Practical parameter identifiability for spatio-temporal models of cell invasion

Abstract

<jats:p>We examine the practical identifiability of parameters in a spatio-temporal reaction–diffusion model of a scratch assay. Experimental data involve fluorescent cell cycle labels, providing spatial information about cell position and temporal information about the cell cycle phase. Cell cycle labelling is incorporated into the reaction–diffusion model by treating the total population as 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 the diffusivities of the subpopulations are identical, but that the parameters are practically non-identifiable when we allow the diffusivities to be distinct. We also assess practical identifiability using a profile likelihood approach, providing similar results to MCMC with the advantage of being an order of magnitude faster to compute. Therefore, we suggest that the profile likelihood ought to be adopted as a screening tool to assess practical identifiability before MCMC computations are performed.</jats:p>

Identifiability analysis for stochastic differential equation models in systems biology

“…In contrast to many studies of identifiability analysis for ODEs, we do not pre-specify parameters in the observation distribution. In a deterministic modelling framework, it is common to assume that all the variability in the data is uncorrelated and sourced from the observation process [44,94,176]. Therefore, for an ODE model, the observation parameters can be reliably estimated using the pooled sample variance.…”

“…This kind of analysis is routinely used in the field of experimental design to assess the nature of data required to adequately identify biophysical parameters [32,54,58,[92][93][94]. Practical identifiability is established in conjunction with an inference technique, such as profile or maximum likelihood [94][95][96][97] or Markov chain Monte Carlo (MCMC) [32,54]. These techniques provide information about the flatness (or otherwise) of the likelihood function-in the Bayesian case, the posterior distribution-that describes knowledge about the parameters after the experimental data is taken into consideration.…”

Identifiability analysis for stochastic differential equation models in systems biology

“…If prior knowledge about the population (i.e., the cell line) is available, perhaps based upon previously conducted experiments, this can be incorporated into the analysis through an informative prior. For example, upper bounds that define reasonable values for biological parameters are routinely applied in this context [82].…”

“…In contrast to many studies of identifiability analysis for ODEs, we do not pre-specify parameters in the observation distribution. In a deterministic modelling framework, it is common to assume that all the variability in the data is uncorrelated and sourced from the observation process [38,82,156]. Therefore, for an ODE model, the observation parameters can be reliably estimated using the pooled sample variance.…”

“…This kind of analysis is routinely used in the field of experimental design to assess the nature of data required to adequately identify biophysical parameters [29,48,52,[80][81][82]. Practical identifiability is established in conjunction with an inference technique, such as profile or maximum likelihood [82][83][84][85] or Markov-chain Monte-Carlo (MCMC) [29,48]. These techniques provide information about the geometry of the likelihood function or, in the Bayesian case, the posterior distribution, that describes knowledge about the parameters after the experimental data is taken into consideration.…”