In the first part of the thesis we focus on a hierarchical analysis on multiple, single cell, Nrf2 reporter levels in nucleus and cytoplasm, observed in human endothelial HMEC-1 in vitro cells (Xue et al., 2015a). Nrf2 is a transcription factor that regulates the expression of several defensive genes protecting against various cellular stresses and forms of oxidation. This analysis aims to gain an insight into this essential cellular protective mechanism. We propose a reaction network based on five reactions, including a distributed delay and a non-linear term, for longitudinal measurements of the amount of Nrf2 in nucleus and cytoplasm. The diffusion approximation (DA) is used to approximate this Markov jump process with a stochastic delay differential equation (SDDE). Since this continuous process is only observed at discrete time points, a second approximation, the Euler-Maruyama approximation (EMA) of the DA, is needed to obtain an approximate likelihood for this bivariate process. Furthermore, to make use of multiple single cell data, we embed the model in a Bayesian hierarchical framework. Moreover, a measurement equation, which involves a proportionality constant and a bivariate normal error, for the nuclear and cytoplasmic measurements, is necessary to relate the original unobserved population levels, X, to the observations, Y. This introduces a hidden Markov process for X and a Bayesian analysis is performed, via a data augmentation procedure, to explore the high dimensional posterior space which includes a bivariate latent process X for every cell. We show results obtained on simulation studies, proving the validity of the methodology, and on a real data application, composed of 35 single cell fluorescent xvi levels under the basal condition, and of 36 under the induction by a stimulant, both observed every two minutes for 1.5-7 hours. In the second part of the thesis we describe the analysis of a switch gene model for mRNA populations. We consider a gene that switches, with exponential waiting times, between a more active ON state and a less active OFF state, where the gene transcribes mRNA at a higher and a lower rate, respectively. We observe, via a measurement equation, the mRNA level in each cell, which is assumed to have reached a steady state. We analytically derive the stationary distribution of such a model and infer its parameters from experimental data, again via hierarchical Bayesian inference. The mRNA populations are only observed up to a proportionality constant and with a second source of white noise attributed to the measurement process. As in the previous case, we use a data augmentation procedure to explore the posterior space of the latent data. The analysis is repeated for different levels of induction by tetracycline, a stimulant, which results in increased gene expression. We particularly focus on studying how the stimulation affects the system.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:731320 |
| Date | January 2016 |
| Creators | Tiberi, Simone |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/95234/ |
Page generated in 0.0019 seconds