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Inference on Low-Rank Data Matrices with Applications to Microarray Data.

ABSTRACT: Probe-level microarray data are usually stored in matrices, where the row and column correspond to array and probe, respectively. Scientists routinely summarize each array by a single index as the expression level of each probe-set (gene). We examine the adequacy of a uni-dimensional summary for characterizing the data matrix of each probe-set. To do so, we propose a low-rank matrix model for the probe-level intensities, and develop a useful framework for testing the adequacy of uni-dimensionality against targeted alternatives. This is an interesting statistical problem where inference has to be made based on one data matrix whose entries are not i.i.d. We analyze the asymptotic properties of the proposed test statistics, and use Monte Carlo simulations to assess their small sample performance. Applications of the proposed tests to GeneChip data show that evidence against a uni-dimensional model is often indicative of practically relevant features of a probe-set.

SUBMITTER: Feng X

PROVIDER: S-EPMC2876352 | biostudies-literature | 2009

REPOSITORIES: biostudies-literature

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Inference on Low-Rank Data Matrices with Applications to Microarray Data.

Feng Xingdong X He Xuming X

The annals of applied statistics 20090101 4

Probe-level microarray data are usually stored in matrices, where the row and column correspond to array and probe, respectively. Scientists routinely summarize each array by a single index as the expression level of each probe-set (gene). We examine the adequacy of a uni-dimensional summary for characterizing the data matrix of each probe-set. To do so, we propose a low-rank matrix model for the probe-level intensities, and develop a useful framework for testing the adequacy of uni-dimensionali ...[more]

PMID: 20508835

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Project description:BackgroundThe cellular signaling pathway (network) is one of the main topics of organismic investigations. The intracellular interactions between genes in a signaling pathway are considered as the foundation of functional genomics. Thus, what genes and how much they influence each other through transcriptional binding or physical interactions are essential problems. Under the synchronous measures of gene expression via a microarray chip, an amount of dynamic information is embedded and remains to be discovered. Using a systematically dynamic modeling approach, we explore the causal relationship among genes in cellular signaling pathways from the system biology approach.ResultsIn this study, a second-order dynamic model is developed to describe the regulatory mechanism of a target gene from the upstream causality point of view. From the expression profile and dynamic model of a target gene, we can estimate its upstream regulatory function. According to this upstream regulatory function, we would deduce the upstream regulatory genes with their regulatory abilities and activation delays, and then link up a regulatory pathway. Iteratively, these regulatory genes are considered as target genes to trace back their upstream regulatory genes. Then we could construct the regulatory pathway (or network) to the genome wide. In short, we can infer the genetic regulatory pathways from gene-expression profiles quantitatively, which can confirm some doubted paths or seek some unknown paths in a regulatory pathway (network). Finally, the proposed approach is validated by randomly reshuffling the time order of microarray data.ConclusionWe focus our algorithm on the inference of regulatory abilities of the identified causal genes, and how much delay before they regulate the downstream genes. With this information, a regulatory pathway would be built up using microarray data. In the present study, two signaling pathways, i.e. circadian regulatory pathway in Arabidopsis thaliana and metabolic shift pathway from fermentation to respiration in yeast Saccharomyces cerevisiae, are reconstructed using microarray data to evaluate the performance of our proposed method. In the circadian regulatory pathway, we identified mainly the interactions between the biological clock and the photoperiodic genes consistent with the known regulatory mechanisms. We also discovered the now less-known regulations between crytochrome and phytochrome. In the metabolic shift pathway, the casual relationship of enzymatic genes could be detected properly.

Dataset Information

Inference on Low-Rank Data Matrices with Applications to Microarray Data.

Publications

Inference on Low-Rank Data Matrices with Applications to Microarray Data.

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