A study of DNA methylation using coagulation-fragmentation based models

DNA methylation occurs when chemical methyl groups attach to DNA at genomic loci known as CpG sites. DNA methylation patterns vary between different types of cells and tissues, and the presence or absence of DNA methylation influences how cells interpret the underlying DNA sequence. In particular, changes in DNA methylation are highly associated with diseases such as cancer, and it has been shown experimentally that alterations in DNA methylation patterns can have very harmful consequences, with total eradication of methylation in mice proving to be fatal.

Previous studies have shown that the methylation state of neighbouring CpG sites are highly correlated, offering the possibility to consider methylation systems in terms of clusters rather than individual CpGs. In this project we will consider methylation and demethylation processes in terms of six events: (a) the birth or death of a methylated cluster; (b) the growth or decay of a methylated cluster; (c) the coagulation or fragmentation of methylated clusters.

An estimation of the rates associated with these reactions could aid in understanding the underlying biological processes associated with methylation and demethylation systems. For example, if the birth rate is small in comparison to the growth and coagulation rates, then that would suggest that methylation events are usually collaborative (i.e. methylated CpGs encourage methylation of neighbouring CpGs), with "spontaneous" methylation occurring less frequently.

We will construct stochastic mathematical models to describe the system and will use these to infer reaction rates from experimental data, allowing biological insights to be made. In particular, we aim to - Describe methylation and demethylation processes in terms of stochastic mathematical models; - Infer reaction rates associated with methylation and demethylation processes from experimental data;

- Gain insight into how methylation and demethylation processes may vary in different genomic regions, cell types and under different conditions.

The results from this project will aid in understanding the complex processes underlying DNA methylation and could shine light on how methylation changes arise in disease.