A novel statistical signal processing approach for analysing high volatile expression profiles.

Abstract

The aim of this research is to introduce new advanced statistical methods for analysing gene expression profiles to consequently enhance our understanding of the spatial gradients of the proteins produced by genes in a gene regulatory network (GRN). To that end, this research has three main contributions. In this thesis, the segmentation Network (SN) in Drosophila melanogaster and the bicoid gene (bcd) as the critical input of this network are targeted to study. The first contribution of this research is to introduce a new noise filtering and signal processing algorithm based on Singular Spectrum Analysis (SSA) for extracting the signal of bicoid gene. Using the proposed SSA algorithm which is based on the minimum variance estimator, the extraction of bcd signal from its noisy profile is considerably improved compared to the most widely accepted model, Synthesis Diffusion Degradation (SDD). The achieved results are evaluated via both simulation studies and empirical results. Given the reliance of this research towards introducing an improved signal extraction approach, it is mandatory to compare the proposed method with the other well-known and widely used signal processing models. Therefore, the results are compared with a range of parametric and non-parametric signal processing methods. The conducted comparison study confirmed the outperformance of the SSA technique. Having the superior performance of SSA, in the second contribution, the SSA signal extraction performance is optimised using several novel computational methods including window length and eigenvalue identification approaches, Sequential and Hybrid SSA and SSA based on Colonial Theory. Each introduced method successfully improves a particular aspect of the SSA signal extraction procedure. The third and final contribution of this research aims at extracting the regulatory role of the maternal effect genes in SN using a variety of causality detection techniques. The hybrid algorithm developed here successfully portrays the interactions which have been previously accredited via laboratory experiments and therefore, suggests a new analytical view to the GRNs.