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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.

Build single-cell trajectories with the software that introduced **pseudotime**. Find out about cell fate decisions and the genes regulated as they're made. Group and classify your cells based on gene expression. Identify new cell types and states and the genes that distinguish them. Find genes that vary between cell types and states, over trajectories, or in response to perturbations using statistically robust, flexible differential analysis. In development, disease, and throughout life, cells transition from one state to another. Monocle introduced the concept of **pseudotime**, which is a measure of how far a cell has moved through biological progress. Many researchers are using single-cell RNA-Seq to discover new cell types. Monocle 3 can help you purify them or characterize them further by identifying key marker genes that you can use in follow-up experiments such as immunofluorescence or flow sorting. **Single-cell trajectory analysis** shows how cells choose between one of several possible end states. The new reconstruction algorithms introduced in Monocle 3 can robustly reveal branching trajectories, along with the genes that cells use to navigate these decisions.

Expanded CRISPR-compatible CITE-seq (ECCITE-seq) which is built upon pooled CRISPR screens, allows to simultaneously measure transcriptomes, surface protein levels, and single-guide RNA (sgRNA) sequences at single-cell resolution. The technique enables multimodal characterization of each perturbation and effect exploration. However, it also encounters heterogeneity and complexity which can cause substantial noise into downstream analyses. Mixscape (Papalexi, Efthymia, et al., 2021) is a computational framework proposed to substantially improve the signal-to-noise ratio in single-cell perturbation screens by identifying and removing confounding sources of variation. In this notebooks, we demonstrate Mixscape's features using pertpy - a Python package offering a range of tools for perturbation analysis. The original pipeline of Mixscape implemented in R can be found here.

InferCNV is used to explore tumor single cell RNA-Seq data to identify evidence for somatic large-scale chromosomal copy number alterations, such as gains or deletions of entire chromosomes or large segments of chromosomes. This is done by exploring expression intensity of genes across positions of tumor genome in comparison to a set of reference 'normal' cells. A heatmap is generated illustrating the relative expression intensities across each chromosome, and it often becomes readily apparent as to which regions of the tumor genome are over-abundant or less-abundant as compared to that of normal cells. **Infercnvpy** is a scalable python library to infer copy number variation (CNV) events from single cell transcriptomics data. It is heavliy inspired by InferCNV, but plays nicely with scanpy and is much more scalable.