Extreme pathways

J. A. Papin, N. D. Price, J. S. Edwards, and B. O. Palsson, The genome scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J. Theor. Biol. 215, 67 82 (2002). 

S. L. Bell and B. 0. Palsson, Expa A program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21(8), 1739 1740 (2005). 

The extreme pathways are a basis (in the sense of vector spaces) for all routes through the reaction network, i.e., ary route can be written as a linear combination of the extreme pathways. When all the reaction steps are irreversible, these two sets are equivalent, i.e., they have the same elements. When some of the steps are reversible, there are more (perhaps far more) elementary modes, though this set is still much smaller than the countably infinite set of all routes. In any event, all routes can be obtained as combinations of the elements of either set, and thus if one studies these relatively small sets of routes, one can hope to obtain results for all routes. 

Two extreme pathways may be envisaged for this transformation. One involves a pericyclic reaction followed by desilylation and elimination of methoxide from the product silyl enol ether. The alternative proceeds via a Lewis acid promoted aldol reaction to give an intermediate which cyclizes to the product dihydropyrone (Figure Si3.6). The actual pathway in an individual case is affected to a considerable degree by the nature of the Lewis acid used and lies somewhere between these two extremes. 

Identifying Pathway Channels in Networks Extreme Pathway Analysis... 

Figure 8 A reaction network and its extreme pathways labeled pi ps (adapted from Schilling et al/ )... 

Due to lack of kinetic parameters, structural metabolic network modeling has been widely applied for analyzing cellular metabolism under steady-state. Depending on what assumptions are made and whether experimental data are required, different techniques have been developed to analyze the invariant of metabohc networks such as metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) including elementary mode and extreme pathway analyses (Lewis et al. 2012 Stephanopoulos et al. 1998 Trinh et al. 2(X)9). 

Behre J, Wilhelm T, von Kamp A, Ruppin E, Schuster S (2008) Stmctuial robustness of metabolic networks with respect to multiple knockouts. J Theor Biol 252 433M41 Bell SL, Palsson BO (2005) Expa a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21 1739-1740 Beurton-Aimar M, Beauvoit B, Monier A, Vallee F Dieuaide-Noubhani M, Colombie S (2011) Comparison between elementary flux modes analysis and 13c-metabolic fluxes measured in bacterial and plant cells. BMC Syst Biol 5 95... 

Jensen P, Lutz K, Papin J (2011) Tiger toolbox for integrating genome-scale metabolic models, expression data, and transcriptional regulatory networks. BMC Syst Biol 5 147 Jevremovic D, Trinh CT, Srienc F, Boley D (2010) On algebraic properties of extreme pathways in metabolic networks. J Comput Biol 17 107-119... 

Llaneras F, Pico J (2010) Which metabolic pathways generate and characterize the flux space A comparison among elementary modes, extreme pathways and minimal generators. J Biomed Biotechnol 753904... 

Extreme pathway analysis and elementary mode analysis... 

In order to extract more information from the steady-state flux model, extreme pathway analysis (EPA) and elementary mode analysis (EMA) have been developed [14,15]. In these approaches, the metaboHc reaction network is decomposed into a collection of small irreversible functional pathways. When these pathways are weighted and superimposed back together, they are able to form the original metaboHc flux network. By examining the elementary pathways, and using Hnear optimization tools, it is possible to better explore the metaboHc capabilities of a network, and this can also be used to suggest useful metaboHc pathway alterations. 

In the second approach, instead of looking for a single solution to the model, all possible steady-state solutions are enumerated via so-called elementary flux modes or extreme pathways using convex analysis. 

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