Lineage Tracing and Manifold Curvature Estimation for Single-Cell Transcriptomics

Abstract

In the first half of this dissertation, an engineered mouse system is described that enables simultaneous readout of recorded lineage histories and full gene expression profiles in single cells. This system uses inducibly expressed Cas9 to stochastically cleave a synthetic target array at a transcribed locus, generating up to 44,000 unique and heritable barcodes. It can be activated at any point in development or adulthood and sequential, pulsed induction results in an accrual of barcode mutations that can be used to determine cellular phylogeny in vivo across a wide range of tissues. These barcodes can be read out efficiently using established single-cell RNA sequencing (scRNAseq) protocols and analyzed using a companion bioinformatics pipeline. Applying this system in embryonic mice unearthed previously unappreciated biases in the expansion patterns of hematopoietic stem cells (HSCs) across different bones. In adult mice subject to myeloablation, blood replenishment was determined to be driven by a few highly active HSCs. By comparing the gene expression profiles of these highly active HSCs to other quiescent HSCs, a transcriptional signature was identified, which included genes associated with HSC activity and previously unidentified potential mediators of quiescence. This is the first time a lineage tracing model has been used to uncover molecular drivers of functional heterogeneity in cellular populations.

In the second half of this dissertation, two approaches are described to estimate the Riemannian curvature of a manifold from a set of sampled datapoints. The first approach uses the Laplace-Beltrami operator, a central tool in intrinsic differential geometry, but is shown to be inaccurate when applied to even constant-curvature manifolds for sample sizes commensurate with current scRNAseq datasets. In contrast, an algorithm using tools from extrinsic differential geometry is presented that can accurately estimate point-wise curvature with controlled error for the same sample size. Furthermore, this algorithm is shown to be robust to non-uniform sampling, reasonable observational noise and high ambient dimension. When applied to scRNAseq datasets, localized regions of non-zero scalar curvature are detected, motivating the development of non-linear dimensionality reduction and visualization tools, which explicitly aim to preserve such non-trivial intrinsic geometry in data manifolds.