Spatial transcriptomics (ST) is a new technology that measures mRNA expression across thousands of spots on a tissue slice, while preserving information about the spatial location of spots. ST is typically applied to several replicates from adjacent slices of a tissue. However, existing methods to analyze ST data do not take full advantage of the similarity in both gene expression and spatial organization across these replicates. We introduce a new method PASTE (Probabilistic Alignment of ST Experiments) to align and integrate ST data across adjacent tissue slices leveraging both transcriptional similarity and spatial distances between spots. First, we formalize and solve the problem of pairwise alignment of ST data from adjacent tissue slices, or layers, using Fused Gromov-Wasserstein Optimal Transport (FGW-OT), which accounts for variability in the composition and spatial location of the spots on each layer. From these pairwise alignments, we construct a 3D representation of the tissue. Next, we introduce the problem of simultaneous alignment and integration of multiple ST layers into a single layer with a low rank gene expression matrix. We derive an algorithm to solve the problem by alternating between solving FGW-OT instances and solving a Non-negative Matrix Factorization (NMF) of a weighted expression matrix. We show on both simulated and real ST datasets that PASTE accurately aligns spots across adjacent layers and accurately estimates a consensus expression matrix from multiple ST layers. PASTE outperforms integration methods that rely solely on either transcriptional similarity or spatial similarity, demonstrating the advantages of combining both types of information.

BackgroundCancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis.ResultsWe model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile to by the minimum number of events needed to transform into . Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum.ConclusionsFor the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances.Availability https://github.com/raphael-group/CNT-ILP Electronic supplementary materialThe online version of this article (doi:10.1186/s13015-017-0103-2) contains supplementary material, which is available to authorized users.

Tumors are highly heterogeneous, consisting of cell populations with both transcriptional and genetic diversity. These diverse cell populations are spatially organized within a tumor, creating a distinct tumor microenvironment. A new technology called spatial transcriptomics can measure spatial patterns of gene expression within a tissue by sequencing RNA transcripts from a grid of spots, each containing a small number of cells. In tumor cells, these gene expression patterns represent the combined contribution of regulatory mechanisms, which alter the rate at which a gene is transcribed, and genetic diversity, particularly copy number aberrations (CNAs) which alter the number of copies of a gene in the genome. CNAs are common in tumors and often promote cancer growth through upregulation of oncogenes or downregulation of tumor-suppressor genes. We introduce a new method STARCH (Spatial Transcriptomics Algorithm Reconstructing Copy-number Heterogeneity) to infer CNAs from spatial transcriptomics data. STARCH overcomes challenges in inferring CNAs from RNA-sequencing data by leveraging the observation that cells located nearby in a tumor are likely to share similar CNAs. We find that STARCH outperforms existing methods for inferring CNAs from RNA-sequencing data without incorporating spatial information.

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Problems of genome rearrangement are central in both evolution and cancer. Most evolutionary scenarios have been studied under the assumption that the genome contains a single copy of each gene. In contrast, tumor genomes undergo deletions and duplications, and thus, the number of copies of genes varies. The number of copies of each segment along a chromosome is called its copy number profile (CNP). Understanding CNP changes can assist in predicting disease progression and treatment. To date, questions related to distances between CNPs gained little scientific attention. Here we focus on the following fundamental problem, introduced by Schwarz et al.: given two CNPs, u and v, compute the minimum number of operations transforming u into v, where the edit operations are segmental deletions and amplifications. We establish the computational complexity of this problem, showing that it is solvable in linear time and constant space.