Elementary Flux Modes Research Articles

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114–120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases. We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.

Elementary flux modes – state-of-the-art implementation and scope of application

Elementary flux modes – state-of-the-art implementation and scope of application

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

BackgroundControl 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.ResultsThe 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.ConclusionThe 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.

From structure to dynamics of metabolic pathways: application to the plant mitochondrial TCA cycle

Mitochondrial metabolism, dominated by the reactions of the tricarboxylic acid (TCA) cycle, is of vital importance for a wide range of metabolic processes. In particular for autotrophic tissue, such as plant leaves, the TCA cycle marks the point of divergence of anabolic pathways and plays an essential role in biosynthesis. However, despite extensive knowledge about its stoichiometric properties, the function and the dynamical capabilities of the TCA cycle remain largely unknown. Based on a recently proposed formalism, we investigate the dynamic and functional properties of the mitochondrial TCA cycle of plants. Starting with the structural properties, as described by the elementary flux modes of the system, we aim for the transition from structure to the dynamics of the TCA cycle. Using a parametric description of the system, encompassing all possible differential equations and parameter values, we detect and quantify regimes of different dynamic behavior. Optimizing the system with respect to dynamic stability, we demonstrate that maximal stability is associated with specific (relative) metabolite concentrations and flux values that are subsequently compared to the experimental literature. Our analysis also serves as a general example how to elucidate the transition from the structure to the dynamics of metabolic pathways.

Identification of flux regulation coefficients from elementary flux modes: A systems biology tool for analysis of metabolic networks

Within a metabolic network, the elementary flux modes enables a unique description of different operations of the network. Thus, the metabolic fluxes can be specified as convex combinations of the elementary flux modes. Here, we describe an approach to identify the set of elementary flux modes that operates in a given metabolic network through the use of measurements of macroscopic fluxes, that is, fluxes in and out of the cell. Besides enabling estimation of the metabolic fluxes, the parameters of the linear combinations of the elementary flux modes provide valuable physiological information; we call these parameters flux regulation coefficients (FRCs). These coefficients indicate which enzyme subsets are important at different growth conditions. We demonstrate how FRCs can be used to map the operation of the metabolic network of the yeast Saccharomyces sp. under different growth conditions.

Analysis of Growth of Lactobacillus plantarum WCFS1 on a Complex Medium Using a Genome-scale Metabolic Model

A genome-scale metabolic model of the lactic acid bacterium Lactobacillus plantarum WCFS1 was constructed based on genomic content and experimental data. The complete model includes 721 genes, 643 reactions, and 531 metabolites. Different stoichiometric modeling techniques were used for interpretation of complex fermentation data, as L. plantarum is adapted to nutrient-rich environments and only grows in media supplemented with vitamins and amino acids. (i) Based on experimental input and output fluxes, maximal ATP production was estimated and related to growth rate. (ii) Optimization of ATP production further identified amino acid catabolic pathways that were not previously associated with free-energy metabolism. (iii) Genome-scale elementary flux mode analysis identified 28 potential futile cycles. (iv) Flux variability analysis supplemented the elementary mode analysis in identifying parallel pathways, e.g. pathways with identical end products but different co-factor usage. Strongly increased flexibility in the metabolic network was observed when strict coupling between catabolic ATP production and anabolic consumption was relaxed. These results illustrate how a genome-scale metabolic model and associated constraint-based modeling techniques can be used to analyze the physiology of growth on a complex medium rather than a minimal salts medium. However, optimization of biomass formation using the Flux Balance Analysis approach, reported to successfully predict growth rate and by product formation in Escherichia coli and Saccharomyces cerevisiae, predicted too high biomass yields that were incompatible with the observed lactate production. The reason is that this approach assumes optimal efficiency of substrate to biomass conversion, and can therefore not predict the metabolically inefficient lactate formation.

Dynamic optimisation of a recombinant BHK-21 culture based on elementary flux analysis and hybrid parametric/nonparametric modeling

Although MFA and MPA techniques have been mainly used for metabolic engineering [1], they may also be useful in other phases of the bioprocess development cycle, namely for advanced bioreactor monitoring and control [2,3]. A number of methods have been developed to study the structure of biochemical networks. From a process optimisation and control point of view, the elementary flux modes (EFMs) method is particularly attractive since it reduces network complexity to a minimal set of reactions. EFMs are unique for a given network and can be considered as nondecomposable steady state flux distributions using a minimal set of reactions.

Metabolic design of macroscopic bioreaction models: application to Chinese hamster ovary cells

The aim of this paper is to present a systematic methodology to design macroscopic bioreaction models for cell cultures based upon metabolic networks. The cell culture is seen as a succession of phases. During each phase, a metabolic network represents the set of reactions occurring in the cell. Then, through the use of the elementary flux modes, these metabolic networks are used to derive macroscopic bioreactions linking the extracellular substrates and products. On this basis, as many separate models are obtained as there are phases. Then, a complete model is obtained by smoothly switching from model to model. This is illustrated with batch cultures of Chinese hamster ovary cells.

HYBMFA: a bioinformatics' tool for batch-to-batch bioprocess optimisation supported by elementary flux analysis

Background The central metabolic pathways of many biological systems with industrial interest are currently known. Knowledge of intracellular fluxes is crucial to understand cell metabolism. Bioreactor dynamic optimisation schemes could profit from the incorporation of this knowledge [1,2]. A number of methods have been developed to study the structure of biochemical networks. The elementary flux modes (EFMs) method is particularly attractive since it allows to reduce network complexity to a minimal set of reactions [3].

Pathway classification of TCA cycle

The structural analysis of large metabolic networks exhibits a combinatorial explosion of elementary modes. A new method of classification has been developed [called aggregation around common motif (ACoM)], which groups elementary modes into classes with similar substructures. This method is applied to the tricarboxylic acid cycle and metabolite carriers. The analysis of this network evidences a great number of elementary flux modes (204) despite the low number of reactions (23). The ACoM is used to class these elementary modes in a low number of sets (8) with biological meanings.

Identification of distributed metabolic objectives in the hypermetabolic liver by flux and energy balance analysis

A methodology for inferring distributed metabolic objectives from time series flux data is developed by combining metabolic flux analysis, pathway identification, free energy balances, and nested optimization. This methodology is used to investigate the metabolic response of the rat liver to burn injury-induced whole body inflammation. Gibbs free energy changes were computed for stoichiometrically balanced sequences of reactions, or pathways, rather than individual reactions, to account for energetic coupling between reactions. Systematic enumeration of pathways proceeded by elementary flux mode (EFM) analysis. Together with stoichiometric balances and external metabolite flux measurements, the Δ G PATH o criterion provided sufficient constraints to solve a series of nested optimization problems on the metabolic goal functions and associated flux distributions of fasted livers during the first-week time course of burn injury. The optimization results suggest that there is a consistent metabolic goal function for the liver that is insensitive to the changing metabolic burdens experienced by the liver during the first-week time course. As defined by the goal function coefficients, the global metabolic objective was to distribute the metabolic resources between amino acid metabolism and ketone body synthesis. These findings point to a role for the time-invariant structure of the metabolic reaction network, expressed as stoichiometric and thermodynamic constraints, in shaping the cellular metabolic objective.

Development of a metabolic network design and optimization framework incorporating implementation constraints: A succinate production case study

We have developed a pathway design and optimization scheme that accommodates genetically and/or environmentally derived operational constraints. We express the full set of theoretically optimal pathways in terms of the underlying elementary flux modes and then examine the sensitivity of the optimal yield to a wide class of physiological perturbations. Though the scheme is general it is best appreciated in a concrete context: we here take succinate production as our model system. The scheme produces novel pathway designs and leads to the construction of optimal succinate production pathway networks. The model predictions compare very favorably with experimental observations.

Adenine and adenosine salvage pathways in erythrocytes and the role of S‐adenosylhomocysteine hydrolase

This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythrocytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of ATP build-up from the recycled substrates and show that the network has considerable redundancy. For example, four different pathways of adenine salvage and 12 different pathways of adenosine salvage are obtained. They give different ATP/glucose yields, the highest being 3:10 for adenine salvage and 2:3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed.

YANA – a software tool for analyzing flux modes, gene-expression and enzyme activities

BackgroundA number of algorithms for steady state analysis of metabolic networks have been developed over the years. Of these, Elementary Mode Analysis (EMA) has proven especially useful. Despite its low user-friendliness, METATOOL as a reliable high-performance implementation of the algorithm has been the instrument of choice up to now. As reported here, the analysis of metabolic networks has been improved by an editor and analyzer of metabolic flux modes. Analysis routines for expression levels and the most central, well connected metabolites and their metabolic connections are of particular interest.ResultsYANA features a platform-independent, dedicated toolbox for metabolic networks with a graphical user interface to calculate (integrating METATOOL), edit (including support for the SBML format), visualize, centralize, and compare elementary flux modes. Further, YANA calculates expected flux distributions for a given Elementary Mode (EM) activity pattern and vice versa. Moreover, a dissection algorithm, a centralization algorithm, and an average diameter routine can be used to simplify and analyze complex networks. Proteomics or gene expression data give a rough indication of some individual enzyme activities, whereas the complete flux distribution in the network is often not known. As such data are noisy, YANA features a fast evolutionary algorithm (EA) for the prediction of EM activities with minimum error, including alerts for inconsistent experimental data. We offer the possibility to include further known constraints (e.g. growth constraints) in the EA calculation process. The redox metabolism around glutathione reductase serves as an illustration example. All software and documentation are available for download at .ConclusionA graphical toolbox and an editor for METATOOL as well as a series of additional routines for metabolic network analyses constitute a new user-friendly software for such efforts.

Algorithmic approaches for computing elementary modes in large biochemical reaction networks

The concept of elementary (flux) modes provides a rigorous description of pathways in metabolic networks and proved to be valuable in a number of applications. However, the computation of elementary modes is a hard computational task that gave rise to several variants of algorithms during the last years. This work brings substantial progresses to this issue. The authors start with a brief review of results obtained from previous work regarding (a) a unified framework for elementary-mode computation, (b) network compression and redundancy removal and (c) the binary approach by which elementary modes are determined as binary patterns reducing the memory demand drastically without loss of speed. Then the authors will address herein further issues. First, a new way to perform the elementarity tests required during the computation of elementary modes which empirically improves significantly the computation time in large networks is proposed. Second, a method to compute only those elementary modes where certain reactions are involved is derived. Relying on this method, a promising approach for computing EMs in a completely distributed manner by decomposing the full problem in arbitrarity many sub-tasks is presented. The new methods have been implemented in the freely available software tools FluxAnalyzer and Metatool and benchmark tests in realistic networks emphasise the potential of our proposed algorithms.

Investigating the dynamic behavior of biochemical networks using model families

Supporting the evolutionary modeling process of dynamic biochemical networks based on sampled in vivo data requires more than just simulation. In the course of the modeling process, the modeler is typically concerned not only with a single model but also with sequences, alternatives and structural variants of models. Powerful automatic methods are then required to assist the modeler in the organization and the evaluation of alternative models. Moreover, the structure and peculiarities of the data require dedicated tool support. To support all stages of an evolutionary modeling process, a new general formalism for the combinatorial specification of large model families is introduced. It allows for automatic navigation in the space of models and excludes biologically meaningless models on the basis of elementary flux mode analysis. An incremental usage of the measured data is supported by using splined data instead of state variables. With MMT2, a versatile tool has been developed as a computational engine intended to be built into a tool chain. Using automatic code generation, automatic differentiation for sensitivity analysis and grid computing technology, a high performance computing environment is achieved. MMT2 supplies XML model specification and several software interfaces. The performance of MMT2 is illustrated by several examples from ongoing research projects. http://www.simtec.mb.uni-siegen.de/ wiechert@simtec.mb.uni-siegen.de.

Rubisco without the Calvin cycle improves the carbon efficiency of developing green seeds

Efficient storage of carbon in seeds is crucial to plant fitness and to agricultural productivity. Oil is a major reserve material in most seeds, and these oils provide the largest source of renewable reduced carbon chains available from nature. However, the conversion of carbohydrate to oil through glycolysis results in the loss of one-third of the carbon as CO2. Here we show that, in developing embryos of Brassica napus L. (oilseed rape), Rubisco (ribulose 1,5-bisphosphate carboxylase/oxygenase) acts without the Calvin cycle and in a previously undescribed metabolic context to increase the efficiency of carbon use during the formation of oil. In comparison with glycolysis, the metabolic conversion we describe provides 20% more acetyl-CoA for fatty-acid synthesis and results in 40% less loss of carbon as CO2. Our conclusions are based on measurements of mass balance, enzyme activity and stable isotope labelling, as well as an analysis of elementary flux modes.

Metabolic pathway analysis of enzyme-deficient human red blood cells

Five enzymopathies (G6PDH, TPI, PGI, DPGM and PGK deficiencies) in the human red blood cells are investigated using a stoichiometric modeling approach, i.e., metabolic pathway analysis. Elementary flux modes (EFMs) corresponding to each enzyme deficiency case are analyzed in terms of functional capabilities. When available, experimental findings reported in literature related to metabolic behavior of the human red blood cells are compared with the results of EFM analysis. Control-effective flux (CEF) calculation, a novel approach which allows quantification and interpretation of determined EFMs, is performed for further analysis of enzymopathies. Glutathione reductase reaction is found to be the most effective reaction in terms of its CEF value in all enzymopathies in parallel with its known essential role for red blood cells. Efficiency profiles of the enzymatic reactions upon the degree of enzyme deficiency are obtained by the help of the CEF approach, as a basis for future experimental studies. CEF analysis, which is found to be promising in the analysis of erythrocyte enzymopathies, has the potential to be used in modeling efforts of human metabolism.

Analysis of structural robustness of metabolic networks

We study the structural robustness of metabolic networks on the basis of the concept of elementary flux modes. It is shown that the number of elementary modes itself is not an appropriate measure of structural robustness. Instead, we introduce three new robustness measures. These are based on the relative number of elementary modes remaining after the knockout of enzymes. We discuss the relevance of these measures with the help of simple examples, as well as with larger, realistic metabolic networks. Thereby we demonstrate quantitatively that the metabolism of Escherichia coli, which must be able to adapt to varying conditions, is more robust than the metabolism of the human erythrocyte, which lives under much more homeostatic conditions.

Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks.

Central carbon metabolism of the yeast Saccharomyces cerevisiae was analyzed using metabolic pathway analysis tools. Elementary flux modes for three substrates (glucose, galactose, and ethanol) were determined using the catabolic reactions occurring in yeast. Resultant elementary modes were used for gene deletion phenotype analysis and for the analysis of robustness of the central metabolism and network functionality. Control-effective fluxes, determined by calculating the efficiency of each mode, were used for the prediction of transcript ratios of metabolic genes in different growth media (glucose-ethanol and galactose-ethanol). A high correlation was obtained between the theoretical and experimental expression levels of 38 genes when ethanol and glucose media were considered. Such analysis was shown to be a bridge between transcriptomics and fluxomics. Control-effective flux distribution was found to be promising in in silico predictions by incorporating functionality and regulation into the metabolic network structure.