A framework for single-cell geometric analysis.

(a) Schematic overview of the TopoMetry algorithm. From an input single-cell dataset (e.g., normalized and scaled scRNAseq data), TopoMetry builds a kNN graph, which is used to learn manifold-adaptive similarities with a decay-adaptive kernel suitable for constructing Laplacian-type and diffusion operators. After estimation of intrinsic dimensionality, these operators are decomposed into a spectral scaffold with up to hundreds of components that jointly explain all of the underlying geometry of the dataset. The spectral scaffolds are used to learn refined Laplacian-type and diffusion operators of the scaffolds themselves, encoding “the geometry of the geometry”. The scaffolds and operators constitute key TopoMetry outputs and can be utilized for downstream tasks, such as clustering, visualization, imputation, evaluation, and diagnostics, in a geometry-aware manner. TopoMetry utilities include (b) estimation of local intrinsic dimensionality, (c) filtering of categorical signals, and (d) imputation and denoising. Crucially, TopoMetry introduces the visualization of manifold diagnostics (e) for single-cell data, in which distortions induced by 2-D embeddings can be identified and investigated from a local, global, and contraction/expansion perspective.

Geometry preservation benchmark.

(a) Schematic representation of the benchmark workflow, in which a corpus composed of 68 scRNAseq datasets was collected, preprocessed, and analyzed with i) the current PCA→UMAP standard, ii) standalone UMAP (graph from high-dimensional gene expression space), iii) scVI (a popular tool for variational inference), and iv) TopoMetry. (b) Violin plots representing geometry-preservation metrics for lower-dimensional latent spaces learned with PCA and scVI, compared to TopoMetry’s spectral scaffolds. TopoMetry’s scaffolds achieved systematically higher scores across all metrics. (c) Violin plots representing geometry-preservation metrics for 2-D visualizations obtained with the evaluated methods. Except for PaCMAP on TopoMetry’s multiscale spectral scaffold, the geometry-aware visualizations achieved systematically higher scores. Visualizations based on scVI and PCA latent space presented the lowest scores.

Inferring cellular lineages with TopoMetry.

(a) TopoMAP and (b) PCA→UMAP visualizations of the Pancreas dataset showing cellular developmental trajectories in the murine pancreas, colored by original cell type annotations. (c) TopoMAP visualization, colored by inferred scores of different phases of the cell cycle, and (d) the predicted phase for each cell with RNA velocity overlay. Note how RNA velocity trajectories largely agree with the identified cell cycle structure and the represented geometry. (e) PCA→UMAP visualization of the Mouse Organogenesis Cell Atlas (MOCA), comprising ∼1.3 million cells collected during murine embryo development, colored by refined subtrajectories annotation. (f–g) TopoMAP visualizations of MOCA, colored by original annotations on refined subtrajectories (f), and TopoMetry’s clustering results (g). Note how the TopoMAP embedding successfully separates main and refined trajectories and adds enhanced detail and resolution on the diversity of subpopulations arising during development.

TopoMetry unveils unexpected transcriptional diversity of T cells.

Analysis of the pbmc68k dataset, comprising approximately 68,000 peripheral blood mononuclear cells from a healthy donor (10X Genomics). (a) TopoMAP visualization colored by TopoMetry’s clustering results. Main cell types are well separated, and T cells present an unexpected high diversity, with approximately a hundred clusters identifying T cell subpopulations. (b) Standard PCA→UMAP visualizations colored by clustering results obtained with the PCA-derived graph (left) and the kNN graph from the high-dimensional gene expression space (right), presenting the same global separation of main cell types but disagreeing on T cells. (c) Matrixplot of the top 3 marker genes found for PCA-based clusters, highlighting the presence of non-specific markers for T cells. (d) Matrixplot of the top 3 marker genes found for TopoMetry clusters, presenting highly specific marker expression. (e) Standalone UMAP visualizations of the same data, colored by PCA-based (left) and kNN-based clustering results (right). Note how the standalone approach detects part, but not all, of the T cell clusters identified with TopoMetry. (f) Contraction/expansion diagnostics of PCA→UMAP (left) and TopoMAP (right) visualizations. Note how the PCA→UMAP approach expands most regions of the cell identity manifold, while TopoMAP contracts the region inhabited by T CD4 lymphocytes when projecting TopoMetry’s refined graphs to a 2-D space.

TopoMetry detects T cell clonal expansion dynamics from gene expression.

Analysis of the ECCITE-TCR dataset, comprising circulating T CD8+ lymphocytes collected from human donors in baseline conditions and after SARS-CoV-2 vaccination or infection. (a) TopoMetry’s default visualizations, colored by TopoMetry’s clustering results. Note how projections derived from the fixed-time scaffold better preserve the local structure of the dataset, while projections derived from the multiscale scaffold better preserve long-range relationships and overall global structure. Despite minor differences, all visualizations correctly represent the cell cycle geometry of proliferating lymphocytes and the transcriptional diversity of central (TCM) and effector memory (TEM) lymphocytes. (b) Matrixplot of the top 3 marker genes found for TopoMetry clusters, presenting highly specific marker expression. (c–f) TopoMAP visualizations colored by original cell type annotations (c), clonal expansion information (d), predicted phase of the cell cycle (e), and contraction/expansion diagnostics. Note how the small clusters of TCM and TEM correspond to smaller clonotypes (ranging from small to medium), how the identified cell cycle geometry agrees with cell cycle predictions, and how the former are contracted while the latter are expanded in the 2-D visualization.