Abstract
We examine the practical identifiability of parameters in a spatiotemporal reaction-diffusion model of a scratch assay where we have access to a relatively large amount of quantitative experimental data. The experiment involves fluorescent cell cycle labels so that the cell cycle is tracked in real time. This provides spatial information about the position of individual cells as well as temporal information about the cell cycle phase of each cell. Cell cycle labelling is incorporated into the reaction-diffusion model by considering the total population to be composed of two interacting subpopulations. Practical identifiability is examined using a Bayesian Markov Chain Monte Carlo (MCMC) framework, confirming that the parameters are identifiable when we assume that the diffusivities of the two subpopulations are identical, but that the parameters are practically non-identifiable when we allow the diffusivities to be distinct. We also assess identifiability using a profile likelihood approach, and show that this provides similar results to MCMC with the advantage of being an order of magnitude faster to compute. Despite the profile likelihood being relatively underutilised in the mathematical biology literature, we suggest that it ought to be adopted as a screening tool to provide a rapid assessment of practical identifiability before more computationally cumbersome MCMC computations are attempted.