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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.
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.
Citations
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Journal ArticleDOI
TL;DR: The proposed framework provides quantitative answers to questions regarding how likely it is to achieve a particular metabolic objective without exceeding a prespecified probability of violating the physiological constraints and indicates the tractability of the method and the significant role that modeling and experimental uncertainty may play in the optimization of networks of metabolic reactions.
Abstract: The S-System formalism provides a popular, versatile and mathematically tractable representation of metabolic pathways. At steady-state, after a logarithmic transformation, the S-System representation reduces into a system of linear equations. Thus, the maximization of a particular metabolite concentration or a flux subject to physiological constraints can be expressed as a linear programming (LP) problem which can be solved explic- itly and exactly for the optimum enzyme activities. So far, the quantitative effect of parametric/experimental uncer- tainty on the S-model predictions has been largely ig- nored. In this work, for the first time, the systematic quantitative description of modeling/experimental un- certainty is attempted by utilizing probability density dis- tributions to model the uncertainty in assigning a unique value to system parameters. This probabilistic descrip- tion of uncertainty renders both objective and physi- ological constraints stochastic, demanding a probabilis- tic description for the optimization of metabolic path- ways. Based on notions from chance-constrained programming and statistics, a novel approach is intro- duced for transforming the original stochastic formula- tion into a deterministic one which can be solved with existing optimization algorithms. The proposed frame- work is applied to two metabolic pathways characterized with experimental and modeling uncertainty in the ki- netic orders. The computational results indicate the trac- tability of the method and the significant role that mod- eling and experimental uncertainty may play in the opti- mization of networks of metabolic reactions. While optimization results ignoring uncertainty sometimes vio- late physiological constraints and may fail to correctly assess objective targets, the proposed framework pro- vides quantitative answers to questions regarding how likely it is to achieve a particular metabolic objective without exceeding a prespecified probability of violating the physiological constraints. Trade-off curves between metabolic objectives, probabilities of meeting these ob- jectives, and chances of satisfying the physiological con- straints, provide a concise and systematic way to guide enzyme activity alterations to meet an objective in the face of modeling and experimental uncertainty. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 145-161, 1997.

35 citations


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

  • ...Recent studies have shown that cell metabolism is close to an optimal state aimed at satisfying a set of particular objectives, for example minimum energy production (Savinell and Palson, 1992), minimum NADH synthesis (Savinell and Palson, 1992), enhanced oxygen transport (Bailey et al., 1990), etc....

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Journal ArticleDOI
TL;DR: Current SC, (log)linear and Lin-log models have less specific methods available to estimate parameter values than the power- law formalism, which implies that more information is needed to parameterize SC models.
Abstract: There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

35 citations


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

  • ...This analysis can improve our understanding of the relationships between genotype and phenotype (Edwards and Palsson, 1999; 2000a,b,c; Famili et al., 2003; Savinell and Palsson, 1992a,b; Varma et al., 1993; Varma and Palsson, 1994)....

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  • ...FBA is a constraint-based approach that uses optimization methods to find appropriate flux distributions that may be compatible with specific stoichiometric matrices (Savinell and Palsson, 1992a,b)....

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Journal ArticleDOI
TL;DR: This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system from an initial state to some target state, which may or may not be a steady state, with BST models in S-system form transformed into affine non- linear control systems, which are subjected to an exact feedback linearization that permits controllable through independent variables.
Abstract: Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.

35 citations

Journal ArticleDOI
TL;DR: This work demonstrates a novel computational approach combining flux balance modeling with statistical methods to identify correlations among fluxes in a metabolic network, providing insight as to how the fluxes should be redirected to achieve maximum product yield.

34 citations

Journal ArticleDOI
TL;DR: This paper proposes to model metabolic networks through classical optimization formulations, such as the classical S-system representation, with an additional constraint to enforce stability within a prespecified neighborhood of the solution point.

34 citations

References
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Book
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

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.

374 citations

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What are some of the theories that support linear kind of development?

Linear optimization theory is a mathematical formalism used to analyze metabolic networks and understand the limitations and behavior of metabolism.