Aligning gene expression time series with time warping algorithms

Abstract

Motivation: Increasingly, biological processes are being studied through time series of RNA expression data collected for large numbers of genes. Because common processes may unfold at varying rates in different experiments or individuals, methods are needed that will allow corresponding expression states in different time series to be mapped to one another. Results: We present implementations of time warping algorithms applicable to RNA and protein expression data and demonstrate their application to published yeast RNA expression time series. Programs executing two warping algorithms are described, a simple warping algorithm and an interpolative algorithm, along with programs that generate graphics that visually present alignment information. We show time warping to be superior to simple clustering at mapping corresponding time states. We document the impact of statistical measurement noise and sample size on the quality of time alignments, and present issues related to statistical assessment of alignment quality through alignment scores. We also discuss directions for algorithm improvement including development of multiple time series alignments and possible applications to causality searches and non-temporal processes (‘concentration warping’). Availability: Academic implementations of alignment programs genewarp and genewarpi and the graphics generation programs grphwarp and grphwarpi are available as Win32 system DOS box executables on our web site along with documentation on their use. The publicly available data on which they were demonstrated may be found at http://genome-www.stanford.edu/cellcycle/. Postscript files generated by grphwarp and grphwarpi may be directly printed or viewed using GhostView software available at http://www.cs.wisc.edu/~ghost/. Contact: church@arep.med.harvard.edu Supplementary information: http://arep.med.harvard.edu/timewarp/supplement.htm. * To whom correspondence should be addressed.