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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01 Jan 2010
TL;DR: An optimal control framework is used to solve dynamic optimization problems associated with metabolic dynamics using a nonlinear control-affine model of a metabolic network with the enzyme concentrations as control inputs and identifies a temporal pattern in the solution that is consistent with previous experimental and numerical observations.
Abstract: The characterization of general control principles that underpin metabolic dynamics is an important part of systems analysis in biology. It has been long argued that many biological regulatory mechanisms have evolved so as to optimize cellular adaptation in response to external stimuli. In this thesis we use an optimal control framework to solve dynamic optimization problems associated with metabolic dynamics. The analysis is based on a nonlinear control-affine model of a metabolic network with the enzyme concentrations as control inputs. We consider the optimization of time-dependent enzyme concentrations to activate an unbranched network and reach a prescribed metabolic flux. The solution accounts for time-resource optimality under constraints in the total enzymatic abundance. We identify a temporal pattern in the solution that is consistent with previous experimental and numerical observations. Our analysis suggests that this behaviour may appear in a broader class of networks than previously considered. In addition, we address the optimization of time-dependent enzyme expression rates for a metabolic network coupled with a model of enzyme dynamics. The formulation accounts for the transition between two metabolic steady states in networks with arbitrary stoichiometries and enzyme kinetics. We consider a finite horizon quadratic cost function that weighs the deviations of metabolites, enzymes and their expression rates from their target values, together with the time-derivative of the expression rates. The problem is recast as an iterative sequence of Linear Quadratic Tracking problems, and we derive conditions under which the iterations converge to a suboptimal solution of the original problem. Additionally, if constant metabolite concentrations are enforced, the nonlinear system can be written as a linear Differential-Algebraic system. In the infinite horizon case the problem can be recast as a standard Linear Quadratic Regulator problem for a lower-dimensional system, the solution of which is readily available.
10 citations
TL;DR: In this paper, the authors study the optimality of biochemical pathways in the H∞ sense, i.e., the effect of a negative feedback loop internally exerted on the system by a self-product of the pathway, and apply the results obtained by their analysis to a linearly unbranched enzyme pathway system.
Abstract: In this paper we study the possible optimality of biochemical pathways in the H∞ sense. We start by presenting simple linearized models of single enzymatic reaction systems, where we apply classical and modern tools of feedback-control theory. We then apply the results obtained by our analysis to a linearly unbranched enzyme pathway system, where we explore the effect of a negative feedback loop internally exerted on the system by a self-product of the pathway. We then probe the sensitivity of the enzymatic system to variations in certain variables and we deal with the problem of assessing the optimality of the static-output feedback control, in the H∞ sense, inherent to the closed-loop system. In this point we demonstrate the applicability of our results via a theoretical example that provides an open-loop and closed-loop analysis of a four-block enzymatic system. We then apply the various tools we developed to the optimal analysis of the Threonine synthesis pathway which is regulated by three feedback loops. We demonstrate that this pathway is optimal in the H∞ sense, in the face of considerable uncertainties in the various enzyme concentrations of the pathway. Copyright © 2007 John Wiley & Sons, Ltd.
10 citations
TL;DR: This work enumerated model parameters that describe key features of cultured mammalian cells – including cellular composition, bioprocess performance metrics, mammalian-specific pathways, and biological assumptions behind model formulation approaches, and found the following considerations to be most critical for accurate parameterization.
Abstract: Genome-scale metabolic models describe cellular metabolism with mechanistic detail Given their high complexity, such models need to be parameterized correctly to yield accurate predictions and avoid overfitting Effective parameterization has been well-studied for microbial models, but it remains unclear for higher eukaryotes, including mammalian cells To address this, we enumerated model parameters that describe key features of cultured mammalian cells - including cellular composition, bioprocess performance metrics, mammalian-specific pathways, and biological assumptions behind model formulation approaches We tested these parameters by building thousands of metabolic models and evaluating their ability to predict the growth rates of a panel of phenotypically diverse Chinese Hamster Ovary cell clones We found the following considerations to be most critical for accurate parameterization: (1) cells limit metabolic activity to maintain homeostasis, (2) cell morphology and viability change dynamically during a growth curve, and (3) cellular biomass has a particular macromolecular composition Depending on parameterization, models predicted different metabolic phenotypes, including contrasting mechanisms of nutrient utilization and energy generation, leading to varying accuracies of growth rate predictions Notably, accurate parameter values broadly agreed with experimental measurements These insights will guide future investigations of mammalian metabolism
8 citations
01 Jan 2008
TL;DR: Constraint-Based reconstruction and analysis A set of approaches for constructing manually curated, stoichiometric network reconstructions and analyzing the resulting models by applying equality and inequal39 constraints and computing functional states.
Abstract: Bibliome The collection of primary literature, review lit19 erature and textbooks on a particular topic. 20 Biochemically, genetically and genomically (BiGG) 21 structured reconstruction A structured genome-scale 22 metabolic network reconstruction which incorpo23 rates knowledge about the genomic, proteomic, and 24 biochemical components, including relationships be25 tween each component in a particular organism or 26 cell (See Sect. “Reconstructions, Knowledge Bases, and 27 Models”). 28 Biomass function A pseudo-reaction representing the 29 stoichiometric consumption of metabolites necessary 30 for cellular growth (i. e., to produce biomass). When 31 this pseudo-reaction is placed in a model, a flux 32 through it represents the in silico growth rate of the 33 organism or population (See Sect. “Constraint-Based 34 Methods of Analysis”). 35 Constraint-Based reconstruction and analysis (COBRA) 36 A set of approaches for constructing manually curated, 37 stoichiometric network reconstructions and analyzing 38 the resulting models by applying equality and inequal39 ity constraints and computing functional states. In 40 general, mass conservation and thermodynamics (for 41 directionality) are the fundamental constraints. Addi42 tional constraints reflecting experimental conditions 43 and other biological constraints (such as regulatory 44 states) can be applied. The analysis approaches gener45 ally fall into two classes: biased and unbiased methods. 46 Biased methods involve the application of various op47 timization approaches which require the definition 48 of an objective function. Unbiased methods do not 49 require an objective function (See Sect. “Constraint50 Based Modeling”). 51 Convex space A multi-dimensional space in which 52 a straight line can be drawn from any two, without 53 leaving the space (see Sect. “Constraint-Based Meth54 ods of Analysis”). 55 Extreme pathways (ExPa) analysis An approach for cal56 culating a unique, linearly independent, but biochem57 ically feasible reaction basis that can describe all pos58 sible steady state flux combinations in a biochemi59 cal network. ExPas are closely related to Elementary 60 Modes (See Sect. “Constraint-Based Methods of Anal61 ysis”). 62 Flux-balance analysis (FBA) The formalism in which 63 a metabolic network is framed as a linear program64 ming optimization problem. The principal constraints 65 in FBA are those imposed by steady state mass con66 servation of metabolites in the system (See Sect. “Con67 straint-Based Methods of Analysis”). 68 Gene-protein-reaction association (GPR) A mathemat69 ical representation of the relationships between gene 70 loci, gene transcripts, protein sub-units, enzymes, and 71 reactions using logical relationships (and/or) (See 72 Sect. “Reconstructions, Knowledge Bases, and Mod73 els”). 74 Genome-scale The characterization of a cellular func75 tion/system on its genome scale, i. e., incorpora76 tion/consideration of all known associated compo77 nents encoded in the organism’s genome. 78 Isocline A line in a phenotypic phase plane diagram, 79 along which the ratio between the shadow prices for 80 two metabolites is fixed (See Sect. “Constraint-Based 81 Methods of Analysis”). 82 Knowledge base A specific type of reconstruction which 83 also accounts for the following information: molecular 84 formulae, subsystem assignments, GPRs, references to 85 primary and review literature, and additional pertinent 86 notes (See Sect. “Reconstructions, Knowledge Bases, 87 and Models”). 88 Line of optimality The isocline in a phenotypic phase 89 plane diagram that achieves the highest value of the ob90 jective in the phase plane (See Sect. “Constraint-Based 91 Methods of Analysis”). 92 Linear programming problem A class of optimization 93 problems in which a linear objective function is max94 imized or minimized subject to linear equality and 95
8 citations
Cites background from "Network analysis of intermediary me..."
..., maximum growth or ATP production)? [53,56,74, 96,100] Energy Balance Analysis How can one evaluate the thermodynamic feasibility of FBA simulation results? [7] ExPa/ElMo How does one define a biochemically feasible, unique set of reactions that span the steady state solution space? [64,81, 85] FBA What is the maximum (or minimum) of a specified cellular objective function? [27,65, 80,97] Flux Confidence Interval What are the confidence intervals of flux values when fluxomic data is mapped to a constraint based model? [4]...
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...Some examples of commonly used objec495 tive functions include biomass production, ATP produc496 tion, or the production of a byproduct of interest [80,100]....
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01 Jan 2012
TL;DR: It is demonstrated that multiple experimental runs distinctively increases reliability and, in turn, the potential to generate meaningful fluxome data and strengthen the position of metabolic flux analysis to be an effective diagnostic tool for metabolic engineering.
Abstract: Metabolic fluxes (i.e. in vivo reaction rates) represent the properties of cellular regulation and are
most suitable for characterizing specific phenotypes of microorganisms. As intracellular fluxes are
not directly measurable they have to be estimated from measured quantities through model-based
evaluation with the aid of computational routines based on13C labeling experiments (13C-MFA).
However, the question might be raised about the biological significance and statistical reliability of
those flux estimations based on single experiments. In addition the medium throughput approach
of13C-MFA leads to a multiplied amount of data, so the used algorithms for data pre-processing
and evaluation of results has to be optimized to increase the efficiency.
Seeking to answer the question and to adopt the challenge of medium throughput13C-MFA a se-
ries of standardized13C-labeling experiments with the model organism Corynebacterium glutami-
cum wildtype (WT) and a lysine producer (LP) was carried out under well-controlled conditions:
continuous cultivation mode with dilution rates of 0.20h−1, 0.15h−1, 0.10h−1and 0.05h−1was
chosen to ensure metabolic and isotopic stationarity. For increasing throughput and minimizing
13C labeling costs a parallel bioreactor setup at small scale (300mL working volume) was uti-
lized. Hence, all experiments were performed in fourfold biological replicates for calculation of
extracellular rates, i.e. substrate uptake and (by-) product formation, including corresponding stan-
dard error. By online FT-IR spectrometry discrimination between13C and12C carbon dioxide was
realized. From each single experiment six technical samples were taken and labeling patterns of
intracellular metabolites were analyzed by LC-MS/MS technology.
To realise data evaluation, processing and storage of such experiments an application-oriented
software package 13CFLUX2-Essentials was developed. The package offers an environment
to handle the huge amount of data, e.g. the graphically aided adjustment and management of
analytical raw data or different functions for comparing results. Calculation of extracellular rates
as well as carbon balances, network modeling, parallel multi-start simulations, evaluation and
visualization of results is automatically performed. Thus,13C-MFA in a medium throughput is
possible now and was developed and used in this work.
From the 20 datasets intracellular fluxes were estimated using the 13CFLUX2 software package.
Comprehensive statistical analysis of error propagation was performed to investigate the influence
of analytical and experimental errors on the determinacy of all fluxes. Label measurements of
intracellular metabolites showed different reproducibility between technical and biological repli-
cations. Carbon balances were closed between 73–102% with an average about 86%. Beside the
extracellulare rates ~66 labeling fragments were included for parameter fitting. 5–7 metabolites
were rejected due to analytical errors. With each dataset 10000 single fittings were performed in
an multi start optimization (MSO). Differences between biological replicas were caused by va-
riations in the fractional labeling of intermediates. 12 out of 20 datasets showed unique global
optimal solutions in the MSO results.
The studies in a small-scale system discover bottle necks and points for improvement for further
investigations. It is demonstrated that multiple experimental runs distinctively increases reliability
and, in turn, the potential to generate meaningful fluxome data. Hence, these results strengthen the
position of metabolic flux analysis to be an effective diagnostic tool for metabolic engineering.
8 citations
Cites background from "Network analysis of intermediary me..."
...Eine tiefergehende Einsicht über die Modellierung biochemischer Netzwerke findet sich in verschiedenen Quellen [71, 84, 184, 230, 238]....
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...Weiterführende Informationen über die geschichtliche Entwicklung finden sich in verschiedenen Quellen [75, 197, 202, 228, 232]....
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...Aktuelle Marktvolumen von biotechnologisch hergestellten Produkten finden sich unter den in [78,114,204] aufgeführten Quellen....
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...Ich habe dabei nur die in der Arbeit angegebenen Quellen und Hilfsmittel benutzt....
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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
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