Practical parameter identifiability for spatio-temporal models of cell invasion.

Understanding how cells move and proliferate is essential in many biological contexts, including wound healing and cancer progression. Mathematical models, such as reaction-diffusion systems, are often used to describe these processes. However, a major challenge is determining whether the parameters in these models can be uniquely estimated from experimental data. Prior research has shown that theoretical identifiability does not always guarantee practical identifiability, especially in complex spatio-temporal systems. This gap motivated the current work, which focuses on a specific biological setup involving fluorescently labeled cell cycle phases. The study addresses the issue of whether parameter estimates remain reliable when modeling assumptions change. No prior work had resolved how varying assumptions about diffusivity affect identifiability. This paper introduces a novel approach by combining Bayesian inference with a faster screening method. The findings aim to improve the reliability of model predictions in cell invasion studies.

The goal of this research is to assess whether parameters in a spatio-temporal reaction-diffusion model of cell invasion can be practically identified from experimental data. The model incorporates fluorescent cell cycle labels to track cell positions and phases over time. The specific problem addressed is whether the parameters remain identifiable under different assumptions about subpopulation diffusivity. The motivation stems from the need to ensure that model outputs are not based on arbitrary or non-identifiable parameters. The study compares two statistical approaches—Bayesian MCMC and profile likelihood—to evaluate identifiability. The researchers aim to determine if one method can serve as a faster alternative to the other. The work also seeks to clarify how modeling assumptions influence identifiability outcomes. By doing so, the study contributes to the broader goal of improving the predictive power of mathematical models in biological systems.

The researchers used a spatio-temporal reaction-diffusion model to simulate cell invasion in a scratch assay. The model divides the cell population into two subpopulations based on cell cycle phases. Fluorescent labeling data provide spatial and temporal information for model calibration. To assess parameter identifiability, the team applied a Bayesian MCMC framework, which estimates parameter distributions based on observed data. They also employed a profile likelihood method, which evaluates how parameter estimates change as one parameter is varied while others are fixed. Both methods were tested under two scenarios: one where subpopulation diffusivities are assumed equal and another where they are allowed to differ. The MCMC approach confirmed identifiability under equal diffusivity but not under distinct diffusivity. The profile likelihood method yielded similar results but required significantly less computational time. These methods together provide a comprehensive assessment of practical identifiability in the model.

The study found that parameters in the model are identifiable when subpopulation diffusivities are assumed to be equal. However, when diffusivities are allowed to vary, the parameters become practically non-identifiable. The Bayesian MCMC analysis confirmed this result, showing that distinct diffusivity assumptions lead to wide posterior distributions for key parameters. The profile likelihood approach produced consistent findings but was an order of magnitude faster to compute. This suggests that profile likelihood can serve as a preliminary screening tool before conducting full MCMC computations. The results highlight the importance of modeling assumptions in determining identifiability outcomes. The computational efficiency of the profile likelihood method makes it a valuable alternative for initial assessments. The study also demonstrates that identifiability is strongly influenced by the structure of the model itself. These findings provide a practical framework for evaluating parameter identifiability in spatio-temporal models of cell invasion.

The authors concluded that parameter identifiability in the spatio-temporal model depends critically on the assumption about subpopulation diffusivity. When diffusivities are assumed equal, the parameters are identifiable, but when they are allowed to differ, identifiability is lost. The Bayesian MCMC framework confirmed these results, showing that distinct diffusivity assumptions lead to non-identifiable parameters. The profile likelihood approach provided similar findings but with much faster computation times. The authors propose that profile likelihood should be used as a screening tool before MCMC computations are performed. This recommendation is based on the computational efficiency of the profile likelihood method and its ability to detect identifiability issues early. The study emphasizes the importance of modeling assumptions in determining identifiability outcomes. The findings suggest that careful consideration of model structure is essential for reliable parameter estimation. These conclusions provide a practical guide for improving the reliability of spatio-temporal models in cell invasion studies.