Unraveling cell differentiation mechanisms through topological exploration of single-cell developmental trajectories

Understanding the circuits that control cell differentiation is a fundamental problem in developmental biology. Single-cell RNA sequencing has emerged as a powerful tool for investigating this problem. However, the reconstruction of developmental trajectories is based on the assumption that cell states traverse a tree-like structure, which may bias our understanding of critical developmental mechanisms. To address this limitation, we developed a framework, TopGen, that enables identifying topological signatures of functional biological circuits as persistent homology groups in transcriptome space. First, we show that TopGen can identify genetic drivers of topological structures in simulated datasets. We then applied our approach to more than ten single-cell developmental atlases and found that topological transcriptome spaces are predominantly path-connected and only sometimes simply connected. Finally, we applied TopGen to analyze gene expression patterns in topological loops representing stem-like, transdifferentiation, and convergent cell circuits, found in C. elegans, H. vulgaris, and N. vectensis, respectively. Our results show that some essential differentiation mechanisms use non-trivial topological motifs, and that these motifs can be conserved in a cell-type-specific manner. Thus, our approach to studying the topological properties of developmental transcriptome atlases opens new possibilities for understanding cell development and differentiation.