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Estimation of the number of extreme pathways for metabolic networks.

Yeung M, Thiele I, Palsson BO - BMC Bioinformatics (2007)

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

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.


Connectivity of Reactions. Diagram describing different types of connectivities. Reaction ri utilizes metabolite A, which is produced by three reactions, and produces metabolite B, which is consumed by three reactions. Reaction ri then has an incoming degree of d-(ri) = 3 due to metabolite A, and outgoing degree of d+(ri) = 3.
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Figure 4: Connectivity of Reactions. Diagram describing different types of connectivities. Reaction ri utilizes metabolite A, which is produced by three reactions, and produces metabolite B, which is consumed by three reactions. Reaction ri then has an incoming degree of d-(ri) = 3 due to metabolite A, and outgoing degree of d+(ri) = 3.

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.


Estimation of the number of extreme pathways for metabolic networks.

Yeung M, Thiele I, Palsson BO - BMC Bioinformatics (2007)

Connectivity of Reactions. Diagram describing different types of connectivities. Reaction ri utilizes metabolite A, which is produced by three reactions, and produces metabolite B, which is consumed by three reactions. Reaction ri then has an incoming degree of d-(ri) = 3 due to metabolite A, and outgoing degree of d+(ri) = 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2089122&req=5

Figure 4: Connectivity of Reactions. Diagram describing different types of connectivities. Reaction ri utilizes metabolite A, which is produced by three reactions, and produces metabolite B, which is consumed by three reactions. Reaction ri then has an incoming degree of d-(ri) = 3 due to metabolite A, and outgoing degree of d+(ri) = 3.
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.

Bottom Line: 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.

View Article: PubMed Central - HTML - PubMed

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.