Stability of Complex Reaction Networks

Clarke, Bruce L.

doi:10.1002/9780470142622.ch1

Cited by 233 publications

(168 citation statements)

References 67 publications

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“…See chapter II, Section C in [47] Geometrically, the part of velocity space where   ν v 0 is a polygonal cone (colloquially: an inverted pyramid of infinite height) extending from origo, and it is generally of lower dimension than the velocity space. This steady-state part of velocity space is known as the current cone, and the velocity vectors defining the edges of the cone are known as the extreme currents ("current" is short for steady-state velocity).…”

Section: Matching the Fluxes Of An Organ Model To A Specific Physiolomentioning

confidence: 94%

A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism

Madsen¹,

Danø²,

Quistorff³

2012

OJAppS

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When realistic mathematical models of whole body metabolism eventually become available, they are likely to add entirely new dimensions to the understanding of the integrated physiological function of the organism, in particular the mechanisms governing the regulation of transitions between different physiological states, like fed-fasted, exercise-rest and normal-diseased. So far the strategy for whole body modelling has primarily been a bottom-up approach where the central problem is an apparently insurmountable barrier of complexity involved in defining and optimising the huge number of parameters. Here we follow a top-down strategy and present a complete mathematical framework for realistic whole body model development. The approach proposed is modular and hierarchical and whole body metabolism is taken as the top level. Next are the organs, where the sum of the contributions from the individual organs must equal the top level metabolism. This hierarchy can be extended to lower levels of organisation, i.e. clusters of cells, individual cells, organelle and individual pathways. Exploiting this hierarchy, metabolism at each level forms an absolute constraint on the contributions from lower level. Importantly, these constraints can in many ways be defined experimentally through mass balance and flux data. Furthermore, the constrained approach allows the lower level models to be developed independently and subsequently adapted to the whole body model. The paper describes the process of whole body modelling in practical terms, centred on a mathematical framework, devised to allow whole-body models of any complexity to be developed. Furthermore, an example of sub-model incorporation in the whole-body framework is illustrated by adapting an existing erythrocyte model to the whole body constraints. Finally, we illustrate the operation of the system by including two sets of whole-body data from humans, reflecting two different physiological states.

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Section: Matching the Fluxes Of An Organ Model To A Specific Physiolomentioning

confidence: 94%

A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism

Madsen¹,

Danø²,

Quistorff³

2012

OJAppS

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“…The set of feasible solutions under bio-chemical constraints form a convex steady-state flux cone. The convex analysis of biochemical networks was founded by Clarke (Clarke, 1980(Clarke, , 1988. The study of convex flux cones utilizes methods and concepts rooting in linear algebra and optimization and forms the underlying mathematical structure for metabolic pathway analysis.…”

Section: Computational Methods For Metabolic Pathway Analysis Using Mmentioning

confidence: 99%

Computational Methods to Interpret and Integrate Metabolomic Data

Li¹,

Wang²,

Zhang³

2012

Metabolomics

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“…To get a first idea consider g = −128x 10 1 x 2 2 + 2x 3 1 x 9 2 − 4096. For g to become positive we need a point p ∈ R 2 where the second term x 3 1 x 9 2 , which has a coefficient with positive sign, dominates in the sense that it has a large absolute value compared to x 10 1 x 2 2 as well as compared to the coefficients −128 and −4096.…”

Section: Heuristically Finding a Positive Pointmentioning

confidence: 99%

“…The variables in our real first-order model corresponded to concentrations of species and reaction rates. 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].…”

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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Stability of Complex Reaction Networks

Cited by 233 publications

References 67 publications

A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism

A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism

Computational Methods to Interpret and Integrate Metabolomic Data

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

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