An elementary metabolite unit (EMU) based method of isotopically nonstationary flux analysis

Nonstationary metabolic flux analysis (NMFA) is at present a very computationally intensive exercise, especially for large reaction networks. We applied elementary metabolite unit (EMU) theory to NMFA, dramatically reducing computational difficulty. We also introduced block decoupling, a new method that systematically and comprehensively divides EMU systems of equations into smaller subproblems to further reduce computational difficulty. These improvements led to a 5000‐fold reduction in simulation times, enabling an entirely new and more complicated set of problems to be analyzed with NMFA. We simulated a series of nonstationary and stationary GC/MS measurements for a large E. coli network that was then used to estimate parameters and their associated confidence intervals. We found that fluxes could be successfully estimated using only nonstationary labeling data and external flux measurements. Addition of near‐stationary and stationary time points increased the precision of most parameters. Contrary to prior reports, the precision of nonstationary estimates proved to be comparable to the precision of estimates based solely on stationary data. Finally, we applied EMU‐based NMFA to experimental nonstationary measurements taken from brown adipocytes and successfully estimated fluxes and some metabolite concentrations. By using NFMA instead of traditional MFA, the experiment required only 6 h instead of 50 (the time necessary for most metabolite labeling to reach 99% of isotopic steady state). Biotechnol. Bioeng. 2008;99: 686–699. © 2007 Wiley Periodicals, Inc.

[1]  N. S. Mendelsohn,et al.  Coverings of Bipartite Graphs , 1958, Canadian Journal of Mathematics.

[2]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[3]  Philip E. Gill,et al.  Practical optimization , 1981 .

[4]  Alex Pothen,et al.  Computing the block triangular form of a sparse matrix , 1990, TOMS.

[5]  W. Wiechert,et al.  Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments. , 1997, Biotechnology and bioengineering.

[6]  U. Sauer,et al.  Metabolic fluxes in riboflavin-producing Bacillus subtilis , 1997, Nature Biotechnology.

[7]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems , 1999 .

[8]  W. Wiechert,et al.  Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. , 1999, Biotechnology and bioengineering.

[9]  W. Wiechert 13C metabolic flux analysis. , 2001, Metabolic engineering.

[10]  J. Nielsen,et al.  Network Identification and Flux Quantification in the Central Metabolism of Saccharomyces cerevisiae under Different Conditions of Glucose Repression , 2001, Journal of bacteriology.

[11]  R. Takors,et al.  Quantification of intracellular metabolites in Escherichia coli K12 using liquid chromatographic-electrospray ionization tandem mass spectrometric techniques. , 2001, Analytical biochemistry.

[12]  Christoph Wittmann,et al.  Genealogy Profiling through Strain Improvement by Using Metabolic Network Analysis: Metabolic Flux Genealogy of Several Generations of Lysine-Producing Corynebacteria , 2002, Applied and Environmental Microbiology.

[13]  G. Stephanopoulos,et al.  Systematic quantification of complex metabolic flux networks using stable isotopes and mass spectrometry. , 2003, European journal of biochemistry.

[14]  Christoph Wittmann,et al.  Comparative Metabolic Flux Analysis of Lysine-Producing Corynebacterium glutamicum Cultured on Glucose or Fructose , 2004, Applied and Environmental Microbiology.

[15]  Gregory Stephanopoulos,et al.  Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements. , 2006, Metabolic engineering.

[16]  Wolfgang Wiechert,et al.  Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions. , 2006, Metabolic engineering.

[17]  J. Morgan,et al.  A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms. , 2007, Phytochemistry.

[18]  G. Stephanopoulos,et al.  Metabolic flux analysis in a nonstationary system: fed-batch fermentation of a high yielding strain of E. coli producing 1,3-propanediol. , 2007, Metabolic engineering.

[19]  Ralf Takors,et al.  Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments. , 2007, Journal of biotechnology.

[20]  G. Stephanopoulos,et al.  Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions. , 2007, Metabolic engineering.

[21]  Gregory Stephanopoulos,et al.  Quantifying Reductive Carboxylation Flux of Glutamine to Lipid in a Brown Adipocyte Cell Line* , 2008, Journal of Biological Chemistry.