Identifiability from a Few Species for a Class of Biochemical Reaction Networks

  • Gabriela Jeronimo
  • Mercedes Pérez MillánEmail author
  • Pablo Solernó


Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of a class of biochemical networks which are abundant, such as multisite phosphorylation systems and phosphorylation cascades (for example, MAPK cascades). For any system of this class, we explicitly exhibit a single species for each connected component of the associated digraph such that the successive total derivatives of its concentration allow us to identify all the parameters occurring in the component. The number of derivatives needed is bounded essentially by the length of the corresponding connected component of the digraph. Moreover, in the particular case of the cascades, we show that the parameters can be identified from a bounded number of successive derivatives of the last product of the last layer. This theoretical result induces also a heuristic interpolation-based identifiability procedure to recover the values of the rate constants from exact measurements.


Chemical reaction networks Mass-action kinetics Identifiability MAPK cascade 



The authors wish to thank the anonymous referees for their thoughtful comments which helped to improve the manuscript.

Supplementary material


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© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de MatemáticaBuenos AiresArgentina
  2. 2.Universidad de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Instituto de Investigaciones Matemáticas “Luis A. Santaló” (IMAS), Facultad de Ciencias Exactas y NaturalesBuenos AiresArgentina
  3. 3.Universidad de Buenos Aires, Ciclo Básico Común, Departamento de Ciencias ExactasBuenos AiresArgentina

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