  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.
