Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching.

Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that many established \textit{in vivo} measurements of protein dynamics average out the spatial dimensions. Here, we are motivated by recent experiments on the binding dynamics of the RNA-binding protein PTBP3 based on fluorescence recovery after photobleaching (FRAP) measurements in RNP granules of frog oocytes. We consider a simple reaction-diffusion model of the protein dynamics, and show the limitations of current methods of structural and practical parameter identifiability for this model and data. We propose a pipeline for assessing parameter identifiability and for learning parameter combinations based on re-parameterization and profile likelihoods analysis. We show that this method is able to recover parameter combinations for synthetic FRAP datasets and investigate its application to real experimental data.