A FRAP model to investigate reaction-diffusion of proteins within a bounded domain: a theoretical approach

TL;DR

This paper introduces a theoretical reaction-diffusion model for analyzing protein transport within cell nuclei using FRAP data, accounting for boundary effects and providing semi-analytical solutions for parameter estimation.

Contribution

It presents a novel reaction-diffusion framework tailored for FRAP experiments in bounded cellular domains, incorporating boundary effects and analytical expressions for rate parameters.

Findings

Model accurately describes protein mobility in bounded domains.

Semi-analytical expressions help define parameter spaces.

Applicable to CLSM-based FRAP experimental data.

Abstract

Temporally and spatially resolved measurements of protein transport inside cells provide important clues to the functional architecture and dynamics of biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique has been used over the past three decades to measure the mobility of macromolecules and protein transport and interaction with immobile structures inside the cell nucleus. A theoretical model is presented that aims to describe protein transport inside the nucleus, a process which is influenced by the presence of a boundary (i.e. membrane). A set of reaction-diffusion equations is employed to model both the diffusion of proteins and their interaction with immobile binding sites. The proposed model has been designed to be applied to biological samples with a Confocal Laser Scanning Microscope (CLSM) equipped with the feature to bleach regions characterised by a scanning beam that has a radially Gaussian distributed profile. The proposed model leads to FRAP curves that depend on the on- and off-rates. Semi-analytical expressions are used to define the boundaries of on- (off-) rate parameter space in simplified cases when molecules move within a bounded domain. The theoretical model can be used in conjunction to experimental data acquired by CLSM to investigate the biophysical properties of proteins in living cells.