Stochastic Models for Eukaryotic DNA Replication

Abstract

We consider eukaryotic DNA replication and in particular the role of replication origins in this process. We focus on origins which are 'active' - that is, trigger themselves in the process before being read by the replication forks of other origins.

We initially consider the spacings of these active replication origins in comparison to certain probability distributions of spacings taken from random matrix theory. We see how the spacings between neighbouring eigenvalues from certain collections of random matrices have some potential for modelling the spacing between active origins. This suitability can be further augmented with the use of uniform thinning which acts as a continuous deformation between correlated eigenvalue spacings and exponential (Poissonian) spacings.

We model the process as a modified 2D Poisson process with an added exclusion rule to identify active points based on their position on the chromosome and trigger time relative to other origins. We see how this can be reduced to a stochastic geometry problem and show analytically that two active origins are unlikely to be close together, regardless of how many non-active points are between them. In particular, we see how these active origins repel linearly.

We compare results from both of these models using genetic data from several different organisms and use regression analyses to highlight their key characteristics, in particular the local repulsion and tail behaviour.

Additionally, we look at related probabilistic models to modelling DNA replication, in particular polynuclear growth, and draw comparisons between the two. We finish our analysis by considering replication time, which is important in the genetics literature, and how this is represented in our stochastic models. We consider possible approaches from extreme value theory as well as results from probability literature.

Date of Award	18 Jun 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Nina C Snaith (Supervisor)