Inference on circular orders with application to cell cycle gene expression data

Abstract

In recent years there has been considerable interest in drawing inferences regarding order relationships among angular parameters. In particular, in biology the interest is to understand genes participating in cell cycle across multiple species and whether they are functionally conserved. The time to peak expression, known as phase angle, of such a gene can be mapped onto a unit circle. Biologists are not only interested in estimating the phase angles but in determining the relative order of expression of various genes. The final aim is to know whether the order of peak expression among cell cycle genes is conserved evolutionarily across species. These questions are challenging due to large variability among studies and to the circular nature of the data. A methodology to find the underlying circular order in a population is presented. We also propose a solution for the problem of testing equality of circular orders among two or more populations. Unbalanced samples and differences in distributions are taken into consideration. The proposed methodology is illustrated by analyzing data sets from three species: Schizosaccharomyces Pombe, Schizosaccharomyces Cerevisiae and Humans. As a result a set of genes is presented where the circular order is conserved across these three species.