We used archetypal analysis to characterize the gradients within and between subtypes. We used partition-based graph abstraction (PAGA) to find those pairs that warranted a gradient-based analysis. PAGA uses the formalism of graph theory and community detection to define a statistic quantifying the presence of connectivity between two clusters.81 To calculate the PAGA graph we ran scanpy.tl.paga on our Seurat integrated data (Figure S3F). We defined subtype pairs as connected if the PAGA edge weight was greater than 0.02. For each pair of connected subtypes – or within a single subtype – we used the Dirichlet Simplex Nest (DSN) implementation of archetype analysis (https://arxiv.org/abs/1905.11009) to define gradients of gene expression. Because we used the raw gene counts, we ran the DSN algorithm in the Poisson configuration.82 Across several runs of the DSN algorithm, we located the archetype most correlated with the subtypes’ annotations and designated those archetypes as the transition axes between the subtype pairs. To determine if the transitions were discrete, we used regression discontinuity design (RDD).83 The null hypothesis of this test is that the gene expression is,
