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

This article is available open access through the publisher’s website through the link below. Copyright @ The Author 2009.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. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online (http://bioinformatics.oxfordjournals.org/cgi/content/full/btp564/DC1).Fundação Calouste Gulbenkian, Fundação para a Ciência e a Tecnologia (FCT) and Siemens SA Portugal

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

Metabolic Pathway Analysis: from small to genome-scale networks

The need for mathematical modelling of biological processes has grown alongside with the achievements in the experimental field leading to the appearance and development of new fields like systems biology. Systems biology aims at generating new knowledge through modelling and integration of experimental data in order to develop a holistic understanding of organisms. In the first part of my PhD thesis, I compare two different levels of abstraction used for computing metabolic pathways, constraint-based and graph theoretical methods. I show that the current representations of metabolism as a simple graph correspond to wrong mathematical descriptions of metabolic pathways. On the other hand, the use of stoichiometric information and convex analysis as modelling framework like in elementary flux mode analysis, allows to correctly predict metabolic pathways. In the second part of the thesis, I present two of the first methods, based on elementary flux mode analysis, that can compute metabolic pathways in such large metabolic networks: the K-shortest EFMs method and the EFMEvolver method. These methods contribute to an enrichment of the mathematical tools available to model cell biology and more precisely, metabolism. The application of these new methods to biotechnological problems is also explored in this part. In the last part of my thesis, I give an overview of recent achievements in metabolic network reconstruction and constraint-based modelling as well as open issues. Moreover, I discuss possible strategies for integrating experimental data with elementary flux mode analysis. Further improvements in elementary flux mode computation on that direction are put forward

Identification of metabolic pathways using pathfinding approaches: A systematic review

Metabolic pathways have become increasingly available for variousmicroorganisms. Such pathways have spurred the development of a wide array of computational tools, in particular, mathematical pathfinding approaches. This article can facilitate the understanding of computational analysis ofmetabolic pathways in genomics. Moreover, stoichiometric and pathfinding approaches inmetabolic pathway analysis are discussed. Threemajor types of studies are elaborated: stoichiometric identification models, pathway-based graph analysis and pathfinding approaches in cellular metabolism. Furthermore, evaluation of the outcomes of the pathways withmathematical benchmarkingmetrics is provided. This review would lead to better comprehension ofmetabolismbehaviors in living cells, in terms of computed pathfinding approaches. © The Author 2016

Random sampling of elementary flux modes in large-scale metabolic networks

Motivation: The description of a metabolic network in terms of elementary (flux) modes (EMs) provides an important framework for metabolic pathway analysis. However, their application to large networks has been hampered by the combinatorial explosion in the number of modes. In this work, we develop a method for generating random samples of EMs without computing the whole set. Results: Our algorithm is an adaptation of the canonical basis approach, where we add an additional filtering step which, at each iteration, selects a random subset of the new combinations of modes. In order to obtain an unbiased sample, all candidates are assigned the same probability of getting selected. This approach avoids the exponential growth of the number of modes during computation, thus generating a random sample of the complete set of EMs within reasonable time. We generated samples of different sizes for a metabolic network of Escherichia coli, and observed that they preserve several properties of the full EM set. It is also shown that EM sampling can be used for rational strain design. A well distributed sample, that is representative of the complete set of EMs, should be suitable to most EM-based methods for analysis and optimization of metabolic networks

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

Analysis of complex metabolic behavior through pathway decomposition

<p>Abstract</p> <p>Background</p> <p>Understanding complex systems through decomposition into simple interacting components is a pervasive paradigm throughout modern science and engineering. For cellular metabolism, complexity can be reduced by decomposition into pathways with particular biochemical functions, and the concept of elementary flux modes provides a systematic way for organizing metabolic networks into such pathways. While decomposition using elementary flux modes has proven to be a powerful tool for understanding and manipulating cellular metabolism, its utility, however, is severely limited since the number of modes in a network increases exponentially with its size.</p> <p>Results</p> <p>Here, we present a new method for decomposition of metabolic flux distributions into elementary flux modes. Our method can easily operate on large, genome-scale networks since it does not require all relevant modes of the metabolic network to be generated. We illustrate the utility of our method for metabolic engineering of <it>Escherichia coli </it>and for understanding the survival of <it>Mycobacterium tuberculosis </it>(MTB) during infection.</p> <p>Conclusions</p> <p>Our method can achieve computational time improvements exceeding 2000-fold and requires only several seconds to generate elementary mode decompositions on genome-scale networks. These improvements arise from not having to generate all relevant elementary modes prior to initiating the decomposition. The decompositions from our method are useful for understanding complex flux distributions and debugging genome-scale models.</p