Sufficiently Exciting Inputs for Structurally Identifiable Systems Biology Models

Abstract A parameter is structurally identifiable if its value can theoretically be estimated by observing the model output. Structural identifiability is a desirable property in biological modelling: if a parameter is structurally unidentifiable, its estimated numerical value is meaningless, and model predictions of unmeasured state variables can be wrong, compromising the ability of the model to provide biological insight. Structural identifiability depends on the system dynamics, observation function (model output), initial conditions, and external inputs. In this paper we focus on the last factor. Methods for structural identifiability analysis typically classify a model as identifiable provided that it is fed with sufficiently exciting inputs. For example, a given model may require a time-varying input to be structurally identifiable, while for another model a constant non-zero input may be enough. Here we present a method that determines how sufficiently exciting an input should be. The approach builds on the STRIKE-GOLDD toolbox, which considers structural identifiability as generalized observability. The approach incorporates extended Lie derivatives, which correctly assess structural identifiability in the case of time-varying inputs. The procedure can also be used to determine the type of input profile that is required to make the parameters identifiable. This capability is helpful when designing new experiments for the purpose of parameter estimation.