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.

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).

MOTIVATION: The analysis of high-throughput molecular data in the context of metabolic pathways is essential to uncover their underlying functional structure. Among different metabolic pathway concepts in systems biology, elementary flux modes (EFMs) hold a predominant place, as they naturally capture the complexity and plasticity of cellular metabolism and go beyond predefined metabolic maps. However, their use to interpret high-throughput data has been limited so far, mainly because their computation in genome-scale metabolic networks has been unfeasible. To face this issue, different optimization-based techniques have been recently introduced and their application to human metabolism is promising. RESULTS: In this article, we exploit and generalize the K-shortest EFM algorithm to determine a subset of EFMs in a human genome-scale metabolic network. This subset of EFMs involves a wide number of reported human metabolic pathways, as well as potential novel routes, and constitutes a valuable database where high-throughput data can be mapped and contextualized from a metabolic perspective. To illustrate this, we took expression data of 10 healthy human tissues from a previous study and predicted their characteristic EFMs based on enrichment analysis. We used a multivariate hypergeometric test and showed that it leads to more biologically meaningful results than standard hypergeometric. Finally, a biological discussion on the characteristic EFMs obtained in liver is conducted, finding a high level of agreement when compared with the literature.

MOTIVATION: The reconstruction of metabolic networks at the genome scale has allowed the analysis of metabolic pathways at an unprecedented level of complexity. Elementary flux modes (EFMs) are an appropriate concept for such analysis. However, their number grows in a combinatorial fashion as the size of the metabolic network increases, which renders the application of EFMs approach to large metabolic networks difficult. Novel methods are expected to deal with such complexity. RESULTS: In this article, we present a novel optimization-based method for determining a minimal generating set of EFMs, i.e. a convex basis. We show that a subset of elements of this convex basis can be effectively computed even in large metabolic networks. Our method was applied to examine the structure of pathways producing lysine in Escherichia coli. We obtained a more varied and informative set of pathways in comparison with existing methods. In addition, an alternative pathway to produce lysine was identified using a detour via propionyl-CoA, which shows the predictive power of our novel approach. AVAILABILITY: The source code in C++ is available upon request.