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Journal ArticleDOI

Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism.

21 Feb 1992-Journal of Theoretical Biology (J Theor Biol)-Vol. 154, Iss: 4, pp 421-454

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.

AbstractAnalysis 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. A stoichiometric matrix accounting for the major pathways involved in energy and mass transformations in the cell was used in our analysis. The auxiliary parameters of linear optimization, the so-called shadow prices, identify the intermediates and cofactors that cause the growth to be limited on each nutrient. This formalism was used to examine how well the cell balances its needs for carbon, nitrogen, and energy during growth on different substrates. The relative values of glucose and glutamine as nutrients were compared by varying the ratio of rates of glucose to glutamine uptakes, and calculating the maximum growth rate. The optimum value of this ratio is between 2-7, similar to experimentally observed ratios. The theoretical maximum growth rate was calculated for growth on each amino acid, and the amino acids catabolized directly to glutamate were found to be the optimal nutrients. The importance of each reaction in the network can be examined both by selectively limiting the flux through the reaction, and by the value of the reduced cost for that reaction. Some reactions, such as malic enzyme and glutamate dehydrogenase, may be inhibited or deleted with little or no adverse effect on the calculated cell growth rate.

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Cleveland State University Cleveland State University
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Chemical & Biomedical Engineering Faculty
Publications
Chemical & Biomedical Engineering Department
2-21-1992
Network Analysis of Intermediary Metabolism Using Linear Network Analysis of Intermediary Metabolism Using Linear
Optimization. I. Development of Mathematical Formalism Optimization. I. Development of Mathematical Formalism
Joanne M. (Savinell) Belovich
Cleveland State University
Bernhard O. Palsson
University of Michigan
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(Savinell) Belovich, Joanne M. and Palsson, Bernhard O., "Network Analysis of Intermediary Metabolism
Using Linear Optimization. I. Development of Mathematical Formalism" (1992).
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. 148.
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Citations
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Journal ArticleDOI
TL;DR: This protocol provides a helpful manual for all stages of the reconstruction process and presents a comprehensive protocol describing each step necessary to build a high-quality genome-scale metabolic reconstruction.
Abstract: Network reconstructions are a common denominator in systems biology. Bottom–up metabolic network reconstructions have been developed over the last 10 years. These reconstructions represent structured knowledge bases that abstract pertinent information on the biochemical transformations taking place within specific target organisms. The conversion of a reconstruction into a mathematical format facilitates a myriad of computational biological studies, including evaluation of network content, hypothesis testing and generation, analysis of phenotypic characteristics and metabolic engineering. To date, genome-scale metabolic reconstructions for more than 30 organisms have been published and this number is expected to increase rapidly. However, these reconstructions differ in quality and coverage that may minimize their predictive potential and use as knowledge bases. Here we present a comprehensive protocol describing each step necessary to build a high-quality genome-scale metabolic reconstruction, as well as the common trials and tribulations. Therefore, this protocol provides a helpful manual for all stages of the reconstruction process.

1,383 citations


Journal ArticleDOI
TL;DR: A predictive algorithm is formulated in order to apply the flux balance model to describe unsteady-state growth and by-product secretion in aerobic batch, fed-batch, and anaerobic batch cultures.
Abstract: Flux balance models of metabolism use stoichiometry of metabolic pathways, metabolic demands of growth, and optimality principles to predict metabolic flux distribution and cellular growth under specified environmental conditions. These models have provided a mechanistic interpretation of systemic metabolic physiology, and they are also useful as a quantitative tool for metabolic pathway design. Quantitative predictions of cell growth and metabolic by-product secretion that are experimentally testable can be obtained from these models. In the present report, we used independent measurements to determine the model parameters for the wild-type Escherichia coli strain W3110. We experimentally determined the maximum oxygen utilization rate (15 mmol of O2 per g [dry weight] per h), the maximum aerobic glucose utilization rate (10.5 mmol of Glc per g [dry weight] per h), the maximum anaerobic glucose utilization rate (18.5 mmol of Glc per g [dry weight] per h), the non-growth-associated maintenance requirements (7.6 mmol of ATP per g [dry weight] per h), and the growth-associated maintenance requirements (13 mmol of ATP per g of biomass). The flux balance model specified by these parameters was found to quantitatively predict glucose and oxygen uptake rates as well as acetate secretion rates observed in chemostat experiments. We have formulated a predictive algorithm in order to apply the flux balance model to describe unsteady-state growth and by-product secretion in aerobic batch, fed-batch, and anaerobic batch cultures. In aerobic experiments we observed acetate secretion, accumulation in the culture medium, and reutilization from the culture medium. In fed-batch cultures acetate is cometabolized with glucose during the later part of the culture period.(ABSTRACT TRUNCATED AT 250 WORDS)

1,073 citations


Cites background from "Network analysis of intermediary me..."

  • ...A metabolic steady state is assumed, in which the metabolic pathway flux leading to the formation of a metabolite and that leading to the degradation of a metabolite must balance, which generates the flux balance equation (3, 13):...

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Journal ArticleDOI
TL;DR: The flux balance methodology allows the quantitative interpretation of metabolic physiology, gives an interpretation of experimental data, provides a guide to metabolic engineering, enables optimal medium formulation, and provides a method for bioprocess optimization.
Abstract: Recently, there has been an increasing interest in stoichiometric analysis of metabolic flux distributions. Flux balance methods only require information about metabolic reaction stoichiometry, metabolic requirements for growth, and the measurement of a few strain–specific parameters. This information determines the domain of stoichiometrically allowable flux distributions that may be taken to define a strain's “metabolic genotype”. Within this domain a single flux distribution is sought based on assumed behavior, such as maximal growth rates. The optimal flux distributions are calculated using linear optimization and may be taken to represent the strain's “metabolic phenotype” under the particular conditions. This flux balance methodology allows the quantitative interpretation of metabolic physiology, gives an interpretation of experimental data, provides a guide to metabolic engineering, enables optimal medium formulation, and provides a method for bioprocess optimization. This spectrum of applications, and its ease of use, makes the metabolic flux balance model a potentially valuable approach for the design and optimization of bioprocesses.

956 citations


Journal ArticleDOI
TL;DR: A generic approach to combine numerical optimization methods with biochemical kinetic simulations is described, suitable for use in the rational design of improved metabolic pathways with industrial significance and for solving the inverse problem of metabolic pathways.
Abstract: MOTIVATION The simulation of biochemical kinetic systems is a powerful approach that can be used for: (i) checking the consistency of a postulated model with a set of experimental measurements, (ii) answering 'what if?' questions and (iii) exploring possible behaviours of a model. Here we describe a generic approach to combine numerical optimization methods with biochemical kinetic simulations, which is suitable for use in the rational design of improved metabolic pathways with industrial significance (metabolic engineering) and for solving the inverse problem of metabolic pathways, i.e. the estimation of parameters from measured variables. RESULTS We discuss the suitability of various optimization methods, focusing especially on their ability or otherwise to find global optima. We recommend that a suite of diverse optimization methods should be available in simulation software as no single one performs best for all problems. We describe how we have implemented such a simulation-optimization strategy in the biochemical kinetics simulator Gepasi and present examples of its application. AVAILABILITY The new version of Gepasi (3.20), incorporating the methodology described here, is available on the Internet at http://gepasi.dbs.aber.ac.uk/softw/Gepasi. html. CONTACT prm@aber.ac.uk

703 citations


Cites methods from "Network analysis of intermediary me..."

  • ...A few groups, notably that of Heinrich, have indeed applied analytical optimization methods (e.g. Heinrich et al., 1987, 1997; Schuster and Heinrich, 1987, 1991; Savinell and Palsson, 1992; Klipp and Heinrich, 1994) to several pathway schemes to investigate the conditions for maximal flux, minimal concentrations, and a series of other criteria....

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  • ...…notably that of Heinrich, have indeed applied analytical optimization methods (e.g. Heinrich et al., 1987, 1997; Schuster and Heinrich, 1987, 1991; Savinell and Palsson, 1992; Klipp and Heinrich, 1994) to several pathway schemes to investigate the conditions for maximal flux, minimal…...

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Journal ArticleDOI
TL;DR: Fundamental issues associated with its formulation and use are reviewed and use to compute optimal growth states are reviewed.
Abstract: Flux balance analysis (FBA) is a mathematical approach for analyzing the flow of metabolites through a metabolic network. To computationally predict cell growth using FBA, one has to determine the biomass objective function that describes the rate at which all of the biomass precursors are made in the correct proportions. Here we review fundamental issues associated with its formulation and use to compute optimal growth states.

508 citations


Cites background or methods from "Network analysis of intermediary me..."

  • ...DOI 10.1016/j.mib.2010.03.003 Introduction Flux balance analysis (FBA) [1] is a widely used approach for studying biochemical networks, in particular the genome-scale metabolic network reconstructions that have been built in the past decade [2,3]....

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  • ...With metabolic models becoming available for a growing number of organisms [5] and high-throughput technologies enabling the construction of many more each year [6], FBA is an important tool for harnessing the knowledge encoded in these models....

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  • ...Available online at www.sciencedirect.com The biomass objective function Adam M Feist1 and Bernhard O Palsson2 Flux balance analysis (FBA) is a mathematical approach for analyzing the flow of metabolites through a metabolic network....

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  • ...of ATP production, (3) minimizing total nutrient uptake, and (4) minimize redox metabolism through minimizing NADH production Linear programming Hybridoma cell line central metabolism (83 reactions, 42 metabolites) [11] (1) Aerobic batch bioreactor with growth, uptake, secretion, and protein production rates [20] Optimization of biomass production can be used to examine growth characteristics and explain observed phenomena [13] 1997 Max....

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  • ...This issue was recognized in the very first paper on large-scale network analysis using FBA [11,12] where a series of selected objective functions were used to find which one fit the data the best....

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References
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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)

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Journal ArticleDOI
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.
Abstract: Little evidence has been available on the oxidative pathways of glutamine and glutamate, the major respiratory substrates of cancer cells. Glutamate formed from glutamine by phosphate-dependent glutaminase undergoes quantitative transamination by aerobic tumor mitochondria to yield aspartate. However, when malate is also added there is a pronounced decrease in aspartate production and a large formation of citrate and alanine, in both state 3 and 4 conditions. In contrast, addition of malate to normal rat heart, liver, or kidney mitochondria oxidizing glutamate causes a marked increase in aspartate production. Further analysis 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. On the other hand intramitochondrial malate generated from glutamate is oxidized quantitatively to oxalacetate by mitochondrial malate dehydrogenase of tumors. Acetyl-CoA derived from extramitochondrial malate via pyruvate and oxalacetate derived from glutamate via intramitochondrial malate are quantitatively converted into citrate, which is extruded. No evidence was found that malic enzyme of tumor mitochondria converts glutamate-derived malate into pyruvate as postulated in other reports. Possible mechanisms for the integration of mitochondrial malic enzyme and malate dehydrogenase activities in tumors are discussed.

350 citations