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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.

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 .

In the realm of transcriptional dynamics, understanding the intricate interplay of regulatory proteins is crucial for deciphering processes ranging from normal development to disease progression. However, traditional RNA velocity methods often overlook the underlying regulatory drivers of gene expression changes over time. This gap in knowledge hinders our ability to unravel the mechanistic intricacies of these dynamic processes. scKINETICs (Key regulatory Interaction NETwork for Inferring Cell Speed) (Burdziak et al, 2023) offers a dynamic model for gene expression changes that simultaneously learns per-cell transcriptional velocities and a governing gene regulatory network. By employing an expectation-maximization approach, scKINETICS quantifies the impact of each regulatory element on its target genes, incorporating insights from epigenetic data, gene-gene coexpression patterns and constraints dictated by the phenotypic manifold.

Classification of tumor and normal cells in the tumor microenvironment from scRNA-seq data is an ongoing challenge in human cancer study. Copy number karyotyping of aneuploid tumors (***copyKAT***) (Gao, Ruli, et al., 2021) is a method proposed for identifying copy number variations in single-cell transcriptomics data. It is used to predict aneuploid tumor cells and delineate the clonal substructure of different subpopulations that coexist within the tumor mass. In this notebook, we will illustrate a basic workflow of CopyKAT based on the tutorial provided on CopyKAT's repository. We will use a dataset of triple negative cancer tumors sequenced by 10X Chromium 3'-scRNAseq (GSM4476486) as an example. The dataset contains 20,990 features across 1,097 cells. We have modified the notebook to demonstrate how the tool works on BioTuring's platform.