Optimal experiment design for practical parameter identifiability and model discrimination

Mechanistic mathematical models of biological systems usually contain a number of unknown parameters whose values need to be estimated from available experimental data in order for the models to be validated and used to make quantitative predictions. This requires that the models are practically identifiable, that is, the values of the parameters can be confidently determined, given available data. A well-designed experiment can produce data that are much more informative for the purpose of inferring parameter values than a poorly designed experiment. It is, therefore, of great interest to optimally design experiments such that the resulting data maximise the practical identifiability of a chosen model. Experimental design is also useful for model discrimination, where we seek to distinguish between multiple distinct, competing models of the same biological system in order to determine which model better reveals insight into the underlying biological mechanisms. In many cases, an external stimulus can be used as a control input to probe the behaviour of the system. In this paper, we will explore techniques for optimally designing such a control for a given experiment, in order to maximise parameter identifiability and model discrimination, and demonstrate these techniques in the context of commonly applied ordinary differential equation models. We use a profile likelihood-based approach to assess parameter identifiability. We then show how the problem of optimal experimental design for model discrimination can be formulated as an optimal control problem, which can be solved efficiently by applying Pontryagin's Maximum Principle.