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The shape of things to come: Topological data analysis and biology, from molecules to organisms
Author(s) -
Amézquita Erik J.,
Quigley Michelle Y.,
Ophelders Tim,
Munch Elizabeth,
Chitwood Daniel H.
Publication year - 2020
Publication title -
developmental dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.634
H-Index - 141
eISSN - 1097-0177
pISSN - 1058-8388
DOI - 10.1002/dvdy.175
Subject(s) - topological data analysis , biology , similarity (geometry) , measure (data warehouse) , function (biology) , persistent homology , limiting , topology (electrical circuits) , computational biology , computer science , data mining , evolutionary biology , artificial intelligence , mathematics , algorithm , combinatorics , mechanical engineering , engineering , image (mathematics)
Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub‐disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data‐driven era where the meaningful interpretation of large data sets is a limiting factor.