  The problem of finding periodically expressed genes from time course
microarray experiments is at the center of numerous efforts to identify the
molecular components of biological clocks. We present a new approach to this
problem based on the cyclohedron test, which is a rank test inspired by recent
advances in algebraic combinatorics. The test has the advantage of being robust
to measurement errors, and can be used to ascertain the significance of
top-ranked genes. We apply the test to recently published measurements of gene
expression during mouse somitogenesis and find 32 genes that collectively are
significant. Among these are previously identified periodic genes involved in
the Notch/FGF and Wnt signaling pathways, as well as novel candidate genes that
may play a role in regulating the segmentation clock. These results confirm
that there are an abundance of exceptionally periodic genes expressed during
somitogenesis. The emphasis of this paper is on the statistics and
combinatorics that underlie the cyclohedron test and its implementation within
a multiple testing framework.
