Metabolic states with maximal specific rate carry flux through an elementary flux mode

Authors

  • Meike T. Wortel,

    1. Systems Bioinformatics, IBIVU, VU University, Amsterdam, The Netherlands
    2. Kluyver Centre for Genomics of Industrial Fermentation, Delft, The Netherlands
    3. Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), VU University, The Netherlands
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  • Han Peters,

    1. Korteweg de Vries Institute for Mathematics, University of Amsterdam, The Netherlands
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  • Josephus Hulshof ,

    1. Department of Mathematics, VU University, Amsterdam, The Netherlands
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  • Bas Teusink,

    1. Systems Bioinformatics, IBIVU, VU University, Amsterdam, The Netherlands
    2. Kluyver Centre for Genomics of Industrial Fermentation, Delft, The Netherlands
    3. Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), VU University, The Netherlands
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  • Frank J. Bruggeman

    Corresponding author
    1. Systems Bioinformatics, IBIVU, VU University, Amsterdam, The Netherlands
    2. Kluyver Centre for Genomics of Industrial Fermentation, Delft, The Netherlands
    3. Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), VU University, The Netherlands
    4. Department of Mathematics, VU University, Amsterdam, The Netherlands
    • Correspondence F. J. Bruggeman, Amsterdam Institute for Molecules, Medicines and Systems (AIMMS), VU University Amsterdam, de Boelelaan 1085, NL-1081HV Amsterdam, The Netherlands Fax: +31(0) 205987229 Tel: +31(0) 205987229 E-mail: f.j.bruggeman@vu.nl Website:http://www.ibi.vu.nl/sysbio

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  • We dedicate this work to the memory of Professor Dr Reinhart Heinrich, who pioneered the study of the optimization of metabolic pathways using kinetic mathematical models.

Abstract

Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product yields, any prediction of optimal specific rates at the genome scale is currently computationally intractable, even if the kinetic properties of all enzymes are available. In the present study, we characterize maximal-specific-rate states of metabolic networks of arbitrary size and complexity, including genome-scale kinetic models. We report that optimal states are elementary flux modes, which are minimal metabolic networks operating at a thermodynamically-feasible steady state with one independent flux. Remarkably, elementary flux modes rely only on reaction stoichiometry, yet they function as the optimal states of mathematical models incorporating enzyme kinetics. Our results pave the way for the optimization of genome-scale kinetic models because they offer huge simplifications to overcome the concomitant computational problems.

Database

The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.mib.ac.uk/database/wortel2/index.html free of charge.

[Database section added 14 May 2014 after original online publication]

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