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Bioinformatics Advance Access published online on November 22, 2005

Bioinformatics, doi:10.1093/bioinformatics/bti789
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© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received June 13, 2005
Revised October 26, 2005
Accepted November 15, 2005

Article

Detecting periodic patterns in unevenly spaced gene expression time series using Lomb-Scargle periodograms

Earl F. Glynn 1, Jie Chen 2 *, and Arcady R. Mushegian 3

1 Stowers Institute for Medical Research, 1000 East 50th Street, Kansas City, MO 64110, USA
2 Stowers Institute for Medical Research, 1000 East 50th Street, Kansas City, MO 64110, USA; Department of Mathematics and Statistics, University of Missouri-Kansas City, 5100 Rockhill Road, Kansas City, MO 64110, USA
3 Stowers Institute for Medical Research, 1000 East 50th Street, Kansas City, MO 64110, USA; Department of Microbiology, Immunology and Molecular Genetics, University of Kansas Medical Center, Kansas City, KS 66160, USA

* To whom correspondence should be addressed.
Jie Chen, E-mail: chenj{at}umkc.edu


   Abstract

Motivation: Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spaced gene expression time series has not been well substantiated.

Methods: The Lomb-Scargle periodogram approach is used to search time series of gene expression to quantify the periodic behavior of every gene represented on the DNA array. The Lomb-Scargle periodogram analysis provides a direct method to treat missing values and unevenly spaced time points. We propose the combination of a Lomb-Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene patterns.

Results: We analyzed the Plasmodium falciparum gene expression dataset. In the Quality Control Dataset of 5080 expression patterns, we found 4112 periodic probes. In addition, we identified 243 probes with periodic expression in the Complete Dataset, which could not be examined in the original study by the FFT analysis due to an excessive number of missing values. While most periodic genes had a period of about 48 hr, some had a period close to 24 hr. Our approach should be applicable for detection and quantification of periodic patterns in any unevenly spaced gene expression time series data.

Availability: The computations were performed in R. The R code is available from http://research.stowers-institute.org/efg/2005/LombScargle.


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