Nonnegative linear elimination for chemical reaction networks

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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
JournalSIAM Journal on Applied Mathematics
Issue number6
Pages (from-to)2434-2455
Publication statusPublished - 2019

    Research areas

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

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