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Identifying unique parameters for mathematical models describing biologicaldata can be challenging and often impossible. Parameter identifiability forpartial differential equations models in cell biology is especially difficultgiven that many established \textit{in vivo} measurements of protein dynamicsaverage out the spatial dimensions. Here, we are motivated by recentexperiments on the binding dynamics of the RNA-binding protein PTBP3 based onfluorescence recovery after photobleaching (FRAP) measurements in RNP granulesof frog oocytes. We consider a simple reaction-diffusion model of the proteindynamics, and show the limitations of current methods of structural andpractical parameter identifiability for this model and data. We propose apipeline for assessing parameter identifiability and for learning parametercombinations based on re-parameterization and profile likelihoods analysis. Weshow that this method is able to recover parameter combinations for syntheticFRAP datasets and investigate its application to real experimental data.

Parameter identifiability in PDE models of fluorescence recovery after photobleaching