Inferring geometric embeddings for single cell data

Massively multiplexed sequencing of RNA in individual cells is transforming basic and clinical life sciences. However, in standard experiments sequenced cells do not retain information about their original spatial context although it is crucial for understanding cellular function. Recent attempts to overcome this fundamental problem rely on employing additional imaging data which can guide spatial mapping. Here we present a conceptually different approach that allows to reconstruct spatial positions of cells in a variety of tissues without using reference imaging data. We first show for several complex biological systems that distances of single cells in expression space monotonically increase with their distances across tissues. We therefore seek to map cells to tissue space such that this principle is optimally preserved, while incorporating imaging data when available. We show that this optimization problem can be cast as an optimal transport problem and solved efficiently. We apply our approach successfully to reconstruct the mammalian liver and intestinal epithelium as well as the fly embryo. Our results demonstrate a simple spatial expression organization principle that can be used to infer meaningful spatial position probabilities from the sequencing data alone.