The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies

Aaron P. Wlaschin, Cong T. Trinh, Ross Carlson, Friedrich Srienc

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The metabolism of a cell can be viewed as a weighted sum of elementary modes. Due to the multiplicity of modes the identification of the individual weights represents a non-trivial problem. To enable the determination of weighting factors we have identified and implemented two gene deletions in combination with defined growth conditions that limit the metabolism from 4374 original elementary modes to 24 elementary modes for a non-PHB synthesizing control and 40 modes for a PHB synthesizing strain. These remaining modes can be further grouped into five families that have the same overall stoichiometry. Thus, the complexity of the problem is significantly reduced, and weighting factors for each family of modes could be determined from the measurement of accumulation rates of metabolites. Moreover, it is shown that individual weights are inversely correlated with the entropy generated by the operation of the used pathways defined in elementary modes. This suggests that evolution developed cellular regulatory patterns that permit diversity of pathways while favoring efficient pathways with low entropy generation. Furthermore, such correlation provides a rational way of estimating metabolic fluxes based on the thermodynamic properties of elementary modes. This is demonstrated with an example in which experimentally determined, intracellular fluxes are shown to be highly correlated with fluxes computed based on elementary modes and reaction entropies. The analysis suggests that the set of elementary modes can be interpreted analogous to a metabolic ensemble of quantum states of a macroscopic system.

Original languageEnglish (US)
Pages (from-to)338-352
Number of pages15
JournalMetabolic Engineering
Issue number4
StatePublished - Jul 2006

Bibliographical note

Funding Information:
The authors would like to thank Bernhard Sonnleitner for providing useful insight during the preparation of the manuscript. We are also grateful to the National Science Foundation (BES-0109383) and to the Minnesota Supercomputing Institute for supporting parts of this work. Ross Carlson and Aaron Wlaschin are recipients of NIH training grant fellowships in Biotechnology.


  • 3-hydroxybutryic acid
  • 3HB
  • Anaerobic metabolism
  • Elementary mode analysis
  • Entropy
  • Escherichia coli metabolism
  • Metabolic modeling
  • PHB
  • Poly (R)-3-hydroxybutyric acid
  • Statistical thermodynamics
  • Weighting factors


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