Finding Groups in Gene Expression Data

The vast potential of the genomic insight offered by microarray technologies has led to their widespread use since they were introduced a decade ago. Application areas include gene function discovery, disease diagnosis, and inferring regulatory networks. Microarray experiments enable large-scale, high-throughput investigations of gene activity and have thus provided the data analyst with a distinctive, high-dimensional field of study. Many questions in this field relate to finding subgroups of data profiles which are very similar. A popular type of exploratory tool for finding subgroups is cluster analysis, and many different flavors of algorithms have been used and indeed tailored for microarray data. Cluster analysis, however, implies a partitioning of the entire data set, and this does not always match the objective. Sometimes pattern discovery or bump hunting tools are more appropriate. This paper reviews these various tools for finding interesting subgroups

Mathematical Modelling of Spatially Coherent Transcription

Genetics and epigenetics are widely expected to revolutionise our understanding of health and disease. However any attempt to extract relevant information from noisy data requires a combination of modelling and statistical techniques. Given the number of genes and the complexity involved in the genome, sophisticated methods will be needed to properly capture the information that is contained. Many mechanisms and variables can affect and control the expression of a gene. In this thesis, it is specifically spatially coherent variations in transcription which are investigated. Several different areas were examined, producing a broad set of results. Important findings include the demonstration of spatial coherence as the result of epigenetic effects, the creation and validation of a technique to detect spatial coherence, and the extension of spatial modelling to epigenetic data. Other important results include the detection of spatial coherence variation due to confounding variables (PMI and neuronal concentration) and the development of new spatial modelling techniques. The results indicate that spatial modelling provides a useful approach to investigating unusual and unknown aspects of epigenetic and transcriptional regulation

Wavelet-based noise reduction of cDNA microarray images

The advent of microarray imaging technology has lead to enormous progress in the life sciences by allowing scientists to analyze the expression of thousands of genes at a time. For complementary DNA (cDNA) microarray experiments, the raw data are a pair of red and green channel images corresponding to the treatment and control samples. These images are contaminated by a high level of noise due to the numerous noise sources affecting the image formation. A major challenge of microarray image analysis is the extraction of accurate gene expression measurements from the noisy microarray images. A crucial step in this process is denoising, which consists of reducing the noise in the observed microarray images while preserving the signal information as much as possible. This thesis deals with the problem of developing novel methods for reducing noise in cDNA microarray images for accurate estimation of the gene expression levels. Denoising methods based on the wavelet transform have shown significant success when applied to natural images. However, these methods are not very efficient for reducing noise in cDNA microarray images. An important reason for this is that existing methods are only capable of processing the red and green channel images separately. In doing so. they ignore the signal correlation as well as the noise correlation that exists between the wavelet coefficients of the two channels. The primary objective of this research is to design efficient wavelet-based noise reduction algorithms for cDNA microarray images that take into account these inter-channel dependencies by 'jointly' estimating the noise-free coefficients in both the channels. Denoising algorithms are developed using two types of wavelet transforms, namely, the frequently-used discrete wavelet transform (DWT) and the complex wavelet transform (CWT). The main advantage of using the DWT for denoising is that this transform is computationally very efficient. In order to obtain a better denoising performance for microarray images, however, the CWT is preferred to DWT because the former has good directional selectivity properties that are necessary for better representation of the circular edges of spots. The linear minimum mean squared error and maximum a posteriori estimation techniques are used to develop bivariate estimators for the noise-free coefficients of the two images. These estimators are derived by utilizing appropriate joint probability density functions for the image coefficients as well as the noise coefficients of the two channels. Extensive experimentations are carried out on a large set of cDNA microarray images to evaluate the performance of the proposed denoising methods as compared to the existing ones. Comparisons are made using standard metrics such as the peak signal-to-noise ratio (PSNR) for measuring the amount of noise removed from the pixels of the images, and the mean absolute error for measuring the accuracy of the estimated log-intensity ratios obtained from the denoised version of the images. Results indicate that the proposed denoising methods that are developed specifically for the microarray images do, indeed, lead to more accurate estimation of gene expression levels. Thus, it is expected that the proposed methods will play a significant role in improving the reliability of the results obtained from practical microarray experiments

Wavelet analysis of gene expression (WAGE)

The wavelet transform (WT) is the mathematical operator of choice for the analysis of nonstationary signals. At the same time, it is also a modelling operator that may be used to impose functional constraints on data to unveil hidden groupings and relationships. In this work, we apply the WT to the chromosomal sequences of gene expression values measured with microarray technology. The application of the wavelet operator aims to uncover clusters of genes that interact by vicinity, either because of a shared regulatory mechanism or because of common susceptibility to environmental factors. Application of the method to data on the expression of human brain genes in neuro-degeneration validates the technique and, at the same time, illustrates the potential of the method

Wavelet analysis of gene expression (WAGE)

The wavelet transform (WT) is the mathematical operator of choice for the analysis of nonstationary signals. At the same time, it is also a modelling operator that may be used to impose functional constraints on data to unveil hidden groupings and relationships. In this work, we apply the WT to the chromosomal sequences of gene expression values measured with microarray technology. The application of the wavelet operator aims to uncover clusters of genes that interact by vicinity, either because of a shared regulatory mechanism or because of common susceptibility to environmental factors. Application of the method to data on the expression of human brain genes in neuro-degeneration validates the technique and, at the same time, illustrates the potential of the method