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Processes 2017, 5(2), 29; doi:10.3390/pr5020029

Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions

Bioprocess Engineering Group, IIM-CSIC, Vigo 36208, Spain
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Received: 12 May 2017 / Revised: 26 May 2017 / Accepted: 31 May 2017 / Published: 2 June 2017
(This article belongs to the Special Issue Biological Networks)
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Abstract

Abstract: Dynamic modelling is a powerful tool for studying biological networks. Reachability (controllability), observability, and structural identifiability are classical system-theoretic properties of dynamical models. A model is structurally identifiable if the values of its parameters can in principle be determined from observations of its outputs. If model parameters are considered as constant state variables, structural identifiability can be studied as a generalization of observability. Thus, it is possible to assess the identifiability of a nonlinear model by checking the rank of its augmented observability matrix. When such rank test is performed symbolically, the result is of general validity for almost all numerical values of the variables. However, for special cases, such as specific values of the initial conditions, the result of such test can be misleading—that is, a structurally unidentifiable model may be classified as identifiable. An augmented observability rank test that specializes the symbolic states to particular numerical values can give hints of the existence of this problem. Sometimes it is possible to find such problematic values analytically, or via optimization. This manuscript proposes procedures for performing these tasks and discusses the relation between loss of identifiability and loss of reachability, using several case studies of biochemical networks. View Full-Text
Keywords: identifiability; controllability; reachability; observability; parameter estimation; nonlinear systems; differential geometry identifiability; controllability; reachability; observability; parameter estimation; nonlinear systems; differential geometry
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Villaverde, A.F.; Banga, J.R. Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions. Processes 2017, 5, 29.

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