Maggs, K.; Youssef, M. K.; Pulver, C.; Isma, J.; Nguyen, T. J.; Karthaus, W.; Hess, K.; Dotto, G. P.

In this paper we introduce cocycle hunter (cHunter), a tool for identifying and exploiting diverse circular structure in single-cell RNAseq data. Our method is based on persistent cohomology in dimension one, which we use to define a system of statistically enriching gene sets for circular structure. We also develop a powerful, cohomology-based technique for estimating the phase of genes exhibiting cyclic expression patterns. We validate our method on synthetic RNA transcription models, as well as real datasets studying the cell cycle, tissue regeneration and senescence in diverse experimental conditions. Our work points towards cocycles as pervasive mathematical structures of the transcriptional program.