David A. Fell

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of ‘elementary flux modes’ provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.

The Small World Inside Large Metabolic Networks

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics efforts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and find that this network is a small–world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The small-world architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.

Metabolic pathways in the post-genome era

Metabolic pathways are a central paradigm in biology. Historically, they have been defined on the basis of their step-by-step discovery. However, the genome-scale metabolic networks now being reconstructed from annotation of genome sequences demand new network-based definitions of pathways to facilitate analysis of their capabilities and functions, such as metabolic versatility and robustness, and optimal growth rates. This demand has led to the development of a new mathematically based analysis of complex, metabolic networks that enumerates all their unique pathways that take into account all requirements for cofactors and byproducts. Applications include the design of engineered biological systems, the generation of testable hypotheses regarding network structure and function, and the elucidation of properties that can not be described by simple descriptions of individual components (such as product yield, network robustness, correlated reactions and predictions of minimal media). Recently, these properties have also been studied in genome-scale networks. Thus, network-based pathways are emerging as an important paradigm for analysis of biological systems.

Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells

Although epidermal growth factor (EGF) induces transient activation of Ras and the mitogen‐activated protein kinase (MAPK) cascade in PC12 cells, whereas nerve growth factor (NGF) stimulates sustained activation, the basis for these contrasting responses is not known. We have developed a computer simulation of EGF‐induced MAPK cascade activation, which provides quantitative evidence that feedback inhibition of the MAPK cascade is the most important factor in determining the duration of cascade activation. Hence, we propose that the observed quantitative differences in EGF and NGF signalling can be accounted for by differential feedback regulation of the MAPK cascade.

A Genome-Scale Metabolic Model of Arabidopsis and Some of Its Properties

We describe the construction and analysis of a genome-scale metabolic model of Arabidopsis (Arabidopsis thaliana) primarily derived from the annotations in the Aracyc database. We used techniques based on linear programming to demonstrate the following: (1) that the model is capable of producing biomass components (amino acids, nucleotides, lipid, starch, and cellulose) in the proportions observed experimentally in a heterotrophic suspension culture; (2) that approximately only 15% of the available reactions are needed for this purpose and that the size of this network is comparable to estimates of minimal network size for other organisms; (3) that reactions may be grouped according to the changes in flux resulting from a hypothetical stimulus (in this case demand for ATP) and that this allows the identification of potential metabolic modules; and (4) that total ATP demand for growth and maintenance can be inferred and that this is consistent with previous estimates in prokaryotes and yeast.

Is maximization of molar yield in metabolic networks favoured by evolution

Stoichiometric analysis of metabolic networks allows the calculation of possible metabolic flux distributions in the absence of kinetic data. In order to predict which of the possible fluxes are present under certain conditions, additional constraints and optimization principles can be applied. One approach of calculating unknown fluxes (frequently called flux balance analysis) is based on the optimality principle of maximizing the molar yield of biotransformations. Here, the relevance and applicability of that approach are examined, and it is compared with the principle of maximizing pathway flux. We discuss diverse experimental evidence showing that, often, those biochemical pathways are operative that allow fast but low-yield synthesis of important products, such as fermentation in Saccharomyces cerevisiae and several other yeast species. Together with arguments based on evolutionary game theory, this leads us to the conclusion that maximization of molar yield is by no means a universal principle.

Increasing the flux in metabolic pathways: A metabolic control analysis perspective

The problems of engineering increased flux in metabolic pathways are analyzed in terms of the understanding provided by metabolic control analysis. Over-expression of a single enzyme is unlikely to be effective unless it is known to have a high flux control coefficient, which can be used as an approximate predictive tool. This is likely to rule out enzymes subject to feedback inhibition, because it transfers control downstream from the inhibited enzyme to the enzymes utilizing the feedback metabolite. Although abolishing feedback inhibition can restore flux control to an enzyme, it is also likely to cause large increases in the concentrations of metabolic intermediates. Simultaneous and coordinated over-expression of most of the enzymes in a pathway can, in principle, produce substantial flux increases without changes in metabolite levels, though technically it may be difficult to achieve. It is, however, closer to the method used by cells to change flux levels, where coordinated changes in the level of activity of pathway enzymes are the norm. Another option is to increase the demand for the pathway product, perhaps by increasing its rate of excretion or removal. Copyright 1998 John Wiley & Sons, Inc.

A Genome-Scale Metabolic Model Accurately Predicts Fluxes in Central Carbon Metabolism under Stress Conditions

Flux is a key measure of the metabolic phenotype. Recently, complete (genome-scale) metabolic network models have been established for Arabidopsis (Arabidopsis thaliana), and flux distributions have been predicted using constraints-based modeling and optimization algorithms such as linear programming. While these models are useful for investigating possible flux states under different metabolic scenarios, it is not clear how close the predicted flux distributions are to those occurring in vivo. To address this, fluxes were predicted for heterotrophic Arabidopsis cells and compared with fluxes estimated in parallel by 13C-metabolic flux analysis (MFA). Reactions of the central carbon metabolic network (glycolysis, the oxidative pentose phosphate pathway, and the tricarboxylic acid [TCA] cycle) were independently analyzed by the two approaches. Net fluxes in glycolysis and the TCA cycle were predicted accurately from the genome-scale model, whereas the oxidative pentose phosphate pathway was poorly predicted. MFA showed that increased temperature and hyperosmotic stress, which altered cell growth, also affected the intracellular flux distribution. Under both conditions, the genome-scale model was able to predict both the direction and magnitude of the changes in flux: namely, increased TCA cycle and decreased phosphoenolpyruvate carboxylase flux at high temperature and a general decrease in fluxes under hyperosmotic stress. MFA also revealed a 3-fold reduction in carbon-use efficiency at the higher temperature. It is concluded that constraints-based genome-scale modeling can be used to predict flux changes in central carbon metabolism under stress conditions.

Getting to grips with the plant metabolic network

Research into plant metabolism has a long history, and analytical approaches of ever-increasing breadth and sophistication have been brought to bear. We now have access to vast repositories of data concerning enzymology and regulatory features of enzymes, as well as large-scale datasets containing profiling information of transcripts, protein and metabolite levels. Nevertheless, despite this wealth of data, we remain some way off from being able to rationally engineer plant metabolism or even to predict metabolic responses. Within the past 18 months, rapid progress has been made, with several highly informative plant network interrogations being discussed in the literature. In the present review we will appraise the current state of the art regarding plant metabolic network analysis and attempt to outline what the necessary steps are in order to further our understanding of network regulation.

Can sugars be produced from fatty acids? A test case for pathway analysis tools

MOTIVATION In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis. RESULTS Elementary modes analysis (EMA) of a set of enzymes corresponding to the Krebs cycle, glycolysis and gluconeogenesis supports the scientific evidence showing that there is no pathway capable of converting acetyl-CoA to glucose at steady state. This conversion is possible after the addition of isocitrate lyase and malate synthase (forming the glyoxylate shunt) to the system. Dealing with the same example, we compare EMA with two tools based on graph theory available online, PathFinding and Pathway Hunter Tool. These automated network generating tools do not succeed in predicting the conversions known from experiment. They sometimes generate unbalanced paths and reveal problems identifying side metabolites that are not responsible for the carbon net flux. This shows that, for metabolic pathway analysis, it is important to consider the topology (including bimolecular reactions) and stoichiometry of metabolic systems, as is done in EMA. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.