Positional Information from Single Cell RNASeq Data via Manifold Learning

The connection between developmental cell fate and embryonic position has led many to propose that early gene expression patterns encode an intrinsic coordinate system within each cell. The spatial patterns of early developmental gene expression have been mapped out in several model systems, and recent work has addressed the inverse problem of inferring the position of a cell from its gene expression with the aid of pre-existing maps quantifying the expression of "marker" genes as a function of position. In our work, we pursue the goal of de novo inference of positional information, based on the assumption of continuity in gene expression space combined with the hypothesis that gene expression data approximately lies on a low dimensional manifold. Our method involves two stages: (i) a preliminary dimensional reduction step to de-noise the data and (ii) a machine learning algorithm to parameterize a low-dimensional manifold that approximates the high-dimensional sequencing data. We do not assume an isometry between the high-dimensional dataset and its low-dimensional representation; instead, we take a novel approach by enforcing monotonicity in neighborhood rankings. We verify our methods on early Drosophila embryos using FISH and scRNAseq data, finding good linear agreement between positional coordinates and our learned transcriptomic manifold.