Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism.
TL;DR: Analysis of metabolic networks using linear optimization theory allows one to quantify and understand the limitations imposed on the cell by its metabolic stoichiometry, and to understand how the flux through each pathway influences the overall behavior of metabolism.
About: This article is published in Journal of Theoretical Biology.The article was published on 1992-02-21 and is currently open access. It has received 255 citations till now.
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TL;DR: This review is intended as an overview of the field and as a starting point for tissue engineers wishing to learn about and eventually employ this methodology to get a comprehensive view of a cell s metabolic state.
Abstract: In recent years, metabolic flux analysis has been widely used in bioprocess engineering to monitor cell viability and improve strain activity. Metabolic flux analysis refers to a methodology for investigating cellular metabolism whereby intracellular fluxes are calculated using a stoichiometric model for the major intracellular reactions and applying mass balances around intracellular metabolites. A powerful feature of this methodology is its ability to consider cellular biochemistry in terms of reaction networks. By considering the stoichiometry of biochemical reactions, it is possible to estimate the degree of engagement of each pathway participating in overall cellular activity, and hence obtain a comprehensive view of a cell s metabolic state. Given the potential impact of cellular energy metabolism on the function of engineered tissues, such comprehensive analysis of metabolic activity can be an extremely useful tool for tissue engineers. Estimates of intracellular fluxes under various environmental conditions could be used to optimize function in vivo as well as culture conditions in vitro. In this review, we provide a brief theoretical background of metabolic flux analysis and summarize the most widely used experimental approaches to obtain flux data. This review is intended as an overview of the field and as a starting point for tissue engineers wishing to learn about and eventually employ this methodology.
52 citations
01 Jan 2009
TL;DR: The double description method is an algorithm to enumerate extreme rays of a polyhedral cone—or of elementary modes in biological terminology, which has proven efficient especially for degenerate problems, where points and constraints are not in general (e.g. random) position.
Abstract: Approaching biological systems quantitatively using mathematical modeling techniques has gained increasing popularity in recent years. In systems biology, the biological complex is considered as a whole, as opposed to studying individual components and interactions. However, this can be very challenging even for simple bacteria, and various modeling techniques have been proposed approaching the enormous complexity at different levels. Simple methods at a high level of abstraction many times lack predictability and significance; detailed models capturing thermodynamic particulars are often limited due to gappy mechanistic knowledge and unknown kinetic parameters. Structural analysis as an intermediate attempt is based on usually wellknown network stoichiometries. Constraint-based methods like linear or convex optimization are able to predict reaction fluxes, growth rates or viability of knockout mutants with high confidence. However, their significance depends heavily on the underlying objectives, and alternative solutions in the flux space are mostly ignored. Comprehensive approaches exist, aiming at analyzing the flux space as a whole. The flux space is a high dimensional solution space for reaction fluxes, bounded by linear constraints on the flux values. Pathway analysis methods define minimal functional modes in the network that are able to comply with the constraints. All possible operation modes are superpositions of such elementary modes. Methods performing the analysis are transforming the descriptive constraints into generative basis vectors. Mathematically, the flux cone shapes a polyhedral cone, and algorithms arise from computational geometry, performing a representation conversion for the cone. Extreme ray enumeration, facet enumeration, vertex enumeration and convex hull are representatives of this family, and they are all related, if not equivalent. Unfortunately, the computation struggles with combinatorial explosion and is computationally intensive. At the beginning of this work, no implementation was applicable to genome scale metabolic networks. Improving the algorithms towards genome scale application is the declared goal of this thesis. The double description method is an algorithm to enumerate extreme rays of a polyhedral cone—or of elementary modes in biological terminology. It has proven efficient especially for degenerate problems, where points and constraints are not in general (e.g. random) position. Most biochemical networks lead to degenerate problems, hence the double description method is usually chosen for pathway computations. Our own implementation is also based on this method, and the present work describes the most important aspects to attain an efficient implementation. Various parts of the algorithm are performance critical and must be considered: it starts with input data, and we review and propose methods to sort and compress the data structures. We also show how to deal with different number types, since we need exact arithmetic for certain ill conditioned problem cases. A central part of the algorithm deals with elementarity of the
51 citations
Cites background from "Network analysis of intermediary me..."
...Many different objective functions have been tested for their utility in predicting phenotypic behavior, relying on smaller-scale network models (Schuetz et al., 2007; Savinell and Palsson, 1992)....
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TL;DR: The results show that the regulation of fluxes in central metabolism of mammalian cells occurs mainly through modulation of enzyme activity and, to a much lesser extent, by enzyme synthesis.
Abstract: Activities of enzymes in glycolysis, the pentose phosphate pathway, the tricarboxylic acid cycle, and glutaminolysis have been determined in the mouse myeloma SP2/0.Ag14. Cells were grown on IMDM medium with 5% serum in steady-state chemostat culture at a fixed dilution rate of 0.03 h-1. Three culture conditions, which differed in supply of glucose and oxygen, were chosen so as to change catabolic fluxes in the central metabolism, while keeping anabolic fluxes constant. In the three steady-state situations, the ratio between specific rates of glucose and glutamine consumption differed by more than twentyfold. The specific rates of glucose consumption and lactate production were highest at low oxygen supply, whereas the specific rate of glutamine consumption was highest in the culture fed with low amounts of glucose. Under low oxygen conditions, the specific production of ammonia increased and the consumption pattern of amino acids showed large changes compared with the other two cultures. For the three steady states, activities of key enzymes in glycolysis, the pentose phosphate pathway, glutaminolysis, and the TCA cycle were measured. The differences in the in vivo fluxes were only partially reflected in changes in enzyme levels. The largest differences were observed in the levels of glycolytic enzymes, which were elevated under conditions of low oxygen supply. High activities of phosphoenolpyruvate carboxykinase (E.C. 4.1.1.32) in all cultures suggest an important role for this enzyme as a link between glutaminolysis and glycolysis. For all enzymes, in vitro activities were found that could accommodate the estimated maximum in vivo fluxes. These results show that the regulation of fluxes in central metabolism of mammalian cells occurs mainly through modulation of enzyme activity and, to a much lesser extent, by enzyme synthesis.
50 citations
TL;DR: In this article, a review enumerates various important considerations for designing and interpreting cellular and mitochondrial bioenergetics experiments, some common challenges and pitfalls in data interpretation, and some potential "next steps" to be taken that can address these highlighted challenges.
50 citations
TL;DR: A detailed mass flux balance-based general stoichiometric model based on the proposed metabolic reaction network starting with the alternative five carbon sources for the synthesis of each enzyme in Bacillus licheniformis that simulates the behaviour of the metabolic pathways with 107 metabolites and 150 reaction fluxes is developed.
49 citations
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01 Jan 1984
TL;DR: Strodiot and Zentralblatt as discussed by the authors introduced the concept of unconstrained optimization, which is a generalization of linear programming, and showed that it is possible to obtain convergence properties for both standard and accelerated steepest descent methods.
Abstract: This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters.From the reviews of the Third Edition: this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn. (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)
4,908 citations
TL;DR: Analysis of oxidative pathways of glutamine and glutamate showed that extramitochondrial malate is oxidized almost quantitatively to pyruvate + CO2 by NAD(P)+-linked malic enzyme, present in the mitochondria of all tumors tested, but absent in heart, liver, and kidney mitochondria.
374 citations