1,331 research outputs found
Inference of Ancestral Recombination Graphs through Topological Data Analysis
The recent explosion of genomic data has underscored the need for
interpretable and comprehensive analyses that can capture complex phylogenetic
relationships within and across species. Recombination, reassortment and
horizontal gene transfer constitute examples of pervasive biological phenomena
that cannot be captured by tree-like representations. Starting from hundreds of
genomes, we are interested in the reconstruction of potential evolutionary
histories leading to the observed data. Ancestral recombination graphs
represent potential histories that explicitly accommodate recombination and
mutation events across orthologous genomes. However, they are computationally
costly to reconstruct, usually being infeasible for more than few tens of
genomes. Recently, Topological Data Analysis (TDA) methods have been proposed
as robust and scalable methods that can capture the genetic scale and frequency
of recombination. We build upon previous TDA developments for detecting and
quantifying recombination, and present a novel framework that can be applied to
hundreds of genomes and can be interpreted in terms of minimal histories of
mutation and recombination events, quantifying the scales and identifying the
genomic locations of recombinations. We implement this framework in a software
package, called TARGet, and apply it to several examples, including small
migration between different populations, human recombination, and horizontal
evolution in finches inhabiting the Gal\'apagos Islands.Comment: 33 pages, 12 figures. The accompanying software, instructions and
example files used in the manuscript can be obtained from
https://github.com/RabadanLab/TARGe
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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
Rewriting Systems and the Modelling of Biological Systems
This paper gives a brief survey of the use of algebraic rewriting systems for modelling
and simulating various biological processes, particularly at the cellular level
Tangled Up: Womenās Experiences in Mathematics
This thesis is a bridge between two disciplines: Women\u27s, Gender, and Sexuality Studies, and Mathematics. The first portion of the work synthesizes both theory and previously done studies to describe the state of women in mathematics as a whole, as well as historicizing the role of women in mathematics. Obstacles to the full and equal participation of women in mathematics are examined through a feminist lens. The second part of the thesis is a feminist biography crafted from an interview with a professor of mathematics, Dr. Erica Flapan. This provides information about her personal experiences as a woman in mathematics education in the late 1970s and early 1980s, and her perception of the field today and the status of women within it. Finally, the topological work of this professor is examined. This section introduces and explains some basics of knot theory and then begins to explore the work of Dr. Flapan in applications of knot theory to DNA in the process of site-specific recombination
P systems and computational algebraic topology
Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P systems. In this paper we calculate some algebraic-topological information of 2D and 3D images in a general and parallel manner using P systems. First, we present a new way to obtain the homology groups of 2D digital images in time logarithmic with respect to the input data involving an improvement with respect to the algorithms development by S. Peltier et al. Second, we obtain an edge-segmentation of 2D and 3D digital images in constant time with respect to the input data
Equation of state for polymer liquid crystals: theory and experiment
The first part of this paper develops a theory for the free energy of
lyotropic polymer nematic liquid crystals. We use a continuum model with
macroscopic elastic moduli for a polymer nematic phase. By evaluating the
partition function, considering only harmonic fluctuations, we derive an
expression for the free energy of the system. We find that the configurational
entropic part of the free energy enhances the effective repulsive interactions
between the chains. This configurational contribution goes as the fourth root
of the direct interactions. Enhancement originates from the coupling between
bending fluctuations and the compressibility of the nematic array normal to the
average director. In the second part of the paper we use osmotic stress to
measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl
solutions. These measurements cover 5 orders of magnitude in DNA osmotic
pressure. At high osmotic pressures the equation of state, dominated by
exponentially decaying hydration repulsion, is independent of the ionic
strength. At lower pressures the equation of state is dominated by fluctuation
enhanced electrostatic double layer repulsion. The measured equation of state
for DNA fits well with our theory for all salt concentrations. We are able to
extract the strength of the direct electrostatic double layer repulsion. This
is a new and alternative way of measuring effective charge densities along
semiflexible polyelectrolytes.Comment: text + 5 figures. Submitted to PR
Translational Oncogenomics and Human Cancer Interactome Networks
An overview of translational, human oncogenomics, transcriptomics and cancer interactomic networks is presented together with basic concepts and potential, new applications to Oncology and Integrative Cancer Biology. Novel translational oncogenomics research is rapidly expanding through the application of advanced technology, research findings and computational tools/models to both pharmaceutical and clinical problems. A self-contained presentation is adopted that covers both fundamental concepts and the most recent biomedical, as well as clinical, applications. Sample analyses in recent clinical studies have shown that gene expression data can be employed to distinguish between tumor types as well as to predict outcomes. Potentially important applications of such results are individualized human cancer therapies or, in general, ‘personalized medicine’. Several cancer detection techniques are currently under development both in the direction of improved detection sensitivity and increased time resolution of cellular events, with the limits of single molecule detection and picosecond time resolution already reached. The urgency for the complete mapping of a human cancer interactome with the help of such novel, high-efficiency / low-cost and ultra-sensitive techniques is also pointed out
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Topology of Reticulate Evolution
The standard representation of evolutionary relationships is a bifurcating tree. However, many types of genetic exchange, collectively referred to as reticulate evolution, involve processes that cannot be modeled as trees. Increasing genomic data has pointed to the prevalence of reticulate processes, particularly in microorganisms, and underscored the need for new approaches to capture and represent the scale and frequency of these events.
This thesis contains results from applying new techniques from applied and computational topology, under the heading topological data analysis, to the problem of characterizing reticulate evolution in molecular sequence data. First, we develop approaches for analyzing sequence data using topology. We propose new topological constructions specific to molecular sequence data that generalize standard constructions such as Vietoris-Rips. We draw on previous work in phylogenetic networks and use homology to provide a quantitative measure of reticulate events. We develop methods for performing statistical inference using topological summary statistics.
Next, we apply our approach to several types of molecular sequence data. First, we examine the mosaic genome structure in phages. We recover inconsistencies in existing morphology-based taxonomies, use a network approach to construct a genome-based representation of phage relationships, and identify conserved gene families within phage populations. Second, we study influenza, a common human pathogen. We capture widespread patterns of reassortment, including nonrandom cosegregation of segments and barriers to subtype mixing. In contrast to traditional influenza studies, which focus on the phylogenetic branching patterns of only the two surface-marker proteins, we use whole-genome data to represent influenza molecular relationships. Using this representation, we identify unexpected relationships between divergent influenza subtypes. Finally, we examine a set of pathogenic bacteria. We use two sources of data to measure rates of reticulation in both the core genome and the mobile genome across a range of species. Network approaches are used to represent the population of S. aureus and analyze the spread of antibiotic resistance genes. The presence of antibiotic resistance genes in the human microbiome is investigated
Designer Gene Networks: Towards Fundamental Cellular Control
The engineered control of cellular function through the design of synthetic
genetic networks is becoming plausible. Here we show how a naturally occurring
network can be used as a parts list for artificial network design, and how
model formulation leads to computational and analytical approaches relevant to
nonlinear dynamics and statistical physics.Comment: 35 pages, 8 figure
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