CIRCUST: a novel methodology for reconstruction of temporal order of molecular rhythms; validation and application towards a human circadian gene expression atlas

The circadian system drives near-24-h oscillations in behaviors and biological processes. The underlying core molecular clock regulates the expression of other genes, and it has been shown that the expression of more than 50 percent of genes in mammals display 24-h rhythmic patterns, with the specific genes that cycle varying from one tissue to another. Determining rhythmic gene expression patterns in human tissues sampled as single timepoints has several challenges, including the reconstruction of temporal order or highly noisy data. Previous methodologies have attempted to address these challenges in one or a small number of tissues for which clock gene evolutionary conservation is preserved. Here we propose CIRCUST, a novel CIRCular-robUST methodology for analyzing molecular rhythms, that relies on circular statistics, is highly robust against noise and requires fewer assumptions than existing methodologies. First, we describe the method, then we validate it against {two} controlled experiments in which sampling times were known, and finally CIRCUST was applied to 34 tissues from the Genotype-Tissue Expression (GTEx) dataset with the aim towards building a comprehensive human circadian expression atlas. The validation and application shown here indicate that CIRCUST provide a flexible framework to formulate and solve the issues related to the analysis of molecular rhythms in human tissues. CIRCUST methodology is publicly available at \url{https://github.com/yolandalago/CIRCUST/ ### Competing Interest Statement Y.L. C.R. and I.M. declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. F.A.J.L.S. served on the Board of Directors for the Sleep Research Society and has received consulting fees from the University of Alabama at Birmingham. F.A.J.L.S. interests were reviewed and managed by Brigham and Women Hospital and Partners HealthCare in accordance with their conflict of interest policies. F.A.J.L.S. consultancies are not related to the current work. R.S. is a founder of Magnet Biomedicine, which is not related to the current work.