A passivity-based stability criterion for a class of biochemical reaction networks

Murat Arcak, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stability test is illustrated on a mitogen-activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of diffusion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the diffusion terms between the compartments.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalMathematical Biosciences and Engineering
Issue number1
StatePublished - Jan 2008

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


  • Biochemical reaction networks
  • Global stability
  • Large-scale systems
  • Lyapunov stability

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