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Motivation The circadian rhythm drives the oscillatory expression of thousands of genes across all tissues. The recent revolution in high-throughput transcriptomics, coupled with the significant implications of the circadian clock for human health, has sparked an interest in circadian profiling studies to discover genes under circadian control. Result We present TimeCycle: a topology-based rhythm detection method designed to identify cycling transcripts. For a given time-series, the method reconstructs the state space using time-delay embedding, a data transformation technique from dynamical systems theory. In the embedded space, Takens’ theorem proves that the dynamics of a rhythmic signal will exhibit circular patterns. The degree of circularity of the embedding is calculated as a persistence score using persistent homology, an algebraic method for discerning the topological features of data. By comparing the persistence scores to a bootstrapped null distribution, cycling genes are identified. Results in both synthetic and biological data highlight Time-Cycle’s ability to identify cycling genes across a range of sampling schemes, number of replicates, and missing data. Comparison to competing methods highlights their relative strengths, providing guidance as to the optimal choice of cycling detection method. Availability and Implementation A fully documented open-source R package implementing Time-Cycle is available at: https://nesscoder.github.io/TimeCycle/.