Nonoverlapping clusters: approximate distribution and application to molecular biology

An iterative data mining approach for mining overlapping coexpression patterns in noisy gene expression data

Clustering is concerned with the discovery of groupings of records in a database. Many clustering problems are defined as partitioning problems in the sense that the similar records are grouped into nonoverlapping partitions. However, the clustering of gene expression data to discover coexpressed genes may not always be meaningful if this problem is reduced into a partitioning problem. Due to the complexity of the underlying biological processes, a protein can interact with one or more other proteins belonging to different functional classes in order to perform a particular biological role. For this reason, when responding to different external stimulants, a gene that produces a particular protein can coexpress with more than one group of other genes. The gene can therefore belong to more than one group of coexpressed genes. This poses a challenge to many clustering algorithms as they are not originally developed to discover overlapping clusters in noisy gene expression data. In this paper, we propose an iterative data mining approach that consists of two phases as follows. In phase 1, a clustering algorithm is used to discover the initial, nonoverlapping partitioning of gene expression profiles in gene expression data. Then, the partition memberships of genes are redetermined iteratively in phase 2 by a pattern discovery technique so as to determine that if a gene should remain in the same partition, be moved to another partition, or be also grouped together with other genes in another partitions. The proposed approach has been tested with both artificial and real datasets. Experimental results show that it can improve the performances of existing clustering algorithms and is able to effectively discover overlapping clusters in noisy gene expression data.

A latent model to detect multiple clusters of varying sizes

This article develops a latent model and likelihood-based inference to detect temporal clustering of events. The model mimics typical processes generating the observed data. We apply model selection techniques to determine the number of clusters, and develop likelihood inference and a Monte Carlo expectation-maximization algorithm to estimate model parameters, detect clusters, and identify cluster locations. Our method differs from the classical scan statistic in that we can simultaneously detect multiple clusters of varying sizes. We illustrate the methodology with two real data applications and evaluate its efficiency through simulation studies. For the typical data-generating process, our methodology is more efficient than a competing procedure that relies on least squares.

A Fast Implementation of a Scan Statistic for Identifying Chromosomal Patterns of Genome Wide Association Studies

In order to take into account the complex genomic distribution of SNP variations when identifying chromosomal regions with significant SNP effects, a single nucleotide polymorphism (SNP) association scan statistic was developed. To address the computational needs of genome wide association (GWA) studies, a fast Java application, which combines single-locus SNP tests and a scan statistic for identifying chromosomal regions with significant clusters of significant SNP effects, was developed and implemented. To illustrate this application, SNP associations were analyzed in a pharmacogenomic study of the blood pressure lowering effect of thiazide-diuretics (N=195) using the Affymetrix Human Mapping 100K Set. 55,335 tagSNPs (pair-wise linkage disequilibrium R(2)<0.5) were selected to reduce the frequency correlation between SNPs. A typical workstation can complete the whole genome scan including 10,000 permutation tests within 3 hours. The most significant regions locate on chromosome 3, 6, 13 and 16, two of which contain candidate genes that may be involved in the underlying drug response mechanism. The computational performance of ChromoScan-GWA and its scalability were tested with up to 1,000,000 SNPs and up to 4,000 subjects. Using 10,000 permutations, the computation time grew linearly in these datasets. This scan statistic application provides a robust statistical and computational foundation for identifying genomic regions associated with disease and provides a method to compare GWA results even across different platforms.

A scan statistic for identifying chromosomal patterns of SNP association

We have developed a single nucleotide polymorphism (SNP) association scan statistic that takes into account the complex distribution of the human genome variation in the identification of chromosomal regions with significant SNP associations. This scan statistic has wide applicability for genetic analysis, whether to identify important chromosomal regions associated with common diseases based on whole-genome SNP association studies or to identify disease susceptibility genes based on dense SNP positional candidate studies. To illustrate this method, we analyzed patterns of SNP associations on chromosome 19 in a large cohort study. Among 2,944 SNPs, we found seven regions that contained clusters of significantly associated SNPs. The average width of these regions was 35 kb with a range of 10-72 kb. We compared the scan statistic results to Fisher's product method using a sliding window approach, and detected 22 regions with significant clusters of SNP associations. The average width of these regions was 131 kb with a range of 10.1-615 kb. Given that the distances between SNPs are not taken into consideration in the sliding window approach, it is likely that a large fraction of these regions represents false positives. However, all seven regions detected by the scan statistic were also detected by the sliding window approach. The linkage disequilibrium (LD) patterns within the seven regions were highly variable indicating that the clusters of SNP associations were not due to LD alone. The scan statistic developed here can be used to make gene-based or region-based SNP inferences about disease association.

ChromoScan: a scan statistic application for identifying chromosomal regions in genomic studies

ChromoScan is an implementation of a genome-based scan statistic that detects genomic regions, which are statistically significant for targeted measurements, such as genetic associations with disease, gene expression profiles, DNA copy number variations, as well as other genome-based measurements. A Java graphic user interface (GUI) is provided to allow users to select appropriate data transformations and thresholds for defining the significant events.

AVAILABILITY

ChromoScan is freely available from http://www.epidkardia.sph.umich.edu/software/chromoscan/

Homotypic regulatory clusters in Drosophila

Cis-regulatory modules (CRMs) are transcription regulatory DNA segments (approximately 1 Kb range) that control the expression of developmental genes in higher eukaryotes. We analyzed clustering of known binding motifs for transcription factors (TFs) in over 60 known CRMs from 20 Drosophila developmental genes, and we present evidence that each type of recognition motif forms significant clusters within the regulatory regions regulated by the corresponding TF. We demonstrate how a search with a single binding motif can be applied to explore gene regulatory networks and to discover coregulated genes in the genome. We also discuss the potential of the clustering method in interpreting the differential response of genes to various levels of transcriptional regulators.