🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.001223s)

  1. Identification of Relevant Genetic Alterations in Cancer Using Topological Data Analysis (2020)

    Raúl Rabadán, Yamina Mohamedi, Udi Rubin, Tim Chu, Adam N. Alghalith, Oliver Elliott, Luis Arnés, Santiago Cal, Álvaro J. Obaya, Arnold J. Levine, Pablo G. Cámara
    Abstract Large-scale cancer genomic studies enable the systematic identification of mutations that lead to the genesis and progression of tumors, uncovering the underlying molecular mechanisms and potential therapies. While some such mutations are recurrently found in many tumors, many others exist solely within a few samples, precluding detection by conventional recurrence-based statistical approaches. Integrated analysis of somatic mutations and RNA expression data across 12 tumor types reveals that mutations of cancer genes are usually accompanied by substantial changes in expression. We use topological data analysis to leverage this observation and uncover 38 elusive candidate cancer-associated genes, including inactivating mutations of the metalloproteinase ADAMTS12 in lung adenocarcinoma. We show that ADAMTS12−/− mice have a five-fold increase in the susceptibility to develop lung tumors, confirming the role of ADAMTS12 as a tumor suppressor gene. Our results demonstrate that data integration through topological techniques can increase our ability to identify previously unreported cancer-related alterations., Rare cancer mutations are often missed using recurrence-based statistical approaches, but are usually accompanied by changes in expression. Here the authors leverage this information to uncover several elusive candidate cancer-associated genes using topological data analysis.

  2. Inference of Ancestral Recombination Graphs Through Topological Data Analysis (2016)

    Pablo G. Cámara, Arnold J. Levine, Raúl Rabadán
    Abstract 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 Galápagos Islands., Evolution occurs through different mechanisms, including point mutations, gene duplication, horizontal gene transfer, and recombinations. Some of these mechanisms cannot be captured by tree graphs. We present a framework, based on the mathematical tools of computational topology, that can explicitly accommodate both recombination and mutation events across the evolutionary history of a sample of genomic sequences. This approach generates a new type of summary graph and algebraic structures that provide quantitative information on the evolutionary scale and frequency of recombination events. The accompanying software, TARGet, is applied to several examples, including migration between sexually-reproducing populations, human recombination, and recombination in Darwin’s finches.

  3. Single-Cell Topological RNA-Seq Analysis Reveals Insights Into Cellular Differentiation and Development (2017)

    Abbas H. Rizvi, Pablo G. Camara, Elena K. Kandror, Thomas J. Roberts, Ira Schieren, Tom Maniatis, Raul Rabadan
    Abstract Transcriptional programs control cellular lineage commitment and differentiation during development. Understanding cell fate has been advanced by studying single-cell RNA-seq, but is limited by the assumptions of current analytic methods regarding the structure of data. We present single-cell topological data analysis (scTDA), an algorithm for topology-based computational analyses to study temporal, unbiased transcriptional regulation. Compared to other methods, scTDA is a non-linear, model-independent, unsupervised statistical framework that can characterize transient cellular states. We applied scTDA to the analysis of murine embryonic stem cell (mESC) differentiation in vitro in response to inducers of motor neuron differentiation. scTDA resolved asynchrony and continuity in cellular identity over time, and identified four transient states (pluripotent, precursor, progenitor, and fully differentiated cells) based on changes in stage-dependent combinations of transcription factors, RNA-binding proteins and long non-coding RNAs. scTDA can be applied to study asynchronous cellular responses to either developmental cues or environmental perturbations.

  4. Topological Data Analysis Generates High-Resolution, Genome-Wide Maps of Human Recombination (2016)

    Pablo G. Camara, Daniel I. S. Rosenbloom, Kevin J. Emmett, Arnold J. Levine, Raul Rabadan
    Abstract Meiotic recombination is a fundamental evolutionary process driving diversity in eukaryotes. In mammals, recombination is known to occur preferentially at specific genomic regions. Using topological data analysis (TDA), a branch of applied topology that extracts global features from large data sets, we developed an efficient method for mapping recombination at fine scales. When compared to standard linkage-based methods, TDA can deal with a larger number of SNPs and genomes without incurring prohibitive computational costs. We applied TDA to 1,000 Genomes Project data and constructed high-resolution whole-genome recombination maps of seven human populations. Our analysis shows that recombination is generally under-represented within transcription start sites. However, the binding sites of specific transcription factors are enriched for sites of recombination. These include transcription factors that regulate the expression of meiosis- and gametogenesis-specific genes, cell cycle progression, and differentiation blockage. Additionally, our analysis identifies an enrichment for sites of recombination at repeat-derived loci matched by piwi-interacting RNAs.