Structural Identifiability of Dynamic Systems Biology Models

Abstract

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.

How to deal with parameters for whole-cell modelling

“…tens to hundreds of species and parameters) due to the computational demands of these methods. Similarly, methods to assess identifiability of models and to characterize the impact of parameter uncertainties tend to be limited to similar size models, although some more recent developments can deal with slightly larger scale models of a few hundred parameters [92,98]. Of course, such methods are currently not compatible with the size and complex hybrid nature of WCMs.…”

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

“…if all its parameters are s.l.i. If (13) does not hold in any neighbourhood of p * , parameter p i is structurally unidentifiable. A model M is structurally unidentifiable if at least one of its parameters is structurally unidentifiable.…”

“…Therefore methods based in the OIC [10,11,13] classify the model as observable and identifiable for generic values of the states and parameters. However, note that for the particular initial conditions {x 1 (0) = 0, x 2 (0) = 10}, two of the states remain at zero {x 1 (t) = 0, x 2 (t) = 0} ∀t ≥ 0, and in this case only p 1 appears in the equations.…”

“…Indeed, it is possible to check simultaneously the observability and structural identifiability of a model by including its parameters in the state variables vector, and calculating the rank of the resulting (augmented) observability matrix. Several computational methods that build on this idea have been presented in the last decade [10][11][12][13].…”

“…In the present work we have carried the rank calculations using a recently presented tool called STRIKE-GOLDD [13]. STRIKE-GOLDD is a methodology for local structural identifiability analysis that evaluates the OIC symbolically.…”