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Open Access Highly Accessed Research article

Estimation of the number of extreme pathways for metabolic networks

Matthew Yeung1, Ines Thiele12 and Bernard Ø Palsson1*

Author Affiliations

1 Dept. of Bioengineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA

2 Program in Bioinformatics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA

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BMC Bioinformatics 2007, 8:363  doi:10.1186/1471-2105-8-363

Published: 27 September 2007

Abstract

Background

The set of extreme pathways (ExPa), {pi}, defines the convex basis vectors used for the mathematical characterization of the null space of the stoichiometric matrix for biochemical reaction networks. ExPa analysis has been used for a number of studies to determine properties of metabolic networks as well as to obtain insight into their physiological and functional states in silico. However, the number of ExPas, p = |{pi}|, grows with the size and complexity of the network being studied, and this poses a computational challenge. For this study, we investigated the relationship between the number of extreme pathways and simple network properties.

Results

We established an estimating function for the number of ExPas using these easily obtainable network measurements. In particular, it was found that log [p] had an exponential relationship with <a onClick="popup('http://www.biomedcentral.com/1471-2105/8/363/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/8/363/mathml/M1">View MathML</a>, where R = |Reff| is the number of active reactions in a network, <a onClick="popup('http://www.biomedcentral.com/1471-2105/8/363/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/8/363/mathml/M2">View MathML</a> and <a onClick="popup('http://www.biomedcentral.com/1471-2105/8/363/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/8/363/mathml/M3">View MathML</a> the incoming and outgoing degrees of the reactions ri Reff, and ci the clustering coefficient for each active reaction.

Conclusion

This relationship typically gave an estimate of the number of extreme pathways to within a factor of 10 of the true number. Such a function providing an estimate for the total number of ExPas for a given system will enable researchers to decide whether ExPas analysis is an appropriate investigative tool.