Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.     

ReacKnock: Identifying Reaction Deletion Strategies for Microbial Strain Optimization Based on Genome-Scale Metabolic Network

Gene knockout has been used as a common strategy to improve microbial strains for producing chemicals. Several algorithms are available to predict the target reactions to be deleted. Most of them apply mixed integer bi-level linear programming (MIBLP) based on metabolic networks, and use duality theory to transform bi-level optimization problem of large-scale MIBLP to single-level programming. However, the validity of the transformation was not proved. Solution of MIBLP depends on the structure of inner problem. If the inner problem is continuous, Karush-Kuhn-Tucker (KKT) method can be used to reformulate the MIBLP to a single-level one. We adopt KKT technique in our algorithm ReacKnock to attack the intractable problem of the solution of MIBLP, demonstrated with the genome-scale metabolic network model of E. coli for producing various chemicals such as succinate, ethanol, threonine and etc. Compared to the previous methods, our algorithm is fast, stable and reliable to find the optimal solutions for all the chemical products tested, and able to provide all the alternative deletion strategies which lead to the same industrial objective.     

Minimal cut sets in biochemical reaction networks

MOTIVATION: Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the network structure and to find suitable targets for repressing undesired metabolic functions. RESULTS: We introduce the concept of minimal cut sets for biochemical networks. A minimal cut set (MCS) is a minimal (irreducible) set of reactions in the network whose inactivation will definitely lead to a failure in certain network functions. We present an algorithm which enables the computation of the MCSs in a given network related to user-defined objective reactions. This algorithm operates on elementary modes. A number of potential applications are outlined, including network verifications, phenotype predictions, assessing structural robustness and fragility, metabolic flux analysis and target identification in drug discovery. Applications are illustrated by the MCSs in the central metabolism of Escherichia coli for growth on different substrates. AVAILABILITY: Computation and analysis of MCSs is an additional feature of the FluxAnalyzer (freely available for academic users upon request, special contracts for industrial companies; see web page below). Supplementary information: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer     

Decision tree modeling predicts effects of inhibiting contractility signaling on cell motility

Background

Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking.

Results

Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks.

Conclusion

CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use.     

NIBBS-search for fast and accurate prediction of phenotype-biased metabolic systems

Understanding of genotype-phenotype associations is important not only for furthering our knowledge on internal cellular processes, but also essential for providing the foundation necessary for genetic engineering of microorganisms for industrial use (e.g., production of bioenergy or biofuels). However, genotype-phenotype associations alone do not provide enough information to alter an organism's genome to either suppress or exhibit a phenotype. It is important to look at the phenotype-related genes in the context of the genome-scale network to understand how the genes interact with other genes in the organism. Identification of metabolic subsystems involved in the expression of the phenotype is one way of placing the phenotype-related genes in the context of the entire network. A metabolic system refers to a metabolic network subgraph; nodes are compounds and edges labels are the enzymes that catalyze the reaction. The metabolic subsystem could be part of a single metabolic pathway or span parts of multiple pathways. Arguably, comparative genome-scale metabolic network analysis is a promising strategy to identify these phenotype-related metabolic subsystems. Network Instance-Based Biased Subgraph Search (NIBBS) is a graph-theoretic method for genome-scale metabolic network comparative analysis that can identify metabolic systems that are statistically biased toward phenotype-expressing organismal networks. We set up experiments with target phenotypes like hydrogen production, TCA expression, and acid-tolerance. We show via extensive literature search that some of the resulting metabolic subsystems are indeed phenotype-related and formulate hypotheses for other systems in terms of their role in phenotype expression. NIBBS is also orders of magnitude faster than MULE, one of the most efficient maximal frequent subgraph mining algorithms that could be adjusted for this problem. Also, the set of phenotype-biased metabolic systems output by NIBBS comes very close to the set of phenotype-biased subgraphs output by an exact maximally-biased subgraph enumeration algorithm ( MBS-Enum ). The code (NIBBS and the module to visualize the identified subsystems) is available at http://freescience.org/cs/NIBBS.     

Interplay between Constraints,Objectives, and Optimality for Genome-Scale Stoichiometric Models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.     

Analysis of Metabolic Capabilities Using Singular Value Decomposition of Extreme Pathway Matrices

It is now possible to construct genome-scale metabolic networks for particular microorganisms. Extreme pathway analysis is a useful method for analyzing the phenotypic capabilities of these networks. Many extreme pathways are needed to fully describe the functional capabilities of genome-scale metabolic networks, and therefore, a need exists to develop methods to study these large sets of extreme pathways. Singular value decomposition (SVD) of matrices of extreme pathways was used to develop a conceptual framework for the interpretation of large sets of extreme pathways and the steady-state flux solution space they define. The key results of this study were: 1), convex steady-state solution cones describing the potential functions of biochemical networks can be studied using the modes generated by SVD; 2), Helicobacter pylori has a more rigid metabolic network (i.e., a lower dimensional solution space and a more dominant first singular value) than Haemophilus influenzae for the production of amino acids; and 3), SVD allows for direct comparison of different solution cones resulting from the production of different amino acids. SVD was used to identify key network branch points that may identify key control points for regulation. Therefore, SVD of matrices of extreme pathways has proved to be a useful method for analyzing the steady-state solution space of genome-scale metabolic networks.     

Analysis of Metabolic Subnetworks by Flux Cone Projection

Background

Analysis of elementary modes (EMs) is proven to be a powerful constraint-based method in the study of metabolic networks. However, enumeration of EMs is a hard computational task. Additionally, due to their large number, EMs cannot be simply used as an input for subsequent analysis. One possibility is to limit the analysis to a subset of interesting reactions. However, analysing an isolated subnetwork can result in finding incorrect EMs which are not part of any steady-state flux distribution of the original network. The ideal set to describe the reaction activity in a subnetwork would be the set of all EMs projected to the reactions of interest. Recently, the concept of "elementary flux patterns" (EFPs) has been proposed. Each EFP is a subset of the support (i.e., non-zero elements) of at least one EM.

Results

We introduce the concept of ProCEMs (Projected Cone Elementary Modes). The ProCEM set can be computed by projecting the flux cone onto a lower-dimensional subspace and enumerating the extreme rays of the projected cone. In contrast to EFPs, ProCEMs are not merely a set of reactions, but projected EMs. We additionally prove that the set of EFPs is included in the set of ProCEM supports. Finally, ProCEMs and EFPs are compared for studying substructures of biological networks.

Conclusions

We introduce the concept of ProCEMs and recommend its use for the analysis of substructures of metabolic networks for which the set of EMs cannot be computed.     

Computation of condition-dependent proteome allocation reveals variability in the macro and micro nutrient requirements for growth

Sustaining a robust metabolic network requires a balanced and fully functioning proteome. In addition to amino acids, many enzymes require cofactors (coenzymes and engrafted prosthetic groups) to function properly. Extensively validated resource allocation models, such as genome-scale models of metabolism and gene expression (ME-models), have the ability to compute an optimal proteome composition underlying a metabolic phenotype, including the provision of all required cofactors. Here we apply the ME-model for Escherichia coli K-12 MG1655 to computationally examine how environmental conditions change the proteome and its accompanying cofactor usage. We found that: (1) The cofactor requirements computed by the ME-model mostly agree with the standard biomass objective function used in models of metabolism alone (M-models); (2) ME-model computations reveal non-intuitive variability in cofactor use under different growth conditions; (3) An analysis of ME-model predicted protein use in aerobic and anaerobic conditions suggests an enrichment in the use of peroxyl scavenging acids in the proteins used to sustain aerobic growth; (4) The ME-model could describe how limitation in key protein components affect the metabolic state of E. coli. Genome-scale models have thus reached a level of sophistication where they reveal intricate properties of functional proteomes and how they support different E. coli lifestyles.     

Literature mining supports a next-generation modeling approach to predict cellular byproduct secretion

The metabolic byproducts secreted by growing cells can be easily measured and provide a window into the state of a cell; they have been essential to the development of microbiology, cancer biology, and biotechnology. Progress in computational modeling of cells has made it possible to predict metabolic byproduct secretion with bottom-up reconstructions of metabolic networks. However, owing to a lack of data, it has not been possible to validate these predictions across a wide range of strains and conditions. Through literature mining, we were able to generate a database of Escherichia coli strains and their experimentally measured byproduct secretions. We simulated these strains in six historical genome-scale models of E. coli, and we report that the predictive power of the models has increased as they have expanded in size and scope. The latest genome-scale model of metabolism correctly predicts byproduct secretion for 35/89 (39%) of designs. The next-generation genome-scale model of metabolism and gene expression (ME-model) correctly predicts byproduct secretion for 40/89 (45%) of designs, and we show that ME-model predictions could be further improved through kinetic parameterization. We analyze the failure modes of these simulations and discuss opportunities to improve prediction of byproduct secretion.     

An engineered non-oxidative glycolysis pathway for acetone production in <Emphasis Type="Italic">Escherichia coli</Emphasis>

Objectives

To find new metabolic engineering strategies to improve the yield of acetone in Escherichia coli.

Results

Results of flux balance analysis from a modified Escherichia coli genome-scale metabolic network suggested that the introduction of a non-oxidative glycolysis (NOG) pathway would improve the theoretical acetone yield from 1 to 1.5 mol acetone/mol glucose. By inserting the fxpk gene encoding phosphoketolase from Bifidobacterium adolescentis into the genome, we constructed a NOG pathway in E.coli. The resulting strain produced 47 mM acetone from glucose under aerobic conditions in shake-flasks. The yield of acetone was improved from 0.38 to 0.47 mol acetone/mol glucose which is a significant over the parent strain.

Conclusions

Guided by computational analysis of metabolic networks, we introduced a NOG pathway into E. coli and increased the yield of acetone, which demonstrates the importance of modeling analysis for the novel metabolic engineering strategies.

     

Computing complex metabolic intervention strategies using constrained minimal cut sets

The model-driven search for gene deletion strategies that increase the production performance of microorganisms is an essential part of metabolic engineering. One theoretical approach is based on Minimal Cut Sets (MCSs) which are minimal sets of knockouts disabling the operation of a specified set of target elementary modes. A limitation of the current approach is that MCSs can induce side effects disabling also desired functionalities. We, therefore, generalize MCSs to Constrained MCSs (cMCSs) allowing for the additional definition of a set of desired modes of which a minimum number must be preserved. Exemplarily for ethanol production by Escherichia coli, we demonstrate that this approach offers enormous flexibility in defining and solving knockout problems. Moreover, many existing methods can be reformulated as special cMCS problems. The cMCSs approach allows systematic enumeration of all equivalent gene deletion combinations and also helps to determine robust knockout strategies for coupled product and biomass synthesis.     

Generation of an atlas for commodity chemical production in Escherichia coli and a novel pathway prediction algorithm,GEM-Path

The production of 75% of the current drug molecules and 35% of all chemicals could be achieved through bioprocessing (Arundel and Sawaya, 2009). To accelerate the transition from a petroleum-based chemical industry to a sustainable bio-based industry, systems metabolic engineering has emerged to computationally design metabolic pathways for chemical production. Although algorithms able to provide specific metabolic interventions and heterologous production pathways are available, a systematic analysis for all possible production routes to commodity chemicals in Escherichia coli is lacking. Furthermore, a pathway prediction algorithm that combines direct integration of genome-scale models at each step of the search to reduce the search space does not exist. Previous work (Feist et al., 2010) performed a model-driven evaluation of the growth-coupled production potential for E. coli to produce multiple native compounds from different feedstocks. In this study, we extended this analysis for non-native compounds by using an integrated approach through heterologous pathway integration and growth-coupled metabolite production design. In addition to integration with genome-scale model integration, the GEM-Path algorithm developed in this work also contains a novel approach to address reaction promiscuity. In total, 245 unique synthetic pathways for 20 large volume compounds were predicted. Host metabolism with these synthetic pathways was then analyzed for feasible growth-coupled production and designs could be identified for 1271 of the 6615 conditions evaluated. This study characterizes the potential for E. coli to produce commodity chemicals, and outlines a generic strain design workflow to design production strains.     

Identifying All Moiety Conservation Laws in Genome-Scale Metabolic Networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell''s metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.     

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.     

The degree of redundancy in metabolic genes is linked to mode of metabolism

An understanding of the factors favoring the maintenance of duplicate genes in microbial genomes is essential for developing models of microbial evolution. A genome-scale flux-balance analysis of the metabolic network of Saccharomyces cerevisiae has suggested that gene duplications primarily provide increased enzyme dosage to enhance metabolic flux because the incidence of gene duplications in essential genes is no higher than that in nonessential genes. Here, we used genome-scale metabolic models to analyze the extent of genetic and biochemical redundancy in prokaryotes that are either specialists, with one major mode of energy generation, or generalists, which have multiple metabolic strategies for conservation of energy. Surprisingly, the results suggest that generalists, such as Escherichia coli and Bacillus subtilis, are similar to the eukaryotic generalist, S. cerevisiae, in having a low percentage (<10%) of essential genes and few duplications of these essential genes, whereas metabolic specialists, such as Geobacter sulfurreducens and Methanosarcina barkeri, have a high percentage (>30%) of essential genes and a high degree of genetic redundancy in these genes compared to nonessential genes. Furthermore, the specialist organisms appear to rely more on gene duplications rather than alternative-but-equivalent metabolic pathways to provide resilience to gene loss. Generalists rely more on alternative pathways. Thus, the concept that the role of gene duplications is to boost enzymatic flux rather than provide metabolic resilience may not be universal. Rather, the degree of gene duplication in microorganisms may be linked to mode of metabolism and environmental niche.     

Genome-scale reconstruction and <Emphasis Type="Italic">in silico</Emphasis> analysis of the <Emphasis Type="Italic">Clostridium acetobutylicum</Emphasis> ATCC 824 metabolic network

To understand the metabolic characteristics of Clostridium acetobutylicum and to examine the potential for enhanced butanol production, we reconstructed the genome-scale metabolic network from its annotated genomic sequence and analyzed strategies to improve its butanol production. The generated reconstructed network consists of 502 reactions and 479 metabolites and was used as the basis for an in silico model that could compute metabolic and growth performance for comparison with fermentation data. The in silico model successfully predicted metabolic fluxes during the acidogenic phase using classical flux balance analysis. Nonlinear programming was used to predict metabolic fluxes during the solventogenic phase. In addition, essential genes were predicted via single gene deletion studies. This genome-scale in silico metabolic model of C. acetobutylicum should be useful for genome-wide metabolic analysis as well as strain development for improving production of biochemicals, including butanol. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. J. L. and H. Y. equally contributed to this work.