TreeEFM: calculating elementary flux modes using linear optimization in a tree-based algorithm.

MOTIVATION: Elementary flux modes (EFMs) analysis constitutes a fundamental tool in systems biology. However, the efficient calculation of EFMs in genome-scale metabolic networks (GSMNs) is still a challenge. We present a novel algorithm that uses a linear programming-based tree search and efficiently enumerates a subset of EFMs in GSMNs. RESULTS: Our approach is compared with the EFMEvolver approach, demonstrating a significant improvement in computation time. We also validate the usefulness of our new approach by studying the acetate overflow metabolism in the Escherichia coli bacteria. To do so, we computed 1 million EFMs for each energetic amino acid and then analysed the relevance of each energetic amino acid based on gene/protein expression data and the obtained EFMs. We found good agreement between previous experiments and the conclusions reached using EFMs. Finally, we also analysed the performance of our approach when applied to large GSMNs. AVAILABILITY AND IMPLEMENTATION: The stand-alone software TreeEFM is implemented in C++ and interacts with the open-source linear solver COIN-OR Linear program Solver (CLP).

Advances in network-based metabolic pathway analysis and gene expression data integration.

With the emergence of metabolic networks, novel mathematical pathway concepts were introduced in the past decade, aiming to go beyond canonical maps. However, the use of network-based pathways to interpret 'omics' data has been limited owing to the fact that their computation has, until very recently, been infeasible in large (genome-scale) metabolic networks. In this review article, we describe the progress made in the past few years in the field of network-based metabolic pathway analysis. In particular, we review in detail novel optimization techniques to compute elementary flux modes, an important pathway concept in this field. In addition, we summarize approaches for the integration of metabolic pathways with gene expression data, discussing recent advances using network-based pathway concepts.

Refining carbon flux paths using atomic trace data.

MOTIVATION: Pathway analysis tools are a powerful strategy to analyze 'omics' data in the field of systems biology. From a metabolic perspective, several pathway definitions can be found in the literature, each one appropriate for a particular study. Recently, a novel pathway concept termed carbon flux paths (CFPs) was introduced and benchmarked against existing approaches, showing a clear advantage for finding linear pathways from a given source to target metabolite. CFPs are simple paths in a metabolite-metabolite graph that satisfy typical constraints in stoichiometric models: mass balancing and thermodynamics (irreversibility). In addition, CFPs guarantee carbon exchange in each of their intermediate steps, but not between the source and the target metabolites and consequently false positive solutions may arise. These pathways often lack biological interest, particularly when studying biosynthetic or degradation routes of a metabolite. To overcome this issue, we amend the formulation in CFP, so as to account for atomic fate information. This approach is termed atomic CFP (aCFP). RESULTS: By means of a side-by-side comparison in a medium scale metabolic network in Escherichia Coli, we show that aCFP provides more biologically relevant pathways than CFP, because canonical pathways are more easily recovered, which reflects the benefits of removing false positives. In addition, we demonstrate that aCFP can be successfully applied to genome-scale metabolic networks. As the quality of genome-scale atomic reconstruction is improved, methods such as the one presented here will undoubtedly be of value to interpret 'omics' data.

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

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.

Path finding methods accounting for stoichiometry in metabolic networks.

Graph-based methods have been widely used for the analysis of biological networks. Their application to metabolic networks has been much discussed, in particular noting that an important weakness in such methods is that reaction stoichiometry is neglected. In this study, we show that reaction stoichiometry can be incorporated into path-finding approaches via mixed-integer linear programming. This major advance at the modeling level results in improved prediction of topological and functional properties in metabolic networks.

Computing the shortest elementary flux modes in genome-scale metabolic networks.

MOTIVATION: Elementary flux modes (EFMs) represent a key concept to analyze metabolic networks from a pathway-oriented perspective. In spite of considerable work in this field, the computation of the full set of elementary flux modes in large-scale metabolic networks still constitutes a challenging issue due to its underlying combinatorial complexity. RESULTS: In this article, we illustrate that the full set of EFMs can be enumerated in increasing order of number of reactions via integer linear programming. In this light, we present a novel procedure to efficiently determine the K-shortest EFMs in large-scale metabolic networks. Our method was applied to find the K-shortest EFMs that produce lysine in the genome-scale metabolic networks of Escherichia coli and Corynebacterium glutamicum. A detailed analysis of the biological significance of the K-shortest EFMs was conducted, finding that glucose catabolism, ammonium assimilation, lysine anabolism and cofactor balancing were correctly predicted. The work presented here represents an important step forward in the analysis and computation of EFMs for large-scale metabolic networks, where traditional methods fail for networks of even moderate size. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A critical examination of stoichiometric and path-finding approaches to metabolic pathways.

Advances in the field of genomics have enabled computational analysis of metabolic pathways at the genome scale. Singular attention has been devoted in the literature to stoichiometric approaches, and path-finding approaches, to metabolic pathways. Stoichiometric approaches make use of reaction stoichiometry when trying to determine metabolic pathways. Stoichiometric approaches involve elementary flux modes and extreme pathways. In contrast, path-finding approaches propose an alternative view based on graph theory in which reaction stoichiometry is not considered. Path-finding approaches use shortest path and k-shortest path concepts. In this article we give a critical overview of the theory, applications and key research challenges of stoichiometric and path-finding approaches to metabolic pathways.

Recovering metabolic pathways via optimization.

A metabolic pathway is a coherent set of enzyme catalysed biochemical reactions by which a living organism transforms an initial (source) compound into a final (target) compound. Some of the different metabolic pathways adopted within organisms have been experimentally determined. In this paper, we show that a number of experimentally determined metabolic pathways can be recovered by a mathematical optimization model.