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

  • Received: 01 May 2007 Accepted: 29 June 2018 Published: 01 January 2008
  • MSC : Primary: 34D23, 93A15,93D30; Secondary: 34D20, 05C50.

  • 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 diag- onal 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 encom- passes the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stabil- ity 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 di®usion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the di®usion terms between the compartments.

    Citation: Murat Arcak, Eduardo D. Sontag. A passivity-based stability criterion for a class of biochemical reaction networks[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 1-19. doi: 10.3934/mbe.2008.5.1

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  • 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 diag- onal 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 encom- passes the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stabil- ity 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 di®usion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the di®usion terms between the compartments.
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    © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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