🍩 Database of Original & Non-Theoretical Uses of Topology

(found 10 matches in 0.001655s)

  3. 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.

  4. 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.

  5. Delineation of a Conserved Arrestin-Biased Signaling Repertoire in Vivo (2015)

    Stuart Maudsley, Bronwen Martin, Diane Gesty-Palmer, Huey Cheung, Calvin Johnson, Shamit Patel, Kevin G. Becker, William H. Wood, Yongqing Zhang, Elin Lehrmann, Louis M. Luttrell
    Abstract Biased G protein–coupled receptor agonists engender a restricted repertoire of downstream events from their cognate receptors, permitting them to produce mixed agonist-antagonist effects in vivo. While this opens the possibility of novel therapeutics, it complicates rational drug design, since the in vivo response to a biased agonist cannot be reliably predicted from its in cellula efficacy. We have employed novel informatic approaches to characterize the in vivo transcriptomic signature of the arrestin pathway-selective parathyroid hormone analog [d-Trp12, Tyr34]bovine PTH(7-34) in six different murine tissues after chronic drug exposure. We find that [d-Trp12, Tyr34]bovine PTH(7-34) elicits a distinctive arrestin-signaling focused transcriptomic response that is more coherently regulated across tissues than that of the pluripotent agonist, human PTH(1-34). This arrestin-focused network is closely associated with transcriptional control of cell growth and development. Our demonstration of a conserved arrestin-dependent transcriptomic signature suggests a framework within which the in vivo outcomes of arrestin-biased signaling may be generalized.

  6. Histopathological Cancer Detection With Topological Signatures (2023)

    Ankur Yadav, Faisal Ahmed, Ovidiu Daescu, Reyhan Gedik, Baris Coskunuzer
    Abstract We present a transformative approach to histopathological cancer detection and grading by introducing a very powerful feature extraction method based on the latest topological data analysis tools. By analyzing the evolution of topological patterns in different color channels, we discovered that every tumor class leaves its own topological footprint in histopathological images, allowing to extract feature vectors that can be used to reliably identify tumor classes.Our topological signatures, even when combined with traditional machine learning methods, provide very fast and highly accurate results in various settings. While most DL models work well for one type of cancer, our model easily adapts to different scenarios, and consistently gives highly competitive results with the state-of-the-art models on benchmark datasets across multiple cancer types including bone, colon, breast, cervical (cytopathology), and prostate cancer. Unlike most DL models, our proposed Topo-ML model does not need any data augmentation or pre-processing steps and works perfectly on small datasets. The model is computationally very efficient, with end-to-end processing taking only a few hours for datasets consisting of thousands of images.

  7. Persistent Voids: A New Structural Metric for Membrane Fusion (2007)

    Peter M. Kasson, Afra Zomorodian, Sanghyun Park, Nina Singhal, Leonidas J. Guibas, Vijay S. Pande
    Abstract Motivation: Membrane fusion constitutes a key stage in cellular processes such as synaptic neurotransmission and infection by enveloped viruses. Current experimental assays for fusion have thus far been unable to resolve early fusion events in fine structural detail. We have previously used molecular dynamics simulations to develop mechanistic models of fusion by small lipid vesicles. Here, we introduce a novel structural measurement of vesicle topology and fusion geometry: persistent voids.Results: Persistent voids calculations enable systematic measurement of structural changes in vesicle fusion by assessing fusion stalk widths. They also constitute a generally applicable technique for assessing lipid topological change. We use persistent voids to compute dynamic relationships between hemifusion neck widening and formation of a full fusion pore in our simulation data. We predict that a tightly coordinated process of hemifusion neck expansion and pore formation is responsible for the rapid vesicle fusion mechanism, while isolated enlargement of the hemifusion diaphragm leads to the formation of a metastable hemifused intermediate. These findings suggest that rapid fusion between small vesicles proceeds via a small hemifusion diaphragm rather than a fully expanded one.Availability: Software available upon request pending public release.Contact:kasson@cmgm.stanford-edu or pande@stanford.eduSupplementary information: Supplementary data are available on Bioinformatics online.

  8. Omics-Based Strategies in Precision Medicine: Toward a Paradigm Shift in Inborn Errors of Metabolism Investigations (2016)

    Abdellah Tebani, Carlos Afonso, Stéphane Marret, Soumeya Bekri
    Abstract The rise of technologies that simultaneously measure thousands of data points represents the heart of systems biology. These technologies have had a huge impact on the discovery of next-generation diagnostics, biomarkers, and drugs in the precision medicine era. Systems biology aims to achieve systemic exploration of complex interactions in biological systems. Driven by high-throughput omics technologies and the computational surge, it enables multi-scale and insightful overviews of cells, organisms, and populations. Precision medicine capitalizes on these conceptual and technological advancements and stands on two main pillars: data generation and data modeling. High-throughput omics technologies allow the retrieval of comprehensive and holistic biological information, whereas computational capabilities enable high-dimensional data modeling and, therefore, accessible and user-friendly visualization. Furthermore, bioinformatics has enabled comprehensive multi-omics and clinical data integration for insightful interpretation. Despite their promise, the translation of these technologies into clinically actionable tools has been slow. In this review, we present state-of-the-art multi-omics data analysis strategies in a clinical context. The challenges of omics-based biomarker translation are discussed. Perspectives regarding the use of multi-omics approaches for inborn errors of metabolism (IEM) are presented by introducing a new paradigm shift in addressing IEM investigations in the post-genomic era.

  9. 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.

  10. Persistent Topology for Cryo-Em Data Analysis (2015)

    Kelin Xia, Guo-Wei Wei
    Abstract SummaryIn this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal-to-noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows that are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure Electron Microscopy Data (EMD 1129). Three helix models, an alpha-tubulin monomer model, an alpha-tubulin and beta-tubulin model, and an alpha-tubulin and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another, play little role in the traditional density fitting or optimization but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is topologically favored. The present work offers persistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems. Copyright © 2015 John Wiley & Sons, Ltd.