Structural vs Practical Identifiability of Nonlinear Differential Equation Models in Systems Biology

This paper reappraises two different viewpoints adopted for testing identifiability of nonlinear differential equation models. The aim is to take advantage through their joint use of the complementary information provided. The common objective is to assess whether model parameters can be estimated from specific input/output (I/O) experiments. The structural identifiability analysis investigates whether unknown model parameters can be identified uniquely, at all, with a particular I/O configuration. This is investigated using differential algebra, e.g., as implemented in the software DAISY (Differential Algebra for Identifiability of SYstems). In contrast, practical identifiability analysis is a data-based approach to assess the precision of parameter estimates obtainable from experimental data. It is based on simulated model outputs and their sensitivities with respect to parameters. The relevant novelty of using both methodologies together is that structural identifiability analysis allows a clearer understanding of the practical identifiability results. This result is shown in the identifiability analysis of a much quoted biological model describing the erythropoietin(Epo)-induced activation of the JAK-STAT signaling pathway, which is known to play a role in the regulation of cell proliferation, differentiation, chemotaxis, and apoptosis and is important for hematopoiesis, and immune development. This study shows that some results on practical identifiability tests can be proven in an analytical way by a differential algebra test and that this test can provide additional information helpful for the experiment design.