Parameter identifiability in PDE models of fluorescence recovery after photobleaching

TL;DR

This paper addresses the challenge of parameter identifiability in PDE models of protein dynamics from FRAP data, proposing a new pipeline for assessing and learning parameter combinations, validated on synthetic and real data.

Contribution

It introduces a novel pipeline combining re-parametrization and profile likelihoods to improve parameter identifiability analysis in PDE models of FRAP experiments.

Findings

The pipeline successfully recovers parameter combinations from synthetic datasets.

Application to real FRAP data demonstrates practical utility.

Current methods offer limited insights into parameter identifiability.

Abstract

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 in RNP granules of frog oocytes based on fluorescence recovery after photobleaching (FRAP) measurements. FRAP is a widely-used experimental technique for probing protein dynamics in living cells, and is often modeled using simple reaction-diffusion models of the protein dynamics. We show that current methods of structural and practical parameter identifiability provide limited insights into identifiability of kinetic parameters for these PDE models and spatially-averaged FRAP data. We thus propose a pipeline for assessing parameter identifiability and for learning parameter combinations based on re-parametrization 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.