The DOI matches its Crossref record; 143 of the 143 references it cites were found in a registry or an index.
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
Open accessAbstract
This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.
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“We applied convolutional neural networks and multi-task learning in our predictions which further advanced the capability of our models [22, 23].”
From Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges (2019) · cites this paper as [23]
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“For the characterization of small molecules, we can use a multilevel element specific persistent homology to both describe the covalent bonds and noncovalent interactions in the molecule [23].”
From Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges (2019) · cites this paper as [23]
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“Such a characterization can help machine learning-based SFs consistently maintain their accuracy in binding affinity predictions for a variety of protein–ligand complexes [19–23].”
From Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges (2019) · cites this paper as [23]
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Cites
Very Deep Convolutional Networks for Large-Scale Image Recognition
Simonyan, K., & Zisserman, A. (2014) · arXiv · doi:10.48550/arxiv.1409.1556 · Cited by 114,148
ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Scikit-learn: Machine Learning in Python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Müller, A., Nothman, J., Louppe, G., et al. (2012) · arXiv · doi:10.48550/arxiv.1201.0490 · Cited by 71,016
Berman, H. M. (2000) · Nucleic Acids Research · doi:10.1093/nar/28.1.235 · Cited by 40,196
Trott, O., & Olson, A. J. (2010) · Journal of Computational Chemistry · doi:10.1002/jcc.21334 · Cited by 38,412
AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility
Morris, G. M., Huey, R., Lindstrom, W., Sanner, M. F., Belew, R. K., Goodsell, D. S., & Olson, A. J. (2009) · Journal of Computational Chemistry · doi:10.1002/jcc.21256 · Cited by 26,294
Advances in neural information processing systems 7
Cios, K. J., & Shields, M. E. (1997) · Neurocomputing · doi:10.1016/s0925-2312(97)90018-7 · Cited by 22,093
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
Advances in Neural Information Processing Systems 25
Zhang, Y., Sutton, C. A., Storkey, A., & Zoubin Ghahramani, A. (2012) · Cited by 12,653
Flagged first, then by citations
Research works printed but not linked: 6
- Q Zheng, 2012, Molecular surface generation using PDE transform, International Journal for Numerical Methods in Biomedical Engineering, 28, 291
- X Shi, 2011, Geometry and topology for modeling biomolecular surfaces, Far East J Applied Math, 50, 1
- T Kaczynski, 2004, vol. 157 of Applied Mathematical Sciences
- VD Silva, 2005, In Proceedings of Robotics: Science and Systems, 01
- B Krishnamoorthy, 2007, Data Mining in Biomedicine, Springer Optimization and Its Applications, 431
- PM Kasson, 2007, Persistent voids: a new structural metric for membrane fusion, Bioinformatics, 23, 1753, 10.1093/bioinformatics/btm250 · DOI
Cited by
Sorted by citations
Items 201–250 of 250
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EGGNet, a Generalizable Geometric Deep Learning Framework for Protein Complex Pose Scoring
Wang, Z., Brand, R., Adolf-Bryfogle, J., Grewal, J., Qi, Y., Combs, S. A., Golovach, N., Alford, R., Rangwala, H., & Clark, P. M. (2024) · ACS Omega · doi:10.1021/acsomega.3c04889 · Cited by 3
Identification of coenzyme-binding proteins with machine learning algorithms
Liu, Y., Munteanu, C. R., Kong, Z., Tao, R., Sahagún-Ruiz, A., He, Z., Zhou, C., & Tan, Z. (2019) · Computational Biology and Chemistry · doi:10.1016/j.compbiolchem.2019.01.014 · Cited by 3
Shiota, K., & Akutsu, T. (2023) · Bioinformatics Advances · doi:10.1093/bioadv/vbad155 · Cited by 2
Francoeur, P. G., & Koes, D. R. (2023) · ACS Omega · doi:10.1021/acsomega.3c05931 · Cited by 2
Topology-Enhanced Machine Learning Model (Top-ML) for Anticancer Peptide Prediction
Tan, J. Z. E., Wee, J., Gong, X., & Xia, K. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5c00476 · Cited by 4
PLNet : Persistent Laplacian neural network for protein–protein binding free energy prediction
Xu, X., Wang, C., Wei, G., & Chen, J. (2025) · Protein Science · doi:10.1002/pro.70377 · Cited by 4
Self-citationLi, G., Yuan, Y., & Zhang, R. (2025) · Interdisciplinary Sciences Computational Life Sciences · doi:10.1007/s12539-025-00745-z · Cited by 2
PHoS: Persistent Homology for Virtual ScreeningPreprint
Keller, B., Lesnick, M., & Willke, T. L. (2018) · ChemRxiv · doi:10.26434/chemrxiv.6969260.v1 · Cited by 2
Structure‐Based Ultra‐Large Virtual Screenings
Gorgulla, C. (2024) · Wiley eBooks · doi:10.1002/9783527840748.ch19 · Cited by 2
Classification of Hand Movements Based on EMG Signals using Topological Features
Li, J., Yang, L., He, Y., & Fukuda, O. (2023) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2023.0140405 · Cited by 1
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Segura-Alabart, N., & Serratosa, F. (2026) · Molecules · doi:10.3390/molecules31122025 · Cited by 1
Suay‐García, B., & Falcó, A. (2026) · Briefings in Bioinformatics · doi:10.1093/bib/bbag370 · Cited by 1
Stability for Inference with Persistent Homology Rank Functions
Wang, Q., García‐Redondo, I., Faugère, P., Henselman‐Petrusek, G., & Monod, A. (2024) · Computer Graphics Forum · doi:10.1111/cgf.15142 · Cited by 1
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Sharma, A., Hsiao, Y.-C., & Dutta, A. (2025) · Drugs and Drug Candidates · doi:10.3390/ddc4030028 · Cited by 2
Meng, Y., Zhang, Z., Li, J., Tang, X., Lu, C., Zhang, Z., Cui, F., Zeng, P., Li, B., & Xu, J. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5c01974 · Cited by 1
Gao, L.-G., & Liu, S. (2026) · Electronics · doi:10.3390/electronics15071487 · Cited by 1
Application of Machine Learning Algorithms in Audit Data Analysis
Zhou, J. (2021) · International Conference on Aviation Safety and Information Technology (ICASIT) · doi:10.1145/3510858.3510881 · Cited by 1
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Topology-Informed Pre-training of Graph Neural Networks
Liang, P., Gel, Y. R., & Chen, Y. (2025) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp49660.2025.10890271 · Cited by 1
Topological potentials guiding protein self-assembly
Spirandelli, I., Nigmetov, A., Morozov, D., & Evans, M. E. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014709 · Cited by 1
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Liu, R., Liu, X. Y., Li, J., Wu, R., & Wu, J. (2026) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2026.3717266 · Cited by 1
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Onchiş, D. M., Istin, C., & Real, P. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-29888-3_50 · Cited by 1
Characterizing Protein Conformational Spaces using Efficient Data Reduction and Algebraic Topology
Joshi, A., Haspel, N., & González, E. (2022) · Journal of Human Earth and Future · doi:10.28991/hef-sp2022-01-01 · Cited by 1
A Unified Topological Approach to Data SciencePreprint
Grbić, J., Wu, J., Xia, K., & Wei, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.16926 · Cited by 1
Self-citationOmicron BA.2 (B.1.1.529.2): high potential to becoming the next dominating variant.Preprint
Chen, J., & Wei, G. (2022) · PubMed · Cited by 1
Self-citationChiew, K. J. (2019) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/83241
Khan, S. U., Khan, A. U., Kamal, M. A., & Htar, T. T. (2023) · Elsevier eBooks · doi:10.1016/b978-0-323-99137-7.00005-8
Geometric and topological AI for molecular sciences
Wee, J. (2023) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/165903
Merkurjev, E. (2023) · International Journal of Machine Learning and Cybernetics · doi:10.1007/s13042-023-01894-7
Pull-back Geometry of Persistent Homology EncodingsPreprint
Liang, S., Turkeš, R., Li, J., Otter, N., & Montúfar, G. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2310.07073
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Moreira, R. A., Braddell, R., Santos, F. A. N., Fülöp, T., Desroches, M., Ubarretxena‐Belandia, I., & Rodrigues, S. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.11.27.568841
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Lamine, Z., Mamouni, M. I., & Mansouri, M. W. (2023) · International Journal of Analysis and Applications · doi:10.28924/2291-8639-21-2023-136
Alawam, A. S., & Alamri, M. A. (2025) · Crystals · doi:10.3390/cryst15060507
Yu, Y., Jiang, Y., Yang, Y. K., Xie, Z., & Lu, Q. (2025) · Applied Soft Computing · doi:10.1016/j.asoc.2025.113983
Additional file 1 of Learning protein-ligand binding affinity with atomic environment vectors
Meli, R., Anighoro, A., Bodkin, M. J., Morris, G. M., & Biggin, P. C. (2021) · Figshare · doi:10.6084/m9.figshare.15178929
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Liang, P., Chen, Y., & He, X. (2025) · IEEE International Conference on Big Data (BigData) · doi:10.1109/bigdata66926.2025.11402319
Persistent Local Laplacian Prediction of Protein–Ligand Binding Affinities
Liu, J., & Feng, H. (2026) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.6c02460 · Cited by 1
Design and application of deep learning methods to structure-based drug design
Volkov, M. (2023) · theses.fr (ABES) · doi:10.70675/d4a7b752z9818z4196zab21z61e5493b7907
Wang, Y., Cai, M., Ma, Y., Wang, X., & Wei, K. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.04.07.717117
Yu, C., Li, H., T, J., Tang, S., Hu, Y., & Huang, J. (2026) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp55912.2026.11463600
Deep Learning-Based Denoising for QPSK Signals Using LSTM Networks
Zhou, C. (2026) · International Conference on Communications, Information System and Computer Engineering (CISCE) · doi:10.1109/cisce69494.2026.11504898
He, Z., Liu, X., Jiang, Y., Xu, J. H., Lin, Y., Jin, S., Wei, L., & Wang, Y. (2026) · Bioinformatics · doi:10.1093/bioinformatics/btag290
Persistent sheaf Laplacian analysis of protein stability and solubility changes upon mutation
Ren, Y., Wee, J., Chen, X., Qian, G., & Wei, G. (2026) · Protein Science · doi:10.1002/pro.70700
Self-citationAn algebraic graph neural network model for protein-ligand binding affinity prediction
Ouru, A., Chen, X., Yeagle, C., & Chen, J. (2026) · Computational and Mathematical Biophysics · doi:10.1515/cmb-2025-0035
DHST: A Deep Hybrid Structure–Topology Framework for Accurate Protein Function Prediction
Lu, B., Xiang, F., Wang, H., Wang, D., & Wang, Q. (2026) · Applied Sciences · doi:10.3390/app16178437
Evolutionary Weighted Hodge Laplacian Descriptors for rs-fMRI Brain Networks
Ma, L., Li, F., Zhang, X., Lei, F., Liang, L., & Mao, X. (2026) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.6c02573
Data-driven modeling of spatiotemporal dynamics using multimodal imaging data
Li, C., Mao, Y., Liu, X., & Hao, W. (2026) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1014751
Abbasi, K., Banadkuki, H., Sepahvand, R., & Rashidi, S. (2026) · PLoS ONE · doi:10.1371/journal.pone.0357278
Metadata
- Authors
- Cang, Z., Mu, L., & Wei, G.-W.
- Affiliations
- Michigan State University (US)
- Oak Ridge National Laboratory (US)
- Corresponding author
- Wei, Guo-Wei
- Venue
- PLOS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2018-01-08
- Volume
- 14
- Issue
- 1
- Pages
- e1005929
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC5774846
- OpenAlex
- W2963833291
- Cited by
- 257
- References
- 140
- Citations by year
- 2026: 21 · 2025: 34 · 2024: 28 · 2023: 37 · 2022: 35 · 2021: 35 · 2020: 39 · 2019: 17 · 2018: 11
- FWCI
- 18.85
- Type
- journal article
- Language
- en
- Update notices
- new_version (2018-01-19)
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- National Science Foundation (DMS-1721024, IIS-1302285)
- Topics
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Machine Learning in Bioinformatics
- Keywords
- algebraic topology, persistent homology, Wasserstein distance, protein-ligand binding affinity prediction, virtual screening, biomolecular complexes, PDBbind
- MeSH terms
- Machine Learning, Algorithms, Humans, Ligands, Models, Neurological, Nucleic Acids, Protein Binding, Proteins, Neural Networks, Computer, Computational Biology, Area Under Curve, Protein Interaction Mapping, Databases, Protein, Static Electricity, Molecular Dynamics Simulation
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