On Algebraic Properties of Extreme Pathways in Metabolic Networks

Overview

Journal J Comput Biol

Specialties Biology
Molecular Biology

Date 2010 Feb 23

PMID 20170399

Citations 7

Authors

Dimitrije Jevremovic

Cong T Trinh

Friedrich Srienc

Daniel Boley

Affiliations

Soon will be listed here.

Abstract

We give a concise development of some of the major algebraic properties of extreme pathways (pathways that cannot be the result of combining other pathways) of metabolic networks, contrasting them to those of elementary flux modes (pathways involving a minimal set of reactions). In particular, we show that an extreme pathway can be recognized by a rank test as simple as the existing rank test for elementary flux modes, without computing all the modes. We make the observation that, unlike elementary flux modes, the property of being an extreme pathway depends on the presence or absence of reactions beyond those involved in the pathway itself. Hence, the property of being an extreme pathway is not a local property. As a consequence, we find that the set of all elementary flux modes for a network includes all the elementary flux modes for all its subnetworks, but that this property does not hold for the set of all extreme pathways.

Citing Articles

decomposition of biochemical reaction networks within growing cells.

Walton J, Lindahl P iScience. 2024; 27(1):108506.

PMID: 38161422 PMC: 10757263. DOI: 10.1016/j.isci.2023.108506.

Towards scaling elementary flux mode computation.

Ullah E, Yosafshahi M, Hassoun S Brief Bioinform. 2019; 21(6):1875-1885.

PMID: 31745550 PMC: 8499997. DOI: 10.1093/bib/bbz094.

Finding MEMo: minimum sets of elementary flux modes.

Rohl A, Bockmayr A J Math Biol. 2019; 79(5):1749-1777.

PMID: 31388689 DOI: 10.1007/s00285-019-01409-5.

Efficient estimation of the maximum metabolic productivity of batch systems.

St John P, Crowley M, Bomble Y Biotechnol Biofuels. 2017; 10:28.

PMID: 28163785 PMC: 5282707. DOI: 10.1186/s13068-017-0709-0.

A depth-first search algorithm to compute elementary flux modes by linear programming.

Quek L, Nielsen L BMC Syst Biol. 2014; 8:94.

PMID: 25074068 PMC: 4236763. DOI: 10.1186/s12918-014-0094-2.

References

Terzer M, Stelling J . Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics. 2008; 24(19):2229-35. DOI: 10.1093/bioinformatics/btn401. View

Palsson B, Price N, Papin J . Development of network-based pathway definitions: the need to analyze real metabolic networks. Trends Biotechnol. 2003; 21(5):195-8. DOI: 10.1016/S0167-7799(03)00080-5. View

Urbanczik R, Wagner C . An improved algorithm for stoichiometric network analysis: theory and applications. Bioinformatics. 2004; 21(7):1203-10. DOI: 10.1093/bioinformatics/bti127. View

Schilling C, Letscher D, Palsson B . Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J Theor Biol. 2000; 203(3):229-48. DOI: 10.1006/jtbi.2000.1073. View

Wiback S, Palsson B . Extreme pathway analysis of human red blood cell metabolism. Biophys J. 2002; 83(2):808-18. PMC: 1302188. DOI: 10.1016/S0006-3495(02)75210-7. View

Schuster S, Hilgetag C, Woods J, Fell D . Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism. J Math Biol. 2002; 45(2):153-81. DOI: 10.1007/s002850200143. View

Gagneur J, Klamt S . Computation of elementary modes: a unifying framework and the new binary approach. BMC Bioinformatics. 2004; 5:175. PMC: 544875. DOI: 10.1186/1471-2105-5-175. View

Klamt S, Gagneur J, von Kamp A . Algorithmic approaches for computing elementary modes in large biochemical reaction networks. Syst Biol (Stevenage). 2006; 152(4):249-55. DOI: 10.1049/ip-syb:20050035. View

von Kamp A, Schuster S . Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics. 2006; 22(15):1930-1. DOI: 10.1093/bioinformatics/btl267. View

10.

Schuster S, Dandekar T, Fell D . Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol. 1999; 17(2):53-60. DOI: 10.1016/s0167-7799(98)01290-6. View

11.

Trinh C, Carlson R, Wlaschin A, Srienc F . Design, construction and performance of the most efficient biomass producing E. coli bacterium. Metab Eng. 2006; 8(6):628-38. DOI: 10.1016/j.ymben.2006.07.006. View

12.

Carlson R, Srienc F . Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions. Biotechnol Bioeng. 2004; 85(1):1-19. DOI: 10.1002/bit.10812. View

13.

Bell S, Palsson B . Expa: a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics. 2004; 21(8):1739-40. DOI: 10.1093/bioinformatics/bti228. View

14.

Pfeiffer T, Nuno J, MONTERO F, Schuster S . METATOOL: for studying metabolic networks. Bioinformatics. 1999; 15(3):251-7. DOI: 10.1093/bioinformatics/15.3.251. View

15.

Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles E . Metabolic network structure determines key aspects of functionality and regulation. Nature. 2002; 420(6912):190-3. DOI: 10.1038/nature01166. View

16.

Urbanczik R . Enumerating constrained elementary flux vectors of metabolic networks. IET Syst Biol. 2007; 1(5):274-9. DOI: 10.1049/iet-syb:20060073. View

17.

Klamt S, Stelling J . Two approaches for metabolic pathway analysis?. Trends Biotechnol. 2003; 21(2):64-9. DOI: 10.1016/s0167-7799(02)00034-3. View

18.

Urbanczik R, Wagner C . Functional stoichiometric analysis of metabolic networks. Bioinformatics. 2005; 21(22):4176-80. DOI: 10.1093/bioinformatics/bti674. View

19.

Klamt S, Stelling J, Ginkel M, Gilles E . FluxAnalyzer: exploring structure, pathways, and flux distributions in metabolic networks on interactive flux maps. Bioinformatics. 2003; 19(2):261-9. DOI: 10.1093/bioinformatics/19.2.261. View

20.

Schuster S, Fell D, Dandekar T . A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat Biotechnol. 2000; 18(3):326-32. DOI: 10.1038/73786. View