Elementary flux modes

B. Flux Balance Analysis and Elementary Flux Modes... 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

Equation (64) justifies the application of flux-balance analysis even in the face of (i) fast short-term fluctuations and (ii) periodic long term for example, circadian variability. The steady state balance condition restricts the feasible steady-state flux distributions to the flux cone P = v° G IRr IVv0 = 0. The reduction of the admissible flux space, with some of its algebraic properties already summarized in Section III.B, is exploited by several computational approaches, most notably Flux Balance Analysis (FBA) [61, 71, 235] and elementary flux modes (EFMs) [96, 236 238],... 

Aiming at a network-based pathway analysis, the elementary flux modes provide a handle on the set of possible pathways through a metabolic network. In particular, each feasible steady-state flux distribution can be represented by a nonnegative combination of generating vectors that span the flux cone defined... 

The concept of elementary flux modes has resulted in a vast number of applications to analyze and predict the functionality of metabolic networks [64, 65, 138, 241 243]. Software resources that allow for the computation of elementary flux modes are fisted in Table V [178, 224], It should be noted that, due to their definition as an exhaustive enumeration of possible flux distributions,... 

S. Schuster and C. Hilgetag, On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165 182 (1994). 

S. Schuster, T. Dandekar, and D. A. Fell, Detection of elementary flux modes in biochemical networks A promising tool for pathway analysis and metabolic engineering. TIBTECH 17, 53 60 (1999). 

The catabolism of 2 includes 118 reactions many of which are reversible (Fig. 3.5). Since kinetic data on micro-metabolites are difficult to determine experimentally, and in order to obtain an overall view of the xenobiotic metabolism, a stoichiometric model of the full network of degradation pathways of 2 was set up in addition to the network shown in Fig. 3.5. This network was then analyzed by means of elementary flux mode analysis [78]. 

Using the modeling platform Copasi, the reaction network was encoded in the language SBML and the elementary flux modes were calculated, i.e. minimum sets... 

Elementary flux mode analysis on a recombinant strain Polyhydroxybutyrate production [363]... 

Somewhat related to FBA is an approach for the determination of so-called elementary flux modes [Schuster, Dandekar, and Fell 1999 Schuster, Fell, and Dandekar 2000]. Generally speaking, an elementary flux mode is a minimal set of enzymes that can operate at steady state. In contrast to FBA, which produces a set of vectors spanning the possible steady-state fluxes, the elementary mode vectors are uniquely determined (up to a multiplication by a positive real number). Any steady-state flux distribution can be then represented as a linear combination of these modes with nonnegative coefficients. 

The methods of FBA and elementary flux modes study interactions between different routes in a metabolic network and the quantification of flux distributions but do not evaluate how fluxes are controlled. In Metabolic Control Analysis (MCA), the control exerted by the rate of a reaction over a substrate flux or any other system parameter (e.g., metabolite concentration or cell proliferation) can be described quantitatively as a control coefficient. The control coefficient is a relative measure of how much a perturbation affects a system variable and is defined as the fractional change in the system property over the fractional change in the reaction rate [e.g., Bums et al. 1985],... 

Elementary flux mode analysis (EFMA) has emerged as a powerful tool in the family of CBMs [2, 3]. The particular power of an EFMA is based on the ability to... 

C. (2013) Elementary flux modes in a nutshell properties, calculation and applications. Biotechnol. /., 8 (9), 1009-1016,... 

Hunt, K.A., Folsom, J.P., Taflfe, R.L., and Carlson, R.P. (2014) Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition. Bioinformatics, 30 (11), 1569-1578. 

Machado, D., Soons, Z., Patil, K.R., Ferreira, E.C., and Rocha, I. (2012) Random sampling of elementary flux modes in large-scale metabolic networks. Bioinformatics, 28 (18), 1515-1521,... 

J., and Schuster, S. (2009) EFMEvolver computing elementary flux modes in genome-scale metabolic networks, in Proceedings of the German Conference on Bioinformatics, Lecture Notes in Informatics (LNI) P-1S7, Gesellschaft fiir Informatik, Bonn, pp. 179-190. 

Pey, J., Villar, J.A., Tobalina, L., Rezola, A., Garcia, J.M., Beasley, J.E., and Planes, F.J. (2015) TreeEFM calculating elementary flux modes using linear optimization in a tree-based algorithm. Bioinformatics, 31 (6), 897-904. 

David, L. and Bockmayr, A. (2014) Computing elementary flux modes involving a set of target reactions. lEEE/ACM Trans. Comput. 

Pey, J. and Planes, F.J. (2014) Direct calculation of elementary flux modes satisfying several biological constraints... 

Terzer, M. and Stelling, J. (2008) Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics, 24 (19), 2229-2235, doi 10.1093/bioinformatics/btn401. 

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