Parameter Identifiability of RNA Dynamics in PDE Transport Models of Fluorescence Recovery After Photobleaching

TL;DR

The study develops a pipeline to assess parameter identifiability in a reaction-diffusion-advection model of RNA FRAP in Xenopus laevis oocytes, revealing region-dependent identifiability for transport and binding dynamics. By combining one- and two-dimensional profile likelihoods with subset profiles, slope vector fields, and a reparameterization via an identifiable curve, the work distinguishes globally identifiable quantities ($c$, $D$) from regionally non-identifiable binding rates ($\beta_1$, $\beta_2$). The approach is validated on synthetic FRAP data and applied to real FRAP datasets, demonstrating that meaningful biological inferences can be drawn for diffusion and transport while highlighting data limitations for kinetic rates. This framework provides a practical, region-aware method for linking PDE-based transport models to FRAP measurements and suggests additional data or experiments to resolve non-identifiable parameters in RNA localization studies.

Abstract

The transport and localization of RNA molecules, crucial for cellular function and development, involve a combination of diffusion and active transport mechanisms. Here, we are motivated by understanding the dynamics of RNA in Xenopus laevis oocytes. Fluorescence Recovery After Photobleaching (FRAP) is an experimental technique that is widely used to investigate the dynamics of molecular movement within cells by observing the recovery of fluorescence intensity in a photobleached region over time. To advance the understanding of RNA dynamics, we develop a reaction-diffusion-advection partial differential equation (PDE) model integrating both transport and diffusion mechanisms. We propose a pipeline for identifiability analysis to assess the model's ability to uniquely determine parameter values from observed FRAP data. Based on profile likelihood analysis and reparametrization, we examine the relationship between non- identifiable parameters, which improves the robustness of parameter estimation. We find out that the identifiability of the four parameters of interest is not exactly the same in different regions of the cell. Specifically, transport velocity and diffusion coefficient are identifiable in all regions of the cell, while some combinations of binding rate and unbinding rate are found to be identifiable near the nucleus.

Figures (16)

• Figure 1: FRAP analysis showing: (1) Initial uniform fluorescence, (2) Sharp intensity drop after photobleaching, (3) Gradual recovery as molecules diffuse into the bleached region, and (4) Final equilibrium fluorescence. The recovery kinetics can reveal molecular mobility and binding dynamics.
• Figure 1: Cartoon of the active transport of RNA, consisting of a population of diffusing particles with diffusion coefficient $D$, a population of moving particles with velocity $c$, as well as switching rates $\beta_1$ and $\beta_2$ between the two population. In the moving state, we assume that RNA molecules are attached to motor proteins and microtubules, while in the diffusion state, we assume they are detached from microtubules.
• Figure 1: Interpretation of profile likelihoods. A flat likelihood (left) corresponds to structural non-identifiability, a profile that does not decrease to 0 on one or both sides of the maximum (center) indicates practical non-identifiability, and a profile with a fast decrease to 0 on both sides of the maximum (right) shows both structural and practical identifiability.
• Figure 1: Subset profiles for interest parameter $\beta_1$ on the x-axis and the corresponding optimized $\beta_2$ on the y-axis for each region given noiseless FRAP data synthetically generated using \ref{['eq: PDEs']} and the parameter set in \ref{['tab:baseline']}. Baseline values are indicated as red stars in each plot (top-left: Region 1, top-right: Region 2, bottom: Region 3).
• Figure 1: Profile likelihoods for each interest parameter $c$, $D$ and $s$ in Region 1 given real experimental FRAP data in \ref{['fig:combined1']} (top-left and top-right). $s$ achieves the maximum at $s^* = -1.7551$, corresponding to the point $Q$ on the yellow curve $\tau$, as well as the trace of error-minimizing green contour curve (bottom).