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Entropy
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Applications of Topological Data Analysis in the Life Sciences
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Applications of Topological Data Analysis in the Life Sciences

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Signal and Data Analysis".

Deadline for manuscript submissions: closed (15 April 2022) | Viewed by 7726

Special Issue Editors

Prof. Dr. Kathryn Hess Bellwald

E-Mail Website
Guest Editor
SV BMI UPHESS, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Interests: algebraic topology; applications of topology in life sciences; category theory
Prof. Dr. Pablo G. Camara

E-Mail Website
Guest Editor
Department of Genetics and Institute for Biomedical Informatics, University of Pennsylvania, Philadelphia, PA 19104, USA
Interests: computational biology; single-cell biology; cancer genomics; topology and metric geometry applications

Special Issue Information

Topological data analysis (TDA) is a relatively new field of research, at the intersection of data science and algebraic topology, and it provides robust mathematical, statistical, and algorithmic methods to infer, analyze, and interpret the topological and geometric structures underlying complex data. TDA provides a set of powerful, efficient tools that can be used in combination with other data science methods. TDA techniques are applied primarily to point clouds in metric spaces, but can also be extended to geometric objects such as graphs. TDA has convincingly proved its utility in a wide range of applications in the life sciences, including in neuroscience, genomics, proteomics, evolution, and cancer biology, among other areas of research. Given these recent successes, the time is ripe for this Special Issue, devoted to surveying the remarkable insights into life sciences that have already been provided by TDA, and to explore promising new developments.

Prof. Dr. Kathryn Hess Bellwald
Prof. Dr. Pablo G. Camara
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topological data analysis
  • genomics
  • proteomics
  • neuroscience
  • cancer biology
  • developmental biology
  • metabolomics

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Published Papers (2 papers)

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Research

29 pages, 8277 KiB  
Article
Multiscale Methods for Signal Selection in Single-Cell Data
by Renee S. Hoekzema, Lewis Marsh, Otto Sumray, Thomas M. Carroll, Xin Lu, Helen M. Byrne and Heather A. Harrington
Entropy 2022, 24(8), 1116; https://doi.org/10.3390/e24081116 - 13 Aug 2022
Cited by 3 | Viewed by 3577
Abstract
Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not [...] Read more.
Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores (eigi) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them. Full article
(This article belongs to the Special Issue Applications of Topological Data Analysis in the Life Sciences)
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30 pages, 4404 KiB  
Article
TAaCGH Suite for Detecting Cancer—Specific Copy Number Changes Using Topological Signatures
by Jai Aslam, Sergio Ardanza-Trevijano, Jingwei Xiong, Javier Arsuaga and Radmila Sazdanovic
Entropy 2022, 24(7), 896; https://doi.org/10.3390/e24070896 - 29 Jun 2022
Cited by 2 | Viewed by 2157
Abstract
Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable [...] Read more.
Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris–Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A. These segments are validated by the TCGA BRCA cohort dataset except for those found for Luminal A. Full article
(This article belongs to the Special Issue Applications of Topological Data Analysis in the Life Sciences)
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