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Observability and Structural Identifiability of Nonlinear Biological Systems

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  • Alejandro F. Villaverde

Abstract

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.

Suggested Citation

  • Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    • Handle: RePEc:hin:complx:8497093
    DOI: 10.1155/2019/8497093
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    References listed on IDEAS

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    1. Walter, Eric & Lecourtier, Yves, 1982. "Global approaches to identifiability testing for linear and nonlinear state space models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(6), pages 472-482.
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    3. Alejandro F Villaverde & Antonio Barreiro & Antonis Papachristodoulou, 2016. "Structural Identifiability of Dynamic Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 12(10), pages 1-22, October.
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    6. Maria Pia Saccomani & Karl Thomaseth, 2018. "The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study," Complexity, Hindawi, vol. 2018, pages 1-10, February.
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    Cited by:

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    2. Michael W Irvin & Arvind Ramanathan & Carlos F Lopez, 2023. "Model certainty in cellular network-driven processes with missing data," PLOS Computational Biology, Public Library of Science, vol. 19(4), pages 1-31, April.
    3. Liu, Jie & Boutat, Driss & Liu, Da-Yan & Zhang, Xue-Feng, 2025. "Nonlinear MIMO observable normal forms with output injection and output diffeomorphism," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    4. Nathaniel J Linden & Boris Kramer & Padmini Rangamani, 2022. "Bayesian parameter estimation for dynamical models in systems biology," PLOS Computational Biology, Public Library of Science, vol. 18(10), pages 1-48, October.
    5. Nerea Martínez & Alejandro F. Villaverde, 2020. "Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation," Mathematics, MDPI, vol. 8(11), pages 1-27, October.

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