Members Research Teaching Activities


Welcome to Xia's research group of Molecular Based Mathematical Biology at the School of Physical and Mathematical Sciences, School of Biological Sciences in Nanyang Technological University (NTU) in Singapore!

The last century has witnessed the tremendous advancement of Biological Sciences. The availability of massive biological data, high-performance computers, efficient computational algorithms, and  mathematical and physical models have paved the way for Biological Sciences to undertake a historic transition from being qualitative, phenomenological, and descriptive to being quantitative, analytical, and predictive. Under this transition, modern Mathematical Biology will be fundamentally changed from macroscale modelings (of species, population, disease, blood fluid, etc) to molecular based analysis (of protein, DNA, gene, virus, etc). A brief introduction of the Molecular Based Mathematical Biology can be found in SIAM news Sep 2016, Dec 2017, and Prof Wei's Harvard talk.

Our group focuses on Molecular Based Mathematical Biology. We use computational tools from PDE, Differential Geometry, Algebraic Topology and Statistical Learning to study the biomolecular structure, flexibility, dynamics, and functions. In particular, we are interested in topology based machine learning for biomolecular data analysis and chromosome hierarchical structures. We sincerely welcome highly motivated students and postdocs to join our group.

Principal Investigator

Kelin_Xia Kelin Xia (Google Scholar Profile; Reseacher ID; CV)

Assistant Professor,
School of Physical and Mathematical Sciences,
School of Biological Sciences,
Nanyang Technological University

SPMS-MAS-05-18, 21 Nanyang Link, Singapore 637371
Phone:  +65 6513-7464
Email: xiakelin@ntu.edu.sg

Research Interests
Grants and Research Funds

 (After joining NTU)
  • PI, MOE AcRF Tier 2,"Persistent homology based topological approaches for biomolecular data analysis", 2018-2021
  • PI, MOE AcRF Tier 1, "Modeling and analyzing environmental effects and self-assembly mechanism of large-sized biomolecules", 2018-2020
  • PI, MOE AcRF Tier 1, "A unified framework for multiscale geometric modeling of biomolecular complex", 2017-2019
  • Co-PI, ASPIRE League Research Grant, "Functional Design of Protein Cage for Sustainable Bionanomaterial", 2017-2018
  • PI, NTU-SUG, "Geometric and topological modeling of biomolecular structure, dynamics and function", 2016-2021
 (Before joining NTU)
  • Co-PI (PI: Guo-Wei Wei), National Science Foundation, DMS-1160352, "FRG: Collaborative research: Variational multiscale approaches to biomolecular structure, dynamics and transport", 09/2012-08/2015. 
  • Co-PI (PI: Guo-Wei Wei), NIH/NIGMS, 3R01GM090208-04S1, "Geometric flow approach to implicit solvation modeling", 07/2014-062015
Publication list

(After joining NTU)
Under Review
40. Chi Seng Pun, Kelin Xia, Si Xian Lee, "Persistent Homology based Machine Learning and its Applications – A Survey", arXiv (2018)
39. Jiajie Peng, Jinjin Yang, Kelin Xia, "Flexibility and rigidity index for chromosome packing, flexibility and dynamics analysis", bioRxiv (2018)
38. Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia,"Weighted fundamental group", arXiv (2018)
37. Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia,"Weighted (Co)homology and Weighted Laplacian", arXiv (2018)
36. Kelin Xia, Guowei Wei, "A review of geometric, topological and graph theory apparatuses for the modeling and analysis of biomolecular data", arXiv  (2018)
35. Kelin Xia,"Persistent similarity for biomolecular structure comparison", Comunications in information and systems, 18 (4), 251-280 (2018)
34. Kelin Xia, "Persistent homology analysis of ion aggregation and hydrogen-bonding network", Physical Chemistry Chemical Physics, 20, 13448-13460 (2018)
33. Kelin Xia, "Sequence-based Multiscale Modeling for high-throughput Chromosome Conformation Capture (Hi-C) Data Analysis",  PLOS ONE, 13(2), 0191899  (2018)
32. Kelin Xia, "Multiscale virtual particle based elastic network model (MVP-ENM) for biomolecular normal mode analysis" , Physical Chemistry Chemical Physics, 20(1), 658-669 (2018)
31. Kelin Xia, Zhiming Li, Lin Mu, "Multiscale persistent functions for biomolecular structure characterization", Bulletin of Mathematical Biology, 80(1),1-31 (2018)
30. Yin Cao, Bao Wang, Kelin Xia and Guo-Wei Wei, "Finite volume formulation of the MIB method for elliptic interface problems", Journal of Computational and  Applied Mathematics, 321, 60-77 (2017)
29. Lin Mu,Kelin Xia, Guowei Wei, "Geometric and electrostatic modeling using molecular rigidity functions", Journal of Computational and  Applied Mathematics, 313, 18-37 (2017)
28. Duc D Nguyen, Kelin Xia and Guo-Wei Wei, "Generalized flexibility-rigidity index", Journal of Chemical Physics, 144, 234106 (2016). 

27. Kristopher Opron, Kelin Xia, Zachary F. Burton and Guo-Wei Wei, "Flexibility-rigidity index for protein-nucleic acid flexibility and fluctuation analysis", Journal of Computational Chemistry, 37, 1283-1295 (2016).

(Before joining NTU)
26. Zixuan Cang, Lin Mu, Kedi Wu, Kristopher Opron, Kelin Xia and Guo-Wei Wei, "A topological approach to protein classification", Molecular Based Mathematical Biology, 3, 140-162 (2015). PDF
25. Kelin Xia, Kristopher Opron and Guo-Wei Wei, "Multiscale Gaussian network model (mGNM) and multiscale anisotropic network  model (mANM)", Journal of Chemical Physics, 143, 204106(2015). PDF
24. Kelin Xia, Zhixiong Zhao and Guo-Wei Wei, "Multiresolution persistent homology for excessively large biomolecular datasets", Journal of Chemical Physics, 143, 134103(2015).PDF
23. Kelin Xia and Guo-Wei Wei, "Multiresolution topological simplification", Journal of Computational Biology, 22(9), 1-5 (2015).PDF
22. Kelin Xia and Guo-Wei Wei, "Multidimensional persistence in biomolecular data", Journal of Computational Chemistry, 36, 1502-1520(2015).PDF
21. Kelin Xia and Guo-Wei Wei, "Persistent homology for cryo-EM data analysis", International Journal for Numerical Methods in Biomedical Engineering, 31(8), e02719(2015).PDF
20. Jinkyoung Park, Kelin Xia and Guo-Wei Wei, "Atomic scale design and three-dimensional simulations of nanofluidic  systems", Microfluidics and Nanofluidics, 19(3), 665-692(2015).PDF
19. Kristopher Opron, Kelin Xia and Guo-Wei Wei, "Communication: Capturing protein multiscale thermal fluctuations", Journal of Chemical Physics, 142, 211101(2015).PDF
18. Bao Wang, Kelin Xia and Guo-Wei Wei, "Second order method for solving 3D elasticity equations with complex interfaces", J. Comput. Phys., 294, 405-438(2015).PDF
17. Kelin Xia, Xin Feng, Yiying Tong and Guo-Wei Wei, "Persistent homology for the quantitative prediction of fullerene stability", Journal of Computational Chemistry, 36, 408-422(2015).PDF
16. Bao Wang, Kelin Xia and Guo-Wei Wei, "Matched interface and boundary method for elasticity interface problems", Journal of Computational and Applied Mathematics, 285, 203-225(2015).PDF
15. Kelin Xia and Guo-Wei Wei, "A Galerkin formulation of the MIB method for three dimensional elliptic interface problems", Computers and Mathematics with Applications, 68, 719-745(2014).PDF
14. Kelin Xia and Guo-Wei Wei, "Persistent homology analysis of protein structure, flexibility and folding", International Journal for Numerical Methods in Biomedical Engineering, 30(8):814-844(2014).PDF
13. Kristopher Opron, Kelin Xia and Guo-Wei Wei, "Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis", J. Chem. Phys., 140, 234105(2014) .PDF
12. Kelin Xia, Meng Zhan and Guo-Wei Wei, "MIB Galerkin method for elliptic interface problem", Journal of Computational and Applied Mathematics, 272, 195-220(2014).PDF
11. Kelin Xia and Guo-Wei Wei, "Molecular nonlinear dynamics and protein thermal uncertainty quantification", Chaos: 24, 013103(2014).PDF
10. Kelin Xia and Guo-Wei Wei, "Stochastic model for protein flexibility analysis", Physical Review E, 88, 062709(2013).PDF
9. Kelin Xia, Kristopher Opron and Guo-Wei Wei, "Multiscale multiphysics and multidomain models-Flexibility and rigidity", Journal of Chemical Physics, 139, 194109(2013).PDF
8. Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong and Guo-Wei Wei, "Multiscale geometric modeling of macromolecules I: Cartesian representation", J. Comput. Phys., 257, 912-936(2014).PDF
7. Xin Feng, Kelin Xia, Zhan Chen, Yiying Tong and Guo-Wei Wei, "Multiscale geometric modeling of macromolecules II: Lagrangian representation", Journal of Computational Chemistry, 34, 2100-2120(2013).PDF
6. Xin Feng, Kelin Xia, Yiying Tong and Guo-Wei Wei, "Geometric modeling of organelles, subcellular structures and multiprotein complexes", International Journal for Numerical Methods in Biomedical Engineering, 28(12), 1198-1223(2012). PDF
5. Guo-Wei Wei, Qiong Zheng, Zhan Chen and Kelin Xia, "Variational multiscale models for charge transport", SIAM Review, 54(4), 699-754(2012).PDF
4. Kelin Xia, Meng Zhan, Decheng Wan and Guo-Wei Wei, "Adaptively deformed mesh based matched interface and boundary (MIB) method for elliptic interface problems", J. Comput. Phys., 231(4), 1440-1461(2012).PDF
3. Kelin Xia, Meng Zhan and Guo-Wei Wei, "MIB method for elliptic equations with multimaterial interfaces", J. Comput. Phys., 230(12), 4588-4615(2011).PDF
2. Ming Yi, Kelin Xia and Meng Zhan, "Theoretical study for regulatory property of scaffold protein on MAPK cascade: a qualitative modeling", Biophysical Chemistry, 147(3), 130-139(2010).PDF
1. Qi Zhao, Ming Yi, Kelin Xia and Meng Zhan, "Information propagation from IP3 to target protein: A combined model  for encoding and decoding of Ca2+ signal", Physica A, 388, 4105-4114(2009).PDF


(After joining NTU)
(Invited speaker) "Computational and Mathematical Approaches for Bioinformatics and Biophysics" workshop at Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, Dec 10-14, 2018
(Academic Committee, Speaker) The First National Conference on Molecular Biology and Topology, Shijiazhuang, Hebei, China, Oct 26-29, 2018
(Invited speaker) Mini-symposium "Applied and Computational Topology" at the SIAM Central States Section Meeting, Norman, Oklahoma, USA, Oct 5-7, 2018
(Invited speaker) Complexity community Share session, NTU, Singapore, Sep 25, 2018
(Invited speaker) Strategic Partnership with IIT Madras, IISc and IIT Bombay and Joint Workshops, India, Sep 17-20, 2018
(Invited speaker) Workshop on Algebraic Topology and Geometric Topology, Dalian, China, Aug 9-13, 2018
(Invited speaker, declines due to time conflict) Mathematics of Drug Design/Discovery, The Fields Institute for Research in Mathematical Sciences, Toronto, Canada, June 4 - 7, 2018
(Invited speaker)  Workshop on Algebraic Topology and Applied Topology, NUS, Singapore, Jan 23, 2018
(Invited speaker) ASPIRE League Research Workshop, School of Life Science and Technology, Tokyo Institute of Technology, Yokohama, Japan, Nov 24, 2017
(Invited speaker) Mini-symposium "Molecular Bioscience and Biophysics: Modeling and Computation" at the 3rd SIAM CSS annual meeting, Fort Collins, Colorado, Sep 29 - Oct 1, 2017
(Invited speaker) NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, September 7, 2017
(Invited speaker) Workshop on "Topology of the Biomolecular World", American Institute of Mathematics, San Jose, CA, July 24-28, 2017
(Invited speaker)
International Symposium on Computational Mathematics, Optimization, and Computational Intelligence (CMOCI 2017), IIT Indore, India, July 17 - 19, 2017
(Invited speaker) "Mathematics Biophysics and Molecular Biosciences" Workshop at Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, Dec 19-23, 2016
(Poster) "Topological, Geometric, and Statistical Techniques in Biological Data Analysis", Mathematical Biosciences Institute, September 12-September 16, 2016
(Invited speaker) Department of Mathematics, National University of Singapore, Singapore, August 31, 2016 
(Invited speaker) Bioinformatics Institute, A*STAR, Singapore, August 23, 2016
(Invited speaker) School of Biological Science, Nanyang Technological University, Singapore, August 15, 2016
Mini-symposium "Molecular Biosciences and Biophysics: Topological and Geometic methods" at SIAM Conference on Life Sciences, Boston, Masschusetts, July 13, 2016 (Co-organizer: Prof. Natasha Jonoska)

(Before joining NTU)
(Invited speaker) Department of Mathematics and Statistics, University of North Carolina Charlotte, April 25, 2016
(Invited speaker) School of Mathematical Science, Monash University, April 21, 2016
(Invited speaker) School of Physical and Mathematical Science, Nanyang Technological University, March 8, 2016
(Invited speaker) Department of Mathematics, The university of Tennessee at Chattanooga, February 30, 2016
(Invited speaker) Department of Mathematical Science, Georgia Sourthern University, February 22, 2016
(Invited speaker) Department of Mathematics, North Carolina State University, January 21, 2016
(Invited speaker) Geometric and Topological Modeling of Biomolecules, Mathematical Biosciences Institute, September 28-October 2, 2015 (Video)
(Invited speaker) IMA hot topic workshop on "Mathematics of Biological Charge Transport: Molecular and Beyond", IMA, Twin Cities, July 20-24, 2015
(PosterAdvanced Numerical Methods in the Mathematical Sciences, Texas A&M, College Station, TX, May 4-7, 2015
(Invited speaker) "Modeling, Numerics and Analysis of Electrodiffusion Phenomena" at AMS Central Spring Sectional Meeting, Michigan State University, East Lansing, Michigan, March 14-15, 2015
(Organizer) Workshop on persistent homology for biosciences, East Lansing, October 18, 2014 (With Prof.Guowei Wei and Prof. Yiying Tong)
(Organizer) Mini-symposium "Molecular Biosciences: Topological modeling of biomolecules" at SIAM Conference on Life Sciences, Charlotte, North Carolina, August 4-7, 2014(Co-organizer: Prof.Yuanan Diao)
(Invited speaker
) Mini-symposium "Modeling and computation of problems in mathematical biology" at the 38th annual meeting of the SIAM Southeastern Atlantic Section, Florida Institute of Technology in Melbourne, Florida, March 28-30, 2014
Poster) IMA Annual Program Year Workshop Topological Structures in Computational Biology, December 9-13, 2013 
(Poster) 2013 Great Lakes SIAM Conference on "Computational Mathematics: Modeling, Algorithms and Applications", Central Michigan University, April 20, 2013
(Invited speaker) Mathematical Challenges in Biomolecular/Biomedical Imaging and Visualization, Mathematical Biosciences Institute, February 18-22, 2013
(Invited speaker) 12th International Symposium on Mathematical and Computational Biology, Tempe, Arizona, November 7-10, 2012
(Speaker) SMB Annual Meeting and Conference, Knoxville, Tennessee, July 25-28, 2012
(Participation) 2nd Midwest Conference on "Mathematical Methods for Images and Surfaces", East Lansing, August 27-28, 2011
(Traveling award) Modeling and Computation of Biomolecular Structure and Dynamics, Mathematical Biosciences Institute, Ohio State University, April 25-29, 2011
(Poster,traveling award) Fluid Motion Driven by Immersed Structures, University of Toronto, August 9-13, 2010
(Participation) Workshop on Nano-Bio Mathematics and Mechanics, Michigan State University, August 5, 2010
(Participation) Modeling and Numerical PDEs in Mathematical Biology and Applications, Oakland University, April 16, 2011
(Participation) Frontiers in Mathematical Biology: NSF-NIH PIs Meeting 2010, University of Maryland, College Park, April 26-27, 2010
) SIAM Great Lakes Conference: Modeling and numerical PDEs in Mathematical Biology, University of Michigan at Dearborn, April 17, 2010