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.

Advances in multi-omics have led to an explosion of multimodal datasets to address questions from basic biology to translation. While these data provide novel opportunities for discovery, they also pose management and analysis challenges, thus motivating the development of tailored computational solutions. `muon` is a Python framework for multimodal omics. It introduces multimodal data containers as `MuData` object. The package also provides state of the art methods for multi-omics data integration. `muon` allows the analysis of both unimodal omics and multimodal omics.

Power analyses are considered important factors in designing high-quality experiments. However, such analyses remain a challenge in single-cell RNA-seq studies due to the presence of hierarchical structure within the data (Zimmerman et al., 2021). As cells sampled from the same individual share genetic and environmental backgrounds, these cells are more correlated than cells sampled from different individuals. Currently, most power analyses and hypothesis tests (e.g., differential expression) in scRNA-seq data treat cells as if they were independent, thus ignoring the intra-sample correlation, which could lead to incorrect inferences. Hierarchicell (Zimmerman, K.D. and Langefeld, C.D., 2021) is an R package proposed to estimate power for testing hypotheses of differential expression in scRNA-seq data while considering the hierarchical correlation structure that exists in the data. The method offers four important categories of functions: data loading and cleaning, empirical estimation of distributions, simulating expression data, and computing type 1 error or power. In this notebook, we will illustrate an example workflow of Hierarchicell. The notebook is inspired by Hierarchicell's vignette and modified to demonstrate how the tool works on BioTuring's platform.