Biomolecular topology: modelling and analysis

With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structur...

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Main Authors: Liu, Jian, Xia, Ke-Lin, Wu, Jie, Yau, Stephen Shing-Toung, Wei, Guo-Wei
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
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Online Access:https://hdl.handle.net/10356/170357
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1703572023-09-08T08:16:13Z Biomolecular topology: modelling and analysis Liu, Jian Xia, Ke-Lin Wu, Jie Yau, Stephen Shing-Toung Wei, Guo-Wei School of Physical and Mathematical Sciences Science::Mathematics Biomolecular Topology Protein Structure With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structures, protein folding configurations, chromosomes, DNA origami, molecular assembly, to others at the macromolecular level, pose a severe challenge in their analysis and characterization. In the past few decades, mathematical concepts, models, algorithms, and tools from algebraic topology, combinatorial topology, computational topology, and topological data analysis, have demonstrated great power and begun to play an essential role in tackling the biomolecular data challenge. In this work, we introduce biomolecular topology, which concerns the topological problems and models originated from the biomolecular systems. More specifically, the biomolecular topology encompasses topological structures, properties and relations that are emerged from biomolecular structures, dynamics, interactions, and functions. We discuss the various types of biomolecular topology from structures (of proteins, DNAs, and RNAs), protein folding, and protein assembly. A brief discussion of databanks (and databases), theoretical models, and computational algorithms, is presented. Further, we systematically review related topological models, including graphs, simplicial complexes, persistent homology, persistent Laplacians, de Rham-Hodge theory, Yau-Hausdorff distance, and the topology-based machine learning models. Ministry of Education (MOE) Nanyang Technological University Ke-lin Xia is supported by Nanyang Technological University Startup Grant M4081842 and Singapore Ministry of Education Academic Research fund Tier 1 RG109/19, MOE-T2EP20120-0013 and MOE-T2EP20220-0010. 2023-09-08T08:16:13Z 2023-09-08T08:16:13Z 2022 Journal Article Liu, J., Xia, K., Wu, J., Yau, S. S. & Wei, G. (2022). Biomolecular topology: modelling and analysis. Acta Mathematica Sinica, English Series, 38(10), 1901-1938. https://dx.doi.org/10.1007/s10114-022-2326-5 1439-8516 https://hdl.handle.net/10356/170357 10.1007/s10114-022-2326-5 36407804 2-s2.0-85141442249 10 38 1901 1938 en M4081842 RG109/19 MOE-T2EP20120-0013 MOE-T2EP20220-0010 Acta Mathematica Sinica, English Series © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2022. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Biomolecular Topology
Protein Structure
spellingShingle Science::Mathematics
Biomolecular Topology
Protein Structure
Liu, Jian
Xia, Ke-Lin
Wu, Jie
Yau, Stephen Shing-Toung
Wei, Guo-Wei
Biomolecular topology: modelling and analysis
description With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structures, protein folding configurations, chromosomes, DNA origami, molecular assembly, to others at the macromolecular level, pose a severe challenge in their analysis and characterization. In the past few decades, mathematical concepts, models, algorithms, and tools from algebraic topology, combinatorial topology, computational topology, and topological data analysis, have demonstrated great power and begun to play an essential role in tackling the biomolecular data challenge. In this work, we introduce biomolecular topology, which concerns the topological problems and models originated from the biomolecular systems. More specifically, the biomolecular topology encompasses topological structures, properties and relations that are emerged from biomolecular structures, dynamics, interactions, and functions. We discuss the various types of biomolecular topology from structures (of proteins, DNAs, and RNAs), protein folding, and protein assembly. A brief discussion of databanks (and databases), theoretical models, and computational algorithms, is presented. Further, we systematically review related topological models, including graphs, simplicial complexes, persistent homology, persistent Laplacians, de Rham-Hodge theory, Yau-Hausdorff distance, and the topology-based machine learning models.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Liu, Jian
Xia, Ke-Lin
Wu, Jie
Yau, Stephen Shing-Toung
Wei, Guo-Wei
format Article
author Liu, Jian
Xia, Ke-Lin
Wu, Jie
Yau, Stephen Shing-Toung
Wei, Guo-Wei
author_sort Liu, Jian
title Biomolecular topology: modelling and analysis
title_short Biomolecular topology: modelling and analysis
title_full Biomolecular topology: modelling and analysis
title_fullStr Biomolecular topology: modelling and analysis
title_full_unstemmed Biomolecular topology: modelling and analysis
title_sort biomolecular topology: modelling and analysis
publishDate 2023
url https://hdl.handle.net/10356/170357
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