Structural Identifiability of Dynamic Systems Biology Models

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas.Author Summary: Advances in computing power have facilitated the development of increasingly larger dynamic models of biological processes, which usually have many unknown parameters. Often times, such models contain parameters that are structurally unidentifiable, i.e., they cannot be uniquely determined from experiments. Any parameter estimation algorithm will fail when trying to estimate unidentifiable parameters, leading to waste of resources and possibly wrong model predictions. Hence, it is essential to assess structural identifiability before exploiting a model. However, performing such analysis can be hard, especially as models become increasingly complicated. To address this challenge, we developed a methodology for structural identifiability analysis that aims at generality—it can handle any analytic model written as a set of ordinary differential equations—and computational efficiency—it includes features that facilitate the analysis of large systems. We provide an implementation of the methodology as a MATLAB toolbox called STRIKE-GOLDD. We illustrate its applicability to systems biology models of genetic, signalling, metabolic, and pharmacokinetic networks, showing which of them are unidentifiable and how they can be made identifiable.