Stochastic modelling of repeat-mediated phase variation in Campylobacter jejuni

Howitt, Ryan (2018) Stochastic modelling of repeat-mediated phase variation in Campylobacter jejuni. PhD thesis, University of Nottingham.

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It is of interest to determine how populations of bacteria whose genes exhibit an ON/OFF switching property (phase variation) evolve over time from an initial population. By statistical analysis of two in vitro experimental Campylobacter jejuni datasets containing 28 genes assumed to be phase variable, we find evidence of small networks of genes which exhibit dependent evolutionary behaviour. This violates the assumption that the genes in these datasets do not interact with one another in the way they mutate during the division of cells, motivating the development of a model which attempts to explain evolution of such genes with factors other than mutation alone.

We show that discrete probability distributions at observation times can be estimated by utilising two stochastic models. One model provides an explanation with mutation rates in genes, resembling a Markov chain under the assumption of having a near infinite population size. The second provides an explanation with both mutation and natural selection. However, the addition of selection parameters makes this model resemble a non-linear Markov process, which makes further analysis less straight-forward. An algorithm is constructed to test whether the mutation-only model can sufficiently explain evolution of single phase variable genes, using distributions and mutation rates from data as examples. This algorithm shows that applying this model to the same phase variable genes believed to show dependent evolutionary behaviour is inadequate. We use Approximate Bayesian Computation to estimate selection parameters for the mutation with selection model, whereby inference is derived from samples drawn from an approximation of the joint posterior distribution of the model parameters.

We illustrate this method on an example of three genes which show evidence of dependent evolutionary behaviour from our two datasets.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Tretyakov, Michael
Fallaize, Chris
Subjects: Q Science > QA Mathematics > QA276 Mathematical statistics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 52218
Depositing User: Howitt, Ryan
Date Deposited: 19 Jul 2018 04:40
Last Modified: 07 May 2020 18:32

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