Quantitative Approaches to the Genomics of Clonal Evolution

Many problems in the biological sciences reduce to questions of genetic evolution. Entire classes of medical pathology, such as malignant neoplasia or infectious disease, can be viewed in the light of Darwinian competition of genomes. With the benefit of today's maturing sequencing technologies we can observe and quantify genetic evolution with nucleotide resolution. This provides a molecular view of genetic material that has adapted, or is in the process of adapting, to its local selection pressures. A series of problems will be discussed in this thesis, all involving the mathematical modeling of genomic data derived from clonally evolving populations. We use a variety of computational approaches to characterize over-represented features in the data, with the underlying hypothesis that we may be detecting fitness-conferring features of the biology. In Part I we consider the cross-sectional sampling of human tumors via RNA-sequencing, and devise computational pipelines for detecting oncogenic gene fusions and oncovirus infections. Genomic translocation and oncovirus infection can each be a highly penetrant alteration in a tumor's evolutionary history, with famous examples of both populating the cancer biology literature. In order to exert a transforming influence over the host cell, gene fusions and viral genetic programs need to be expressed and thus can be detected via whole transcriptome sequencing of a malignant cell population. We describe our approaches to predicting oncogenic gene fusions (Chapter 2) and quantifying host-viral interactions (Chapter 3) in large panels of human tumor tissue. The alterations that we characterize prompt the larger question of how the genetics of tumors and viruses might vary in time, leading us to the study of serially sampled populations. In Part II we consider longitudinal sampling of a clonally evolving population. Phylogenetic trees are the standard representation of a clonal process, an evolutionary picture as old as Darwin's voyages on the Beagle. Chapter 4 first reviews phylogenetic inference and then introduces a certain phylogenetic tree space that forms the starting point of our work on the topic. Specifically, Chapter 4 describes the construction of our projective tree space along with an explicit implementation for visualizing point clouds of rescaled trees. The Chapter finishes by defining a method for stable dimensionality reduction of large phylogenies, which is useful for analyzing long genomic time series. In Chapter 5 we consider medically relevant instances of clonal evolution and the longitudinal genetic data sets to which they give rise. We analyze data from (i) the sequencing of cancers along their therapeutic course, (ii) the passaging of a xenografted tumor through a mouse model, and (iii) the seasonal surveillance of H3N2 influenza's hemagglutinin segment. A novel approach to predicting influenza vaccine effectiveness is demonstrated using statistics of point clouds in tree spaces. Our investigations into clonal processes may be extended beyond naturally occurring genomes. In Part III we focus on the directed clonal evolution of populations of synthetic RNAs in vitro. Analogous to the selection pressures exerted upon malignant cells or viral particles, these synthetic RNA genomes can be evolved against a desired fitness objective. We investigate fitness objectives related to reprogramming ribosomal translation. Chapter 6 identifies high fitness RNA pseudoknot geometries capable of inducing ribosomal frameshift, while Chapter 7 takes an unbiased approach to evolving sequence and structural elements that promote stop codon readthrough