Galton-Watson-processen och åldrande celler

Abstract

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.