🍩 Database of Original & Non-Theoretical Uses of Topology

(found 7 matches in 0.002853s)
  1. From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives (2020)

    Lida Kanari, Adélie Garin, Kathryn Hess
    Abstract Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this article we study in detail the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm, gaining both theoretical and computational insights into the relation between the two. We propose a new approach to classify barcodes using symmetric groups, which provides a concrete language to formulate our results. We investigate to what extent the TNS recovers a geometric tree from its TMD and describe the effect of different types of noise on the process of tree generation from persistence diagrams. We prove moreover that the TNS algorithm is stable with respect to specific types of noise.
  2. Two-Tier Mapper, an Unbiased Topology-Based Clustering Method for Enhanced Global Gene Expression Analysis (2019)

    Rachel Jeitziner, Mathieu Carrière, Jacques Rougemont, Steve Oudot, Kathryn Hess, Cathrin Brisken
    Abstract MOTIVATION: Unbiased clustering methods are needed to analyze growing numbers of complex datasets. Currently available clustering methods often depend on parameters that are set by the user, they lack stability, and are not applicable to small datasets. To overcome these shortcomings we used topological data analysis, an emerging field of mathematics that discerns additional feature and discovers hidden insights on datasets and has a wide application range. RESULTS: We have developed a topology-based clustering method called Two-Tier Mapper (TTMap) for enhanced analysis of global gene expression datasets. First, TTMap discerns divergent features in the control group, adjusts for them, and identifies outliers. Second, the deviation of each test sample from the control group in a high-dimensional space is computed, and the test samples are clustered using a new Mapper-based topological algorithm at two levels: a global tier and local tiers. All parameters are either carefully chosen or data-driven, avoiding any user-induced bias. The method is stable, different datasets can be combined for analysis, and significant subgroups can be identified. It outperforms current clustering methods in sensitivity and stability on synthetic and biological datasets, in particular when sample sizes are small; outcome is not affected by removal of control samples, by choice of normalization, or by subselection of data. TTMap is readily applicable to complex, highly variable biological samples and holds promise for personalized medicine. AVAILABILITY AND IMPLEMENTATION: TTMap is supplied as an R package in Bioconductor. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
  3. The Architecture of the Endoplasmic Reticulum Is Regulated by the Reversible Lipid Modification of the Shaping Protein CLIMP-63 (2018)

    Patrick A. Sandoz, Robin A. Denhardt-Eriksson, Laurence Abrami, Luciano Abriata, Gard Spreemann, Catherine Maclachlan, Sylvia Ho, Béatrice Kunz, Kathryn Hess, Graham Knott, Vassily Hatzimanikatis, F. Gisou van der Goot
    Abstract \textlessh3\textgreaterAbstract\textless/h3\textgreater \textlessp\textgreaterThe endoplasmic reticulum (ER) has a complex morphology generated and maintained by membrane-shaping proteins and membrane energy minimization, though not much is known about how it is regulated. The architecture of this intracellular organelle is balanced between large, thin sheets that are densely packed in the perinuclear region and a connected network of branched, elongated tubules that extend throughout the cytoplasm. Sheet formation is known to involve the cytoskeleton-linking membrane protein 63 (CLIMP-63), though its regulation and the depth of its involvement remain unknown. Here we show that the post-translational modification of CLIMP-63 by the palmitoyltransferase ZDHHC6 controls the relative distribution of CLIMP-63 between the ER and the plasma membrane. By combining data-driven mathematical modeling, predictions, and experimental validation, we found that the attachment of a medium chain fatty acid, so-called S-palmitoylation, to the unique CLIMP-63 cytoplasmic cysteine residue drastically reduces its turnover rate, and thereby controls its abundance. Light microscopy and focused ion beam electron microcopy further revealed that enhanced CLIMP-63 palmitoylation leads to strong ER-sheet proliferation. Altogether, we show that ZDHHC6-mediated S-palmitoylation regulates the cellular localization of CLIMP-63, the morphology of the ER, and the interconversion of ER structural elements in mammalian cells through its action on the CLIMP-63 protein.\textless/p\textgreater\textlessh3\textgreaterSignificance Statement\textless/h3\textgreater \textlessp\textgreaterEukaryotic cells subcompartmentalize their various functions into organelles, the shape of each being specific and necessary for its proper role. However, how these shapes are generated and controlled is poorly understood. The endoplasmic reticulum is the largest membrane-bound intracellular compartment, accounting for more than 50% of all cellular membranes. We found that the shape and quantity of its sheet-like structures are controlled by a specific protein, cytoskeleton-linking membrane protein 63, through the acquisition of a lipid chain attached by an enzyme called ZDHHC6. Thus, by modifying the ZDHHC6 amounts, a cell can control the shape of its ER. The modeling and prediction technique used herein also provides a method for studying the interconnected function of other post-translational modifications in organelles.\textless/p\textgreater
  4. Cliques of Neurons Bound Into Cavities Provide a Missing Link Between Structure and Function (2017)

    Michael W. Reimann, Max Nolte, Martina Scolamiero, Katharine Turner, Rodrigo Perin, Giuseppe Chindemi, Paweł Dłotko, Ran Levi, Kathryn Hess, Henry Markram
    Abstract The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission into account, constructing graphs of a network that reflect the direction of information flow, and analyzing these directed graphs using algebraic topology. Applying this approach to a local network of neurons in the neocortex revealed a remarkably intricate and previously unseen topology of synaptic connectivity. The synaptic network contains an abundance of cliques of neurons bound into cavities that guide the emergence of correlated activity. In response to stimuli, correlated activity binds synaptically connected neurons into functional cliques and cavities that evolve in a stereotypical sequence towards peak complexity. We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities.