Analysis of Circular Data from Cell Cycle Transcripts Using Order Restricted Statistical Procedures
Miguel A. Fernández1, Sandra Barragán1, Cristina Rueda1, Shyamal D. Peddada2
1Statistics and Operations Research, Universidad de Valladolid, Valladolid, Spain; 2Biostatistics Branch, National Institute of Environmental Health Sciences, NC, United States

A cell division cycle in eukaryotes is a well-coordinated process where cells go through 4 distinct phases before dividing. Genes with periodic expression are known as cell-cycle genes. To discover evolutionarily conserved cell-cycle genes, biologists are interested in identifying genes that are periodic in multiple organisms. There has been considerable discussion in the literature on genes that are periodic in fission yeast (S. pombe) as well as in budding yeast (S. cerevisiae). Based on recent microarray studies, a conservative estimate of the number of genes that are periodic in both yeasts is 35 (known as a “core set”). Phase angle of peak expression of a cell-cycle gene is of interest as it may be associated with its function. Since the cell cycle is a carefully orchestrated process, we hypothesize that the relative order of the phase angles (isotropic order) among the core set of genes is conserved in the two yeasts.

We expose a novel statistical methodology that integrates order restricted inference and circular data procedures. This methodology that has been developed in Rueda et al. (2009) and Fernández et al. (2011) allows performing a statistical test to check the isotropy hypothesis. We demonstrate that the isotropic order is conserved for at least 80% of genes in the core set. Surprisingly at most 33% of fission yeast genes appear to satisfy the isotropic order of the corresponding human orthologs.

Together with the statistical methodology, we present an R package (see Barragán et al. (2011)) that makes available to researchers these procedures. In this way biologists can formulate and test their own hypotheses on cell cycle order conservation.


Barragán, S., Rueda, C., Fernández, M. and Peddada, S. (2011). isocir: An R package for Isotonic Inference in Circular data. An application to the analysis of cell cycle expression data. Submitted to Journal of Statistical Software.

Fernández, M., Rueda, C. and Peddada, S. (2011). Isotropic order among a core set of cell-cycle transcripts conserved between budding and fission yeast. Submitted to PNAS.

Rueda, C., Fernández, M. and Peddada, S. (2009). Estimation of Parameters subject to Order Restrictions on a Circle with Application to Estimation of Phase Angles od Cell-cycle Genes. Journal of the American Statistical Association, 104(495), 338-347.

Keywords: Cell-cycle Genes; Circular Isotonic Regression; Phase Angles

Biography: Miguel A. Fernández earned a PhD in Statistical Science from the Universidad de Valladolid (Spain) in 1995. He received the BS in Mathematics also from the Universidad de Valladolid. He is currently Profesor Titular de Universidad at the Department of Statistics and Operational Research of the Universidad de Valladolid. His research interests include Statistical Inference methods under restrictions and Reliability and Maintenance of complex and extended systems.