Graphical reduction of reaction networks by linear elimination of species

Meritxell Sáez, Carsten Wiuf, Elisenda Feliu

Research output: Indexed journal article Articlepeer-review

20 Citations (Scopus)


The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the “fast” species are assumed effectively to be at steady state with respect to the “slow” species. Under this assumption the steady state equations can be used to eliminate the “fast” variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.

Original languageEnglish
Pages (from-to)195-237
Number of pages43
JournalJournal of Mathematical Biology
Issue number1-2
Publication statusPublished - 1 Jan 2017
Externally publishedYes


  • Dynamical system
  • Noninteracting
  • Positivity
  • Quasi-steady-state
  • Reduced network
  • Species graph


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