Journal: Nature Methods

Article Title: Spatial transition tensor of single cells

doi: 10.1038/s41592-024-02266-x

Figure Lengend Snippet: a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors. In pathway similarity graph, Dim. denotes the coordinates in reduced dimensions.

Article Snippet: Fig. 1 Overview of STT. a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors.

Techniques: Comparison, Gene Expression

Journal: Nature Methods

Article Title: Spatial transition tensor of single cells

doi: 10.1038/s41592-024-02266-x

Figure Lengend Snippet: a , Comparison between streamlines of STT and other methods for toggle-switch dataset. The cells are colored by attractor in STT, or Leiden clustering results in scVelo and UniTVelo. The STT, scVelo and ground-truth results are embedded in PCA on joint spliced and unspliced counts, and UniTVelo result is plotted on the coordinates of spliced counts. b , The box plots across all cells ( n = 10,010) of cosine similarity between calculated velocity and ground truth in different methods. The central box represents the interquartile range, from the 25th percentiles (bottom bounds) to 75th percentiles (top bounds), and horizontal line within the box indicates the median (50th percentile). The whiskers stretch out to the values that fall within 1.5 times the interquartile range from the lower and upper quartiles. The dots indicate outliers. c , d , Comparison between streamlines of STT and other methods for synthetic EMT circuit dataset. c , The cells are colored with attractor assignment by STT, and the low-dimensional embedding is the UMAP based on the joint of spliced and unspliced counts. The streamlines are visualized using the averaged velocity over attractors. d , The cells are colored with Leiden clustering output, and the low-dimensional embedding is the UMAP of spliced counts only. The streamlines are visualized using RNA velocity.

Article Snippet: Fig. 1 Overview of STT. a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors.

Techniques: Comparison

Journal: Nature Methods

Article Title: Spatial transition tensor of single cells

doi: 10.1038/s41592-024-02266-x

Figure Lengend Snippet: a , The global transition path analysis of EMT. Cells are embedded in the constructed transition coordinates (trans. coord.) of dynamical manifold and the number indicates fraction of transition flux. Cells are colored by STT attractor. b , Transition coordinates with cells colored by collection time. c , Violin plot of cell-membership entropy in different attractors. d , Absorption probabilities of cells into different attractors using multistability kernel induced random walk by STT. e , Top genes that are consistent with the multistability of attractors in EMT. f , The streamlines of various components of transition tensors, including the attractor-averaged and attractor-specific tensors. The low-dimensional embedding is the UMAP of both spliced and unspliced counts. In the left panel, the cells are colored by the attractor assignment. In the right panel, the cells are colored by their membership in each attractor, and only the tensors of cells whose memberships are greater than 0.2 in the attractors are shown.

Article Snippet: Fig. 1 Overview of STT. a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors.

Techniques: Construct

Journal: Nature Methods

Article Title: Spatial transition tensor of single cells

doi: 10.1038/s41592-024-02266-x

Figure Lengend Snippet: a , b , The spatial annotation of data and detected attractor by STT with cells colored by different categories: attractor ( a ) and region ( b ). c , Local transition tensor streamlines in specific attractors 6 and 3. The cells are colored by their memberships in corresponding attractors. d , Similarity of transition tensors across KEGG pathways. The left shows 2D embedding indicating the clustering of similar biological pathways in mouse brain development spatial dynamics, with the averaged tensor streamlines from various pathways displaying different transition dynamics. Pathways that have at least three genes overlapped with STT multistability genes are shown in the low-dimensional embeddings. The right shows the streamlines of specific pathways from different clusters, with cells embedded in spatial coordinates.

Article Snippet: Fig. 1 Overview of STT. a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors.

Techniques:

Journal: Nature Methods

Article Title: Spatial transition tensor of single cells

doi: 10.1038/s41592-024-02266-x

Figure Lengend Snippet: a , b , The spatial spots of the analyzed data, with spots colored by detected attractor by STT regions ( a ) or annotation in original research ( b ). c , The constructed dynamical landscape of data, with spots colored by attractors. d , The spatial spots colored by cell type annotations in original research. e , The Sankey plot displaying the relation between STT attractors (left) and spatial region annotations (right). The width of links indicates the number of cells that share the connected attractor label and region annotation label simultaneously. f , Local transition tensor streamlines in specific attractors 1, 2, 3 and 4. The cells are colored by their memberships to corresponding attractors.

Article Snippet: Fig. 1 Overview of STT. a , Comparison between the RNA velocity (linear and single equilibrium) versus STT tensor model (multistable and multiple attractors). b , Definition of transition tensor and induced RNA velocity by averaging cell’s membership in different attractors. c – f , Workflow of the STT. c , The input U and S count matrices. d , e , Iterative scheme between kinetic parameter estimation of transition tensor ( d ) and dynamics decomposition and coarse-graining ( e ). f , Output of STT. g , Analysis of spatial transcriptomics data using STT where the spatial-similarity kernel based on spatial cell coordinates is combined with the tensor-induced and gene expression-induced kernel to infer a cell’s membership in attractors.

Techniques: Construct