An improved rhythmicity analysis method using Gaussian Processes detects cell-density dependent circadian oscillations in stem cells.

Detecting oscillations in time series datasets remains a challenging problem even after decades of research. Development of improved statistical algorithms, therefore, remains an exciting avenue of research, especially in fields such as chronobiology where gene expression oscillations tend to be low amplitude, noisy and non-stationary. Here we introduce a new method, ODeGP ( O scillation De tection using G aussian P rocesses), which combines Gaussian Process (GP) regression with Bayesian inference to provide a flexible approach to the problem. Besides naturally incorporating measurement errors and non-uniformly sampled data, ODeGP uses a recently developed kernel to improve the detection of non-stationary waveforms. An additional advantage is that it circumvents issues related to p-value based rhythmicity classification by using the Bayes factor instead. Using a variety of synthetic datasets we first demonstrate that ODeGP almost always outperforms eight commonly used methods in detecting stationary as well as nonstationary oscillations. Next, by analyzing existing qPCR datasets with known (non)oscillatory behavior, we find that the ODeGP Bayes factors show a large separation between oscillatory and non-oscillatory datasets, providing a good metric for the classification problem. In qPCR datasets that exhibit low amplitude and noisy oscillations, we demonstrate that our method is more sensitive compared to the existing methods at detecting weak oscillations. Finally, we generate new qPCR time-series datasets on pluripotent mouse embryonic stem cells, which are expected to exhibit no oscillations of the core circadian clock genes. Surprisingly, we discover using ODeGP that increasing cell density can result in the generation of oscillations in the Bmal1 gene, thus highlighting our method’s ability to discover new and unexpected patterns. We make ODeGP available for open-source use as an easy to run R-package.