Galton-Watson-processen och åldrande celler
Typ
Examensarbete för kandidatexamen
Program
Publicerad
2022
Författare
Eriksson, Lotta
Hildingsson, Joel
Ibahim, Taha
Varghaei, Laleh
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The theory of the multitype Galton-Watson-process has been applied to build a mathematical
model for describing biological aging in cells. We also study the phenomenon of
rejuvenation. The theoretical results of the model have been applied and populations have
been simulated in order to study how biological aging affects cell populations and individual
cells.
This project investigates how different parameters of the model affect the properties of
cell populations. We study what the distribution of different biological ages looks like in the
population, guaranteed extinction of populations and the distribution of life lengths in cells.
We also introduce a rejuvenation index to provide a formal measure of rejuvenation in the
populations.
The rate of accumulation of damage and how frequently the cells divide is essential in
whether or not the population becomes extinct. In the surviving populations, asymmetric
distribution of damage between the mother and daughter cells results in smaller populations
but with a higher proportion of biologically young cells. The individual cells live for a shorter
period of time but rejuvenation occurs to a higher extent. In populations where the damage is
distributed symmetrically, populations become larger and the individual cells live longer but
rejuvenation does not occur.
Aging in cells has been modeled in a simple but insightful way but there is still some
sensitivity in the choice of parameters. The mathematical model that has been developed has
also compared the aging and rejuvenation with the yeast cell. We suggest that future research
aims at adjusting the parameters of the model in order to be able to describe the mechanisms
behind the aging of the yeast and gain an insight into human aging.