Topology identifies concurrent cyclic processes in single-cell transcriptomics and androgen receptor function

Standard single-cell RNA-seq analysis frameworks aggregate over-lapping biological processes and impose a single parametrization, conflating distinct programs. Here, we introduce a topological framework that detects and disentangles multiple cyclic processes directly from single-cell transcriptomic data. We validate this approach on synthetic datasets and scRNA-seq profiles of human dermal fibroblasts under control conditions and following androgen receptor (AR) silencing, as well as in vivo mouse prostate regeneration under androgen receptor add-back. We show robust cell cycle structure across conditions, identify an unbiased AR-linked stress signature related to the senescence and proliferation across organisms, and uncover cholesterol homeostasis as an AR-linked program in tissue regeneration. This framework enables identification and separation of concurrent cyclic processes from snapshot single-cell data, revealing complex multi-dimensional regulatory dynamics inaccessible to standard clustering analysis.