Lyndsay Kerr

I will describe the use of cluster mean-field models in approximating stochastic mathematical models involving spatial interactions. In particular, I will discuss the use of cluster mean-field models in approximating DNA methylation systems. DNA methylation is an epigenetic mark and large-scale alternations in DNA methylation patterns are observed in development, ageing and diseases such as cancer. Previous mathematical models have aided in understanding methylation patterns, but the computational expense associated with these studies have limited their use to the study of small-scale patterns. During this talk, I will discuss how to construct a cluster mean-field model that can be used to quickly, and accurately, predict statistical properties associated with large-scale DNA methylation patterns. I will then discuss the general use of cluster mean-field models in describing spatial interactions on a 1D lattice. Much of my talk is based on the publication https://royalsocietypublishing.org/doi/10.1098/rsif.2021.0707.