Nonnegative linear elimination for chemical reaction networks

Meritxell Sáez, Carsten Wiuf, Elisenda Feliu

Research output: Indexed journal article Articlepeer-review

3 Citations (Scopus)


We consider linear elimination of variables in the steady state equations of a chem- ical reaction network. Particular subsets of variables corresponding to sets of so-called reactant- noninteracting species, are introduced. The steady state equations for the variables in such a set, taken together with potential linear conservation laws in the variables, define a linear system of equa- tions. We give conditions that guarantee that the solution to this system is nonnegative, provided it is unique. The results are framed in terms of spanning forests of a particular multidigraph derived from the reaction network and thereby conditions for uniqueness and nonnegativity of a solution are derived by means of the multidigraph. Though our motivation comes from applications in systems biology, the results have general applicability in applied sciences.

Original languageEnglish
Pages (from-to)2434-2455
Number of pages22
JournalSIAM Journal on Applied Mathematics
Issue number6
Publication statusPublished - 2019
Externally publishedYes


  • Elimination
  • Linear system
  • Noninteracting
  • Positive solution
  • Spanning forest


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