Journal of Mathematical Chemistry

, Volume 6, Issue 1, pp 17-40

First online:

Detecting strictly detailed balanced subnetworks in open chemical reaction networks

  • Stefan SchusterAffiliated withSektion Biologie, Bereich Biophysik, Humboldt-Universität zu Berlin
  • , Ronny SchusterAffiliated withInstitut für Biochemie, Humboldt-Universität zu Berlin

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The notion “strictly detailed balanced subnetwork” is introduced, for chemical reaction networks which are open and spatially homogeneous, to refer to any set of reactions the net rates of which vanish in each asymptotically stable steady state, regardless of the kinetic parameters of any reaction in the whole network. Necessary and sufficient conditions for sets of reactions to be strictly detailed balanced subnetworks are derived. An algorithm for detecting all reactions belonging to such subnetworks in systems of arbitrary stoichiometry is given, justified and applied to a realistic biochemical system. A computer program in PASCAL, performing the essential parts of this algorithm, is added.