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Bioinformatics Advance Access published online on April 15, 2004

Bioinformatics, doi:10.1093/bioinformatics/bth274
Bioinformatics © Oxford University Press 2004; all rights reserved
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Received February 13, 2004
Revised March 24, 2004
Accepted March 26, 2004

Article

A geometric approach to determine association and coherence of the activation times of cell-cycling genes under differing experimental conditions

Delong Liu 1, Clarice R. Weinberg 1, Shyamal D. Peddada 1*

1 Biostatistics Branch, MD:A3-03, National Institute of Environmental Health Sciences, National Institutes of Health, P.O.Box 12233, Research Triangle Park, NC 27709

* To whom correspondence should be addressed. E-mail: peddada{at}niehs.nih.gov.


   Abstract

Differing arresting agents and protocols can be used to synchronize cells in cultures to specific phases of the cell when studying cell cycle gene expressions. Often, data derived from individual experiments are analyzed separately, since no appropriate statistical methodology is available at the moment to analyze the data from all such experiments simultaneously. The focus of this paper is to determine the association and coherence of the relative activation times of cell-cycling genes under different experimental conditions. Using the circular-circular regression model of Downs and Mardia (2002), we define two parameters, a rotation parameter for the angular difference between cells' arresting times (phases) in two cell cycle experiments, and an association parameter to describe the correspondence between the cycle times of maximal expression (phase angles) for a set of genes studied in two experiments. Further, we propose a procedure to assess coherence across multiple experiments, that is, to what extent the circular ordering of the phase angles of genes is maintained across multiple experiments. Coherence of genes across experiments suggests that functionally these genes tend to respond in a stereotypically sequenced way under different experimental conditions. Our proposed methodology is illustrated by applying it to the HeLa cell cycle gene expression data described in Whitfield et al. (2002).


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