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Analysis of the pathway structure of metabolic networks.

Metabolic networks comprise a multitude of enzymatic reactions carrying out various functions related to cell growth and product formation. Although such reactions are occasionally organized into biochemical pathways, a formal procedure is desired to identify the independent pathways in a bioreaction network and the degree of engagement of each individual reaction in these pathways. We present a procedure for the identification of the independent pathways of bioreaction networks of any size and complexity. The method makes use of the steady-state internal metabolite stoichiometry matrix and defines the independent pathways through the reaction membership of its kernel matrix. Examples from the aromatic amino acid biosynthetic pathway and central carbon metabolism of cells in culture are provided to illustrate the method. Applications to the analysis of the control structure of bioreaction networks are also discussed.

Adenosine Triphosphate↗

Hierarchical analysis of dependency in metabolic networks.

MOTIVATION: Elucidation of metabolic networks for an increasing number of organisms reveals that even small networks can contain thousands of reactions and chemical species. The intimate connectivity between components complicates their decomposition into biologically meaningful sub-networks. Moreover, traditional higher-order representations of metabolic networks as metabolic pathways, suffers from the lack of rigorous definition, yielding pathways of disparate content and size. RESULTS: We introduce a hierarchical representation that emphasizes the gross organization of metabolic networks in largely independent pathways and sub-systems at several levels of independence. The approach highlights the coupling of different pathways and the shared compounds responsible for those couplings. By assessing our results on Escherichia coli (E.coli metabolic reactions, Genetic Circuits Research Group, University of California, San Diego, http://gcrg.ucsd.edu/organisms/ecoli.html, 'model v 1.01. reactions') against accepted biochemical annotations, we provide the first systematic synopsis of an organism's metabolism. Comparison with operons of E.coli shows that low-level clusters are reflected in genome organization and gene regulation. AVAILABILITY: Source code, data sets and supplementary information are available at http://www.mas.ecp.fr/labo/equipe/gagneur/hierarchy/hierarchy.html

Algorithms↗

On the analysis of the inverse problem of metabolic pathways using artificial neural networks.

Here we develop the use of artificial neural networks for solving the inverse metabolic problem, in other words, given a set of steady-state metabolite levels and fluxes in a pathway of known structure to obtain the parameters of the system, in this case the enzymatic limiting rate and Michaelis constants. This requires two main procedures: first the development of a computer program with which one can model metabolism in the forward direction (i.e. given the internal and parameters to determine the steady-state fluxes and metabolite concentrations), and second, given arrays of associated parameters and variables thereby obtained, to exploit artificial neural networks to form a model capable of obtaining the parameters from the variables. We studied 2-step pathways exhibiting first-order kinetics, 2-step pathways exhibiting reversible Michaelis-Menten kinetics and then 3-step pathways (again exhibiting reversible Michaelis-Menten kinetics), modelled using the program Gepasi. Whilst it was fairly easy for the networks to learn most of the parameters in the 2-step pathway, it was found helpful for the Michaelis-Menten case to vary the concentration of the starting pathway substrate for each set of internal parameters, and to train separate networks for each parameter. Some parameters were much easier to learn than others, reverse K(m) and V(max) values normally being the most difficult. For the 3-step pathway learning sometimes required as much as 3 days, and occasionally convergence was not obtained. Overall, neural networks of the present type, with fully interconnected feedforward architectures and trained according to the backpropagation algorithm, scaled poorly as the problem size was increased.

Algorithms↗

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks.

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.

Algorithms↗

SBML-PET: a Systems Biology Markup Language-based parameter estimation tool.

UNLABELLED: The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in systems biology. We present a Systems Biology Markup Language (SBML) based Parameter Estimation Tool (SBML-PET). The tool is designed to enable parameter estimation for biological models including signaling pathways, gene regulation networks and metabolic pathways. SBML-PET supports import and export of the models in the SBML format. It can estimate the parameters by fitting a variety of experimental data from different experimental conditions. SBML-PET has a unique feature of supporting event definition in the SMBL model. SBML models can also be simulated in SBML-PET. Stochastic Ranking Evolution Strategy (SRES) is incorporated in SBML-PET for parameter estimation jobs. A classic ODE Solver called ODEPACK is used to solve the Ordinary Differential Equation (ODE) system. AVAILABILITY: http://sysbio.molgen.mpg.de/SBML-PET/. The website also contains detailed documentation for SBML-PET.

Algorithms↗

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

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

Amino Acids↗

Dynamic profiling of the glucose metabolic network in fasted rat hepatocytes using [1,2-13C2]glucose.

Recent studies in metabolic profiling have underscored the importance of the concept of a metabolic network of pathways with special functional characteristics that differ from those of simple reaction sequences. The characterization of metabolic functions requires the simultaneous measurement of substrate fluxes of interconnecting pathways. Here we present a novel stable isotope method by which the forward and reverse fluxes of the futile cycles of the hepatic glucose metabolic network are simultaneously determined. Unlike previous radio-isotope methods, a single tracer [1,2-13C2]D-glucose and mass isotopomer analysis is used. Changes in fluxes of substrate cycles, in response to several gluconeogenic substrates, in isolated fasted hepatocytes from male Wistar rats were measured simultaneously. Incubation with these substrates resulted in a change in glucose-6-phosphatase/glucokinase and glycolytic/gluconeogenic flux ratios. Different net redistributions of intermediates in the glucose network were observed, resulting in distinct metabolic phenotypes of the fasted hepatocytes in response to each substrate condition. Our experimental observations show that the constraints of concentrations of shared intermediates, and enzyme kinetics of intersecting pathways of the metabolic network determine substrate redistribution throughout the network when it is perturbed. These results support the systems-biology notion that network analysis provides an integrated view of the physiological state. Interaction between metabolic intermediates and glycolytic/gluconeogenic pathways is a basic element of cross-talk in hepatocytes, and may explain some of the difficulties in genotype and phenotype correlation.

Animals↗

Text mining for metabolic pathways, signaling cascades, and protein networks.

The complexity of the information stored in databases and publications on metabolic and signaling pathways, the high throughput of experimental data, and the growing number of publications make it imperative to provide systems to help the researcher navigate through these interrelated information resources. Text-mining methods have started to play a key role in the creation and maintenance of links between the information stored in biological databases and its original sources in the literature. These links will be extremely useful for database updating and curation, especially if a number of technical problems can be solved satisfactorily, including the identification of protein and gene names (entities in general) and the characterization of their types of interactions. The first generation of openly accessible text-mining systems, such as iHOP (Information Hyperlinked over Proteins), provides additional functions to facilitate the reconstruction of protein interaction networks, combine database and text information, and support the scientist in the formulation of novel hypotheses. The next challenge is the generation of comprehensive information regarding the general function of signaling pathways and protein interaction networks.

Animals↗

A metabolic network in the evolutionary context: multiscale structure and modularity.

The enormous complexity of biological networks has led to the suggestion that networks are built of modules that perform particular functions and are "reused" in evolution in a manner similar to reusable domains in protein structures or modules of electronic circuits. Analysis of known biological networks has revealed several modules, many of which have transparent biological functions. However, it remains to be shown that identified structural modules constitute evolutionary building blocks, independent and easily interchangeable units. An alternative possibility is that evolutionary modules do not match structural modules. To investigate the structure of evolutionary modules and their relationship to functional ones, we integrated a metabolic network with evolutionary associations between genes inferred from comparative genomics. The resulting metabolic-genomic network places metabolic pathways into evolutionary and genomic context, thereby revealing previously unknown components and modules. We analyzed the integrated metabolic-genomic network on three levels: macro-, meso-, and microscale. The macroscale level demonstrates strong associations between neighboring enzymes and between enzymes that are distant on the network but belong to the same linear pathway. At the mesoscale level, we identified evolutionary metabolic modules and compared them with traditional metabolic pathways. Although, in some cases, there is almost exact correspondence, some pathways are split into independent modules. On the microscale level, we observed high association of enzyme subunits and weak association of isoenzymes independently catalyzing the same reaction. This study shows that evolutionary modules, rather than pathways, may be thought of as regulatory and functional units in bacterial genomes.

Biological Evolution↗

Determination of redundancy and systems properties of the metabolic network of Helicobacter pylori using genome-scale extreme pathway analysis.

The capabilities of genome-scale metabolic networks can be described through the determination of a set of systemically independent and unique flux maps called extreme pathways. The first study of genome-scale extreme pathways for the simultaneous formation of all nonessential amino acids or ribonucleotides in Helicobacter pylori is presented. Three key results were obtained. First, the extreme pathways for the production of individual amino acids in H. pylori showed far fewer internal states per external state than previously found in Haemophilus influenzae, indicating a more rigid metabolic network. Second, the degree of pathway redundancy in H. pylori was essentially the same for the production of individual amino acids and linked amino acid sets, but was approximately twice that of the production of the ribonucleotides. Third, the metabolic network of H. pylori was unable to achieve extensive conversion of amino acids consumed to the set of either nonessential amino acids or ribonucleotides and thus diverted a large portion of its nitrogen to ammonia production, a potentially important result for pH regulation in its acidic habitat. Genome-scale extreme pathways elucidate emergent system-wide properties. Extreme pathway analysis is emerging as a potentially important method to analyze the link between the metabolic genotype and its phenotypes.

Amino Acids↗

Composite control of cell function: metabolic pathways behaving as single control units.

This paper shows that under some conditions the control exerted by a part of a metabolic network (a pathway) on a flux or concentration in any other part can be described through a single (overall) control coefficient. This has the following implications: (i) the relative contributions of a pathway enzyme to the regulation of the pathway (output) flux and of any flux or concentration outside are identical; therefore, the control analysis of the pathway 'in isolation' allows one to determine the control exerted by any pathway enzyme on the rest of the cell by estimation of the control efficient of just one, arbitrarily chosen enzyme; (ii) the relative control of any two metabolic variables outside the pathway (measured as the ratio of the control coefficients over these two variables outside) is the same for all pathway enzymes. These properties allow one to substitute effectively a pathway by a single (super)reaction and make it possible to consider such a pathway as a metabolic unit within the cellular enzyme network.

Cells↗

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.

Algorithms↗

The large-scale organization of metabolic networks.

In a cell or microorganism, the processes that generate mass, energy, information transfer and cell-fate specification are seamlessly integrated through a complex network of cellular constituents and reactions. However, despite the key role of these networks in sustaining cellular functions, their large-scale structure is essentially unknown. Here we present a systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variation in their individual constituents and pathways, these metabolic networks have the same topological scaling properties and show striking similarities to the inherent organization of complex non-biological systems. This may indicate that metabolic organization is not only identical for all living organisms, but also complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.

Animals↗