An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in re...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 178; H. 2; S. 502 - 537
Hauptverfasser: Akbari, Amir, Barton, Paul I.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2018
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computation
E coli
Engineering
Flux
Genomes
Linear algebra
Linear programming
Mathematics
Mathematics and Statistics
Matrix methods
Metabolism
Networks
Operations Research/Decision Theory
Optimization
Scale models
Software
Space bases
Stoichiometry
Theory of Computation
90C20
90C06
Multi-parametric programming
Flux balance analysis
90C05
Metabolic networks
ISSN:0022-3239, 1573-2878
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Zusammenfassung:Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse; thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli . We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than fivefold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.
Bibliographie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1281-x