Parameter identifiability and model selection for partial differential equation models of cell invasion.

Area of Science:

• Mathematical Biology
• Computational Biology
• Cellular Mechanobiology

Background:

• Mechanistic models are vital for biological research, enabling predictions and understanding of complex phenomena.
• Practical parameter identifiability is essential for the reliability of these models, especially when extrapolating to new scenarios.
• The Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) model is frequently used to describe phenomena like cell invasion.

Purpose of the Study:

• To investigate the parameter identifiability of four extensions of the Fisher-KPP model using experimental cell invasion data.
• To assess how model complexity influences parameter identifiability and the need for experimental data.
• To provide a framework for selecting appropriate mechanistic models based on identifiability criteria.

Main Methods:

• Utilized a profile-likelihood approach to systematically evaluate parameter identifiability.
• Applied the method to four distinct extensions of the Fisher-KPP model.
• Analyzed experimental data from a cell invasion assay to ground the identifiability assessment in empirical evidence.

Main Results:

• Demonstrated that increased model complexity generally leads to decreased parameter identifiability.
• Found that parameter estimates for more complex models are more sensitive to experimental variations.
• Showed that complex models necessitate larger datasets to achieve practical parameter identifiability.

Conclusions:

• Parameter identifiability is a critical factor in selecting mechanistic biological models.
• Model complexity should be balanced against identifiability and data requirements during model selection.
• The findings advocate for incorporating parameter identifiability alongside goodness-of-fit and complexity in model evaluation.