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 topol-ogy,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,inter-actions,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 system-atically review related topological models,including graphs,simplicial complexes,persistent homology,persistent Laplacians,de Rham-Hodge theory,Yau-Hausdorff distance,and the topology-based ma-chine learning models.

Jian LIU;Ke-Lin XIA;Jie WU;Stephen Shing-Toung YAU;Guo-Wei WEI

School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,P.R.China;Yanqi Lake Beijing Institute of Mathematical Sciences and Applications,Beijing 101408,P.R.China;School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore 639798;Department of Mathematical Sciences,Tsinghua University,Beijing 100084,P.R.China;Department of Mathematics&Department of Biochemistry and Molecular Biology&Department of Electrical and Computer Engineering,Michigan State University,Wells Hall 619 Red Cedar Road East Lansing,MI 48824-1027,US

数学学报（英文版）

[1]Jian LIU;Ke-Lin XIA;Jie WU;Stephen Shing-Toung YAU;Guo-Wei WEI-.Biomolecular Topology:Modelling and Analysis)[J].数学学报（英文版）,2022(10):1901-1938

topol,databanks,simplicial,Laplacians,Rham

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