Approximate Bayesian computation and agent based modelling for inference of size dependence in stochastic gene expressionof Size Dependence in Stochastic Gene Expression

Abstract

Gene expression is an inherently stochastic process, but it is also subject to sources of extrinsic noise. Chief among these sources is the cell cycle, both through its different stages, but also through the change in cell size that happens throughout it. In order to fully understand these sources of variability, mathematical modelling and quantitative gene expression data must be combined. Unfortunately, when working with agent-based models of gene expression that incorporate the cell cycle, we do not have access to an analytical likelihood function. These types of models can only be simulated. Approximate Bayesian computation (ABC) is a class of simulation-based likelihood free inference methods that is useful for dealing with problems of this nature. In this thesis we have firstly developed more efficient ABC methods for model selection that can help us decide among different competing biological mechanisms. Secondly we have integrated models of gene expression, including the totally asymmetric exclusion process (TASEP), into the cell cycle. We have done so by developing agent-based models of growing and dividing cells, where each cell contains biochemical reactions. In this way, we are able to couple gene expression to cell size and the cell cycle. Finally, in collaboration with biologists, we have applied these models and our ABC methods to single cell transcription and cell size snapshot data in S.pombe, in order to uncover the precise molecular mechanisms that control transcription rates scaling with cell size. We find that transcription of both constitutive and periodic genes is a Poisson process with transcription rates scaling with cell size and without evidence for transcriptional off states. Modelling and experimental data indicate that scaling relies on the coordination of RNA polymerase II (RNAPII) transcription initiation rates with cell size and that RNAPII is a limiting factor. Our modeling results are validated by real-time quantitative imaging that shows size increase is accompanied by a rapid concentrationindependent recruitment of RNAPII onto chromatin. Overall, this thesis highlights applications of mathematical modelling and statistical inference to biological data, to uncover biological mechanisms