Topological analysis of mass-balanced signaling networks: a framework to obtain network properties including crosstalk

Signal transduction networks have only been studied at a small scale because large-scale reconstructions and suitable in silico analysis methods have not been available. Since reconstructions of large signaling networks are progressing well there is now a need to develop a framework for analysing structural properties of signaling networks. One such framework is presented here, one that is based on systemically independent pathways and a mass-balanced representation of signaling events. This approach was applied to a prototypic signaling network and it allowed for: (1) a systemic analysis of all possible input/output relationships, (2) a quantitative evaluation of network crosstalk, or the interconnectivity of systemically independent pathways, (3) a measure of the redundancy in the signaling network, (4) the participation of reactions in signaling pathways, and (5) the calculation of correlated reaction sets. These properties emerge from network structure and can only be derived and studied within a defined mathematical framework. The calculations presented are the first of their kind for a signaling network, while similar analysis has been extensively performed for prototypic and genome-scale metabolic networks. This approach does not yet account for dynamic concentration profiles. Due to the scalability of the stoichiometric formalism used, the results presented for the prototypic signaling network can be obtained for large signaling networks once their reconstruction is completed.     

Identification of possible two-reactant sources of oscillations in the Calvin photosynthesis cycle and ancillary pathways

A systematic search for possible sources of experimentally observed oscillations in the photosynthetic reaction system has been performed by application of recent theoretical results characterizing the transient-state rate behaviour of metabolic reactions involving two independent concentration variables. All subsystems involving two independent reactants in metabolically fundamental parts of the Calvin cycle and the ancillary pathways of starch and sucrose synthesis have been examined in order to decide on basis of their kinetic and stoichiometric structure whether or not they may trigger oscillations. The results show that no less than 20 possible oscillators can be identified in the examined reaction system, only three of which have been previously considered as potential sources of experimentally observed oscillations. This illustrates the superiority of the method now applied over those previously used to identify possible two-reactant sources of metabolic oscillations and indicates that there should be no difficulty in complex metabolic pathways to point to a multitude of interactions that may trigger an oscillatory rate behaviour of the system.     

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.     

Mathematical and computational techniques to deduce complex biochemical reaction mechanisms

Time series data can now be routinely collected for biochemical reaction pathways, and recently, several methods have been proposed to infer reaction mechanisms for metabolic pathways and networks. In this paper we provide a survey of mathematical techniques for determining reaction mechanisms for time series data on the concentration or abundance of different reacting components, with little prior information about the pathways involved.     

Phylogenetic Analysis of Metabolic Pathways

The information provided by completely sequenced genomes can yield insights into the multi-level organization of organisms and their evolution. At the lowest level of molecular organization individual enzymes are formed, often through assembly of multiple polypeptides. At a higher level, sets of enzymes group into metabolic networks. Much has been learned about the relationship of species from phylogenetic trees comparing individual enzymes. In this article we extend conventional phylogenetic analysis of individual enzymes in different organisms to the organisms' metabolic networks. For this purpose we suggest a method that combines sequence information with information about the underlying reaction networks. A distance between pathways is defined as incorporating distances between substrates and distances between corresponding enzymes. The new analysis is applied to electron-transfer and amino acid biosynthesis networks yielding a more comprehensive understanding of similarities and differences between organisms. Received: 14 August 2000 / Accepted: 4 January 2001     

Gradient Descent Optimization in Gene Regulatory Pathways

Background

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms.

Methodology

In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings.

Conclusions

We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example.     

An efficient network querying method based on conditional random fields

MOTIVATION: A large amount of biomolecular network data for multiple species have been generated by high-throughput experimental techniques, including undirected and directed networks such as protein-protein interaction networks, gene regulatory networks and metabolic networks. There are many conserved functionally similar modules and pathways among multiple biomolecular networks in different species; therefore, it is important to analyze the similarity between the biomolecular networks. Network querying approaches aim at efficiently discovering the similar subnetworks among different species. However, many existing methods only partially solve this problem. RESULTS: In this article, a novel approach for network querying problem based on conditional random fields (CRFs) model is presented, which can handle both undirected and directed networks, acyclic and cyclic networks and any number of insertions/deletions. The CRF method is fast and can query pathways in a large network in seconds using a PC. To evaluate the CRF method, extensive computational experiments are conducted on the simulated and real data, and the results are compared with the existing network querying methods. All results show that the CRF method is very useful and efficient to find the conserved functionally similar modules and pathways in multiple biomolecular networks.     

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.     

Engineering primary metabolic pathways of industrial micro-organisms

Metabolic engineering is a powerful tool for the optimisation and the introduction of new cellular processes. This is mostly done by genetic engineering. Since the introduction of this multidisciplinary approach, the success stories keep accumulating. The primary metabolism of industrial micro-organisms has been studied for long time and most biochemical pathways and reaction networks have been elucidated. This large pool of biochemical information, together with data from proteomics, metabolomics and genomics underpins the strategies for design of experiments and choice of targets for manipulation by metabolic engineers. These targets are often located in the primary metabolic pathways, such as glycolysis, pentose phosphate pathway, the TCA cycle and amino acid biosynthesis and mostly at major branch points within these pathways. This paper describes approaches taken for metabolic engineering of these pathways in bacteria, yeast and filamentous fungi.     

Dynamic modeling of complex biological systems: a link between metabolic and macroscopic description

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples.     

Motif search in graphs: application to metabolic networks

The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks     

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     

A Text-Mining System for Extracting Metabolic Reactions from Full-Text Articles

ABSTRACT: BACKGROUND: Increasingly biological text mining research is focusing on the extraction of complex relationships relevant to the construction and curation of biological networks and pathways. However, one important category of pathway - metabolic pathways - has been largely neglected. Here we present a relatively simple method for extracting metabolic reaction information from free text that scores different permutations of assigned entities (enzymes and metabolites) within a given sentence based on the presence and location of stemmed keywords. This method extends an approach that has proved effective in the context of the extraction of protein-protein interactions. RESULTS: When evaluated on a set of manually-curated metabolic pathways using standard performance criteria, our method performs surprisingly well. Precision and recall rates are comparable to those previously achieved for the well-known protein-protein interaction extraction task. CONCLUSIONS: We conclude that automated metabolic pathway construction is more tractable than has often been assumed, and that (as in the case of protein-protein interaction extraction) relatively simple text-mining approaches can prove surprisingly effective. It is hoped that these results will provide an impetus to further research and act as a useful benchmark for judging the performance of more sophisticated methods that are yet to be developed.     

Expanding Metabolic Networks: Scopes of Compounds, Robustness, and Evolution

A new method for the mathematical analysis of large metabolic networks is presented. Based on the fact that the occurrence of a metabolic reaction generally requires the existence of other reactions providing its substrates, series of metabolic networks are constructed. In each step of the corresponding expansion process those reactions are incorporated whose substrates are made available by the networks of the previous generations. The method is applied to the set of all metabolic reactions included in the KEGG database. Starting with one or more seed compounds, the expansion results in a final network whose compounds define the scope of the seed. Scopes of all metabolic compounds are calculated and it is shown that large parts of cellular metabolism can be considered as the combined scope of simple building blocks. Analyses of various expansion processes reveal crucial metabolites whose incorporation allows for the increase in network complexity. Among these metabolites are common cofactors such as NAD⁺, ATP, and coenzyme A. We demonstrate that the outcome of network expansion is in general very robust against elimination of single or few reactions. There exist, however, crucial reactions whose elimination results in a dramatic reduction of scope sizes. It is hypothesized that the expansion process displays characteristics of the evolution of metabolism such as the temporal order of the emergence of metabolic pathways. [Reviewing Editor : Dr. David Pollock]     

Metabolic Pathfinding Using RPAIR Annotation

Metabolic databases contain information about thousands of small molecules and reactions, which can be represented as networks. In the context of metabolic reconstruction, pathways can be inferred by searching optimal paths in such networks. A recurrent problem is the presence of pool metabolites (e.g., water, energy carriers, and cofactors), which are connected to hundreds of reactions, thus establishing irrelevant shortcuts between nodes of the network. One solution to this problem relies on weighted networks to penalize highly connected compounds. A more refined solution takes the chemical structure of reactants into account in order to differentiate between side and main compounds of a reaction. Thanks to an intensive annotation effort at KEGG, decompositions of reactions into reactant pairs (RPAIR) categorized by their role (main, trans, cofac, ligase, and leave) are now available.The goal of this article is to evaluate the impact of RPAIR data on pathfinding in metabolic networks. To this end, we measure the impact of different parameters concerning the construction of the metabolic network: mapping of reactions and reactant pairs onto a graph, use of selected categories of reactant pairs, weighting schemes for compounds and reactions, removal of highly connected metabolites, and reaction directionality. In total, we tested 104 combinations of parameters and identified their optimal values for pathfinding on the basis of 55 reference pathways from three organisms.The best-performing metabolic network combines the biochemical knowledge encoded by KEGG RPAIR with a weighting scheme penalizing highly connected compounds. With this network, we could recover reference pathways from Escherichia coli with an average accuracy of 93% (32 pathways), from Saccharomyces cerevisiae with an average accuracy of 66% (11 pathways), and from humans with an average accuracy of 70% (12 pathways). Our pathfinding approach is available as part of the Network Analysis Tools.     

Construction of an E. Coli genome-scale atom mapping model for MFA calculations

Metabolic flux analysis (MFA) has so far been restricted to lumped networks lacking many important pathways, partly due to the difficulty in automatically generating isotope mapping matrices for genome-scale metabolic networks. Here we introduce a procedure that uses a compound matching algorithm based on the graph theoretical concept of pattern recognition along with relevant reaction information to automatically generate genome-scale atom mappings which trace the path of atoms from reactants to products for every reaction. The procedure is applied to the iAF1260 metabolic reconstruction of Escherichia coli yielding the genome-scale isotope mapping model imPR90068. This model maps 90,068 non-hydrogen atoms that span all 2,077 reactions present in iAF1260 (previous largest mapping model included 238 reactions). The expanded scope of the isotope mapping model allows the complete tracking of labeled atoms through pathways such as cofactor and prosthetic group biosynthesis and histidine metabolism. An EMU representation of imPR90068 is also constructed and made available.     

Recreating ancient metabolic pathways before enzymes

The biochemistry of all living organisms uses complex, enzyme-catalyzed metabolic reaction networks. Yet, at life’s origins, enzymes had not yet evolved. Therefore, it has been postulated that non-enzymatic metabolic pathways predated their enzymatic counterparts. In this account article, we describe our recent work to evaluate whether two ancient carbon fixation pathways, the rTCA (reductive tricarboxylic acid) cycle and the reductive AcCoA (Wood-Ljungdahl) pathway, could have operated without enzymes and therefore have originated as prebiotic chemistry. We also describe the discovery of an Fe²⁺-promoted complex reaction network that may represent a prebiotic predecessor to the TCA and glyoxylate cycles. The collective results support the idea that most central metabolic pathways could have roots in prebiotic chemistry.     

Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph

MOTIVATION: Metabolic networks are organized in a modular, hierarchical manner. Methods for a rational decomposition of the metabolic network into relatively independent functional subsets are essential to better understand the modularity and organization principle of a large-scale, genome-wide network. Network decomposition is also necessary for functional analysis of metabolism by pathway analysis methods that are often hampered by the problem of combinatorial explosion due to the complexity of metabolic network. Decomposition methods proposed in literature are mainly based on the connection degree of metabolites. To obtain a more reasonable decomposition, the global connectivity structure of metabolic networks should be taken into account. RESULTS: In this work, we use a reaction graph representation of a metabolic network for the identification of its global connectivity structure and for decomposition. A bow-tie connectivity structure similar to that previously discovered for metabolite graph is found also to exist in the reaction graph. Based on this bow-tie structure, a new decomposition method is proposed, which uses a distance definition derived from the path length between two reactions. An hierarchical classification tree is first constructed from the distance matrix among the reactions in the giant strong component of the bow-tie structure. These reactions are then grouped into different subsets based on the hierarchical tree. Reactions in the IN and OUT subsets of the bow-tie structure are subsequently placed in the corresponding subsets according to a 'majority rule'. Compared with the decomposition methods proposed in literature, ours is based on combined properties of the global network structure and local reaction connectivity rather than, primarily, on the connection degree of metabolites. The method is applied to decompose the metabolic network of Escherichia coli. Eleven subsets are obtained. More detailed investigations of the subsets show that reactions in the same subset are really functionally related. The rational decomposition of metabolic networks, and subsequent studies of the subsets, make it more amenable to understand the inherent organization and functionality of metabolic networks at the modular level. SUPPLEMENTARY INFORMATION: http://genome.gbf.de/bioinformatics/