Bulletin of Mathematical Biology

, Volume 80, Issue 9, pp 2306–2337 | Cite as

Network Translation and Steady-State Properties of Chemical Reaction Systems

  • Elisa Tonello
  • Matthew D. Johnston
Original Article


Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.


Dynamical systems Mass action systems Biochemical reaction graph Robustness Linear programming 

Mathematics Subject Classification

92C42 92C45 90C35 



MDJ was supported by the Henry Woodward Fund. The authors thanks the anonymous reviewers for their helpful comments.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamEngland
  2. 2.Department of MathematicsSan Jose State UniversitySan JoseUSA

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