Charting an organs’ biological atlas requires us to spatially resolve the entire single-cell transcriptome, and to relate such cellular features to the anatomical scale. Single-cell and single-nucleus RNA-seq (sc/snRNA-seq) can profile cells comprehensively, but lose spatial information. Spatial transcriptomics allows for spatial measurements, but at lower resolution and with limited sensitivity. Targeted in situ technologies solve both issues, but are limited in gene throughput. To overcome these limitations we present Tangram, a method that aligns sc/snRNA-seq data to various forms of spatial data collected from the same region, including MERFISH, STARmap, smFISH, Spatial Transcriptomics (Visium) and histological images. Tangram can map any type of sc/snRNA-seq data, including multimodal data such as those from SHARE-seq, which we used to reveal spatial patterns of chromatin accessibility. We demonstrate Tangram on healthy mouse brain tissue, by reconstructing a genome-wide anatomically integrated spatial map at single-cell resolution of the visual and somatomotor areas.

A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics (some with proofs, others conjecturally): skew Schur polynomials; symmetric polynomials associated to reduced words, Redfield-Pólya theory, Witt vectors, and totally nonnegative matrices; resultants; discriminants (up to quartics); Macdonald polynomials; key polynomials; Demazure atoms; Schubert polynomials; and Grothendieck polynomials, among others.Our principal construction is the Schubitope. For any subset of [n] 2 , we describe it by linear inequalities. This generalized permutahedron conjecturally has positive Ehrhart polynomial. We conjecture it describes the Newton polytope of Schubert and key polynomials. We also define dominance order on permutations and study its poset-theoretic properties.

Charting a biological atlas of an organ, such as the brain, requires us to spatially-resolve whole transcriptomes of single cells, and to relate such cellular features to the histological and anatomical scales. Single-cell and single-nucleus RNA-Seq (sc/snRNA-seq) can map cells comprehensively5,6, but relating those to their histological and anatomical positions in the context of an organ’s common coordinate framework remains a major challenge and barrier to the construction of a cell atlas7–10. Conversely, Spatial Transcriptomics allows for in-situ measurements11–13 at the histological level, but at lower spatial resolution and with limited sensitivity. Targeted in situ technologies1–3 solve both issues, but are limited in gene throughput which impedes profiling of the entire transcriptome. Finally, as samples are collected for profiling, their registration to anatomical atlases often require human supervision, which is a major obstacle to build pipelines at scale. Here, we demonstrate spatial mapping of cells, histology, and anatomy in the somatomotor area and the visual area of the healthy adult mouse brain. We devise Tangram, a method that aligns snRNA-seq data to various forms of spatial data collected from the same brain region, including MERFISH1, STARmap2, smFISH3, and Spatial Transcriptomics4 (Visium), as well as histological images and public atlases. Tangram can map any type of sc/snRNA-seq data, including multi-modal data such as SHARE-seq data5, which we used to reveal spatial patterns of chromatin accessibility. We equipped Tangram with a deep learning computer vision pipeline, which allows for automatic identification of anatomical annotations on histological images of mouse brain. By doing so, Tangram reconstructs a genome-wide, anatomically-integrated, spatial map of the visual and somatomotor area with ∼30,000 genes at single-cell resolution, revealing spatial gene expression and chromatin accessibility patterning beyond current limitation of in-situ technologies.

No abstract