Probing the performance limits of the Escherichia coli metabolic network subject to gene additions or deletions.

An optimization-based procedure for studying the response of metabolic networks after gene knockouts or additions is introduced and applied to a linear flux balance analysis (FBA) Escherichia coli model. Both the gene addition problem of optimally selecting which foreign genes to recombine into E. coli, as well as the gene deletion problem of removing a given number of existing ones, are formulated as mixed-integer optimization problems using binary 0-1 variables. The developed modeling and optimization framework is tested by investigating the effect of gene deletions on biomass production and addressing the maximum theoretical production of the 20 amino acids for aerobic growth on glucose and acetate substrates. In the gene deletion study, the smallest gene set necessary to achieve maximum biomass production in E. coli is determined for aerobic growth on glucose. The subsequent gene knockout analysis indicates that biomass production decreases monotonically, rendering the metabolic network incapable of growth after only 18 gene deletions. In the gene addition study, the E. coli flux balance model is augmented with 3,400 non-E. coli reactions from the KEGG database to form a multispecies model. This model is referred to as the Universal model. This study reveals that the maximum theoretical production of six amino acids could be improved by the addition of only one or two genes to the native amino acid production pathway of E. coli, even though the model could choose from 3,400 foreign reaction candidates. Specifically, manipulation of the arginine production pathway showed the most promise with 8.75% and 9.05% predicted increases with the addition of genes for growth on glucose and acetate, respectively. The mechanism of all suggested enhancements is either by: 1) improving the energy efficiency and/or 2) increasing the carbon conversion efficiency of the production route.     

Metabolic network analysis revealed distinct routes of deletion effects between essential and non-essential genes

Interest in essential genes has arisen recently given their importance in antimicrobial drug development. Although knockouts of essential genes are commonly known to cause lethal phenotypes, there is insufficient understanding on the intermediate changes followed by genetic perturbation and to what extent essential genes correlate to other genes. Here, we characterized the gene knockout effects by using a list of affected genes, termed as 'damage lists'. These damage lists were identified through a refined cascading failure approach that was based on a previous topological flux balance analysis. Using an Escherichia coli metabolic network, we incorporated essentiality information into damage lists and revealed that the knockout of an essential gene mainly affects a large range of other essential genes whereas knockout of a non-essential gene only interrupts other non-essential genes. Also, genes sharing common damage lists tend to have the same essentiality. We extracted 72 core functional modules from the common damage lists of essential genes and demonstrated their ability to halt essential metabolites production. Overall, our network analysis revealed that essential and non-essential genes propagated their deletion effects via distinct routes, conferring mechanistic explanation to the observed lethality phenotypes of essential genes.     

Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems

The elucidation of organism-scale metabolic networks necessitates the development of integrative methods to analyze and interpret the systemic properties of cellular metabolism. A shift in emphasis from single metabolic reactions to systemically defined pathways is one consequence of such an integrative analysis of metabolic systems. The constraints of systemic stoichiometry, and limited thermodynamics have led to the definition of the flux space within the context of convex analysis. The flux space of the metabolic system, containing all allowable flux distributions, is constrained to a convex polyhedral cone in a high-dimensional space. From metabolic pathway analysis, the edges of the high-dimensional flux cone are vectors that correspond to systemically defined "extreme pathways" spanning the capabilities of the system. The addition of maximum flux capacities of individual metabolic reactions serves to further constrain the flux space and has led to the development of flux balance analysis using linear optimization to calculate optimal flux distributions. Here we provide the precise theoretical connections between pathway analysis and flux balance analysis allowing for their combined application to study integrated metabolic function. Shifts in metabolic behavior are calculated using linear optimization and are then interpreted using the extreme pathways to demonstrate the concept of pathway utilization. Changes to the reaction network, such as the removal of a reaction, can lead to the generation of suboptimal phenotypes that can be directly attributed to the loss of pathway function and capabilities. Optimal growth phenotypes are calculated as a function of environmental variables, such as the availability of substrate and oxygen, leading to the definition of phenotypic phase planes. It is illustrated how optimality properties of the computed flux distributions can be interpreted in terms of the extreme pathways. Together these developments are applied to an example network and to core metabolism of Escherichia coli demonstrating the connections between the extreme pathways, optimal flux distributions, and phenotypic phase planes. The consequences of changing environmental and internal conditions of the network are examined for growth on glucose and succinate in the face of a variety of gene deletions. The convergence of the calculation of optimal phenotypes through linear programming and the definition of extreme pathways establishes a different perspective for the understanding of how a defined metabolic network is best used under different environmental and internal conditions or, in other words, a pathway basis for the interpretation of the metabolic reaction norm.     

Generalized concept of minimal cut sets in biochemical networks

Recently, the concept of minimal cut sets has been introduced for studying structural fragility and identifying knock-out strategies in biochemical reaction networks. A minimal cut set (MCS) has been defined as a minimal set of reactions whose removal blocks the operation of a chosen objective reaction. In this report the theoretical framework of MCSs is refined and extended increasing the practical applicability significantly. An MCS is now defined as a minimal (irreducible) set of structural interventions (removal of network elements) repressing a certain functionality specified by a deletion task. A deletion task describes unambiguously the flux patterns (or the functionality) to be repressed. It is shown that the MCSs can be computed from the set of target modes, which comprises all elementary modes that exhibit the functionality to be attacked. Since a deletion task can be specified by several Boolean rules, MCSs can now be determined for a large variety of complex deletion problems and may be utilized for inhibiting very special flux patterns. It is additionally shown that the other way around is also possible: the elementary modes belonging to a certain functionality can be computed from the respective set of MCSs. Therefore, elementary modes and MCSs can be seen as dual representations of network functions and both can be converted into each other. Moreover, there exist a strong relationship to minimal hitting sets known from set theory: the MCSs are the minimal hitting sets of the collection of target modes and vice versa. Another generalization introduced herein is that MCSs need not to be restricted to the removal of reactions they may also contain network nodes. In the light of the extended framework of MCSs, applications for assessing, manipulating, and designing metabolic networks in silico are discussed.     

Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective

Cellular metabolism is most often described and interpreted in terms of the biochemical reactions that make up the metabolic network. Genomics is providing near complete information regarding the genes/gene products participating in cellular metabolism for a growing number of organisms. As the true functional units of metabolic systems are its pathways, the time has arrived to define metabolic pathways in the context of whole-cell metabolism for the analysis of the structural design and capabilities of the metabolic network. In this study, we present the theoretical foundations for the identification of the unique set of systemically independent biochemical pathways, termed extreme pathways, based on system stochiometry and limited thermodynamics. These pathways represent the edges of the steady-state flux cone derived from convex analysis, and they can be used to represent any flux distribution achievable by the metabolic network. An algorithm is presented to determine the set of extreme pathways for a system of any complexity and a classification scheme is introduced for the characterization of these pathways. The property of systemic independence is discussed along with its implications for issues related to metabolic regulation and the evolution of cellular metabolic networks. The underlying pathway structure that is determined from the set of extreme pathways now provides us with the ability to analyse, interpret, and perhaps predict metabolic function from a pathway-based perspective in addition to the traditional reaction-based perspective. The algorithm and classification scheme developed can be used to describe the pathway structure in annotated genomes to explore the capabilities of an organism.     

Flux balance analysis of photoautotrophic metabolism

Photosynthesis is the principal process responsible for fixation of inorganic carbon dioxide into organic molecules with sunlight as the energy source. Potentially, many chemicals could be inexpensively produced by photosynthetic organisms. Mathematical modeling of photoautotrophic metabolism is therefore important to evaluate maximum theoretical product yields and to deeply understand the interactions between biochemical energy, carbon fixation, and assimilation pathways. Flux balance analysis based on linear programming is applied to photoautotrophic metabolism. The stoichiometric network of a model photosynthetic prokaryote, Synechocystis sp. PCC 6803, has been reconstructed from genomic data and biochemical literature and coupled with a model of the photophosphorylation processes. Flux map topologies for the hetero-, auto-, and mixotrophic modes of metabolism under conditions of optimal growth were determined and compared. The roles of important metabolic reactions such as the glyoxylate shunt and the transhydrogenase reaction were analyzed. We also theoretically evaluated the effect of gene deletions or additions on biomass yield and metabolic flux distributions.     

Dissecting Germ Cell Metabolism through Network Modeling

Metabolic pathways are increasingly postulated to be vital in programming cell fate, including stemness, differentiation, proliferation, and apoptosis. The commitment to meiosis is a critical fate decision for mammalian germ cells, and requires a metabolic derivative of vitamin A, retinoic acid (RA). Recent evidence showed that a pulse of RA is generated in the testis of male mice thereby triggering meiotic commitment. However, enzymes and reactions that regulate this RA pulse have yet to be identified. We developed a mouse germ cell-specific metabolic network with a curated vitamin A pathway. Using this network, we implemented flux balance analysis throughout the initial wave of spermatogenesis to elucidate important reactions and enzymes for the generation and degradation of RA. Our results indicate that primary RA sources in the germ cell include RA import from the extracellular region, release of RA from binding proteins, and metabolism of retinal to RA. Further, in silico knockouts of genes and reactions in the vitamin A pathway predict that deletion of Lipe, hormone-sensitive lipase, disrupts the RA pulse thereby causing spermatogenic defects. Examination of other metabolic pathways reveals that the citric acid cycle is the most active pathway. In addition, we discover that fatty acid synthesis/oxidation are the primary energy sources in the germ cell. In summary, this study predicts enzymes, reactions, and pathways important for germ cell commitment to meiosis. These findings enhance our understanding of the metabolic control of germ cell differentiation and will help guide future experiments to improve reproductive health.     

Genome-scale metabolic model of Helicobacter pylori 26695

A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes.     

Minimal reaction sets for Escherichia coli metabolism under different growth requirements and uptake environments

A computational procedure for identifying the minimal set of metabolic reactions capable of supporting various growth rates on different substrates is introduced and applied to a flux balance model of the Escherichia coli metabolic network. This task is posed mathematically as a generalized network optimization problem. The minimal reaction sets capable of supporting specified growth rates are determined for two different uptake conditions: (i) limiting the uptake of organic material to a single organic component (e.g., glucose or acetate) and (ii) allowing the importation of any metabolite with available cellular transport reactions. We find that minimal reaction network sets are highly dependent on the uptake environment and the growth requirements imposed on the network. Specifically, we predict that the E. coli network, as described by the flux balance model, requires 224 metabolic reactions to support growth on a glucose-only medium and 229 for an acetate-only medium, while only 122 reactions enable growth on a specially engineered growth medium.     

Genome-scale analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture

A dynamic flux balance model based on a genome-scale metabolic network reconstruction is developed for in silico analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture. Metabolic engineering strategies previously identified for their enhanced steady-state biomass and/or ethanol yields are evaluated for fed-batch performance in glucose and glucose/xylose media. Dynamic analysis is shown to provide a single quantitative measure of fed-batch ethanol productivity that explicitly handles the possible tradeoff between the biomass and ethanol yields. Productivity optimization conducted to rank achievable fed-batch performance demonstrates that the genetic manipulation strategy and the fed-batch operating policy should be considered simultaneously. A library of candidate gene insertions is assembled and directly screened for their achievable ethanol productivity in fed-batch culture. A number of novel gene insertions with ethanol productivities identical to the best metabolic engineering strategies reported in previous studies are identified, thereby providing additional targets for experimental evaluation. The top performing gene insertions were substrate dependent, with the highest ranked insertions for glucose media yielding suboptimal performance in glucose/xylose media. The analysis results suggest that enhancements in biomass yield are most beneficial for the enhancement of fed-batch ethanol productivity by recombinant xylose utilizing yeast strains. We conclude that steady-state flux balance analysis is not sufficient to predict fed-batch performance and that the media, genetic manipulations, and fed-batch operating policy should be considered simultaneously to achieve optimal metabolite productivity.     

Comparative analysis of metabolic network of pathogens

Background

Metabolic networks are complex and system of highly connected chemical reactions and hence it needs a system level computational approach to identify the genotype- phenotype relationship. The study of essential genes and reactions and synthetic lethality of genes and reactions plays a crucial role in explaining functional links between genes and gene function predictions.

Methods

Flux balance analysis (FBA) has been developed as a powerful method for the in silico analyses of metabolic networks. In this study, we present the comparative analysis of the genomic scale metabolic networks of the four microorganisms i.e. Salmonella typhimurium, Mycobacterium tuberculosis, Staphylococcus aureus, and Helicobacter pylori. The fluxes of all reaction were obtained and the growth rate of the organism was calculated by setting the biomass reaction as the objective function.

Results & Conclusions

The average lethality fraction of all the four organisms studied ranged from 0.2 to 0.6. It was also observed that there are very few metabolites which are highly connected. Those metabolites that are highly connected are supposed to be the ‘global players’ similar to the hub protein in the protein–protein interaction network.

     

Regulated redirection of central carbon flux enhances anaerobic production of bioproducts in Zymomonas mobilis

The microbial production of chemicals and fuels from plant biomass offers a sustainable alternative to fossilized carbon but requires high rates and yields of bioproduct synthesis. Z. mobilis is a promising chassis microbe due to its high glycolytic rate in anaerobic conditions that are favorable for large-scale production. However, diverting flux from its robust ethanol fermentation pathway to nonnative pathways remains a major engineering hurdle. To enable controlled, high-yield synthesis of bioproducts, we implemented a central-carbon metabolism control-valve strategy using regulated, ectopic expression of pyruvate decarboxylase (Pdc) and deletion of chromosomal pdc. Metabolomic and genetic analyses revealed that glycolytic intermediates and NADH accumulate when Pdc is depleted and that Pdc is essential for anaerobic growth of Z. mobilis. Aerobically, all flux can be redirected to a 2,3-butanediol pathway for which respiration maintains redox balance. Anaerobically, flux can be redirected to redox-balanced lactate or isobutanol pathways with ≥65% overall yield from glucose. This strategy provides a promising path for future metabolic engineering of Z. mobilis.     

Thermodynamics-based metabolic flux analysis

A new form of metabolic flux analysis (MFA) called thermodynamics-based metabolic flux analysis (TMFA) is introduced with the capability of generating thermodynamically feasible flux and metabolite activity profiles on a genome scale. TMFA involves the use of a set of linear thermodynamic constraints in addition to the mass balance constraints typically used in MFA. TMFA produces flux distributions that do not contain any thermodynamically infeasible reactions or pathways, and it provides information about the free energy change of reactions and the range of metabolite activities in addition to reaction fluxes. TMFA is applied to study the thermodynamically feasible ranges for the fluxes and the Gibbs free energy change, Delta(r)G', of the reactions and the activities of the metabolites in the genome-scale metabolic model of Escherichia coli developed by Palsson and co-workers. In the TMFA of the genome scale model, the metabolite activities and reaction Delta(r)G' are able to achieve a wide range of values at optimal growth. The reaction dihydroorotase is identified as a possible thermodynamic bottleneck in E. coli metabolism with a Delta(r)G' constrained close to zero while numerous reactions are identified throughout metabolism for which Delta(r)G' is always highly negative regardless of metabolite concentrations. As it has been proposed previously, these reactions with exclusively negative Delta(r)G' might be candidates for cell regulation, and we find that a significant number of these reactions appear to be the first steps in the linear portion of numerous biosynthesis pathways. The thermodynamically feasible ranges for the concentration ratios ATP/ADP, NAD(P)/NAD(P)H, and H(extracellular)(+)/H(intracellular)(+) are also determined and found to encompass the values observed experimentally in every case. Further, we find that the NAD/NADH and NADP/NADPH ratios maintained in the cell are close to the minimum feasible ratio and maximum feasible ratio, respectively.     

Elementary Flux Mode Analysis Revealed Cyclization Pathway as a Powerful Way for NADPH Regeneration of Central Carbon Metabolism

NADPH regeneration capacity is attracting growing research attention due to its important role in resisting oxidative stress. Besides, NADPH availability has been regarded as a limiting factor in production of industrially valuable compounds. The central carbon metabolism carries the carbon skeleton flux supporting the operation of NADPH-regenerating enzyme and offers flexibility in coping with NADPH demand for varied intracellular environment. To acquire an insightful understanding of its NADPH regeneration capacity, the elementary mode method was employed to compute all elementary flux modes (EFMs) of a network representative of central carbon metabolism. Based on the metabolic flux distributions of these modes, a cluster analysis of EFMs with high NADPH regeneration rate was conducted using the self-organizing map clustering algorithm. The clustering results were used to study the relationship between the flux of total NADPH regeneration and the flux in each NADPH producing enzyme. The results identified several reaction combinations supporting high NADPH regeneration, which are proven to be feasible in cells via thermodynamic analysis and coincident with a great deal of previous experimental report. Meanwhile, the reaction combinations showed some common characteristics: there were one or two decarboxylation oxidation reactions in the combinations that produced NADPH and the combination constitution included certain gluconeogenesis pathways. These findings suggested cyclization pathways as a powerful way for NADPH regeneration capacity of bacterial central carbon metabolism.     

Design, construction and performance of the most efficient biomass producing E. coli bacterium

Inverse metabolic engineering based on elementary mode analysis was applied to maximize the biomass yield of Escherchia coli MG1655. Elementary mode analysis was previously employed to identify among 1691 possible pathways for cell growth the most efficient pathway with maximum biomass yield. The metabolic network analysis predicted that deletion of only 6 genes reduces the number of possible elementary modes to the most efficient pathway. We have constructed a strain containing these gene deletions and we evaluated its properties in batch and in chemostat growth experiments. The results show that the theoretical predictions are closely matched by the properties of the designed strain.     

The genome‐scale metabolic network of Ectocarpus siliculosus (EctoGEM): a resource to study brown algal physiology and beyond

Brown algae (stramenopiles) are key players in intertidal ecosystems, and represent a source of biomass with several industrial applications. Ectocarpus siliculosus is a model to study the biology of these organisms. Its genome has been sequenced and a number of post‐genomic tools have been implemented. Based on this knowledge, we report the reconstruction and analysis of a genome‐scale metabolic network for E. siliculosus, EctoGEM ( http://ectogem.irisa.fr ). This atlas of metabolic pathways consists of 1866 reactions and 2020 metabolites, and its construction was performed by means of an integrative computational approach for identifying metabolic pathways, gap filling and manual refinement. The capability of the network to produce biomass was validated by flux balance analysis. EctoGEM enabled the reannotation of 56 genes within the E. siliculosus genome, and shed light on the evolution of metabolic processes. For example, E. siliculosus has the potential to produce phenylalanine and tyrosine from prephenate and arogenate, but does not possess a phenylalanine hydroxylase, as is found in other stramenopiles. It also possesses the complete eukaryote molybdenum co‐factor biosynthesis pathway, as well as a second molybdopterin synthase that was most likely acquired via horizontal gene transfer from cyanobacteria by a common ancestor of stramenopiles. EctoGEM represents an evolving community resource to gain deeper understanding of the biology of brown algae and the diversification of physiological processes. The integrative computational method applied for its reconstruction will be valuable to set up similar approaches for other organisms distant from biological benchmark models.     

Selection of objective function in genome scale flux balance analysis for process feed development in antibiotic production

Using flux variability analysis of a genome scale metabolic network of Streptomyces coelicolor, a series of reactions were identified, from disparate pathways that could be combined into an actinorhodin-generating mini-network. Candidate process feed nutrients that might be expected to influence this network were used in process simulations and in silico predictions compared to experimental findings. Ranking potential process feeds by flux balance analysis optimisation, using either growth or antibiotic production as objective function, did not correlate with experimental actinorhodin yields in fed processes. However, the effect of the feeds on glucose assimilation rate (using glucose uptake as objective function) ranked them in the same order as in vivo antibiotic production efficiency, consistent with results of a robustness analysis of the effect of glucose assimilation on actinorhodin production.     

Exploring the overproduction of amino acids using the bilevel optimization framework OptKnock

In this study, we modify and extend the bilevel optimization framework OptKnock for identifying gene knockout strategies in the Escherichia coli metabolic network, leading to the overproduction of representative amino acids and key precursors for all five families. These strategies span not only the central metabolic network genes but also the amino acid biosynthetic and degradation pathways. In addition to gene deletions, the transport rates of carbon dioxide, ammonia, and oxygen, as well as the secretion pathways for key metabolites, are introduced as optimization variables in the framework. Computational results demonstrate the importance of manipulating energy-producing/consuming pathways, controlling the uptake of nitrogen and oxygen, and blocking the secretion pathways of key competing metabolites. The identified pathway modifications include not only straightforward elimination of competing reactions but also a number of nonintuitive knockouts quite distant from the amino acid-producing pathways. Specifically, OptKnock suggests three reactions (i.e., pyruvate kinase, phosphotransacetylase, and ATPase) for deletion, in addition to the straightforward elimination of 2-ketoglutarate dehydrogenase, to generate a glutamate-overproducing mutant. Similarly, phosphofructokinase and ATPase are identified as promising knockout targets to complement the removal of pyruvate formate lyase and pyruvate dehydrogenase for enhancing the yield of alanine. Although OptKnock in its present form does not consider regulatory constraints, it does provide useful suggestions largely in agreement with existing practices and, more importantly, introduces a framework for incorporating additional modeling refinements as they become available.     

Classification and sensitivity analysis of a proposed primary metabolic reaction network for Streptomyces lividans

Constructing a metabolic flux analysis model is in principle fairly straightforward. However, there are a number of mathematical pitfalls. First, dependent reactions are a recurring problem and, second, the choice of reactions to measure may not be straight-forward. A method for systematic identification of dependent reactions and a thorough reactions classification procedure is presented. A well-defined stoichiometric presentation can provide significant insight into metabolic control mechanisms. Two methods for analyzing the impact of perturbations in the measured fluxes on the remaining metabolism and the impact of changes in biomass composition on the calculated metabolic reactions is developed. A metabolic reaction network proposed for Streptomyces lividans is used as an example to demonstrate the outlined analysis. It is concluded that oxygen utilization has the highest influence on the pathway fluxes and that realistic perturbations in the biomass composition do not significantly alter the flux patterns.