A MILP-based flux alternative generation and NMR experimental design strategy for metabolic engineering

Cell scale host-pathogen modeling: another branch in the evolution of constraint-based methods

Constraint-based models have become popular methods for systems biology as they enable the integration of complex, disparate datasets in a biologically cohesive framework that also supports the description of biological processes in terms of basic physicochemical constraints and relationships. The scope, scale, and application of genome scale models have grown from single cell bacteria to multi-cellular interaction modeling; host-pathogen modeling represents one of these examples at the current horizon of constraint-based methods. There are now a small number of examples of host-pathogen constraint-based models in the literature, however there has not yet been a definitive description of the methodology required for the functional integration of genome scale models in order to generate simulation capable host-pathogen models. Herein we outline a systematic procedure to produce functional host-pathogen models, highlighting steps which require debugging and iterative revisions in order to successfully build a functional model. The construction of such models will enable the exploration of host-pathogen interactions by leveraging the growing wealth of omic data in order to better understand mechanism of infection and identify novel therapeutic strategies.

Effect of plasmid replication deregulation via inc mutations on E. coli proteome & simple flux model analysis

When the replication of a plasmid based on sucrose selection is deregulated via the inc1 and inc2 mutations, high copy numbers (7,000 or greater) are attained while the growth rate on minimal medium is negligibly affected. Adaptions were assumed to be required in order to sustain the growth rate. Proteomics indicated that indeed a number of adaptations occurred that included increased expression of ribosomal proteins and 2-oxoglutarate dehydrogenase. The operating space prescribed by a basic flux model that maintained phenotypic traits (e.g. growth, byproducts, etc.) within typical bounds of resolution was consistent with the flux implications of the proteomic changes.

Sampling with poling-based flux balance analysis: optimal versus sub-optimal flux space analysis of Actinobacillus succinogenes

BACKGROUND

Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value.

RESULTS

In this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively "small" characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions. The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol.

CONCLUSIONS

A new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO₂ must be taken into the system. Solutions involving release of CO₂ all give sub-optimal succinic acid production.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

De novo creation of MG1655-derived E. coli strains specifically designed for plasmid DNA production

The interest in plasmid DNA (pDNA) as a biopharmaceutical has been increasing over the last several years, especially after the approval of the first DNA vaccines. New pDNA production strains have been created by rationally mutating genes selected on the basis of Escherichia coli central metabolism and plasmid properties. Nevertheless, the highly mutagenized genetic background of the strains used makes it difficult to ascertain the exact impact of those mutations. To explore the effect of strain genetic background, we investigated single and double knockouts of two genes, pykF and pykA, which were known to enhance pDNA synthesis in two different E. coli strains: MG1655 (wild-type genetic background) and DH5α (highly mutagenized genetic background). The knockouts were only effective in the wild-type strain MG1655, demonstrating the relevance of strain genetic background and the importance of designing new strains specifically for pDNA production. Based on the obtained results, we created a new pDNA production strain starting from MG1655 by knocking out the pgi gene in order to redirect carbon flux to the pentose phosphate pathway, enhance nucleotide synthesis, and, consequently, increase pDNA production. GALG20 (MG1655ΔendAΔrecAΔpgi) produced 25-fold more pDNA (19.1 mg/g dry cell weight, DCW) than its parental strain, MG1655ΔendAΔrecA (0.8 mg/g DCW), in glucose. For the first time, pgi was identified as an important target for constructing a high-yielding pDNA production strain.

Metabolic network reconstruction and flux variability analysis of storage synthesis in developing oilseed rape (Brassica napus L.) embryos

Computational simulation of large-scale biochemical networks can be used to analyze and predict the metabolic behavior of an organism, such as a developing seed. Based on the biochemical literature, pathways databases and decision rules defining reaction directionality we reconstructed bna572, a stoichiometric metabolic network model representing Brassica napus seed storage metabolism. In the highly compartmentalized network about 25% of the 572 reactions are transport reactions interconnecting nine subcellular compartments and the environment. According to known physiological capabilities of developing B. napus embryos, four nutritional conditions were defined to simulate heterotrophy or photoheterotrophy, each in combination with the availability of inorganic nitrogen (ammonia, nitrate) or amino acids as nitrogen sources. Based on mathematical linear optimization the optimal solution space was comprehensively explored by flux variability analysis, thereby identifying for each reaction the range of flux values allowable under optimality. The range and variability of flux values was then categorized into flux variability types. Across the four nutritional conditions, approximately 13% of the reactions have variable flux values and 10-11% are substitutable (can be inactive), both indicating metabolic redundancy given, for example, by isoenzymes, subcellular compartmentalization or the presence of alternative pathways. About one-third of the reactions are never used and are associated with pathways that are suboptimal for storage synthesis. Fifty-seven reactions change flux variability type among the different nutritional conditions, indicating their function in metabolic adjustments. This predictive modeling framework allows analysis and quantitative exploration of storage metabolism of a developing B. napus oilseed.

Genome-scale metabolic networks

During the last decade, models have been developed to characterize cellular metabolism at the level of an entire metabolic network. The main concept that underlies whole-network metabolic modeling is the identification and mathematical definition of constraints. Here, we review large-scale metabolic network modeling, in particular, stoichiometric- and constraint-based approaches. Although many such models have been reconstructed, few networks have been extensively validated and tested experimentally, and we focus on these. We describe how metabolic networks can be represented using stoichiometric matrices and well-defined constraints on metabolic fluxes. We then discuss relatively successful approaches, including flux balance analysis (FBA), pathway analysis, and common extensions or modifications to these approaches. Finally, we describe techniques for integrating these approaches with models of other biological processes.

Systems-level engineering of nonfermentative metabolism in yeast

We designed and experimentally validated an in silico gene deletion strategy for engineering endogenous one-carbon (C1) metabolism in yeast. We used constraint-based metabolic modeling and computer-aided gene knockout simulations to identify five genes (ALT2, FDH1, FDH2, FUM1, and ZWF1), which, when deleted in combination, predicted formic acid secretion in Saccharomyces cerevisiae under aerobic growth conditions. Once constructed, the quintuple mutant strain showed the predicted increase in formic acid secretion relative to a formate dehydrogenase mutant (fdh1 fdh2), while formic acid secretion in wild-type yeast was undetectable. Gene expression and physiological data generated post hoc identified a retrograde response to mitochondrial deficiency, which was confirmed by showing Rtg1-dependent NADH accumulation in the engineered yeast strain. Formal pathway analysis combined with gene expression data suggested specific modes of regulation that govern C1 metabolic flux in yeast. Specifically, we identified coordinated transcriptional regulation of C1 pathway enzymes and a positive flux control coefficient for the branch point enzyme 3-phosphoglycerate dehydrogenase (PGDH). Together, these results demonstrate that constraint-based models can identify seemingly unrelated mutations, which interact at a systems level across subcellular compartments to modulate flux through nonfermentative metabolic pathways.

Pyruvate kinase-deficient Escherichia coli exhibits increased plasmid copy number and cyclic AMP levels

Previously established consequences of abolishing pyruvate kinase (Pyk) activity in Escherichia coli during aerobic growth on glucose include reduced acetate production, elevated hexose monophosphate (HMP) pathway flux, elevated phosphoenolpyruvate carboxylase (Ppc) flux, and an increased ratio of phosphoenolpyruvate (PEP) to pyruvate. These traits inspired two hypotheses. First, the mutant (PB25) may maintain more plasmid than the wild type (JM101) by combining traits reported to facilitate plasmid DNA synthesis (i.e., decreased Pyk flux and increased HMP pathway and Ppc fluxes). Second, PB25 likely possesses a higher level of cyclic AMP (cAMP) than JM101. This is based on reports that connect elevated PEP/pyruvate ratios to phosphotransferase system signaling and adenylate cyclase activation. To test the first hypothesis, the strains were transformed with a pUC-based, high-copy-number plasmid (pGFPuv), and copy numbers were measured. PB25 exhibited a fourfold-higher copy number than JM101 when grown at 37 degrees C. At 42 degrees C, its plasmid content was ninefold higher than JM101 at 37 degrees C. To test the second hypothesis, cAMP was measured, and the results confirmed it to be higher in PB25 than JM101. This elevation was not enough to elicit a strong regulatory effect, however, as indicated by the comparative expression of the pGFPuv-based reporter gene, gfp(uv), under the control of the cAMP-responsive lac promoter. The elevated cAMP in PB25 suggests that Pyk may participate in glucose catabolite repression by serving among all of the factors that tighten gene expression.

Optimization of Fed-Batch Saccharomyces cerevisiae Fermentation Using Dynamic Flux Balance Models

We developed a dynamic flux balance model for fed-batch Saccharomyces cerevisiae fermentation that couples a detailed steady-state description of primary carbon metabolism with dynamic mass balances on key extracellular species. Model-based dynamic optimization is performed to determine fed-batch operating policies that maximize ethanol productivity and/or ethanol yield on glucose. The initial volume and glucose concentrations, the feed flow rate and dissolved oxygen concentration profiles, and the final batch time are treated as decision variables in the dynamic optimization problem. Optimal solutions are generated to analyze the tradeoff between maximal productivity and yield objectives. We find that for both cases the prediction of a microaerobic region is significant. The optimization results are sensitive to network model parameters for the growth associated maintenance and P/O ratio. The results of our computational study motivate continued development of dynamic flux balance models and further exploration of their application to productivity optimization in biochemical reactors.

Effect of carbon source perturbations on transcriptional regulation of metabolic fluxes in Saccharomyces cerevisiae

BACKGROUND

Control effective flux (CEF) of a reaction is the weighted sum of all fluxes through that reaction, derived from elementary flux modes (EFM) of a metabolic network. Change in CEFs under different environmental conditions has earlier been proven to be correlated with the corresponding changes in the transcriptome. Here we use this to investigate the degree of transcriptional regulation of fluxes in the metabolism of Saccharomyces cerevisiae. We do this by quantifying correlations between changes in CEFs and changes in transcript levels for shifts in carbon source, i.e. between the fermentative carbon source glucose and nonfermentative carbon sources like ethanol, acetate, and lactate. The CEF analysis is based on a simple stoichiometric model that includes reactions of the central carbon metabolism and the amino acid metabolism.

RESULTS

The effect of the carbon shift on the metabolic fluxes was investigated for both batch and chemostat cultures. For growth on glucose in batch (respiro-fermentative) cultures, EFMs with no by-product formation were removed from the analysis of the CEFs, whereas those including any by-products (ethanol, glycerol, acetate, succinate) were omitted in the analysis of growth on glucose in chemostat (respiratory) cultures. This resulted in improved correlations between CEF changes and transcript levels. A regression correlation coefficient of 0.60 was obtained between CEF changes and gene expression changes in the central carbon metabolism for the analysis of 5 different perturbations. Out of 45 data points there were no more than 6 data points deviating from the correlation. Additionally, up- or down-regulation of at least 75% of the genes were in qualitative agreement with the CEF changes for all perturbations studied.

CONCLUSION

The analysis indicates that changes in carbon source are associated with a high degree of hierarchical regulation of metabolic fluxes in the central carbon metabolism as the change in fluxes are correlating directly with the change in transcript levels of genes encoding their corresponding enzymes. For amino acid biosynthesis there was, however, not found to exist a similar correlation, and this may point to either post-transcriptional and/or metabolic regulation, or be due to the absence of a direct perturbation on the amino acid pathways in these experiments.

A three-level problem-centric strategy for selecting NMR precursor labeling and analytes

We have developed a sequential set of computational screens that may prove useful for evaluating analyte sets for their ability to accurately report on metabolic fluxes. The methodology is problem-centric in that the screens are used in the context of a particular metabolic engineering problem. That is, flux bounds and alternative flux routings are first identified for a particular problem, and then the information is used to inform the design of nuclear magnetic resonance (NMR) experiments. After obtaining the flux bounds via MILP, analytes are first screened for whether the predicted NMR spectra associated with various analytes can differentiate between different extreme point (or linear combinations of extreme point) flux solutions. The second screen entails determining whether the analytes provide unique flux values or multiple flux solutions. Finally, the economics associated with using different analytes is considered in order to further refine the analyte selection process in terms of an overall utility index, where the index summarizes the cost-benefit attributes by quantifying benefit (contrast power) per cost (e.g., NMR instrument time required). We also demonstrate the use of an alternative strategy, the Analytical Hierarchy Process, for ranking analytes based on the individual experimentalist's-generated weights assigned for the relative value of flux scenario contrast, unique inversion of NMR data to fluxes, etc.

Modelling strategies for the industrial exploitation of lactic acid bacteria

Lactic acid bacteria (LAB) have a long tradition of use in the food industry, and the number and diversity of their applications has increased considerably over the years. Traditionally, process optimization for these applications involved both strain selection and trial and error. More recently, metabolic engineering has emerged as a discipline that focuses on the rational improvement of industrially useful strains. In the post-genomic era, metabolic engineering increasingly benefits from systems biology, an approach that combines mathematical modelling techniques with functional-genomics data to build models for biological interpretation and--ultimately--prediction. In this review, the industrial applications of LAB are mapped onto available global, genome-scale metabolic modelling techniques to evaluate the extent to which functional genomics and systems biology can live up to their industrial promise.

Complementary identification of multiple flux distributions and multiple metabolic pathways

Cell robustness and complexity have been recognized as unique features of biological systems. Such robustness and complexity of metabolic-reaction systems can be explored by discovering, or identifying, the multiple flux distributions (MFD) and redundant pathways that lead to a given external state; however, this is exceedingly cumbersome to accomplish. It is, therefore, highly desirable to establish an effective computational method for their identification, which, in turn, gives rise to a novel insight into the cellular function. An effective approach is proposed for complementarily identifying MFD in metabolic flux analysis and multiple metabolic pathways (MMP) in structural pathway analysis. This approach judiciously integrates flux balance analysis (FBA) based on linear programming and the graph-theoretic method for determining reaction pathways. A single metabolic pathway, with the concomitant flux distribution and the overall reaction manifesting itself as the desired phenotype under some environmental conditions, is determined by FBA from the initial candidate sequence of metabolic reactions. Subsequently, the graph-theoretic method recovers all feasible MMP and the corresponding MFD. The approach's efficacy is demonstrated by applying it to the in silico Escherichia coli model under various culture conditions. The resultant MMP and MFD attaining a unique external state reveal the surprising adaptability and robustness of the intricate cellular network as a key to cell survival against environmental or genetic changes. These results indicate that the proposed approach would be useful in facilitating drug discovery.

Genome-scale models of microbial cells: evaluating the consequences of constraints

Microbial cells operate under governing constraints that limit their range of possible functions. With the availability of annotated genome sequences, it has become possible to reconstruct genome-scale biochemical reaction networks for microorganisms. The imposition of governing constraints on a reconstructed biochemical network leads to the definition of achievable cellular functions. In recent years, a substantial and growing toolbox of computational analysis methods has been developed to study the characteristics and capabilities of microorganisms using a constraint-based reconstruction and analysis (COBRA) approach. This approach provides a biochemically and genetically consistent framework for the generation of hypotheses and the testing of functions of microbial cells.

Fundamental Escherichia coli biochemical pathways for biomass and energy production: creation of overall flux states

We have previously shown that the metabolism for most efficient cell growth can be realized by a combination of two types of elementary modes. One mode produces biomass while the second mode generates only energy. The identity of the four most efficient biomass and energy pathway pairs changes, depending on the degree of oxygen limitation. The identification of such pathway pairs for different growth conditions offers a pathway-based explanation of maintenance energy generation. For a given growth rate, experimental aerobic glucose consumption rates can be used to estimate the contribution of each pathway type to the overall metabolic flux pattern. All metabolic fluxes are then completely determined by the stoichiometries of involved pathways defining all nutrient consumption and metabolite secretion rates. We present here equations that permit computation of network fluxes on the basis of unique pathways for the case of optimal, glucose-limited Escherichia coli growth under varying levels of oxygen stress. Predicted glucose and oxygen uptake rates and some metabolite secretion rates are in remarkable agreement with experimental observations supporting the validity of the presented approach. The entire most efficient, steady-state, metabolic rate structure is explicitly defined by the developed equations without need for additional computer simulations. The approach should be generally useful for analyzing and interpreting genomic data by predicting concise, pathway-based metabolic rate structures.

Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states

The constraint-based analysis of genome-scale metabolic and regulatory networks has been successful in predicting phenotypes and useful for analyzing high-throughput data sets. Within this modeling framework, linear optimization has been used to study genome-scale metabolic models, resulting in the enumeration of single optimal solutions describing the best use of the network to support growth. Here mixed-integer linear programming was used to calculate and study a subset of the alternate optimal solutions for a genome-scale metabolic model of Escherichia coli (iJR904) under a wide variety of environmental conditions. Analysis of the calculated sets of optimal solutions found that: (1) only a small subset of reactions in the network have variable fluxes across optima; (2) sets of reactions that are always used together in optimal solutions, correlated reaction sets, showed moderate agreement with the currently known transcriptional regulatory structure in E. coli and available expression data, and (3) reactions that are used under certain environmental conditions can provide clues about network regulatory needs. In addition, calculation of suboptimal flux distributions, using flux variability analysis, identified reactions which are used under significantly more environmental conditions suboptimally than optimally. Together these results demonstrate the utilization of reactions in genome-scale models under a variety of different growth conditions.

Reconstruction and Functional Characterization of the Human Mitochondrial Metabolic Network Based on Proteomic and Biochemical Data

Diverse datasets including genomic, proteomic, isotopomer, and DNA sequence variation are becoming available for human mitochondria. Thus there is a need to integrate these data within an in silico modeling framework where mitochondrial biology and related disorders can be studied and analyzed. This paper reports a reconstruction and characterization of the human mitochondrial metabolic network based on proteomic and biochemical data. The 189 reactions included in this reconstruction are both elementally and charge-balanced and are assigned to their respective cellular compartments (mitochondrial, cytosol, or extracellular). The capabilities of the reconstructed network to fulfill three metabolic functions (ATP production, heme synthesis, and mixed phospholipid synthesis) were determined. Network-based analysis of the mitochondrial energy conversion process showed that the overall ATP yield per glucose is 31.5. Network flexibility, characterized by allowable variation in reaction fluxes, was evaluated using flux variability analysis and analysis of all of the possible optimal flux distributions. Results showed that the network has high flexibility for the biosynthesis of heme and phospholipids but modest flexibility for maximal ATP production. A subset of all of the optimal network flux distributions, computed with respect to the three metabolic functions individually, was found to be highly correlated, suggesting that this set may contain physiological meaningful fluxes. Examinations of optimal flux distributions also identified correlated reaction sets that form functional modules in the network.

The effects of alternate optimal solutions in constraint-based genome-scale metabolic models

Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.

Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions

Cells grow by oxidizing nutrients using a complex network of biochemical reactions. During this process new biological material is produced along with energy used for maintaining cellular organization. Because the metabolic network is highly branched, these tasks can be accomplished using a wide variety of unique reaction sequences. However, evolutionary pressures under carbon-limited growth conditions likely select organisms that utilize highly efficient pathways. Using elementary-mode analysis, we demonstrate that the metabolism of the bacterium Escherichia coli contains four unique pathways that most efficiently convert glucose and oxygen into new cells and maintenance energy under any level of oxygen limitation. Observed regulatory patterns and experimental findings suggest growing cells use these highly efficient pathways. It is predicted that five knockout mutations generate a strain that supports growth using only the most efficient reaction sequence. The analysis approach should be generally useful for predicting metabolic capabilities and efficient network designs based on only genomic information.

Saccharomyces cerevisiae phenotypes can be predicted by using constraint-based analysis of a genome-scale reconstructed metabolic network

Full genome sequences of prokaryotic organisms have led to reconstruction of genome-scale metabolic networks and in silico computation of their integrated functions. The first genome-scale metabolic reconstruction for a eukaryotic cell, Saccharomyces cerevisiae, consisting of 1,175 metabolic reactions and 733 metabolites, has appeared. A constraint-based in silico analysis procedure was used to compute properties of the S. cerevisiae metabolic network. The computed number of ATP molecules produced per pair of electrons donated to the electron transport system (ETS) and energy-maintenance requirements were quantitatively in agreement with experimental results. Computed whole-cell functions of growth and metabolic by-product secretion in aerobic and anaerobic culture were consistent with experimental data, and thus mRNA expression profiles during metabolic shifts were computed. The computed consequences of gene knockouts on growth phenotypes were consistent with experimental observations. Thus, constraint-based analysis of a genome-scale metabolic network for the eukaryotic S. cerevisiae allows for computation of its integrated functions, producing in silico results that were consistent with observed phenotypic functions for approximately 70-80% of the conditions considered.

Advances in flux balance analysis

Biology is going through a paradigm shift from reductionist to holistic, systems-based approaches. The complete genome sequence for a number of organisms is available and the analysis of genome sequence data is proving very useful. Thus, genome sequencing projects and bioinformatic analyses are leading to a complete 'parts catalog' of the molecular components in many organisms. The next challenge will be to reconstruct and simulate overall cellular functions based on the extensive reductionist information. Recent advances have been made in the area of flux balance analysis, a mathematical modeling approach often utilized by metabolic engineers to quantitatively simulate microbial metabolism.

The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy

Genome-scale metabolic networks can be characterized by a set of systemically independent and unique extreme pathways. These extreme pathways span a convex, high-dimensional space that circumscribes all potential steady-state flux distributions achievable by the defined metabolic network. Genome-scale extreme pathways associated with the production of non-essential amino acids in Haemophilus influenzae were computed. They offer valuable insight into the functioning of its metabolic network. Three key results were obtained. First, there were multiple internal flux maps corresponding to externally indistinguishable states. It was shown that there was an average of 37 internal states per unique exchange flux vector in H. influenzae when the network was used to produce a single amino acid while allowing carbon dioxide and acetate as carbon sinks. With the inclusion of succinate as an additional output, this ratio increased to 52, a 40% increase. Second, an analysis of the carbon fates illustrated that the extreme pathways were non-uniformly distributed across the carbon fate spectrum. In the detailed case study, 45% of the distinct carbon fate values associated with lysine production represented 85% of the extreme pathways. Third, this distribution fell between distinct systemic constraints. For lysine production, the carbon fate values that represented 85% of the pathways described above corresponded to only 2 distinct ratios of 1:1 and 4:1 between carbon dioxide and acetate. The present study analysed single outputs from one organism, and provides a start to genome-scale extreme pathways studies. These emergent system-level characterizations show the significance of metabolic extreme pathway analysis at the genome-scale.