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Abstract Spatial transcriptomics (ST) technologies measure gene expression at thousands of locations within a two-dimensional tissue slice, enabling the study of spatial gene expression patterns. Spatial variation in gene expression is characterized byspatial gradients, or the collection of vector fields describing the direction and magnitude in which the expression of each gene increases. However, the few existing methods that learn spatial gradients from ST data either make restrictive and unrealistic assumptions on the structure of the spatial gradients or do not accurately model discrete transcript locations/counts. We introduce SLOPER (for Score-based Learning Of Poisson-modeled Expression Rates), a generative model for learning spatial gradients (vector fields) from ST data. SLOPER models the spatial distribution of mRNA transcripts with aninhomogeneous Poisson point process (IPPP)and usesscore matchingto learn spatial gradients for each gene. SLOPER utilizes the learned spatial gradients in a novel diffusion-based sampling approach to enhance the spatial coherence and specificity of the observed gene expression measurements. We demonstrate that the spatial gradients and enhanced gene expression representations learned by SLOPER leads to more accurate identification of tissue organization, spatially variable gene modules, and continuous axes of spatial variation (isodepth) compared to existing methods. Software availabilitySLOPER is available athttps://github.com/chitra-lab/SLOPER. 

The selection of marker gene panels is critical for capturing the cellular and spatial heterogeneity in the expanding atlases of single-cell RNA sequencing (scRNA-seq) and spatial transcriptomics data. Most current approaches to marker gene selection operate in a label-based framework, which is inherently limited by its dependency on predefined cell type labels or clustering results. In contrast, existing label-free methods often struggle to identify genes that characterize rare cell types or subtle spatial patterns, and they frequently fail to scale efficiently with large data sets. Here, we introduce geneCover, a label-free combinatorial method that selects an optimal panel of minimally redundant marker genes based on gene-gene correlations. Our method demonstrates excellent scalability to large data sets and identifies marker gene panels that capture distinct correlation structures across the transcriptome. This allows geneCover to distinguish cell states in various tissues of living organisms effectively, including those associated with rare or otherwise difficult-to-identify cell types. We evaluate the performance of geneCover across various scRNA-seq and spatial transcriptomics data sets, comparing it to other label-free algorithms to highlight its utility and potential in diverse biological contexts. 

Definition of cell classes across the tissues of living organisms is central in the analysis of growing atlases of single-cell RNA sequencing (scRNA-seq) data across biomedicine. Marker genes for cell classes are most often defined by differential expression (DE) methods that serially assess individual genes across landscapes of diverse cells. This serial approach has been extremely useful, but is limited because it ignores possible redundancy or complementarity across genes that can only be captured by analyzing multiple genes simultaneously. Interrogating binarized expression data, we aim to identify discriminating panels of genes that are specific to, not only enriched in, individual cell types. To efficiently explore the vast space of possible marker panels, leverage the large number of cells often sequenced, and overcome zero-inflation in scRNA-seq data, we propose viewing marker gene panel selection as a variation of the “minimal set-covering problem” in combinatorial optimization. Using scRNA-seq data from blood and brain tissue, we show that this new method, CellCover, performs as good or better than DE and other methods in defining cell-type discriminating gene panels, while reducing gene redundancy and capturing cell-class-specific signals that are distinct from those defined by DE methods. Transfer learning experiments across mouse, primate, and human data demonstrate that CellCover identifies markers of conserved cell classes in neocortical neurogenesis, as well as developmental progression in both progenitors and neurons. Exploring markers of human outer radial glia (oRG, or basal RG) across mammals, we show that transcriptomic elements of this key cell type in the expansion of the human cortex likely appeared in gliogenic precursors of the rodent before the full program emerged in neurogenic cells of the primate lineage. We have assembled the public datasets we use in this report within the NeMO Analytics multi-omic data exploration environment [1], where the expression of individual genes (NeMO: Individual genes in cortex and NeMO: Individual genes in blood) and marker gene panels (NeMO: Telley 3 CellCover Panels, NeMO: Telley 12 CellCover Panels, NeMO: Sorted Brain Cell CellCover Panels, and NeMO: Blood 34 CellCover Panels) can be freely explored without coding expertise. CellCover is available in CellCover R and CellCover Python. 

This chapter reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of various approaches at building Riemannian spaces of shapes, with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm, the attention is turned to elastic metrics and to growth models that can be derived from it. In the latter context, a new class of metrics, involving the optimization of a growth tensor, is introduced, and some of its properties are studied. 

Abstract This paper explicates a solution to building correspondences between molecular-scale transcriptomics and tissue-scale atlases. This problem arises in atlas construction and cross-specimen/technology alignment where specimens per emerging technology remain sparse and conventional image representations cannot efficiently model the high dimensions from subcellular detection of thousands of genes. We address these challenges by representing spatial transcriptomics data as generalized functions encoding position and high-dimensional feature (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling regions as homogeneous random fields with unknown transcriptomic feature distribution. We solve simultaneously for the minimizing geodesic diffeomorphism of coordinates through LDDMM and for these latent feature densities. We map tissue-scale mouse brain atlases to gene-based and cell-based transcriptomics data from MERFISH and BARseq technologies and to histopathology and cross-species atlases to illustrate integration of diverse molecular and cellular datasets into a single coordinate system as a means of comparison and further atlas construction. 

This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.