Network and Algebraic Topology of Influenza Evolution

Evolution is a force that has molded human existence since its divergence from chimpanzees about 5.4 million years ago. In that same amount of time, an influenza virus, which replicates every six hours, would have undergone an equivalent number of generations over only a hundred years. The fast replication times of influenza, coupled with its high mutation rate, make the virus a perfect model to study real-time evolution at a mega-Darwin scale, more than a million times faster than human evolution. While recent developments in high-throughput sequencing provide an optimal opportunity to dissect their genetic evolution, a concurrent growth in computational tools is necessary to analyze the large influx of complex genomic data. In my thesis, I present novel computational methods to examine different aspects of influenza evolution. I first focus on seasonal influenza, particularly the problems that hamper public health initiatives to combat the virus. I introduce two new approaches: 1. The q2-coefficient, a method of quantifying pathogen surveillance, and 2. FluGraph, a technique that employs network topology to track the spread of seasonal influenza around the world. The second chapter of my thesis examines how mutations and reassortment combine to alter the course of influenza evolution towards pandemic formation. I highlight inherent deficiencies in the current phylogenetic paradigm for analyzing evolution and offer a novel methodology based on algebraic topology that comprehensively reconstructs both vertical and horizontal evolutionary events. I apply this method to viruses, with emphasis on influenza, but foresee broader application to cancer cells, bacteria, eukaryotes, and other taxa