Elementary Flux Modes Research Articles

Structural Control of Metabolic Flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

Enzyme allocation problems in kinetic metabolic networks: Optimal solutions are elementary flux modes

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.

Metabolic analysis of Chlorobium chlorochromatii CaD3 reveals clues of the symbiosis in ‘Chlorochromatium aggregatum’

A symbiotic association occurs in 'Chlorochromatium aggregatum', a phototrophic consortium integrated by two species of phylogenetically distant bacteria composed by the green-sulfur Chlorobium chlorochromatii CaD3 epibiont that surrounds a central β-proteobacterium. The non-motile chlorobia can perform nitrogen and carbon fixation, using sulfide as electron donors for anoxygenic photosynthesis. The consortium can move due to the flagella present in the central β-protobacterium. Although Chl. chlorochromatii CaD3 is never found as free-living bacteria in nature, previous transcriptomic and proteomic studies have revealed that there are differential transcription patterns between the symbiotic and free-living status of Chl. chlorocromatii CaD3 when grown in laboratory conditions. The differences occur mainly in genes encoding the enzymatic reactions involved in nitrogen and amino acid metabolism. We performed a metabolic reconstruction of Chl. chlorochromatii CaD3 and an in silico analysis of its amino acid metabolism using an elementary flux modes approach (EFM). Our study suggests that in symbiosis, Chl. chlorochromatii CaD3 is under limited nitrogen conditions where the GS/GOGAT (glutamine synthetase/glutamate synthetase) pathway is actively assimilating ammonia obtained via N2 fixation. In contrast, when free-living, Chl. chlorochromatii CaD3 is in a condition of nitrogen excess and ammonia is assimilated by the alanine dehydrogenase (AlaDH) pathway. We postulate that 'Chlorochromatium aggregatum' originated from a parasitic interaction where the N2 fixation capacity of the chlorobia would be enhanced by injection of 2-oxoglutarate from the β-proteobacterium via the periplasm. This consortium would have the advantage of motility, which is fundamental to a phototrophic bacterium, and the syntrophy of nitrogen and carbon sources.

Elementary Flux Modes Analysis of Functional Domain Networks Allows a Better Metabolic Pathway Interpretation

Metabolic network analysis is an important step for the functional understanding of biological systems. In these networks, enzymes are made of one or more functional domains often involved in different catalytic activities. Elementary flux mode (EFM) analysis is a method of choice for the topological studies of these enzymatic networks. In this article, we propose to use an EFM approach on networks that encompass available knowledge on structure-function. We introduce a new method that allows to represent the metabolic networks as functional domain networks and provides an application of the algorithm for computing elementary flux modes to analyse them. Any EFM that can be represented using the classical representation can be represented using our functional domain network representation but the fine-grained feature of functional domain networks allows to highlight new connections in EFMs. This methodology is applied to the tricarboxylic acid cycle (TCA cycle) of Bacillus subtilis, and compared to the classical analyses. This new method of analysis of the functional domain network reveals that a specific inhibition on the second domain of the lipoamide dehydrogenase (pdhD) component of pyruvate dehydrogenase complex leads to the loss of all fluxes. Such conclusion was not predictable in the classical approach.

Flux modules in metabolic networks

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.

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.

Fast Computation of Minimal Cut Sets in Metabolic Networks with a Berge Algorithm that Utilizes Binary Bit Pattern Trees

Minimal cut sets are a valuable tool for analyzing metabolic networks and for identifying optimal gene intervention strategies by eliminating unwanted metabolic functions and keeping desired functionality. Minimal cut sets rely on the concept of elementary flux modes, which are sets of indivisible metabolic pathways under steady-state condition. However, the computation of minimal cut sets is nontrivial, as even medium-sized metabolic networks with just 100 reactions easily have several hundred million elementary flux modes. We developed a minimal cut set tool that implements the well-known Berge algorithm and utilizes a novel approach to significantly reduce the program run time by using binary bit pattern trees. By using the introduced tree approach, the size of metabolic models that can be analyzed and optimized by minimal cut sets is pushed to new and considerably higher limits.

On functional module detection in metabolic networks.

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models.

Metabolic pathway analysis and reduction for mammalian cell cultures—Towards macroscopic modeling

First of all, the aim of this paper is to systematically analyze the metabolism of mammalian cell cultures and reduce the complicated metabolic networks to a manageable macroscopic reaction scheme. Herein, the central carbon metabolism (glycolysis, TCA cycle and glutaminolysis) of glucose and amino acids was investigated whereas the synthetic metabolism of cell and antibody was simply represented with macroscopically balanced reactions. Without losing generality, perfusion and fed-batch cultures of two typical cell lines (hybridoma and GS-CHO) were carried out in bioreactor. With macroscopic balance analysis and metabolic flux analysis (stationary and dynamical), the metabolic networks were rationally reduced thanks to the experimental facts that most of the amino acids (except glutamine, glutamate, and alanine) contributed negligibly to the central carbon metabolism, i.e., they were allocated mainly to the syntheses. Finally, with the aid of analysis of elementary flux mode analysis and extreme pathways, nine macro reactions were derived with physiological definitions.Furthermore, the results from above analyses (MBA, MFA, EFM and EPs) support following conclusions: the respiratory quotient value in mammalian cell culture generally should be near one; several potential metabolic bottlenecks (pyruvate to acetyl-CoA, cytosol NADH translocation into mitochondrion, glutamate dehydrogenation into TCA) may control and regulate cellular metabolism. These results will benefit the future study of dynamic modeling for process monitoring and control.

Five-step continuous production of PHB analyzed by elementary flux, modes, yield space analysis and high structured metabolic model

A high structured metabolic model for PHB synthesis by Cupriavidus necator DSM 545 consisting of 43 mass balance equations related to the same number of intracellular compounds was established. The metabolic state of cells cultivated in a continuously operated five stage bioreactor cascade was analyzed by help of elementary flux modes and two-dimensional yield space. Two different C-source feeding strategies were performed. Concerning PHB and biomass yields, values of the more efficient strategy were used as the data source for elementary modes and metabolic flux calculations, respectively. Metabolic fluxes were calculated from experimental yield data using a combination of elementary modes by applying the quadratic programming approach, in which the sum of squared weighting factors was minimized. Two different metabolic situations concerning activity of glucose-6-phosphate isomerase were tested. The high structured metabolic model was validated by comparison of experimental data from 24h batch cultivation and simulated results.

Systems‐wide analysis and engineering of metabolic pathway fluxes in bio‐succinate producing Basfia succiniciproducens

Basfia succiniciproducens has been recently isolated as novel producer for succinate, an important platform chemical. In batch culture, the wild type exhibited a high natural yield of 0.75 mol succinate (mol glucose)⁻¹. Systems-wide ¹³C metabolic flux analysis identified undesired fluxes through pyruvate-formate lyase (PflD) and lactate dehydrogenase (LdhA). The double deletion strain B. succiniciproducens ΔldhA ΔpflD revealed a 45% improved product yield of 1.08 mol mol⁻¹. In addition, metabolic flux analysis unraveled the parallel in vivo activity of the oxidative and reductive branch of the TCA cycle in B. succiniciproducens, whereby the oxidative part mainly served for anabolism. The wild type re-directed surplus NADH via a cycle involving malic enzyme or via transhydrogenase, respectively, to supply NADPH for anabolism, because the fluxes through the oxidative PPP and isocitrate dehydrogenase, that also provide this cofactor, were not sufficient. This was not observed for the deletion mutants, B. succiniciproducens ΔpflD and ΔldhA ΔpflD, where PPP and isocitrate dehydrogenase flux alone matched with the reduced anabolic NADPH demand. The integration of the production performance into the theoretical flux space, computed by elementary flux mode analysis, revealed that B. succiniciproducens ΔldhA ΔpflD reached 62% of the theoretical maximum yield.

Elementary flux modes in a nutshell: Properties, calculation and applications

Elementary flux mode (EFM) analysis allows the unbiased decomposition of a metabolic network into minimal functional units, making it a powerful tool for metabolic engineering. While the use of EFM analysis (EFMA) is still limited by the size of the models it can handle, EFMA has been successfully applied to solve real-world metabolic engineering problems. Here we provide a user-oriented introduction to EFMA, provide examples of recent applications, analyze current research strategies to overcome the computational restrictions and give an overview over current approaches, which aim to identify and calculate only biologically relevant EFMs.

Selection of human tissue-specific elementary flux modes using gene expression data

The analysis of high-throughput molecular data in the context of metabolic pathways is essential to uncover their underlying functional structure. Among different metabolic pathway concepts in systems biology, elementary flux modes (EFMs) hold a predominant place, as they naturally capture the complexity and plasticity of cellular metabolism and go beyond predefined metabolic maps. However, their use to interpret high-throughput data has been limited so far, mainly because their computation in genome-scale metabolic networks has been unfeasible. To face this issue, different optimization-based techniques have been recently introduced and their application to human metabolism is promising. In this article, we exploit and generalize the K-shortest EFM algorithm to determine a subset of EFMs in a human genome-scale metabolic network. This subset of EFMs involves a wide number of reported human metabolic pathways, as well as potential novel routes, and constitutes a valuable database where high-throughput data can be mapped and contextualized from a metabolic perspective. To illustrate this, we took expression data of 10 healthy human tissues from a previous study and predicted their characteristic EFMs based on enrichment analysis. We used a multivariate hypergeometric test and showed that it leads to more biologically meaningful results than standard hypergeometric. Finally, a biological discussion on the characteristic EFMs obtained in liver is conducted, finding a high level of agreement when compared with the literature.

Drug target prediction using elementary mode analysis in Ascaris lumbricoides energy metabolism

Ascariasis, an intestinal worm infection is caused by the parasite Ascaris lumbricoides and a report by World Health Organization (WHO) on soil transmitted helminths suggests that over one billion people are affected by Ascariasis. This disease is prevalent in developing countries, and in places of poor sanitation and unhygienic conditions. Even though anthelminthic drugs are available for the treatment of ascariasis, it is considered as a neglected tropical disease (NTD). Resistance of the parasite to the existing drugs necessitates a detailed study of its energy metabolism for identification of new drug targets. The catabolic pathway of the parasite is an evolved design well suited for parasitic life and obtains constant input from its host. Its energy metabolism is predominantly anaerobic. The parasite mitochondrion plays a key role as it lacks the functional tricarboxylic acid cycle (TCA cycle) and cytochrome oxidase activity. In adult ascarid mitochondrion, there is no external final electron acceptor and endogenously produced fumarate and 2-methyl branched-chain enoyl — CoAs function as the terminal electron acceptors instead of oxygen. In this study, elementary flux mode analysis (EFM), a metabolic pathway analysis tool has been applied to model energy metabolism of the parasite A. lumbricoides. This study identifies a set of enzymes that have been suggested to be essential for the survival of the parasite; the inhibition of these enzymes paralyzes the parasite. The key enzymes of glycolysis and the phosphoenolpyruvate carboxykinase-succinate pathway are identified as drug targets since the knock-out of any of these enzymes results in zero flux value for all EFM that have been identified.

RegEfmtool: Speeding up elementary flux mode calculation using transcriptional regulatory rules in the form of three-state logic

Despite the considerable progress made in recent years, the computation of the complete set of elementary flux modes of large or even genome-scale metabolic networks is still impossible. We present regEfmtool which is an extension to efmtool that utilizes transcriptional regulatory networks for the computation of elementary flux modes. The implemented extension significantly decreases the computational costs for the calculation of elementary flux modes, such as runtime, memory usage and disk space by omitting biologically infeasible solutions. Hence, using the presented regEfmtool pushes the size of metabolic networks that can be studied by elementary flux modes to new limits.

Systems metabolic engineering for the production of bio‐nylon precursor

Systematic approaches for in silico design of metabolic pathways and experimental evaluation of cellular performance are important for the development of industrially useful organisms. In this issue of Biotechnology Journal, Buschke et al. [1] report the production of 1,5-diaminopentane using xylose produced by Corynebacterium glutamicum by employing integration methodologies of rational design for genetic improvement, experimental analysis of metabolic fluxes, and comprehensive gene expression. Recent progress in 'omics sciences has facilitated the analysis of microorganisms for molecular breeding. There has been increasing interest for the integration of in silico and experimental approaches for the development of microbial cells for industrial applications. In silico simulations aid the rational design of metabolic pathways for the production of target compounds. On the basis of the in silico simulation data, the host organism is genetically manipulated to improve target metabolite production [2, 3]. The 13C-metabolic flux analysis method is useful for determining the flux distribution; this method requires experimental data procured from genetically manipulated strains [4, 5]. Identification of the genes that confer useful phenotypes for cells on the basis of DNA microarray analysis is also important [6]. The integration method, which combines in silico and experimental approaches for the development of cell factories is shown in Fig. 1. Many applications of the integration method for the bioproduction of chemicals and fuels have been reported [7, 8]. Concept of systems metabolic engineering. Production of 1,5-diaminopentane, a bio-nylon precursor, is reported by Buschke et al. [1], in this Special Issue “Systems Metabolic Engineering” of Biotechnology Journal. Buschke et al.'s study [1] is a good example of the successful application of bioengineering that contributes to the recent progress in systems metabolic engineering. Diaminopentane is produced by a one-step reaction from lysine by C. glutamicum, which is a well-known amino acid-producing bacterium and has recently used for chemical production as well [9, 10]. The authors have previously developed a high-producing strain that converts glucose to diaminopentane [11]. In the current study [1], a novel strain which produces diaminopentane from xylose was developed. Xylose utilization is particularly useful because xylose is a main component of lignocellulose waste, which is widely available. The previously developed diaminopentane-producing strain, DAP-Xyl1, produce diaminopentane less efficiently from xylose than from glucose. Thus, Buschke et al. [1] apply a systematic approach to improve diaminopentane production. In silico elementary flux mode analysis predicts an ideal metabolic state for diaminopentane production. The theoretical maximum yield from xylose is predicted, and the analysis reveal that the high oxidative pentose phosphate pathway (PPP) flux and the zero flux of the tricarboxylic acid (TCA) cycle are important for diaminopentane production; however, the metabolic flux of these pathways in the strain DAP-Xyl1 does not show good agreement with ideal metabolic flux for diaminopentane production. The small flux of PPP and the large flux of the TCA cycle cause low production of diaminopentane by the strain DAP-Xyl1. Additionally, gene selection is performed on the basis of the transcriptome analysis results. The novel, rationally designed strain DAP-Xyl2 successfully produce more than 100 g/L of diaminopentane after 75 h of cultivation. This study demonstrates the development process of a high performance strain of C. glutamicum and the importance of systems metabolic engineering approach for developing an industrially useful microorganism [7, 12]. The author declares no conflict of interest.

Finding minimal generating set for metabolic network with reversible pathways

Elementary flux modes give a mathematical representation of metabolic pathways in metabolic networks satisfying the constraint of non-decomposability. The large cost of their computation shifts attention to computing a minimal generating set which is a conically independent subset of elementary flux modes. When a metabolic network has reversible reactions and also admits a reversible pathway, the minimal generating set is not unique. A theoretical development and computational framework is provided which outline how to compute the minimal generating set in this case. The method is based on combining existing software to compute the minimal generating set for a “pointed cone” together with standard software to compute the Reduced Row Echelon Form.

Integration of time-resolved transcriptomics data with flux-based methods reveals stress-induced metabolic adaptation in Escherichia coli

BackgroundChanges in environmental conditions require temporal effectuation of different metabolic pathways in order to maintain the organisms’ viability but also to enable the settling into newly arising conditions. While analyses of robustness in biological systems have resulted in the characterization of reactions that facilitate homeostasis, temporal adaptation-related processes and the role of cellular pathways in the metabolic response to changing conditions remain elusive.ResultsHere we develop a flux-based approach that allows the integration of time-resolved transcriptomics data with genome-scale metabolic networks. Our framework uses bilevel optimization to extract temporal minimal operating networks from a given large-scale metabolic model. The minimality of the extracted networks enables the computation of elementary flux modes for each time point, which are in turn used to characterize the transitional behavior of the network as well as of individual reactions. Application of the approach to the metabolic network of Escherichia coli in conjunction with time-series gene expression data from cold and heat stress results in two distinct time-resolved modes for reaction utilization—constantly active and temporally (de)activated reactions. These patterns contrast the processes for the maintenance of basic cellular functioning and those required for adaptation. They also allow the prediction of reactions involved in time- and stress-specific metabolic response and are verified with respect to existing experimental studies.ConclusionsAltogether, our findings pinpoint the inherent relation between the systemic properties of robustness and adaptability arising from the interplay of metabolic network structure and changing environment.

In-silico-driven metabolic engineering of Pseudomonas putida for enhanced production of poly-hydroxyalkanoates

Here, we present systems metabolic engineering driven by in-silico modeling to tailor Pseudomonas putida for synthesis of medium chain length PHAs on glucose. Using physiological properties of the parent wild type as constraints, elementary flux mode analysis of a large-scale model of the metabolism of P. putida was used to predict genetic targets for strain engineering. Among a set of priority ranked targets, glucose dehydrogenase (encoded by gcd) was predicted as most promising deletion target. The mutant P. putida Δgcd, generated on basis of the computational design, exhibited 100% increased PHA accumulation as compared to the parent wild type, maintained a high specific growth rate and exhibited an almost unaffected gene expression profile, which excluded detrimental side effects of the modification. A second mutant strain, P. putida Δpgl, that lacked 6-phosphogluconolactonase, exhibited a substantially decreased PHA synthesis, as was also predicted by the model. The production potential of P. putida Δgcd was assessed in batch bioreactors. The novel strain showed an increase of the PHA yield (+80%), the PHA titer (+100%) and cellular PHA content (+50%) and revealed almost unaffected growth and diminished by-product formation. It was thus found superior in all relevant criteria towards industrial production. Beyond the contribution to more efficient PHA production processes at reduced costs that might replace petrochemical plastics in the future, the study illustrates the power of computational prediction to tailor microbial strains for enhanced biosynthesis of added-value compounds.

Random sampling of elementary flux modes in large-scale metabolic networks.

Motivation: The description of a metabolic network in terms of elementary (flux) modes (EMs) provides an important framework for metabolic pathway analysis. However, their application to large networks has been hampered by the combinatorial explosion in the number of modes. In this work, we develop a method for generating random samples of EMs without computing the whole set.Results: Our algorithm is an adaptation of the canonical basis approach, where we add an additional filtering step which, at each iteration, selects a random subset of the new combinations of modes. In order to obtain an unbiased sample, all candidates are assigned the same probability of getting selected. This approach avoids the exponential growth of the number of modes during computation, thus generating a random sample of the complete set of EMs within reasonable time. We generated samples of different sizes for a metabolic network of Escherichia coli, and observed that they preserve several properties of the full EM set. It is also shown that EM sampling can be used for rational strain design. A well distributed sample, that is representative of the complete set of EMs, should be suitable to most EM-based methods for analysis and optimization of metabolic networks.Availability: Source code for a cross-platform implementation in Python is freely available at http://code.google.com/p/emsampler.Contact: dmachado@deb.uminho.ptSupplementary information: Supplementary data are available at Bioinformatics online.