🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.000813s)

  1. Topological Data Analysis for Genomics and Evolution: Topology in Biology (2019)

    Raul Rabadan, Andrew J. Blumberg
    Abstract Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.

  2. 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.

  3. Multiscale Topology Classifies Cells in Subcellular Spatial Transcriptomics (2024)

    Katherine Benjamin, Aneesha Bhandari, Jessica D. Kepple, Rui Qi, Zhouchun Shang, Yanan Xing, Yanru An, Nannan Zhang, Yong Hou, Tanya L. Crockford, Oliver McCallion, Fadi Issa, Joanna Hester, Ulrike Tillmann, Heather A. Harrington, Katherine R. Bull
    Abstract Spatial transcriptomics measures in situ gene expression at millions of locations within a tissue1, hitherto with some trade-off between transcriptome depth, spatial resolution and sample size2. Although integration of image-based segmentation has enabled impactful work in this context, it is limited by imaging quality and tissue heterogeneity. By contrast, recent array-based technologies offer the ability to measure the entire transcriptome at subcellular resolution across large samples3–6. Presently, there exist no approaches for cell type identification that directly leverage this information to annotate individual cells. Here we propose a multiscale approach to automatically classify cell types at this subcellular level, using both transcriptomic information and spatial context. We showcase this on both targeted and whole-transcriptome spatial platforms, improving cell classification and morphology for human kidney tissue and pinpointing individual sparsely distributed renal mouse immune cells without reliance on image data. By integrating these predictions into a topological pipeline based on multiparameter persistent homology7–9, we identify cell spatial relationships characteristic of a mouse model of lupus nephritis, which we validate experimentally by immunofluorescence. The proposed framework readily generalizes to new platforms, providing a comprehensive pipeline bridging different levels of biological organization from genes through to tissues.