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Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation.

Barrett CL, Herrgard MJ, Palsson B - BMC Syst Biol (2009)

Bottom Line: We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system.This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bioengineering, University of California at San Diego, La Jolla, CA, 92093-0412, USA. cbarrett@bioeng.ucsd.edu

ABSTRACT

Background: Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.

Results: We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system. This decomposition comes in the form of a low number of small reaction sets whose flux variability accounts for nearly all of the flux variability in the entire system. This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.

Conclusion: We demonstrate how our top-down analysis of networks can be used to determine key regulatory requirements independent of specific parameters and mechanisms. Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

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The cumulative fractional eigenvalue distribution. Shown for the variation in the randomly sampled metabolic network flux states before (crosses) and after (squares) eigenvector rotation.
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Figure 2: The cumulative fractional eigenvalue distribution. Shown for the variation in the randomly sampled metabolic network flux states before (crosses) and after (squares) eigenvector rotation.

Mentions: Monte Carlo sampling is a method for generating large numbers of random allowable flux states and has been used to study the properties of metabolic flux states[9,14-19]. We comprehensively sampled the flux space corresponding to a growth rate of at least 90% of the maximum achievable growth rate and generated a large number (~106) of flux vectors. Because the sampling procedure is a linear one and because we sought a basis for the sampled space, we performed Principal Components Analysis using Singular Value Decomposition. The cumulative fractional eigenvalue distribution (Figure 2) reveals that 96% of the variation in the metabolic network flux states can be explained by seven principal components–implying that the post-translational regulatory problem is low-dimensional. That is, by "regulating" a small number of dimensions the flux state of the entire network can be essentially set. The implications and caveats associated with this interpretation are addressed below.


Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation.

Barrett CL, Herrgard MJ, Palsson B - BMC Syst Biol (2009)

The cumulative fractional eigenvalue distribution. Shown for the variation in the randomly sampled metabolic network flux states before (crosses) and after (squares) eigenvector rotation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2667477&req=5

Figure 2: The cumulative fractional eigenvalue distribution. Shown for the variation in the randomly sampled metabolic network flux states before (crosses) and after (squares) eigenvector rotation.
Mentions: Monte Carlo sampling is a method for generating large numbers of random allowable flux states and has been used to study the properties of metabolic flux states[9,14-19]. We comprehensively sampled the flux space corresponding to a growth rate of at least 90% of the maximum achievable growth rate and generated a large number (~106) of flux vectors. Because the sampling procedure is a linear one and because we sought a basis for the sampled space, we performed Principal Components Analysis using Singular Value Decomposition. The cumulative fractional eigenvalue distribution (Figure 2) reveals that 96% of the variation in the metabolic network flux states can be explained by seven principal components–implying that the post-translational regulatory problem is low-dimensional. That is, by "regulating" a small number of dimensions the flux state of the entire network can be essentially set. The implications and caveats associated with this interpretation are addressed below.

Bottom Line: We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system.This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bioengineering, University of California at San Diego, La Jolla, CA, 92093-0412, USA. cbarrett@bioeng.ucsd.edu

ABSTRACT

Background: Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.

Results: We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system. This decomposition comes in the form of a low number of small reaction sets whose flux variability accounts for nearly all of the flux variability in the entire system. This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.

Conclusion: We demonstrate how our top-down analysis of networks can be used to determine key regulatory requirements independent of specific parameters and mechanisms. Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

Show MeSH