SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data.

BACKGROUND: Identifying periodically expressed genes across different processes (e.g. the cell and metabolic cycles, circadian rhythms, etc) is a central problem in computational biology. Biological time series may contain (multiple) unknown signal shapes of systemic relevance, imperfections like noise, damping, and trending, or limited sampling density. While there exist methods for detecting periodicity, their design biases (e.g. toward a specific signal shape) can limit their applicability in one or more of these situations. METHODS: We present in this paper a novel method, SW1PerS, for quantifying periodicity in time series in a shape-agnostic manner and with resistance to damping. The measurement is performed directly, without presupposing a particular pattern, by evaluating the circularity of a high-dimensional representation of the signal. SW1PerS is compared to other algorithms using synthetic data and performance is quantified under varying noise models, noise levels, sampling densities, and signal shapes. Results on biological data are also analyzed and compared. RESULTS: On the task of periodic/not-periodic classification, using synthetic data, SW1PerS outperforms all other algorithms in the low-noise regime. SW1PerS is shown to be the most shape-agnostic of the evaluated methods, and the only one to consistently classify damped signals as highly periodic. On biological data, and for several experiments, the lists of top 10% genes ranked with SW1PerS recover up to 67% of those generated with other popular algorithms. Moreover, the list of genes from data on the Yeast metabolic cycle which are highly-ranked only by SW1PerS, contains evidently non-cosine patterns (e.g. ECM33, CDC9, SAM1,2 and MSH6) with highly periodic expression profiles. In data from the Yeast cell cycle SW1PerS identifies genes not preferred by other algorithms, hence not previously reported as periodic, but found in other experiments such as the universal growth rate response of Slavov. These genes are BOP3, CDC10, YIL108W, YER034W, MLP1, PAC2 and RTT101. CONCLUSIONS: In biological systems with low noise, i.e. where periodic signals with interesting shapes are more likely to occur, SW1PerS can be used as a powerful tool in exploratory analyses. Indeed, by having an initial set of periodic genes with a rich variety of signal types, pattern/shape information can be included in the study of systems and the generation of hypotheses regarding the structure of gene regulatory networks.

Conservation and Diversification of Circadian Rhythmicity Between a Model Crassulacean Acid Metabolism Plant Kalanchoë fedtschenkoi and a Model C3 Photosynthesis Plant Arabidopsis thaliana.

Crassulacean acid metabolism (CAM) improves photosynthetic efficiency under limited water availability relative to C3 photosynthesis. It is widely accepted that CAM plants have evolved from C3 plants and it is hypothesized that CAM is under the control of the internal circadian clock. However, the role that the circadian clock plays in the evolution of CAM is not well understood. To identify the molecular basis of circadian control over CAM evolution, rhythmic gene sets were identified in a CAM model plant species (Kalanchoë fedtschenkoi) and a C3 model plant species (Arabidopsis thaliana) through analysis of diel time-course gene expression data using multiple periodicity detection algorithms. Based on protein sequences, ortholog groups were constructed containing genes from each of these two species. The ortholog groups were categorized into five gene sets based on conservation and diversification of rhythmic gene expression. Interestingly, minimal functional overlap was observed when comparing the rhythmic gene sets of each species. Specifcally, metabolic processes were enriched in the gene set under circadian control in K. fedtschenkoi and numerous genes were found to have retained or gained rhythmic expression in K. fedtsechenkoi. Additonally, several rhythmic orthologs, including CAM-related orthologs, displayed phase shifts between species. Results of this analysis point to several mechanisms by which the circadian clock plays a role in the evolution of CAM. These genes provide a set of testable hypotheses for future experiments.