A Computationally Efficient Algorithm for Testing the Identifiability of Polynomial Systems with Applications to Biological Systems

Mathematical models of physical systems often contain many more parameters than can be estimated from observations. It is useful to check whether such models are structurally identifiable before choosing an experimental plan for parameter estimation. Many identifiability tests have been proposed in the literature. However, the proposed methods are computationally complex, or even intractable, for systems containing more than a handful of states or parameters. In this work, a linear algebra-based approach for testing ordinary differential equations and index-one differential algebraic equation systems with linear output maps for local structural identifiability is presented. The proposed method is computationally efficient, as it does not require repeated differentiation of the model equations. Furthermore, the proposed model can be used by experimenters to determine which set of measurements should be made in order to estimate specific parameters within the model. The effectiveness of the proposed approach is demonstrated by testing the identifiability of a 15-state model describing NF-kappa B regulation. The model is shown to be identifiable even if process measurements are related to the state variables by proportionality constants (themselves unknown). Furthermore, the proposed procedure is used to compute a table that relates to each unknown parameter or parameter set a set of state variables whose observation is sufficient for parameter estimation.