Time ordering of gene coexpression.

Temporal microarray gene expression profiles allow characterization of gene function through time dynamics of gene coexpression within the same genetic pathway. In this paper, we define and estimate a global time shift characteristic for each gene via least squares, inferred from pairwise curve alignments. These time shift characteristics of individual genes reflect a time ordering that is derived from ob- served temporal gene expression profiles. Once these time shift characteristics are obtained for each gene, they can be entered into further analyses, such as clustering. We illustrate the proposed methodology using Drosophila embryonic development and yeast cell-cycle gene expression profiles, as well as simulations. Feasibility is demonstrated through the successful recovery of time ordering. Estimated time shifts for Drosophila maternal and zygotic genes provide excellent discrimination between these two categories and confirm known genetic pathways through the time order of gene expression. The application to yeast cell-cycle data establishes a natural time order of genes that is in line with cell-cycle phases. The method does not require periodicity of gene expression profiles. Asymptotic justifications are also provided.