Abstract
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.
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Dedicated to Professor Banghe Li on His 80th Birthday
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. Guo-Wei Wei is supported by NIH grant GM126189, and NSF grants DMS-2052983, DMS-1761320, and IIS-1900473. Jie Wu and Jian Liu are supported by Natural Science Foundation of China (NSFC) grant (11971144), High-level Scientific Research Foundation of Hebei Province and the Start-up Research Fund from Yanqi Lake Beijing Institute of Mathematical Sciences and Applications. Jian Liu is also supported by Tianjin Natural Science Foundation (Grant No. 19JCYBJC30200). Stephen Shing-Toung Yau is supported by National Natural Science Foundation of China (NSFC) grant (12171275), Tsinghua University Spring Breeze Fund (2020Z99CFY044), Tsinghua University Start-up Fund, and Tsinghua University Education Foundation fund (042202008). Professor Stephen Shing-Toung Yau is grateful to the National Center for Theoretical Sciences (NCTS) for providing an excellent research environment while part of this research was done
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Liu, J., Xia, KL., Wu, J. et al. Biomolecular Topology: Modelling and Analysis. Acta. Math. Sin.-English Ser. 38, 1901–1938 (2022). https://doi.org/10.1007/s10114-022-2326-5
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DOI: https://doi.org/10.1007/s10114-022-2326-5