Mapping out the coarse-grained connectivity structures of complex manifolds Biological systems often change over time, as old cells die and new cells are created through differentiation from progenitor cells. This means that at any given time, not all cells will be at the same stage of development. In this sense, a single-cell sample could contain cells at different stages of differentiation. By analyzing the data, we can identify which cells are at which stages and build a model for their biological transitions. By quantifying the connectivity of partitions (groups, clusters) of the single-cell graph, partition-based graph abstraction (PAGA) generates a much simpler abstracted graph (PAGA graph) of partitions, in which edge weights represent confidence in the presence of connections. In this notebook, we will introduce the concept of single-cell Trajectory Analysis using PAGA (Partition-based graph abstraction) in the context of hematopoietic differentiation.

Single-cell RNA sequencing methods can profile the transcriptomes of single cells but cannot preserve spatial information. Conversely, spatial transcriptomics assays can profile spatial regions in tissue sections but do not have single-cell resolution. Here, Runmin Wei (Siyuan He, Shanshan Bai, Emi Sei, Min Hu, Alastair Thompson, Ken Chen, Savitri Krishnamurthy & Nicholas E. Navin) developed a computational method called CellTrek that combines these two datasets to achieve single-cell spatial mapping through coembedding and metric learning approaches. They benchmarked CellTrek using simulation and in situ hybridization datasets, which demonstrated its accuracy and robustness. They then applied CellTrek to existing mouse brain and kidney datasets and showed that CellTrek can detect topological patterns of different cell types and cell states. They performed single-cell RNA sequencing and spatial transcriptomics experiments on two ductal carcinoma in situ tissues and applied CellTrek to identify tumor subclones that were restricted to different ducts, and specific T-cell states adjacent to the tumor areas.

Recent technological advancements have enabled spatially resolved transcriptomic profiling but at multi-cellular pixel resolution, thereby hindering the identification of cell-type-specific spatial patterns and gene expression variation. To address this challenge, we develop STdeconvolve as a reference-free approach to deconvolve underlying cell types comprising such multi-cellular pixel resolution spatial transcriptomics (ST) datasets. Using simulated as well as real ST datasets from diverse spatial transcriptomics technologies comprising a variety of spatial resolutions such as Spatial Transcriptomics, 10X Visium, DBiT-seq, and Slide-seq, we show that STdeconvolve can effectively recover cell-type transcriptional profiles and their proportional representation within pixels without reliance on external single-cell transcriptomics references. **STdeconvolve** provides comparable performance to existing reference-based methods when suitable single-cell references are available, as well as potentially superior performance when suitable single-cell references are not available. STdeconvolve is available as an open-source R software package with the source code available at https://github.com/JEFworks-Lab/STdeconvolve .