Systems approaches to modelling pathways and networks.

Peer reviewedPreprin

Low Degree Metabolites Explain Essential Reactions and Enhance Modularity in Biological Networks

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints. In the metabolic networks of E. coli, S. cerevisiae and S. aureus, we identified metabolites with a low degree of connectivity, particularly those that are produced and/or consumed in just a single reaction. Using FBA we also determined reactions essential for growth in these metabolic networks. We find that most reactions identified as essential in these networks turn out to be those involving the production or consumption of low degree metabolites. Applying graph theoretic methods to these metabolic networks, we identified connected clusters of these low degree metabolites. The genes involved in several operons in E. coli are correctly predicted as those of enzymes catalyzing the reactions of these clusters. We independently identified clusters of reactions whose fluxes are perfectly correlated. We find that the composition of the latter `functional clusters' is also largely explained in terms of clusters of low degree metabolites in each of these organisms. Our findings mean that most metabolic reactions that are essential can be tagged by one or more low degree metabolites. Those reactions are essential because they are the only ways of producing or consuming their respective tagged metabolites. Furthermore, reactions whose fluxes are strongly correlated can be thought of as `glued together' by these low degree metabolites.Comment: 12 pages main text with 2 figures and 2 tables. 16 pages of Supplementary material. Revised version has title changed and contains study of 3 organisms instead of 1 earlie

Signatures of arithmetic simplicity in metabolic network architecture

Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that several of the properties predicted by the artificial chemistry model hold for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity

On the effects of alternative optima in context-specific metabolic model predictions

Recent methodological developments have facilitated the integration of high-throughput data into genome-scale models to obtain context-specific metabolic reconstructions. A unique solution to this data integration problem often may not be guaranteed, leading to a multitude of context-specific predictions equally concordant with the integrated data. Yet, little attention has been paid to the alternative optima resulting from the integration of context-specific data. Here we present computational approaches to analyze alternative optima for different context-specific data integration instances. By using these approaches on metabolic reconstructions for the leaf of Arabidopsis thaliana and the human liver, we show that the analysis of alternative optima is key to adequately evaluating the specificity of the predictions in particular cellular contexts. While we provide several ways to reduce the ambiguity in the context-specific predictions, our findings indicate that the existence of alternative optimal solutions warrant caution in detailed context-specific analyses of metabolism

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

Integrating gene and protein expression data with genome-scale metabolic networks to infer functional pathways

This article has been made available through the Brunel Open Access Publishing Fund. Copyright @ 2013 Pey et al.; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: The study of cellular metabolism in the context of high-throughput -omics data has allowed us to decipher novel mechanisms of importance in biotechnology and health. To continue with this progress, it is essential to efficiently integrate experimental data into metabolic modeling. Results: We present here an in-silico framework to infer relevant metabolic pathways for a particular phenotype under study based on its gene/protein expression data. This framework is based on the Carbon Flux Path (CFP) approach, a mixed-integer linear program that expands classical path finding techniques by considering additional biophysical constraints. In particular, the objective function of the CFP approach is amended to account for gene/protein expression data and influence obtained paths. This approach is termed integrative Carbon Flux Path (iCFP). We show that gene/protein expression data also influences the stoichiometric balancing of CFPs, which provides a more accurate picture of active metabolic pathways. This is illustrated in both a theoretical and real scenario. Finally, we apply this approach to find novel pathways relevant in the regulation of acetate overflow metabolism in Escherichia coli. As a result, several targets which could be relevant for better understanding of the phenomenon leading to impaired acetate overflow are proposed. Conclusions: A novel mathematical framework that determines functional pathways based on gene/protein expression data is presented and validated. We show that our approach is able to provide new insights into complex biological scenarios such as acetate overflow in Escherichia coli.Basque Governmen