🍩 Database of Original & Non-Theoretical Uses of Topology
(found 4 matches in 0.002176s)
Current Theoretical Models Fail to Predict the Topological Complexity of the Human Genome (2015)Javier Arsuaga, Reyka G. Jayasinghe, Robert G. Scharein, Mark R. Segal, Robert H. Stolz, Mariel Vazquez
AbstractUnderstanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.
Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology (2015)Javier Arsuaga, Tyler Borrman, Raymond Cavalcante, Georgina Gonzalez, Catherine Park
AbstractDNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumor-driving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previously-presented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a two-dimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation of the data permits segmenting the data at different resolutions and identifying CNAs by interrogating the topological properties of these simplicial complexes. We tested our approach on a published dataset with the goal of identifying specific breast cancer CNAs associated with specific molecular subtypes. Identification of CNAs associated with each subtype was performed by analyzing each subtype separately from the others and by taking the rest of the subtypes as the control. Our results found a new amplification in 11q at the location of the progesterone receptor in the Luminal A subtype. Aberrations in the Luminal B subtype were found only upon removal of the basal-like subtype from the control set. Under those conditions, all regions found in the original publication, except for 17q, were confirmed; all aberrations, except those in chromosome arms 8q and 12q were confirmed in the basal-like subtype. These two chromosome arms, however, were detected only upon removal of three patients with exceedingly large copy number values. More importantly, we detected 10 and 21 additional regions in the Luminal B and basal-like subtypes, respectively. Most of the additional regions were either validated on an independent dataset and/or using GISTIC. Furthermore, we found three new CNAs in the basal-like subtype: a combination of gains and losses in 1p, a gain in 2p and a loss in 14q. Based on these results, we suggest that topological approaches that incorporate multiresolution analyses and that interrogate topological properties of the data can help in the identification of copy number changes in cancer.
Topological Analysis of Gene Expression Arrays Identifies High Risk Molecular Subtypes in Breast Cancer (2012)Javier Arsuaga, Nils A. Baas, Daniel DeWoskin, Hideaki Mizuno, Aleksandr Pankov, Catherine Park
AbstractGenomic technologies measure thousands of molecular signals with the goal of understanding complex biological processes. In cancer these molecular signals have been used to characterize disease subtypes, signaling pathways and to identify subsets of patients with specific prognosis. However molecular signals for any disease type are so vast and complex that novel mathematical approaches are required for further analyses. Persistent and computational homology provide a new method for these analyses. In our previous work we presented a new homology-based supervised classification method to identify copy number aberrations from comparative genomic hybridization arrays. In this work we first propose a theoretical framework for our classification method and second we extend our analysis to gene expression data. We analyze a published breast cancer data set and find that that our method can distinguish most, but not all, different breast cancer subtypes. This result suggests that specific relationships between genes, captured by our algorithm, help distinguish between breast cancer subtypes. We propose that topological methods can be used for the classification and clustering of gene expression profiles.