Reconstructing metabolic flux vectors from extreme pathways: Defining the α-spectrum

Sharon J. Wiback, Radhakrishnan Mahadevan, Bernhard Palsson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)


The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the α-spectrum. The α-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the α-spectrum. The α-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Original languageEnglish
Pages (from-to)313-324
Number of pages12
JournalJournal of Theoretical Biology
Issue number3
Publication statusPublished - 7 Oct 2003

Bibliographical note

Funding Information:
We would like to acknowledge the support of the National Science Foundation (BES 01-20363) and the National Institutes of Health (GM 57089). We would also like to thank Iman Famili, Jason Papin, Markus Covert, and Tim Allen for their critical reading of this manuscript.

Other keywords

  • Elementary flux mode
  • Extreme pathway analysis
  • Human red blood cell
  • In silico model
  • Pathway-based perspective


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