Computational Modeling of Fluorescence Photobleaching

Encoded fluorescent proteins, such as the green fluorescent protein (GFP),
have changed and revolutionized the way scientists use microscopes. Today
high resolution live cell fluorescence imaging is used to study intracellular
traffic, which was not possible before. One of the modern microscopy methods
for visualization of transport processes in living cells is Fluorescence Loss In
Photobleaching (FLIP). In FLIP a high-intensity laser is used to bleach a small
cellular area, while images are taken between the bleaches.
This thesis presents several methods, which can be used to model the
intracellular transport observed on FLIP images. A reaction-diffusion system
that models both free and hindered molecules and different models for nuclear
membrane transport have been proposed. In the interest of the development
of an automated analysis of the FLIP images, the cell geometry was extracted
from the FLIP image by use of the Active Contours Without Edges or merely
Chan-Vese algorithm.
To our knowledge, it is the first time a quantitative computational FLIP
(cFLIP) method used to determine transport parameters from the FLIP image
data is presented. The method have been used to determine the diffusion
constant, membrane permeability, local binding rates and bleaching rates for
eGFP. Further, the method is expanded to model intracellular protein aggregates,
which is related to various age-associated neurodegenerative diseases,
such as Alzheimer’s disease, Chorea Huntington, Ataxia and Parkinson disease.
Additionally, an adaptive E-scheme for viscous balance laws originated
from the work on an analysis for the cFLIP method is presented in the thesis.
Numerical experiments are performed to show the improved accuracy of the
adaptive scheme. Moreover, it is proved that E-schemes are monotone and
TVD.
The polyglutamine protein aggregates considered in this thesis do not
move, which makes it possible to apply the cFLIP method on a fixed mesh.
However, recent developments in FEniCS makes it possible to have multiple
meshes, which can move independently. The MultiMesh implementation is explored
and used to simulate wind flow and view of a settlement layout, which
thus gives a measure on how well the houses are placed, in order to find and
design the optimal settlement layout.