The Geometry of the Flux Cone of a Metabolic Network

Wagner, Clemens; Urbanczik, Robert

doi:10.1529/biophysj.104.055129

Cited by 84 publications

(70 citation statements)

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“…Using ideas from stoichiometric network analysis [10], it is possible to analyze the system dynamics in flux space instead of concentration space and to represent the space of steady states with a combination of subnetworks. The subnetworks form a convex cone in flux space [68]. There are techniques for decomposing that cone and limiting the search for Hopf bifurcations to lower dimensional facets [22].…”

Section: Further Applications In Chemistry and The Life Sciencesmentioning

confidence: 99%

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Sturm

2017

Math.Comput.Sci.

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Effective quantifier elimination procedures for first-order theories provide a powerful tool for generically solving a wide range of problems based on logical specifications. In contrast to general first-order provers, quantifier elimination procedures are based on a fixed set of admissible logical symbols with an implicitly fixed semantics. This admits the use of sub-algorithms from symbolic computation. We are going to focus on quantifier elimination for the reals and its applications giving examples from geometry, verification, and the life sciences. Beyond quantifier elimination we are going to discuss recent results with a subtropical procedure for an existential fragment of the reals. This incomplete decision procedure has been successfully applied to the analysis of reaction systems in chemistry and in the life sciences.

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Section: Further Applications In Chemistry and The Life Sciencesmentioning

confidence: 99%

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Sturm

2017

Math.Comput.Sci.

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“…If one is only interested in generating the flux space fulfilling (11), the more reasonably choice is a minimal generating set, a smallest set of vectors holding the property (Urbanczik, 2005). Unfortunately this set is not unique in the general case.…”

Section: Generate the Flux Spacementioning

confidence: 99%

“…In fact, it has been recently shown that the set of extreme currents (ECS) coincide with the set of elementary modes, which will be introduced below, when it is translated to the original vector-space (Wagner, 2005)-when computing the first a set of r spurious cycles appear (pathways formed by the forward and backward reaction of each reversible flux); however, these pathways are not considered meaningful (Schilling, 2000) and they disappear when the ECS are expressed in the original vectorspace R n .…”

Section: Extreme Currentsmentioning

confidence: 99%

“…Which is then the minimal set of vectors that generates P by non-negative combination? The term minimal generating set (MGS) has been recently coined to refer to this set (Wagner, 2005). Wagner et al also shown how to obtain a MGS that is subset of EMS.…”

Section: Minimal Generatorsmentioning

confidence: 99%

“…For example, the MGS has to be recalculated after a gene deletion, and similar difficulties arise in other applications. The advantage of the MGSs against the EMS is its reduced size: considering the central carbon metabolism of E. coli, the computation of the EMS returns more than 500000 EMs, whereas a MGS contains around 3000 MGs (Wagner, 2005). This also implies that obtaining the MGS is computationally more efficient.…”

Section: Minimal Generatorsmentioning

confidence: 99%

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Interval and Possibilistic Methods for Constraint-Based Metabolic Models

Estrada¹

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In the following site the reader will find updated information regarding this thesis. This includes corrections and clarifications, connections with future works, publications, software and tools, etc.http://science.ensilicio.com/Thesis/Thesis.html AgradecimientosLa tesis doctoral es un viaje emocionante, exigente y no exento de riesgos. Por suerte, resulta mucho mejor, más sencillo y más divertido, cuando uno tiene una lista de agradecimientos tan extensa como la mía.Estoy en deuda con mi director, Jesús Picó, por darme la oportunidad de trabajar en lo que me gusta, por descubrirme un tema fascinante y por dirigirme sabiamente en el desarrollo de esta tesis. También con mis supervisores durante mis estancias en el extranjero, Georges Bastin y Vassily Hatzimanikatis, porque me permitieron aprender de su trabajo, conocer sus instituciones y explorar dos países.Le agradezco a Antonio Sala que se acercase un buen día con una propuesta para colaborar (haciendo así fructíferas las reuniones en la biblioteca); y a Marta Tortajada que fuese mi coautora en varias ocasiones y que sea una de las personas cuyas ideas más me han ayudado. He aprendido mil cosas de otras personas -profesores, compañeros, colegas, revisores, etc.-y a todos les estoy agradecido.A los compañeros que encontré camino al doctorado les agradezco, sobretodo, que hicieran mi trabajo divertido. Agradezco cada café y cada conversación. Mención especial merecen mis principales compañeros de viaje, Pepe y Sergio, por su camaradería en el trabajo y en la vida.Es probable que sin el apoyo de otras personas no hubiese terminado esta tesis... y es seguro que de haberlo hecho sería irrelevante. A mi familia -Juan, María, Juan-les agradezco que sean mi refugio, porque la existencia de ese «lugar» me permite el lujo de ser temerario. A mis amigos en la vecindad les agradezco su interés por las victorias de cada día; y tanto a ellos como al resto, les doy las gracias por creer incondicionalmente que lo que hacía, fuese lo que fuese, era digno de admirar. Mi deuda es especial con Lucia porque ella fue la recompensa en los días de trabajo y sacrificio.Por último, y por encima de todo, quiero agradecer a mis padres todo lo que hicieron y el modo preciso en que lo hicieron. Sé que eso excede el ámbito de esta tesis, pero este párrafo es un buen lugar para mostrarles mi gratitud. Gracias. AbstractThis thesis is devoted to the study and application of constraint-based metabolic models. The objective was to find simple ways to handle the difficulties that arise in practice due to uncertainty (knowledge is incomplete, there is a lack of measurable variables, and those available are imprecise). With this purpose, tools have been developed to model, analyse, estimate and predict the metabolic behaviour of cells.The document is structured in three parts. First, related literature is revised and summarised. This results in a unified perspective of several methodologies that use constraint-based representations of the cell metabolism. Three outstanding methods are discussed i...

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Dynamic models of metabolism: Review of the cybernetic approach

Ramkrishna¹,

Song²

2012

AIChE Journal

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in Wiley Online Library (wileyonlinelibrary.com).The cybernetic approach to metabolic modeling tracing its progress from its early beginnings to its current state with regard to its relationship to other modeling approaches, applications to bioprocess modeling, metabolic engineering, and future prospects are described. The framework is shown to handle large metabolic networks in making dynamic predictions from limited data with looming prospects of extending to genome scale networks. V V C 2012 American Institute of Chemical Engineers AIChE J, 58: 986-997, 2012 Keywords: dynamic metabolic models, the cybernetic approach, metabolic engineering, elementary modes, cellular regulation where W j denotes the species whose concentration is w j . Eq. 1 represents n r reactions of metabolism which subsume both transport and chemical reaction with a ij the stoichiometric coefficient which, as per the usual convention, is positive, negative, or zero, in respective accordance with W j being a product, reactant, or nonparticipant in the ith reaction. The rate associated with the ith reaction is denoted by r i . As each reaction is catalyzed by a specific enzyme, the level of this enzyme and its activity would determine the rate of the reaction besides the concentrations (as dictated by the kinetics) of species participating in the reaction.Predictions (a) based on measurements of glucose alone leads to good predictions of biomass, formate, ethanol but not of lactate and succinate. When measurements of glucose and lactate are both used for model identification (b), all predictions (shown in continuous lines) are considerably improved. Figure 13. Cybernetic model simulations of Namjoshi et al. 52 alongside with experimental data of Europa et al., 50 showing multiple steady states in continuous cultures of hybridoma cells.

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The Geometry of the Flux Cone of a Metabolic Network

Cited by 84 publications

References 32 publications

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Interval and Possibilistic Methods for Constraint-Based Metabolic Models

Dynamic models of metabolism: Review of the cybernetic approach

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