Permutation test for periodicity in short time series data

Background: Periodic processes, such as the circadian rhythm, are important factors modulating and coordinating transcription of genes governing key metabolic pathways. Theoretically, even small fluctuations in the orchestration of circadian gene expression patterns among different tissues may result in functional asynchrony at the organism level and may contribute to a wide range of pathologic disorders. Identification of circadian expression pattern in time series data is important, but equally challenging. Microarray technology allows estimation of relative expression of thousands of genes at each time point. However, this estimation often lacks precision and microarray experiments are prohibitively expensive, limiting the number of data points in a time series expression profile. The data produced in these experiments carries a high degree of stochastic variation, obscuring the periodic pattern and a limited number of replicates, typically covering not more than two complete periods of oscillation. Results: To address this issue, we have developed a simple, but effective, computational technique for the identification of a periodic pattern in relatively short time series, typical for microarray studies of circadian expression. This test is based on a random permutation of time points in order to estimate non-randomness of a periodogram. The Permutated time, or Pt-test, is able to detect oscillations within a given period in expression profiles dominated by a high degree of stochastic fluctuations or oscillations of different irrelevant frequencies. We have conducted a comprehensive study of circadian expression on a large data set produced at PBRC, representing three different peripheral murine tissues. We have also re-analyzed a number of similar time series data sets produced and published independently by other research groups over the past few years. Conclusion: The Permutated time test (Pt-test) is demonstrated to be effective for detection of periodicity in short time series typical for high-density microarray experiments. The software is a set of C++ programs available from the authors on the open source basis.