type and the P. fluorescens SBW25 genome-scale metabolic model. Genetic engineering was used to construct selected strains with alterations in both the anti-sigma factor mucA and alginate-specific genes, and the physiological response was characterized by chemostat cultivations and transcriptome analysis. Integration of the metabolic model with the experimental data allowed us to obtain new insight about the metabolism of this producer of the commercially interesting biopolymer alginate. Firstly, we could show that the yields of alginate are close to the theoretical stoichiometric optimum, demonstrating the very high efficiency of the alginate biosynthetic machinery in this organism. We could also, however, see that the biomass production of P. fluorescens SBW25 is markedly suboptimal in the wild-type strain, and by the use of random sampling analysis in the transcriptome data set we could give strong indications that this suboptimality on fructose is related to a cycle in the central metabolism, effectively wasting cellular energy in the form of NADPH. This cycle does not seem to be active when the organism is grown on glycerol. The down-regulation of the suspected NADPH oxidizing cycle was observed in the mucA strains, adding to the putative regulon of this global regulator.We have described the reconstruction and application of a P. aeruginosa and P. putida models. Alginate is a significant virulence factor in P. aeruginosa infections, and the emphasis on alginate biosynthesis in the (non-pathogenic) P. fluorescens system described here could support the clinical research on this important pathogen. Also, alginate is a valuable industrial product, and the optimization of alginate production in bacterial systems is of great commercial interest. As compared to the other major alginate-producing bacterial genus, Azotobacter, the relative simplicity that applies to both engineering and cultivating P. fluorescens – taken together with its highly efficient alginate biosynthesis as described here – should provide an argument for its applicability in an industrial context. The heterologous expression of Azotobacter alginate epimerases could then be used to produce high yields of alginates with tailored monomer sequences.The model described in this work, validated by comprehensive continuous-culture experimental data and integrated with transcriptome analyses, nicely complements the existing E. coli were performed using the rubidium-chloride method (available at http://www.neb.com). Matings and selection of double recombinants were performed as described earlier  by the iSB1139. The model is available for download in both Excel format and in SBML at http://www.sysbio.se/biomet. Flux balance analysis of the SBW25 model was performed with the linear programming solver Mosek  for Matlab .The final model was designated The authors declare that they have no competing interests.SEFB participated in construction of the custom expression array, performed microarray data analysis, contributed to analysis of physiological parameters, constructed the genome-scale metabolic model and performed comparisons with other species, and drafted the manuscript. SB performed the random sampling flux analysis, the calculations about theoretical yields and wrote part of the manuscript. HS and ØJ had major roles in cultivations, while HE was responsible for strain constructions. PB was involved in experimental design. TEE was leading the cultivation activities, JN was leading the modelling parts and SV was project leader for the overall project. All authors were to varying degrees involved in the planning, design and evaluation of the project, and read and approved the final manuscript.An overview of the strains and plasmids used in this study.Click here for fileThe complete microarray data, both in raw and quantile normalized formats.Click here for fileA spreadsheet comparison and alignment of the reactions present in the published Pseudomonas genome-scale models iMO1056, iJN746 and iSB1139.Click here for fileDescription of the growth media used for cultivations, and standard operating procedures used in sampling for transcriptome analysis, as well as analysis of alginate produced and remaining carbon source in the chemostat cultures.Click here for fileThe literature references used in the manual curation of the draft genome-scale metabolic model.Click here for file


Escherichia coli. Experimental data based on microarrays, signaling components and extracellular metabolites are used to estimate kinetic parameters. A newly designed strain was used that adjusts the incoming glucose flux into the system and allows a kinetic analysis. Based on the results, prediction for intracelluar metabolite concentrations over a broad range of the growth rate could be performed and compared with data from literature.Metabolism and signalling are tightly coupled in bacteria. Combining several theoretical approaches, a core model is presented that describes transcriptional and allosteric control of glycolysis in  Glc, represents a good nutritional state of the cell, while a high phosphorylation state represents hunger conditions. In addition to EIIAGlc, another protein coupled to the PTS, the FruR protein , acts as a global regulator. This protein senses the concentration of fructose-1,6-bisphosphate in the cell and controls the expression of several enzymes of glycolysis and gluconeogenesis.In bacteria, metabolism and signaling processes are tightly coupled to allow the cell to adapt efficiently to new environmental conditions. This is especially evident by the tight coupling of the metabolic and signaling functions of the bacterial phosphoenolpyruvate (PEP)-dependent phosphotransferase system (PTS). The PTS is an important uptake system, e.g., for the preferred carbon source glucose, but at the same time it represents a sensory system that signals the metabolic state of the cells. For this function, the coupling of the phosphorylation state of the different PTS proteins to the PEP to pyruvate ratio of the cell is important. A low phosphorylation state of the PTS, especially of EIIAE. coli is well understood from its structural properties, genetic organization and signalling characteristics, and therefore provides excellent conditions for a quantitative modelling approach. Experimental data from array experiments are available and sensor outputs as well as metabolites could also be measured. However, data is still limited to specific experimental conditions. Having a mathematical model available that is validated with experimental data from different sources , it should be possible to predict the behavior for unmeasured (or hardly measurable) metabolites from model simulation studies for a large range of input conditions. Moreover, a model can help understand the architecture and allows designing new properties of the system by genetic modifications.Central metabolism in E. coli can be characterized by two signalling systems where fructose-1,6-bisphosphate, PEP and pyruvate are involved as major signalling molecules. As an extension of the previous work [Glycolysis in ous work ,3,4 thatConsideration of transcriptional control of the glycolytic enzymes via transcription factor FruR and determination of the influence of the activity of FruR on gene expression via network component analysis (NCA).Structural analysis of the extended model. The influence of transcription factor FruR (Cra) on gene expression and metabolism is studied.vs. growth rate) with a newly designed strain.Experimental verification of the characteristic curves for carbohydrate uptake , PEP and pyruvate (both determine the degree of phosphorylation of protein EIIA of the PTS). In addition, glucose 6-phosphate is taken into account as entry component into glycolysis.The model describes the steady state behavior of important metabolites of glycolysis in G6P, phosphoenolpyruvate PEP, pyruvate rvP, and a lumped component of the PTS, enzyme IIA EIIA; E stands for the respective enzyme, r for the rate. The equations consider that a carbohydrate (PTS as well as non-PTS sugars) is fed into glycolysis via glucose-6-phosphate. The carbohydrate is metabolized by a sequence of steps with pyruvate as the final component. In reaction glyr reversible reaction steps catalyzed by the enzymes fructose bisphosphate aldolase, triose phosphate isomerase, glyceraldehyde-3-phosphate dehydrogenase, phosphoglycerate kinase, phophoglycerate mutase and enolase are lumped (glyE).The stoichiometric equations are as follows: for the metabolites are calculated. Matrix D has the following entries:pfkr, glyr, pykr, and pdhr, and the columns consider G6P, F16BP, PEP, and rvP. While in a previous study [D. All other ε values, ε11 and ε33, are based on mass action and have positive values.First the influence of regulation of gene expression and of allosteric control is studied. Based on the approach described in Material and Methods, the derivatives us study  the condE. coli, all entries of the Jacobian matrix were determined and analyzed [ε32. Matrix D is related to the inverse of the Jacobian and a similar pattern can also be found here.The following derivatives are calculated:analyzed . It turnTo further explore these equations, a more detailed analysis was done with the following kinetic approximations :(4)andiκ for genetic control, all other exponents for mass action and allosteric control) which are not necessarily integers. Since PEP is involved in signaling, the behavior of PEP is analyzed in more detail. As discussed in [upr could be obtained under the following conditions:κ3 and α) should be larger than the strength of control on the lumped glycolytic reaction glyr (κ2 and β). The second constraint requires that the latter one is reversible. For a detailed calculation, see Appendix.In many studies, classical saturation kinetics are chosen for the kinetic rate laws. Here, saturation is not explicitly taken into account and kinetic rate laws are approximated with power law exponents  and acetate (squares). Three phases can be seen and are marked with vertical lines: After 10 h, glucose is depleted; at time point 15 h E. coli switches to growth on acetate, and after 20 h acetate is depleted. Plots B/C shows the corresponding activities of the transcription factors Crp and FruR, respectively. During growth on glucose, Crp activity is low and after depletion of glucose, Crp activity becomes more and more active. In contrast, FruR activity is high during growth on glucose andjp as well as the fraction jf (jμ) with j = 1,7 of uptake via the non-PTS system could be estimated. Fraction jf (jμ) is defined as:Considering now a simultaneous growth with both uptake systems, the uptake rate can be written as a sum:ata from ), and mijf could be determined perfectly in experiments 2–6  available allows to estimate parameters of the uptake reaction kinetics for the non-PTS and the PTS uptake systems. Measurements of the degree of phosphorylation of protein EIIA were performed in the exponential growth phase. Here, glucose is abundant and it is expected that the enzymes are saturated. The non-PTS system is assumed constitutive, but based on the experiments the uptake is dependent on PtsG induction. Since no details are available for this lumped kinetic expression, an inhibition by PtsG is taken into account (black box approach). For the PTS system, a two-substrate mechanism is used as before [exGlc >> K1, K21). The respective uptake rates are estimated (see above) and measurements for PtsG and PEIIA are available. Therefore, the four unknown kinetic parameters  could be estimated based on the seven experiments  and the influence of FruR on the kinetic expressions . The latter two parameters are determined above via the NCA approach. From literature [δ = 2. Rearranging Equation (12) and with results from above leads to:β = 1. As a result, the influence of the feedforward activation by fructose-1,6-bisphosphate can be calculated to α = 1.53 . Taking into account that the sigmoidal behavior of the pyruvate kinase was described with δ = 2 that corresponds to the number of domains of the system, the value for α is in good agreement since it should also reflect the number of the domains .From Equation (12) it can be seen that terature , it is kbehavior  and we sPtsK and 0EIIA from literature [. The values show a high capacity of the PTS chain in comparison with glycolytic fluxes. It is expected that sudden changes in the uptake rate should be seen immediately also in the degree of phosphorylation. This was demonstrated experimentally [From Equations (10) and 12) the following estimation could be done: the follmentally . The couHaving the model parameters for the uptake systems available, the complete system including PtsG induction kinetics (see Appendix) was simulated with fine-tuned parameters . First, time course data with simulated and experimental data are shown in Shown are data for optical density (plot A), extracellular glucose concentration (plot B), PtsG (plot C), and EIIA phosphorylated (plot D) for no IPTG (left) and maximal IPTG concentration (right). The calculation of the optical density in plot A shows a very good agreement with the experimental data; glucose uptake for high concentrations of IPTG could not be reproduced accurately as the yield coefficients for each experiment were different and in the calculations, a mean value was used. Furthermore, the fit of the parameters for glucose uptake  also shoSteady state values  are considered and compared with simulation results . Plot A For increasing values of IPTG, the system moves from one curve to the other, indicating a change of the uptake system based on the induction of PtsG: the degree of phosphorylation decreases while the growth rate increases. A comparison of the experimental data with the simulation data reveals differences in the growth rate. The first (experiment 1) and last (experiment 7) data point are fitted with high accuracy while in the other experiments larger deviations could be seen. As indicated before, the main reason for the deviations is most probably the variation in the yield biomass/glucose and the choice of simple rate laws. E. coli to predict semi-quantitatively the steady state behavior for central metabolites in dependence on the growth rate . Glycolysis is an important reaction system since some of the metabolites such as fructose-1,6-bisphosphate, PEP and pyruvate are closely related to signalling units that trigger the important transcription factors FruR and Crp. While experimental data for metabolite concentrations [Mathematical modeling can be a powerful tool to analyze systems that are hardly observable. Here, we use a simple core model for glycolysis of trations  and mathtrations  are avaitrations ,21, howetrations  a detailtrations  was prestrations . To summIn previous studies, we already analyzed the input/output relationship to describe a characteristic curve that relates growth rate for a number of carbohydrates and the degree of phosphorylation of EIIA, an important metabolite of the PTS. Other groups focus on structural properties of the same system  or on thκ. A crucial issue is the verification of the elements of the coupling matrix. In most studies—also in the first publication that introduces the method—the signs of the entries were not validated with entries of databases. In our previous study [icd gene (isocitrate dehydrogenase in the TCA) is different from the data base entry. The values for pfkA, eno, gap, and pyk are determined from the experiments and are taken into account in further parts of the study. Interestingly the values for eno and gap are similar and are integrated into a single value for the lumped glycolytic reaction glyr.Results from NCA allow to determine the influence of transcription factor activities on a set of selected genes. Data that were used in a different study were complemented with new experiments. In this experiment, glucose was pulsed to a culture growing under glucose limitation. Glucose was immediately taken up and after 10 h glucose was depleted. Acetate is produced during growth on glucose and consumed after 15 h. The different energy sources lead to different transcription factor activities that could be estimated with NCA. Furthermore, the influence of each transcription factor on each gene is described with a coupling factor us study  we alreaκ2 and κ3) and kinetic properties .A structural analysis of the core model including all regulatory features was performed to calculate the behaviour of the intracellular metabolites of the core model . While the signs for fructose-1,6-bisphosphate and pyruvate are fixed and show positive values, it is expected that both metabolites show increasing values if the uptake rate is increasing. In contrast, the signs of PEP and glucose-6-phosphate are not fixed. Since PEP is an important metabolite for the PTS and the PEP/pyruvate ratio determines the degree of phosphorylation, the behavior of PEP in dependence on the growth rate was further explored. In a previous study, we analyzed the robustness of a simplified version of the model and it turns out that a monotonous decreasing course of PEP is more favourable with respect to robustness . In thisglyr was studied with numerical simulations. Parameter estimation reveals that condition (6) was fulfilled. Doing so, the course of PEP depends on the value of K20 (equilibrium constant of the reversible glycolytic reaction glyr). K20 (plot A) and the course of phosphorylated EIIA. As can be seen in K20 in the range of the growth rate considered here. In all other cases, PEP is monotonously increasing. The course of phosphorylated EIIA shows a very low sensitivity with respect to K20 (plot B). The same is true for fructose-1,6-bisphosphate (data not shown).Based on the first “rough” estimation of the model parameters, the influence of the reversibility of the glycolytic reaction E. coli was starved for carbohydrates and nitrogen. This situation reflects a move from a high growth rate to a very low growth rate. E. coli is growing on glucose and lactose, the dynamic of PEP could also be monitored. For both growth phases, the level of PEP is nearly constant. In an A-stat experiment different metabolites of central metabolism were monitored [Experimental data to verify the simulations are found. Several studies focus on single growth conditions or on specific stimulations of the system ,19. In  E. coli onitored . AlthougWith a newly designed strain that allows to adjust the level of PtsG, it was possible to “move” from one branch of the characteristic curve of phosphorylated EIIA (non-PTS case) to the other branch (PTS case). The experiments are designed such that glucose is taken up by the PTS and also by non-specific uptake systems. With the data of these experiments, it was possible to approach different points on the uptake kinetics for parameter estimation. While the data for the degree of phosphorylation were taken from previous experiments, the data with the new strain confirmed the relationship already published.The approach shows that an understanding of the intracellular network is required to design and modify such network and offers new possibilities in medical and biotechnological applications. galP gene was transduced from the strain JC7623Δ into the genomes of the strains LJ121 (LJ110Δ(ptsG::cat) man-8 zea-225::Tn10) and LJ130 (LJ110 Δ(manXYZ::cat)) [ptsG transporter gene for glucose uptake. The wild type genes encoding the galactose ABC transporter MglBAC, which is able to transport glucose with very low affinity, are present in all strains. The plasmids pRR48 or pRRGH (pRR48 with the ptsG gene under the control of a tac promoter [A deletion of the Z::cat))  to generpromoter ) were trptsG expression), JGA1/pRRGH , and JGA2/pRR48  were monitored in minimal medium with ampicillin and either glycerol or glucose as a carbon source. Utilizing glycerol as carbon source, the strains showed similar generation times . Whereas the growth rates in minimal medium supplied with glucose revealed the expected differences due to different ptsG genotypes  the addition of IPTG to the medium resulted in an induction of the tac promoter in front of the encoded ptsG gene and hence to an increase in available EIICBGlc protein. This was again correlated with an enhanced rate of glucose uptake and utilization, resulting in increased growth rates .The growth behavior of the strains JGA1/pRR48  to the entire signal of EIIA  for each sample.For determining the degree of phosphorylation, cells were harvested from cultures growing with various induction conditions as described above and tested in a second Western blot analysis. In this case, the sample preparation was carried out according to a protocol that is suitable for immediately freezing the phosphorylation status of proteins in the sample. The final step involved the quantification of the Western blot signals using the LICOR Odyssey software. In each approach and Western blot the amount of EIICBE. coli LJ110 were grown in a 1 L chemostat culture at 28°C with 8 g/L glucose at a dilution rate of 0.072 1/h. Medium composition was essentially as described in [2 and CO2 concentrations in the off gas were monitored continuously. After the culture displayed steady state growth as displayed by stable biomass and stable CO2 production, glucose was pulsed to 10 g/L. Immediately before and at defined time points after the pulse samples were taken for microarray analysis as well as for the determination of extracellular metabolites.Array data for NCA were compiled from a glucose pulse experiment. Cells of Extracellular metabolites glucose, acetate, formate and lactate were measured by using the respective enzymatic test kits of r-biopharm according to the instructions provided by the manufacturer but scaled for the use of 96 well plates. Microarray analysis was performed on microarrays purchased from Agilent.in vitro transcription) reaction using aminoallyl-dUTP antisense aRNA were generated and subsequently coupled with fluorescent dye Cy3. Cy3-labeled aRNA was hybridized to Agilent’s 8 × 15k E. coli microarray  for 16 h at 68°C and scanned using the Agilent DNA Microarray Scanner. Expression values (raw data) were calculated by the software package Feature Extraction 10.5.1.1  using default values for GE1_105_Dec08 extraction protocol.Total RNA was isolated from the cells using the protocol accompanying the RNeasy Mini Kit . Quality and integrity of the total RNA was controlled on an Agilent Technologies 2100 Bioanalyzer . 200 ng of total RNA were applied for Cy3-labelling reaction using the MessageAmp II-Bacteria Kit according to supplier’s recommendation . As a result of IVT   was appldiauxic growth on glucose and lactose glucose pulse experiment (this study)growth on acetate N and the number of selected transcription factors is m. The dynamics of a single gene (i) is described with an ordinary differential equation:jik are related to the strength of each transcription factor jTF binding to the respective control sequence: if jik > 0 then the transcription factor is an activator, while jik < 0 points to an inhibition. Assuming that the dynamics of mRNA is faster than protein synthesis, a steady-state assumption holds true and the following equation results after fixing a set point (subscript 0):2) leads to:K is N × m coupling matrix representing the effect of each transcription factor on the respective gene, and TF is an  m × kt matrix of transcription factor activities (kt is again the number of available data points). The aim is now to decompose matrix mRNA to get both K as well as TF. Note that the entries of K have to be specified before  the algorithm starts, that is, the structure of the model has to be given and NCA determines the coupling strength and the time course of transcription factor activities. To solve the problem, the following objective function is minimised:NCA allows a semi-quantitative description of gene expression based on measured transcriptomic data. In brief, the approach is as follows: The number of selected genes is al paper .m = 3 transcription factors . After filtering out genes with no entry in the database  the final model contains N = 33 genes, representing the central metabolism. The choice is based on prerequisites of the algorithm and the experimental conditions chosen. Therefore, transcription factor Fnr related to genes that are involved in oxygen consumption is not considered. Also, several other transcription factors cannot be integrated or are not significant, e.g., considering transcription factor Fis showed that this transcription factor has only marginal influence on the calculations.The data set considered in this study comprises 50 transcriptional units (75 genes) and c, the non-negative rate vector r'(c) of external and internal rates and a fixed stoichiometric matrix N’ [r' will be partitioned into an unknown rate vector r of internal rates and into a known rate vector rup of free input fluxes, here, uptake rate and known rates for biosynthesis. The stoichiometric matrix N’ will be partitioned accordingly into sub-matrices N and upN. The admissible steady states of the network are then given by the solutions r ofN of the stoichiometric matrix N’ to be an invertible square matrix so thatAccording to a previous study the metabolic network of the form2is consiupr on the concentrations c(upr) in steady-state might be calculated from denotes the Jacobian matrix (or elasticities) of the rates ir with respect to the concentrations jc:D(c(upr)) is invertible, the dependency of the steady-state concentration c(upr) on the input upr is uniquely determined byD. This will be important for the characterization of the steady-state solutions for given uptake rates.The influence of the input Based on the reaction scheme above, differential equations (o.d.e.) are set up and kinetic parameters are either taken from network component analysis or estimated based on the experimental data. The dynamic system comprises differential equations for substrates , biomass, metabolites glucose 6-phosphate, fructose 1,6-bisphosphate, PEP and pyruvate. Furthermore, gene expression and control via FruR of the following enzymes is considered: phosphofruktokinase (PfkA), pyruvate kinase (pykF), and a lumped enzyme for glycolytic reactions. Simulation studies and parameter estimation are performed with MATLAB.F16BP). Therefore, the steady state of the enzyme corresponds directly to ligand concentration and the respective parameter iκ is determined with NCA :iκ being the entry in the coupling matrix K.Some of the enzymes of glycolysis are subject to transcriptional control by FruR. These enzymes are taken into account in the model with additional equations. Taking the simplified form for the enzymes according to , the steThe complete dynamical system reads as follows:μ based on the yield coefficient Y:Y was determined as follows: for the seven experiments, the individual yield coefficients were determined by linear regression, finally a mean value for all experiments was calculated. The following kinetic parameters in In addition to the kinetic expressions given in the text, the following rate law is used to calculate the growth rate


A minimal cut set is a minimal set of reactions whose inactivation would guarantee a failure in a certain network function or functions. Minimal cut sets (MCSs) were initially developed from the metabolic pathway analysis method (MPA) of elementary modes (EMs); they provide a way of identifying target genes for eliminating a certain objective function from a holistic perspective that takes into account the structure of the whole metabolic network. The concept of MCSs is fairly new and still being explored and developed; the initial concept has developed into a generalized form and its similarity to other network characterizations are discussed. MCSs can be used in conjunction with other constraints-based methods to get a better understanding of the capability of metabolic networks and the interrelationship between metabolites and enzymes/genes. The concept could play an important role in systems biology by contributing to fields such as metabolic and genetic engineering where it could assist in finding ways of producing industrially relevant compounds from renewable resources, not only for economical, but also for sustainability, reasons.  Minimal cut sets (MCSs) have been developed from elementary modes (EMs) ,2,3,4, aThis review focuses on MCSs which, together with EMs, form dual representations of metabolic networks with both being able to be converted into each other . The MCSMCSs can be considered the smallest “failure modes” in a system; they were first introduced in 2004 by S. Klamt and Gilles , motivatS. Klamt and E.D. Gilles  defined “We call a set of reactions a cut set (with respect to a defined objective reaction) if after the removal of these reactions from the network no feasible balanced flux distribution involves the objective reaction”; and “A cut set C (related to a defined objective reaction) is a minimal cut set (MCS) if no proper subset of C is a cut set.”In effect, an MCS (with respect to an objective reaction) constitutes the minimal set of reactions whose removal from the network prevents any feasible balanced flux distribution involving the objective reaction; MCSs are the minimal hitting sets of the target EMs  or the mIn terms of the network structure, a continued operation of the objective reaction would not be physiologically possible because it would lead to the depletion or accumulation of metabolite pools and the system would not be able to achieve steady state.The algorithm for calculating MCSs was developed by S. Klamt and E.D. Gilles  and operi.e., cause the dysfunction of the system with respect to the objective reaction, so the corresponding network function is repressed.The theory behind the use of EMs ,2,4 for MCSs can be used for studying the fragility of a network structure and identifying suitable targets for metabolic functionalities. For example, we have used MCSs  to studyNetEx) used in [To illustrate the MCS concept, consider the example network . In order to eliminate the production of P, all the EMs that involve PSynth need to be blocked. By definition, an EM is blocked by removing any of its constituent reactions, therefore, any combination of reactions, one taken from each EM, forms a cut set that disables flux through the EMs. For our network example, NetEx, a MCS for the objective reaction, PSynth, is a set of reactions whose knockout blocks the five EMs involving PSynth, thus disabling flux through PSynth at steady state. As shown in the above figure, there are six EMs for The notion of MCSs does exist in other theories and research areas, particularly in relation to risk analysis. In developing the algorithm for MCSs, S. Klamt and E.D. Gilles  looked aFault Trees are non-recursive Boolean networks studied in reliability and risk assessment of industrial systems ,19, whicAn example of a Fault Tree can be seen in the left hand graph of MCSs  for compMCSs obtained from the RBD are: {1}, {7}, {5,6}, {2,3,4}, {2,3,6} and {3,4,5};The Fault Tree is constructed by connecting the MCSs using the OR gate. Within each set that contains multiple blocks, the multiple blocks are connected with an AND gate. The equivalent Fault Tree is shown in More about Fault Trees and RBDs and the software used in reliability engineering and related fields can be seen in ,22. The difference between MCSs in Fault Trees and those in metabolic networks is that unlike RBDs, there is no definite knowledge of which combinations of the removed reactions would cause the failure of the objective reaction So, Fault Tree algorithms cannot be used to determine MCSs in metabolic networks.ExNet, reactions R6 and R7 have 2:1 (reactants:product) relationships NetEx and identify those that start from a buffered metabolite and lead to the formation of metabolite E or the objective reaction PSynth. Since EMs are non-decomposable, removing one of the reactions from these EM will prevent the system from producing E and subsequently achieving the PSynth.Calculate EMs  in NetExX and the objective reaction.There are six EMs in total, of which five lead to the formation of metabolite (2)PSynth from taking place, i.e. stop the five EMs that involve PSynth from being functional. This can be done in various ways e.g. inactivating one or more reactions in the EMs by deleting genes of certain enzymes or other manipulations that inhibit the enzymes. Different numbers and combination of reactions can be removed to eliminate PSynth.Determine how to prevent The MCSs for a given objective reaction in a large metabolic network, however, cannot be done by a simple examination; an algorithm would be needed to compute the MCSs. The first algorithm was developed by Klamt and Gilles  althoughThe MCS AlgorithmThe MCS algorithm devised by Klamt and Gilles  relies or, can be represented by a non-negative linear combination of elementary modes as illustrated in Equation 1 :N is the number of EMs; andwhere the removal of reactions from the network results in a new set of EMs constituted by those EMs from the original network that do not involve the deleted reactions .Before MCSs are computed, the set of EMs is split into two disjoint sets:tE), i.e., all EMs  involving the objective reaction, tthe set of target modes (ntE), i.e., EMs not involving the objective reaction, ntthe set of non-target modes  comprising the target modes (tE) and the set of EMs  comprising the non-target modes (ntE) [t,jE, only non-target modes nt,kE could survive, which means that all remaining flux distributions r will show zero flux in the objective reaction, objRr. The right-hand side of Equation 2 above, illustrates, respectively, the set of EMs (ees (Ent) . Since rNetEx, discussed in [The pseudocode of the MCS algorithm for calculating MCSs initially developed by S. Klamt and E.D. Gilles is provided in  and furtussed in . NetEx network, the algorithm calculates seven MCSs in addition to the trivial MCS (PSynth itself). To illustrate, one of the MCSs (MCS2) is shown in For the The seven MCSs and the corresponding EMs are shown in the first two tables of a minimal (irreducible) set of structural interventions  repressing a certain functionality specified by a deletion task”. This new definition indicates the key role that the deletion task plays in the difference between the new generalized approach and the initial MCS concept. S. Klamt, in 2006 , redefinThe deletion task can be specified by several Boolean rules that clearly represent and describe, unambiguously, the flux patterns or the functionality to be repressed. This increases the practical applicability of MCSs because they can now be determined for a large variety of complex deletion problems and for inhibiting very special flux patterns instead of just for studying structural fragility and identifying knock-out strategies. The refinements and extensions to the initial MCS concept offer a broader range of possible ways in which MCSs can be used to assess, manipulate and design biochemical networks. A comparison of the concept versions is covered later.Constrained MCSs (cMCSs) that take into consideration side constraints and allow for a set of desired modes, with a minimum number preserved, to be defined.Further refinement of MCSs has also been undertaken  to deal This generalization provides a flexibility for cMCSs to be applied to existing methods, for example Minimal Metabolic Functionalities ,26, OptKThe next section compares the three concepts, to get a better understanding of MCSs and how they have developed.Some properties between the initial and generalized/ refined concepts of MCSs remain the same. For example:there will always be a trivial MCS- the objective reaction itself;some reactions such as the biomass synthesis, are actually pseudo-reactions that are not related to a single gene or enzyme and thus cannot be repressed by inhibitions such as gene deletions;the definition of the MCSs: each MCS provides a minimal (irreducible) set of deletions or EMs from the set of target modes, that will achieve the elimination of the objective reaction.T is a set of constraints that characterize the stationary flux patterns (reactions) r to be repressed while D, derived from T, characterizes the target modes (EMs) to be targeted by MCSs. As such, D (for the target modes) and T (for the flux vectors r) are, in most cases such as in the earlier MCS concept, identical.A deletion task D can either differ from T or T must be transformed into several iD that lead to sub-tasks. So, instead of only dealing with a simple deletion task T where all non-trivial flux distributions for an objective reaction are blocked, other more complicated deletion tasks and intervention goals are possible.In the generalized MCS concept, however, the deletion task i.e., MCSs are EMs in a dual metabolic network [In the initial MCS concept, the MCSs are based on EMs, whereas the generalized MCS concept  sees EMs network .The generalized MCS concept offers a wider range of capacity to assess, manipulate and design biochemical networks. MCSs are no longer restricted to the removal of reactions as shown in P; this is evident when we look at the set of EMs which shows three metabolites as essential for PSynth compared to one essential reaction. This is because removing a metabolite results in eliminating all the reactions connected to it, thus eliminating the corresponding EMs, so MCSs from deleting metabolites would be more effective. MCSs could also be derived from a combination of reactions and metabolites, although these methods could quickly become computationally challenging [From llenging ,31; compConstrained MCSs (cMCSs) provide further flexibility by providing the capacity to specify, not only functionalities to be disabled, but also those that need to be preserved; the combination of these desirable and undesirable functionalities are represented by appropriate sets of target EMs and desired EMs. This allows for systematic enumeration of all equivalent gene deletion combinations and subsequently assists in determining intervention problems and robust knockout strategies for coupled product and biomass synthesis.NetEx  (or the number of steps) it takes to complete a problem of size n. For example the time might be found to be 2-2n+5T(n) = 6n. As n grows large, the 2n term will come to dominate, so that all other terms can be neglected. The coefficients also become irrelevant if T(n) is compared to other orders of expression e.g., 3n or 4n; 3U(n) = n, will always exceed T(n) when n gets larger than 6. The number of steps, on the other hand, depends on the details of the machine model on which the algorithm runs, although different types of machines generally vary by only a constant factor in the number of steps needed to execute an algorithm. So the algorithm has order of 2n time complexity denoted by the big O as:The big O notations have dramatically different meanings:Note: The following two right-hand side big f(m) exhibits polynomial growth, while the second, assuming m > 1, states that g(n) exhibits exponential growth. The first case states that i.e., runs in O(kn)steps for some non-negative integer k, where n is the input size. A deterministic algorithm only has one choice in each step taken to execute the problem, i.e., it would have the same output for every run on the same input instance for the problem.Class P consists of those decision problems whose solution can be obtained using a deterministic algorithm that runs in polynomial time, the guessing phase where a nondeterministic algorithm is used to generate an arbitrary string of characters that may or may not correspond to a solution of the input, and b) the verification phase which uses a deterministic algorithm to check and verify that the generated string is a valid solution or reject it otherwise. Both phases need to be completed in polynomial time (O(jn))where j is a non-negative integer. Class NP consists of those decision problems for which there exists a nondeterministic algorithm that runs in polynomial time with two phases: a) The complexity class P is contained in NP, but NP contains many important problems, the hardest of which are called NP-complete problems, for which no polynomial-time algorithms are known for solving them . The most important open question in complexity theory, the P=NP problem, asks whether such algorithms actually exist for NP-complete, and by corollary, all NP problems. It is widely believed that this is not the case.The complexity of EMs and MCSs in metabolic networks is covered in ,31 and aIn addition to finding EMs being NP-hard, it has also been shown  that finFour MCS computational methods have been developed since the first two ; maii)E.coli.The first method was presented by Imielinski and Belta  and consii)et al. [The second method is by Haus et al.  and invoet al.  and compet al.  and direiii)et al. [The third method, contributed by Ballerstein et al. , also deiv)et al. [The fourth method includes an approximation algorithm for computing the minimum reaction cut and an improvement for enumerating MCSs, recently proposed by Acuña et al. . These eThe algorithm and enumeration improvement aim to avoid having to compute elementary modes in order to obtain reaction cuts; instead of a MCS that disables too many EMs, it would be desirable to find a MCS that cuts the target reaction but leaves certain reactions intact or as many EMs as possible intact. These types of MCSs are NP-hard. The developments in  provide MCSs were developed as an extension of the metabolic pathway analysis methods and thus provide a different, if not improved, approach for studying similar network properties. The application of MCSs, as Klamt describes  it, can i)If the cut occurred naturally, e.g., a reaction malfunctioning due to spontaneous mutation, the MCS would serve as an internal failure mode with respect to a certain functionality and could be applied to study structural fragility and robustness on a local and global scale.ii)If, on the other hand, the cut is a deliberate intervention e.g., gene deletion, enzyme inhibition or RNA interference, then the MCS would be seen as a target set that could, for example, be suitable for blocking metabolic functionalities, and thus have significant potential in metabolic engineering and drug discovery. These applications can be extended to enable the MCSs to be used for assessing/verifying, manipulating and designing biochemical networks.Because a complex network provides many alternate pathways, there are generally several different MCSs for a single collection of objective reaction(s). All of these MCSs would be effective but their efficiencies would differ. In this respect, MCSs can be used in conjunction with other metabolic pathway methods to gain more information on the structural capability of the network in relation to the objective function. Since the mathematics guarantees that the collection of MCSs is complete, we can use quantitative analysis to compare and investigate the effect that each MCS has on the remaining non-target set of EMs. Along with other different MPA methods, these effects can be utilized in exploring things such as which MCSs would achieve loss-of-function most efficiently and whether this was related to the position of the genes in the pathway. Other investigations could include correlating different MCSs to different structures and/or situations. We could also analyze the properties of the genes concerned and the impact that their suppression would have on other processes in the network. The next part looks at areas in which MCSs have been applied.One area in which MCSs have been applied is fragility. Fragility is the vulnerability of a system to failure due to external or internal perturbations. It is inversely related to robustness , the capiF, defined as the reciprocal of the average size of all MCSs in which reaction i participates [iF would be closest to 0 where reaction i is one of many reactions occurring in a MCS, and the highest is 1 where reaction i is the only reaction in a MCS and therefore essential for the objective function. The average fragility over all the reactions is taken as the overall structural fragility of the network.The application of MCSs to measure fragility can be found in ,12,16. TNetEx, reaction R1 has two MCSs: the first MCS is MCS2 which has 2 reactions and the second is MCS6 which consists of 3 reactions; the fragility coefficient (1F) for R1 would therefore be 2/(2+3) which would be 2/5 or 0.4. The specific fragility coefficients of reactions in NetEx with respect to the production of P are as follows:For example, in the network example P as is obviously the case for Psynth. This indicates that the loss of function of R3 would automatically render the other reactions meaningless for the production of P.The above table shows that reaction R3 is essential for the production of E.coli, earlier investigated by Stelling et al to study robustness using EMs. They found the number of MCSs to vary for different compound substrates that E.coli was growing on. For example, there were more MCSs, including the largest MCS for growth, on glucose than on acetate for which the lower number of MCSs were predominantly smaller. This indicated that E.coli growth on glucose was less fragile than on acetate. S. Klamt and E.D. Gilles  applied In the generalized MCS concept , Klamt fMCSs can be used to verify a network because the minimal sets of target reactions/genes they provide are mathematically complete in relation to the structure of the network. Thus, the simultaneous removal of genes making up each MCS should lead to the elimination of the objective function. If the prediction is incorrect in an experiment and the phenotype is still viable, it means that the network structure is incorrect or incomplete. NetEx  for the objective function, and depends on the chosen substrate. Past work on network verification has been done using Flux Balance analysis (FBA) ,47 and eur) to be calculated or observed in a steady state flux distribution. The process includes first calculating all EMs and selecting those where the unknown reaction rate exists (ur≠0); the set of rates to be measured are then constructed such that they contain at least one of the reactions participating in each of the selected EMs. These sets of rates to be measured are in fact the MCSs with respect to the reaction rate (ur is the objective reaction) so, the sets of possible measurements will be minimal and non-redundant. As such, the MCSs can be screened to determine the most appropriate sets of measurement for FBA [Another use of the MCS concept is in finding the necessary information that can be used to make stationary network fluxes observable. As shown in , EM anal for FBA ,50. NetEx  and then an element-by-element multiplication is performed with each of the P  rows of E to form G. The EMs ensure that the sequence of reactions in the entire pathway is in one direction and assist FBA in identifying the objective function(s) driving the metabolic behavior of tissue cells, especially multi-functional ones [To assist FBA, EMs have been used to place thermodynamics constraints at the pathway level  where a nal ones . The relnal ones .Along with their role in obtaining a deeper understanding of the structural fragility of cellular networks, MCSs can also be seen as minimal target sets for efficiently repressing cellular functions. The generalized concept  allows MNetEx, the set of MCSs (cMCSs) can be identified that would repress the synthesis of P and redirect fluxes to maximize the production of X. MCSs provide the capacity to identify an optimal intervention strategy by providing, from a structural perspective, the most efficient set of manipulations to achieve a certain deletion task. In addition to being efficient, an ideal MCS would be one that is small and therefore does not affect or weakly affect other network functions; also an MCS that does not involve network functions that are hard to eliminate e.g., a reaction with many isozymes.For example, as illustrated in the intervention in The growing importance of MCSs in metabolic engineering is evident in ,12,15, fThis generalization can be applied to existing methods which can be reformulated as special cMCS problems, providing the capacity for systematic enumeration of all equivalent gene deletion combinations and determining robust knockout strategies for coupled product and biomass synthesis, altogether offering great flexibility in defining and solving knock out problems. Other examples of MCSs in metabolic engineering can be seen in ,29, discin degree which refers to the number of links forwarded to the node under consideration, out degree which refers to the number of links going out of the node, and betweenness which measures the number of “shortest paths” [Bottlenecks characterize a point of congestion in a system that happens when workloads arrive at a given point more quickly than can be handled at that point. In a metabolic network consisting of enzymes (nodes) and substrate-product metabolite fluxes , three topological centralities that are used to measure the importance of nodes in controlling information transfer are: t paths”  going tha and b in a or b is knocked out, the network would collapse. In effect, bottlenecks indicate essentiality of the nodes.For example, the bottleneck nodes in degree of node a is 4 and the out degree is 1; these centralities only consider the partners connected directly to a particular node, whereas the betweenness considers a node’s position in the network and, as shown for a, is much higher e.g. 28. Thus, bottlenecks in metabolic networks could be defined as nodes with a high betweenness centrality. The essentiality of the bottleneck nodes is illustrated in the above graph which shows that they are “AND” nodes, traversed in series and you cannot get from the input nodes to the output except through node a “AND” node b. The One importance of bottlenecks is in relation to whole genome duplication (WGD) ,55, wherNetEx, . For example, to use MCSs to calculate the essentiality of reactions/enzymes for a whole network, the objective function to repress would be the formation of all end products in the network, which would likely lead to combinatorial problems in larger networks. For the example network, refer to , the objNetEx. Bottlenecks would require a fragility coefficient of 1 because they represent an essential reaction that forms a bridge or tunnel to get from the input side of the network to the output. MCSs don’t necessarily have to, as shown by the fragility coefficients in The above table shows no reaction with a fragility coefficient  of 1, inPSynth) in NetEx, R3 is the reaction with the highest fragility coefficient of 0.5. When we look at the corresponding EMs, R3 is also involved in the highest number of 5 EMs. Characterising that as a bottleneck does not seem unreasonable when looking at the NetEx diagram. In fact, adding the number of 1’s in the EM table is somewhat like the “betweenness” index that bottlenecks are based on. For example, ignoring the outermost reactions connected to the products The input domain (substrate subset (S)), which contains substrates that can be converted reversibly to intermediates or directly to metabolites in the GSC, but those directly connected to the GSC cannot be produced from the GSC.(2)The knot or GSC, which is the metabolite converting hub , where p(3)The output domain (product subset (P)), which contains products from metabolites in the GSC and can also have intermediate metabolites but the products cannot be converted back into the GSC . In othe(4)The resulting metabolites that are not in the GSC, S or P subsets form an isolated subset (IS), the simplest structured of the four bow-tie components , which cThe bow-tie decomposition of a network can assist with the problem of combinatorial explosion encountered when calculating EMs and MCSs in large sized metabolic networks. For example, suppose that EMs are calculated separately for each of the three subnets , a typical EM for the full network can then be reconstituted by joining a substrate mode and product mode to one of their connecting GSC modes. The large number of ways in which this can be done is a manifestation of the combinatorial explosion, and demonstrates that the bow-tie splitting will substantially reduce the computational effort of calculating EMs and the resulting MCSs. More explicitly, the reactions constituting MCSs of a whole network can be classified in terms of the blocked reactions’ locations in the bow-tie decomposition:(1)All substrate reactions (S subnet) plus GSC reactions blocking any cyclic EMs that could take place without inputs from the substrate reactions. In this case, no product reactions (P subnet) need blocking;(2)All product reactions(P subnet) plus GSC reactions blocking the cyclic EMs- in this case no substrate (S subnet) need to be blocked;(3)All GSC reactions that connect the S to the P subnet. No substrate or product reactions need to be blocked;(4)A combination of S reactions plus GSC reactions reached from the unblocked S reactions. P reactions don’t need to be blocked;(5)A combination of P reactions plus GSC reactions that could reach the unblocked P reactions. S reactions don’t need blocking.These classifications can be used to investigate the question of whether a bow-tie decomposition can be derived from a known MCSs table. For example, a plausible strategy to identify GSC reactions is as follows:From all MCS, eliminate any that involve reactions that are known to belong to S or P;Order the remainder by increasing size and/or decreasing mean fragility coefficient;Choose a cutoff value in this sequence, and allocate all reactions that belong to MCSs in the top section of the sequence to the GSC.If the bow-tie structure is pronounced, there should be a clear separation between the small, high fragility coefficient MCSs that belong to the GSC and the rest, otherwise the choice of a cutoff may be problematic. An MCS analysis may be helpful to examine if a bow-tie structure exists and partially detect members of its main components, but not to make a full partitioning.Noting that bow-ties can assist with combinatorial explosion by decomposing large networks into subnets that can be analyzed by MCSs and EMs, we conclude that despite some overlap in the concepts and applications of bow-ties and MCSs, there is no clear cut correspondence between the two network descriptions. While bow-ties try to extract subsets of nodes that are of importance in the metabolic network, the EM and MCS approaches focus on comprehensive sets that are in different ways essential. Moreover, EMs are, by construction, the “constituents” of a steady metabolic state. So they, and MCSs, reflect the stoichiometry underlying the network and describe the metabolism, not just the topology of the network. In this respect, MCS (and EM) analysis is more powerful than bow-ties that just characterize network topology.et al. [‘Weak nutrient sets’ is a concept analogous to MCSs, that was developed by Imielinski et al.  to demonC for an objective reaction j is a set of reactions whose elimination renders flux through j infeasible at steady state so, a necessary and sufficient condition for C to be a cut set for j is that C is a hitting set for all j-containing elementary modes. Similarly, U is a weak nutrient set for species or metabolite i if and only if U is a hitting set for all of the i-containing ESCRs.Weak nutrient sets are analogous to MCSs in a metabolic network in that a MCS The ‘weak nutrient sets’ algorithm identified all minimal nutrient media that left an arbitrary metabolite weakly producible with respect to a given metabolic network. Details of the concept and its application can be seen in . Flux balance analysis (FBA) ,64,65 shCalculating EMs and MCSs for larger networks can lead to problems with combinatorial explosion. However, because they are unique for a given network structure, they provide the full range of potential functionalities of the metabolic system and are therefore useful for investigating all physiological states that are meaningful for the cell in the long term. FBA, on the other hand, is more efficient, providing good predictions of mutant phenotypes and using linear programming to obtain a single (not necessarily unique) solution to an optimization problem. However, because it focuses on a specific behavior, FBA cannot cope with cellular regulation without additional constraints; it fails whenever network flexibility has to be taken into account, e.g., in the analysis of pathway redundancy or in quantitative prediction of gene expression .We conclude that MCSs and EMs offer a convenient way of interpreting metabolic functions while FBA can be used to explore the relationship between the metabolic genotype and phenotype of organisms. MCSs, EMs and FBA can also be used together to interpret shifts in metabolic routing that could occur in response to environmental and internal/genetic challenges. Because they are mathematically equivalent, the predictions from the three methods would be the same except that MCSs enable the systematic search of more than one mutation.MCSs are an extension of metabolic pathway analysis (MPA) methods and provide a way of identifying target genes for eliminating a certain objective function from a holistic perspective that takes into account the structure of the whole metabolic network and all the reactions taking place in the cell. The objective function can be represented by a set of EMs which is then used to calculate the MCSs used for studying structural fragility and identifying knock out strategies from a whole cell perspective. Such exhaustive characterization is very hard to achieve experimentally because, regardless of how many examples of a phenomenon one has observed, there might always be others not yet observed. This aspect of completeness by MCSs and EMs, subject only to a complete knowledge of the network itself, makes it possible to make quantitative assessments e.g. of the relative importance of reactions and their corresponding enzymes/genes. Looking in detail at the MCS concept and how it has developed in relation to similar concepts, it is easy to see its importance in systems biology and how it can contribute to fields such as metabolic engineering. Without needing prior knowledge of genes, MCSs can provide a complete list of loss of function(s) target genes that can then be investigated by other methods to analyze the properties of those genes and the impact that their suppression would have on other processes in the network. Thus, MCSs can assist in finding ways of producing industrially relevant compounds from renewable resources, not only for economical but also for sustainability reasons. The concept of MCSs is fairly new and still being explored; its similarity to other concepts and the fact that it has developed from the well established MPA method of EMs, means that MCSs can be used in conjunction with FBA and other MPA methods to get a better understanding of the capability of metabolic networks and the interrelationship between metabolites and enzymes/genes. The MCS concept also opens an avenue for developing new novel systems biology methods for use in genetic engineering.


Chlamydomonas reinhardtii.Although the number of reconstructed metabolic networks is steadily growing, experimental data integration into these networks is still challenging. Based on elementary flux mode analysis, we combine sequence information with metabolic pathway analysis and include, as a novel aspect, circadian regulation. While minimizing the need of assumptions, we are able to predict changes in the metabolic state and can hypothesise on the physiological role of circadian control in nitrogen metabolism of the green alga  Metabolic pathway analysis is a well established and very useful tool in Systems Biology Beside a growing number of methods for the analysis of metabolic networks, connecting experimental data to reconstructed models remains a major task to systems biology Chlamydomonas reinhardtii, a model process for green crop plants. Assimilating nitrogen is a key step of metabolism required by phototrophic organisms in order to grow and survive in natural habitats To demonstrate the usefulness of our method with a case study, we describe the analysis of a reconstructed metabolic network of nitrogen uptake in the green algae C. reinhardtii or contain a high nitrogen content in their side chain and, thus, are particularly suitable for nitrogen storage.Here, we combine genome based sequence and metabolic pathway analyses by computing EFMs. This allows us to evaluate the changes in nitrogen assimilation and amino acid anabolism that are caused by CHLAMY1 binding and thus, determine the physiological role of this circadian RNA-binding factor. We study amino acid biosynthesis of alanine, glycine, asparagine, lysine and arginine, which permits physiological interpretation and comparison to known data from other organisms. These amino acids were chosen as they are either overrepresented in As we will show, the application of optimality principles that solely focus on analysing maximum yields like in Flux Balance Analysis C. reinhardtii using elementary flux mode analysis, we first had to confine our model. C. reinhardtii is able to grow either autotrophically, heterotrophically or mixotrophically. As we simulate only metabolism during the night here, we have chosen acetate and glucose-6-phosphate (G6P) as carbon sources. G6P is provided by starch degradation. The degradation is not explicitly included into the model.As it is not feasible to analyse the complete metabolism of C. reinhardtii and identified glycine and alanine as most abundant and highly overrepresented amino acids compared to other organisms  into glycine, alanine, asparagine, lysine or arginine . During Beside glycine, the maximum yields for biosynthesis of all amino acids are reduced, if complete downregulation by CHLAMY1 was assumed. However, analysing maximum yields only uses a very small portion of the information about the network's metabolic capabilities. In contrast, EFMs offer a more detailed view on the metabolic capacity. This significant advantage will be exploited below.To make use of the full potential of flux distribution, we first took all EFMs and respective yields into account, rather than analysing solely optimised fluxes with respect to carbon yields. Again, as ASL is a key step in arginine biosynthesis that is inactivated by CHLAMY1, we did not conduct any further analysis of arginine metabolism.From Note that until now all EFMs were discarded that contain at least one reaction that is under influence of CHLAMY1. However, such drastic downregulation is questionable and asks for a more realistic modelling.In the following calculations we therefore circumvented the need to inactivate fluxes, regulated by CHLAMY1, which is usually enforced by EFM analysis. We now assume downregulation of the corresponding fluxes to 10% due to CHLAMY1 binding, rather than complete inactivation. We reduced the impact of inhibited EFMs by weighting EFMs differently, depending on whether they are under CHLAMY1 control or not . The extAdditionally, we calculated the mean of molar yields by using the formula for weighted means given by Eq. (3). This enables us to weight every derived yield and hence, also the underlying flux, represented by its respective EFM. We applied a weight of 10% to EFMs affected by CHLAMY1 and a unity weight to all remaining fluxes. The resulting mean yield is considerably increased upon CHLAMY1 binding .C. reinhardtii, which is under the control of the circadian clock. The calculated elementary flux modes provide a data set that is well-suited for quantifying and understanding the complex architecture of this network. The large number of modes (e. g. 1352352 for arginine) point to a considerable redundancy of this network. Intriguingly, our results show that downregulation of circadian controlled enzymes improves carbon distribution and thus, decreases energy consumption. The somewhat counter-intuitive result that knocking out or downregulating several enzymes may lead to an increase in average yield arises, because poor pathways are deleted or downregulated, so that more efficient pathways become more dominant. A similar phenomenon was observed earlier in the context of strain optimisation In this study, we have outlined a method that interconnects sequence based knowledge with metabolic pathway analysis. The method has been illustrated by nitrogen metabolism of Escherichia coli or Saccharomyces cerevisiae, but might be virtually infeasible for higher organisms, when regulatory complexity becomes more sophisticated. Thus, our approach proves to be an easy-to-use, helpful method to determine the type and impact of influences of regulatory factors.Additionally, we have considered information derived from sequence data. Since it is known that many regulatory proteins bind to specific motifs in the mRNA or to promoters, such information is extremely useful in modelling regulation of metabolism. Moreover, measuring fluxes in detail is already a demanding task for simple model organisms, like C. reinhardtii remains able to synthesise glycine, alanine, asparagine and lysine but with reduced theoretical effectiveness while not being able to synthesis arginine if one assumes complete downregulation by CHLAMY1 at night-time. However, as there are more than three million possible routes within the network producing the target amino acids and the main portion of all EFMs  prediction data in fasta file format. The fasta files from C. reinhardtii Click here for additional data file.Table S2http://genome.jgi-psf.org/Chlre4/). The code of the UGOverview of modelled enzymes and corresponding EC–numbers, abbreviations as well as JGI database IDs Click here for additional data file.


Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development. Cellular metabolism is a key element in human physiology. Ideally the metabolic network needs to be considered within the context of the surrounding tissue and organism since the various levels of biological organization are mutually influencing each other. To mechanistically describe the interplay between intracellular space and extracellular environment, we here integrate the genome-scale metabolic network model HepatoNet1 at the cellular scale into physiologically-based pharmacokinetic models at the whole-body level. The resulting multiscale model allows the quantitative description of metabolic behavior in the context of time-resolved metabolite concentration profiles in the body and the surrounding liver tissue. The model has been applied to three case studies covering fundamental aspects of medicine and pharmacology: drug administration, biomarker identification and drug-induced toxication. Most notably, our multiscale approach fosters an improved quantitative understanding of drug action and the impact of metabolic disorders at an organism level, based on a genome-scale representation of cellular metabolism. Computational models such as the one presented include various aspects of human physiology and may therefore significantly support rational approaches in medical diagnostics and pharmaceutical drug development in the future. Human metabolism is an integral component of whole-body physiology and its dysfunction plays a key role in many systemic diseases. Frequent symptoms of metabolic diseases are changes in exometabolism In recent years, modeling approaches have been developed describing biological processes at different levels of physiological organization based on multiple, divergent mathematical formalisms For analyses at the cellular level, metabolic network reconstructions are an important tool of bottom-up systems biology. Cellular metabolism gathers a multitude of upstream regulatory events onto the various layers of cellular organization such as the transcriptome and metabolome representing an important angle point in the physiology of an organism. Metabolic networks are typically described by stoichiometric matrices and intracellular flux distributions are inherent variables in such models. First stoichiometric models on human metabolism at genome-scale encompassed generic collections of metabolic biochemistry in human cells in vitro experiments with more or less well-defined media conditions, they do not suffice for considerations of in vivo metabolism, where the cell is embedded in the ever-changing environment of the surrounding tissue and organism. Therefore, human metabolism can only be fully understood by an integrative analysis which simultaneously considers the whole-body context. This allows in particular the quantification of cellular boundary conditions and the interference with intracellular states and processes. Several approaches for combining models covering different levels of biological organization have been described before While metabolic network models are applicable to the investigation of We here apply dFBA to describe human metabolic networks within the context of whole-body PBPK models . The relative enzyme activity (relE(t)) is the time-resolved ratio of the inhibited reaction rate v(t) and the uninfluenced reaction rate 0v (I = 0 µM). Next, relE(t) is used to quantify the effect of enzyme inhibition in the metabolic network. The additional constraint for the FBA step imposed on the specific flux in the metabolic network is defined as:E(t)v corresponds to the flux through the affected enzyme at each time step which is defined as the product of the unperturbed flux E(0)v which is calculated by FBA and the relative enzyme activity relE(t). Therefore, the set of constraints changes over time such that the extracellular exchange rates identified with FBA also evolve dynamically. This allows on the one hand quantifying the effect of compound-induced extracellular perturbations on metabolic states. On the other hand, time-resolved exchange fluxes determined with FBA may interfere with the mass balance of the PBPK model such that direct coupling needs to be considered (see section below).Indirect coupling is used for the simulation of regulatory modifications such as drug-induced inhibition of metabolic enzymes , 2. In tMetabolic clearance and formation processes are simulated by direct coupling since they directly interfere with the mass balance of the PBPK model. Direct coupling therefore describes the influence of active processes at the cellular level on the distribution of compounds at the whole-body scale. To this end, a feedback update loop is considered which consists of the following steps : (1) TheWhile the exchange rates in the PBPK model and metabolic network are identical for the metabolic reference state, these rates will differ if internal and external network perturbations are imposed. Without any impairment of enzyme reactions in the metabolic network, the clearance or production rates calculated by FBA will reach the upper bound (step 2). In this case, the rates of the coupled model are identical to those of the PBPK model alone. In contrast, the rates calculated by FBA will decrease if for instance enzyme activities are impaired due to restricted functionality or structural network errors . ConsequAs a first example we analyzed drug action of allopurinol in the treatment of hyperuricemia with a multiscale PK/PD model. Purine metabolism provides a large number of drug targets In clinical practice, high plasma levels of uric acid (above 470 µM) are referred to as hyperuricemia which may result from inborn errors of purine metabolism and even more often from impaired renal excretion of uric acid, which is considered in the following. Hyperuricemia can lead to diseases like gout where uric acid is deposited into tissues, especially in the joints To estimate the inhibitory concentration of allopurinol and its active metabolite oxypurinol, a coupled PBPK model was developed see . ExperimIn the next step, a PBPK model for uric acid was created, which allowed describing changes in uric acid concentration as a mechanistic consequence of allopurinol inhibition in hepatic purine metabolism  resulting in a reduced ammonia detoxification capacity. Pathogenesis of UCD was exemplarily assumed as a linear decrease of the enzyme activity of ornithine transcarbamylase (OTC), leading to complete impairment of the enzyme  [56]. SiWith the coupled model and the above described constraints, simulation was performed within a time range of 21 days. After 24 h, UCD starts developing which led to a decreasing urea production rate after 30 h. At the same time, the glutamine and alanine fluxes began to rise and the rate of ammonia uptake began to decrease. In the new steady state (after 6.5 days), ammonia uptake rate was 0.072 µmol/L/min  and glutAbove model is a representation for an average patient. Since the model, however, structurally includes many potential causes for inter-individual variability at a large level of mechanistic detail, it may be used to analyze pathogenesis on a populations scale as well. Such individual differences may include physiology Our final example deals with drug-induced toxication by addressing downstream effects of drug dosing on metabolic functionality at the cellular level. We here chose overdosing of paracetamol, one of the most common reasons for liver failure To quantify the metabolic impact of perturbations in the enzyme activities on whole liver functionality, indirect coupling of a paracetamol PBPK model and HepatoNet1 was used to determine the effect of a paracetamol overdose on a large amount of functional liver objectives. HepatoNet1 was previously validated with 123 physiological functions which represent essential tasks for liver metabolism We started our analyses with the development of PBPK models of the parent drug paracetamol the three metabolites  and NAPQI , respectively as well as time of trough concentrations at 24 h after drug administration (t24h)  . Out of We next analyzed, whether the flux underlying the different optimal values changed during the application of different doses of paracetamol. This could explain why more objective functions are affected after the toxic dose of paracetamol, which is to be expected by network robustness We here integrate genome-scale metabolic networks, comprising thousands of biochemical reactions, into PBPK models to analyze metabolism at the level of the human organism. The approach is based on dFBA Our approach combines well-established computational modeling approaches from different biological scales. At the organism scale, standardized PBPK models which are routinely used in pharmaceutical drug development provide a generalized description of the distribution of substances within the human body. At the cellular scale, metabolic network reconstructions represent core building blocks of bottom-up systems biology which describe fundamental cellular biochemistry. Our coupling approach therefore provides a generic framework for a wide range of possible applications. Notably, all these applications can be addressed without the need for further model curation or modification.To illustrate our approach, we exemplarily integrate HepatoNet1 In a first application example we investigate a multiscale PK/PD approach, where indirect coupling is used to mechanistically describe the pharmacological effect of the purine analogue allopurinol on the biosynthesis of uric acid. The PK of the exogenous drug as well as its resulting downstream PD effect on the formation of endogenous metabolites are quantified allowing a comprehensive evaluation of drug safety and drug efficiency. For multiple oral administrations of 200 mg allopurinol we predict a 69.3% decrease of uric acid concentration in the venous plasma which is in quantitative agreement with clinical data The identification of quantitative biomarkers for metabolic disorders is the second application example. As a complement to classical qualitative biomarker identification Drug-induced toxication following paracetamol overdose is the third application example. We demonstrate how paracetamol impairs metabolic capacity by affecting a broad range of different metabolic functions. The specific metabolic impact is illustrated for a therapeutic (1 g) and a toxic (15 g) dose of paracetamol. The results show a larger metabolic impact on single hepatic functions following the toxic dose of paracetamol. Also, more metabolic functions are affected after the higher dose (24 vs. 20 functions). Since a considerable number of fluxes is affected, we conclude that paracetamol toxication induces flux rerouting which is used by the hepatocyte to compensate for network perturbations thereby conferring cellular robustness. Notably, this effect which has been shown before for microorganisms Describing the impact of a compound on the body and the cell is the fundamental question in pharmacodynamics. Classical approaches describe this interference with rather phenomenological models Taken together, the presented approach integrating organ-specific metabolic networks into PBPK models provides many opportunities for scientific research, clinical applications and drug development as outlined by the prototypical examples discussed above. It is only by such multiscale models that a mechanistic understanding of organ dysfunction and disease etiology at a system level will be achieved. This will be greatly supported by the reconstruction of further genome-scale metabolic networks which will become available in the future At the whole-body level, PBPK modeling quantitatively describes all ADME-related processes of endogenous and exogenous compounds within mammalian organisms The PBPK models considered in this study were all built with the software tools PK-Sim and MoBi for which academic licenses are available free of charge  usually less literature data is available and (2) these parameters often have significant sensitivity although the overall dynamic behavior of the PBPK models is robust  and v represents the intracellular flux distribution. The overall solution space is confined by a set of additional constraints (A·v≤b) which represent for example substrate availability.Stoichiometric models provide a mathematically formal way to capture the basic biochemistry of cellular metabolism into an analytical framework. Assuming steady state of the system, all intracellular metabolites can be balanced in linear systems of equations, which are usually underdetermined since they encompass much more unknown reaction rates than linear independent mass balance equations. Flux distributions can be identified with stoichiometric models by using FBA To illustrate our approach, we here exemplarily use HepatoNet1, a tissue-specific network reconstruction of hepatic metabolism Text S1Important additional texts, tables, equations and figures.(PDF)Click here for additional data file.