Geometric optimization methods for the analysis of gene expression data

DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the most popular algorithms to perform ICA. These algorithms are then applied on a microarray breast-cancer data set. Some issues about the application of ICA and the evaluation of biological relevance of the results are discussed. This study indicates that ICA significantly outperforms Principal Component Analysis (PCA).

Epigenetic remodeling of meiotic crossover frequency in Arabidopsis thaliana DNA methyltransferase mutants.

Meiosis is a specialized eukaryotic cell division that generates haploid gametes required for sexual reproduction. During meiosis, homologous chromosomes pair and undergo reciprocal genetic exchange, termed crossover (CO). Meiotic CO frequency varies along the physical length of chromosomes and is determined by hierarchical mechanisms, including epigenetic organization, for example methylation of the DNA and histones. Here we investigate the role of DNA methylation in determining patterns of CO frequency along Arabidopsis thaliana chromosomes. In A. thaliana the pericentromeric regions are repetitive, densely DNA methylated, and suppressed for both RNA polymerase-II transcription and CO frequency. DNA hypomethylated methyltransferase1 (met1) mutants show transcriptional reactivation of repetitive sequences in the pericentromeres, which we demonstrate is coupled to extensive remodeling of CO frequency. We observe elevated centromere-proximal COs in met1, coincident with pericentromeric decreases and distal increases. Importantly, total numbers of CO events are similar between wild type and met1, suggesting a role for interference and homeostasis in CO remodeling. To understand recombination distributions at a finer scale we generated CO frequency maps close to the telomere of chromosome 3 in wild type and demonstrate an elevated recombination topology in met1. Using a pollen-typing strategy we have identified an intergenic nucleosome-free CO hotspot 3a, and we demonstrate that it undergoes increased recombination activity in met1. We hypothesize that modulation of 3a activity is caused by CO remodeling driven by elevated centromeric COs. These data demonstrate how regional epigenetic organization can pattern recombination frequency along eukaryotic chromosomes.

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.