Bulletin of Mathematical Biology

, Volume 77, Issue 12, pp 2180–2211 | Cite as

A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions

  • Satya Swarup Samal
  • Dima Grigoriev
  • Holger Fröhlich
  • Andreas Weber
  • Ovidiu Radulescu
Original Article


Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low-dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.


Model reduction Algebraic systems biology Complexity 



This work has been supported by the French ModRedBio CNRS Peps, and EPIGENMED Excellence Laboratory projects. D.G. is grateful to the Max-Planck Institut für Mathematik, Bonn for its hospitality during writing this paper and to Labex CEMPI (ANR-11-LABX-0007-01).


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  • Satya Swarup Samal
    • 1
  • Dima Grigoriev
    • 2
  • Holger Fröhlich
    • 1
  • Andreas Weber
    • 3
  • Ovidiu Radulescu
    • 4
  1. 1.Algorithmic BioinformaticsBonn-Aachen International Center for ITBonnGermany
  2. 2.CNRS, Mathématiques, Université de LilleVilleneuve d’AscqFrance
  3. 3.Institut für Informatik IIUniversity of BonnBonnGermany
  4. 4.DIMNP UMR CNRS 5235University of MontpellierMontpellierFrance

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