Deconstructing Complexity: A Computational Topology Approach to Trajectory Inference in the Human Thymus with tviblindi

Understanding complex, organ-level single-cell datasets represents a formidable interdisciplinary challenge. This study aims to describe developmental trajectories of thymocytes and mature T cells. We developed tviblindi, a trajectory inference algorithm that integrates several autonomous modules - pseudotime inference, random walk simulations, real-time topological classification using persistent homology, and autoencoder-based 2D visualization using the vaevictis algorithm. This integration facilitates interactive exploration of developmental trajectories, revealing not only the canonical CD4 and CD8 development but also offering insights into checkpoints such as TCR{beta} selection and positive/negative selection. Furthermore, tviblindi allowed us to thoroughly characterize thymic regulatory T cells, tracing their development passed the negative selection stage to mature thymic regulatory T cells. At the very end of the developmental trajectory we discovered a previously undescribed subpopulation of thymic regulatory T cells. Experimentally, we confirmed its extensive proliferation history and an immunophenotype characteristic of activated and recirculating cells. tviblindi represents a new class of methods that is complementary to fully automated trajectory inference tools. It offers a semi-automated tool that leverages features derived from data in an unbiased and mathematically rigorous manner. These features include pseudotime, homology classes, and appropriate low-dimensional representations. These features can be integrated with expert knowledge to formulate hypotheses regarding the underlying dynamics, tailored to the specific trajectory or biological process under investigation.