Estimation of the number of extreme pathways for metabolic networks.
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In particular, it was found that log [p] had an exponential relationship with log[ summation operatori=1Rd-id+ici] where R = /Reff/ is the number of active reactions in a network, d-i and d+i the incoming and outgoing degrees of the reactions ri in 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.
Affiliation: Dept, of Bioengineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA. palsson@ucsd.edu.
ABSTRACT
ABSTRACT: BACKGROUND: The set of extreme pathways (ExPa), {pi}, defines the convex basis vectors used for the mathematical characterization of the 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 log[ summation operatori=1Rd-id+ici] where R = /Reff/ is the number of active reactions in a network, d-i and d+i the incoming and outgoing degrees of the reactions ri in 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. No MeSH data available. |
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Mentions: From Figure 4, it can be seen that the number of possible pathways through a given reaction ri is given by . It is tempting to conclude that the number of pathways calculated is given by . However, this would be similar to the number derived in [14], which typically over-estimated the number of elementary modes, of which the set of ExPas {pi} is a subset, by a factor of 6 × 107. Here, we instead looked into the relationship between p = /{pi}/ and the sum of these terms to avoid such an overestimation. |
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Affiliation: Dept, of Bioengineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA. palsson@ucsd.edu.
No MeSH data available.