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A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation
Open accessAbstract
The ability to predict protein–protein interactions is crucial to our understanding of a wide range of biological activities and functions in the human body, and for guiding drug discovery. Despite considerable efforts to develop suitable computational methods, predicting protein–protein interaction binding affinity changes following mutation (ΔΔG) remains a severe challenge. Algebraic topology, a champion in recent worldwide competitions for protein–ligand binding affinity predictions, is a promising approach to simplifying the complexity of biological structures. Here we introduce element- and site-specific persistent homology (a new branch of algebraic topology) to simplify the structural complexity of protein–protein complexes and embed crucial biological information into topological invariants. We also propose a new deep learning algorithm called NetTree to take advantage of convolutional neural networks and gradient-boosting trees. A topology-based network tree is constructed by integrating the topological representation and NetTree for predicting protein–protein interaction ΔΔG. Tests on major benchmark datasets indicate that the proposed topology-based network tree is an important improvement over the current state of the art in predicting ΔΔG. Persistent homology provides an efficient approach to simplifying the complexity of protein structure. Wang et al. combine this approach with convolutional neural networks and gradient-boosting trees to improve predictions of protein–protein interactions.
Overview
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Written from the paper’s full text.
TL;DR
The paper introduces TopNetTree, combining element- and site-specific persistent homology with CNN-assisted gradient-boosting trees to predict protein–protein binding affinity changes upon mutation (ΔΔG). It reports improved Pearson correlations over prior methods on AB-Bind and SKEMPI benchmarks, including RP 0.65 on AB-Bind S645 and RP 0.82 on SKEMPI 2.0 S4947.
Key findings
- On the AB-Bind S645 set, TopNetTree achieved an RP of 0.65, about 22% better than the previous best RP of 0.53 from mCSM-AB; excluding 27 non-binders increased RP to 0.68, and a blind test on homology structures gave RP 0.55.
- On the SKEMPI S1131 set, the method was reported as about 15% more accurate than the best existing method in tenfold cross-validation.
- On SKEMPI 2.0, TopNetTree achieved RP 0.82 and r.m.s.e. 1.11 kcal mol−1 on S4947; RP 0.79 and r.m.s.e. 1.13 kcal mol−1 on S4169 versus mCSM-PPI2’s RP 0.76 and r.m.s.e. 1.19 kcal mol−1; and RP 0.85 and r.m.s.e. 1.11 kcal mol−1 on S8338 versus mCSM-PPI2’s RP 0.82 and r.m.s.e. 1.18 kcal mol−1.
- Cross-validation analyses showed inter-protein average/median RP of 0.508/0.541 and intra-protein leave-one-out average/median RP of 0.170/0.215; mutation-region RP values were 0.60 (core), 0.66 (rim), 0.66 (support), 0.65 (interior) and 0.48 (surface).
Methods
- The model uses element- and site-specific persistent homology: atoms are classified into mutation-site, neighbourhood, antibody, antigen and element-type subsets, with modified distance matrices excluding same-set interactions; H0 barcodes come from Vietoris–Rips filtration, while H1 and H2 barcodes come from alpha complex filtration.
- H0 barcodes are vectorized by binning the filtration range (for example, [0, 12] Å into 0.5 Å bins) and counting persistence intervals, birth events and death events; H1 and H2 barcodes are summarized by statistics such as sum, maximum, minimum, mean and standard deviation of bar lengths, birth values and death values.
- A CNN extracts higher-level features from H0; these are combined with H1/H2 statistics and fed into a gradient-boosting tree (GBT) for final prediction. The paper evaluates on AB-Bind S645, SKEMPI S2317/S1131, and SKEMPI 2.0 S4947/S4169/S8338/S787 using RP and r.m.s.e., with tenfold, inter-protein, intra-protein and blind-test protocols.
Limitations
- Stated: the characterization of birth and death may not be stable against different discretizations, so only H0 barcodes from Vietoris–Rips filtration are used; datasets are relatively small and complex; non-binders are outliers that strongly affect accuracy; intra-protein cross-validation is limited by small per-complex training sets (average 27 samples); surface mutations have small data and small average energy disturbance; model prediction variance is generally lower than experimental variance.
- Evident from reported results: performance varies strongly across protein families, with negative RP for 1FFW (−0.043) and 1YY9 (−0.068); inter-protein cross-validation (average RP 0.508) and blind tests (homology RP 0.55; S787 RP 0.53) are lower than the main tenfold results.
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Claims the paper makes
17 Own result · 15 Not checked yet · 12 Own interpretation · 9 No basis given · 3 Own method · 1 Partly supported · accuracy not yet measured
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We also applied a blind test on homology structures using the rest of the samples as the training set, achieving an RP of 0.55, as shown in Fig. 4.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“Tests on major benchmark datasets indicate that the proposed topology-based network tree is an important improvement over the current state of the art in predicting ΔΔG.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
hedged- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The individual learners in an ensemble are likely to make different mistakes, so summing weak learners reduces overall error.
- Rests on an assumption: PPI ΔΔG prediction data are highly complex due to 3D structures, whereas the datasets are relatively small.
In the paper
“Our method is about 22% more accurate than the best-existing score of RP = 0.53 (given by mCSM-AB), indicating the power of our TopNetTree.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites Pires et al.21 Pires, D. E. & Ascher, D. B. mCSM-AB: a web server for predicting antibody–antigen affinity changes upon mutation with graph-based signatures. Nucleic Acids Res. 44, W469–W473 (2016). source
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In the paper
“In comparison with non-machine learning methods such as Rosetta and bASA, our method is over 100% more accurate in terms of RP indicating that our topology-based machine learning methods have a better predictive power for PPI systems.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“In our case, the RP increased from 0.65 to 0.68 for the same treatment as shown in Fig. 4.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“Our model achieved an RP of 0.65 on the AB-Bind S645 dataset, which is significantly better than those of other existing methods as shown in Table 1.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“It is found that the proposed TopNetTree is about 15% more accurate than the best-existing method.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“however, the performance of the model varies among different protein families”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different protein complexes.
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In the paper
“we find that most mutations from polar to hydrophobic residues have a positive free energy change (for example, S to M)”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation types.
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In the paper
“The ΔΔG of 27 non-binders (−8 kcal mol−1) did not follow the distribution of the whole dataset.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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- Probably not a substantial claim. 17
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In the paper
“There are 2,317 single point mutation data entries among the whole database, which are referred to as the SKEMPI S2317 set.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Partly supportedcites [11] Moal, I. H. & Fernández-Recio, J. SKEMPI: a structural kinetic and energetic database of mutant protein interactions and its use in empirical models. Bioinformatics 28, 2600–2607 (2012). sourceExperimental — accuracy not yet measured
The Results section reports that the database contains 2,317 single mutants, supporting the count and mutation type. Our copy does not call these entries the “SKEMPI S2317 set,” so the attributed name is not supported. (LLM, conf=0.88)
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In the paper
“We achieved an average RP of 0.53 and r.m.s.e. of 1.45 kcal mol−1 on this blind test (further details are given in the Supplementary Information).”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“We tested set S4947 with the regular tenfold cross-validation, achieving an average RP of 0.82 and an r.m.s.e. of 1.11 kcal mol−1 for the tenfold cross-validation.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“For set S4169, we obtained an average RP of 0.79 and r.m.s.e. of 1.13 kcal mol−1, compared with the average RP of 0.76 and r.m.s.e. of 1.19 kcal mol−1 achieved by mCSM-PPI2.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites David et al.48
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In the paper
“This dataset, called the AB-Bind S645 set, consists of about 20% stabilizing mutations and 80% destabilizing ones; there are 27 non-binders in the whole dataset, which are variants determined not to bind within the sensitivity of the assay.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“It is interesting to note that all the mutations to alanine have a positive energy change”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation types.
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In the paper
“In experimental data, mutations at the core or support region have a higher average energy change of around 1.8 kcal mol−1 (1.72 kcal mol−1 and 1.91 kcal mol−1, respectively), whereas mutations at the rim or interior region have an average energy change of around 0.8 kcal mol−1 (0.82 kcal mol−1 and 0.83 kcal mol−1, respectively)”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation regions.
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In the paper
“Overall, our predicted patterns are remarkably similar to those of experimental data in terms of both average binding energy changes and variance of binding energy changes, as shown in Fig. 5.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation types.
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In the paper
“For this test, our model reached average/median RP values of 0.170/0.215, which are significantly lower than the tenfold cross-validation result over the entire dataset.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different protein complexes.
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In the paper
“For this test, our model reached an average RP of 0.508 and a median RP of 0.541.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different protein complexes.
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In the paper
“We demonstrate that the proposed TopNetTree achieves an RP of 0.65, which is about 22% better than the previous best result for the AB-Bind dataset.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Conclusion
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In the paper
“Sirin et al.10 collected an AB-Bind database of mutation-induced antibody–antigen complex binding free energy changes. This database contains 1,101 mutation data entries, including 645 single-point mutations on 32 different antibody–antigen complexes.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
What the sources say
- Not checked yetcites Sirin et al.10 Sirin, S., Apgar, J. R., Bennett, E. M. & Keating, A. E. AB-bind: antibody binding mutational database for computational affinity predictions. Protein Sci. 25, 393–409 (2016). source
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In the paper
“This dataset contains 7,085 entries, including single- and multi-point mutations.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites [39] Jankauskaitė, J., Jiménez-García, B., Dapkūnas, J., Fernández-Recio, J. & Moal, I. H. SKEMPI 2.0: an updated benchmark of changes in protein–protein binding energy, kinetics and thermodynamics upon mutation. Bioinformatics 35, 462–469 (2018). source
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In the paper
“Pires et al.21 found that excluding non-binders from the dataset would significantly increase the performance of a prediction model.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites Pires et al.21 Pires, D. E. & Ascher, D. B. mCSM-AB: a web server for predicting antibody–antigen affinity changes upon mutation with graph-based signatures. Nucleic Acids Res. 44, W469–W473 (2016). source
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“SKEMPI is a more general database for protein–protein binding affinity changes following mutation (ΔΔG)11, it contains 3,047 mutation data entries for protein–protein heterodimeric complexes with experimentally determined structures.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
What the sources say
- Not checked yetcites [11] Moal, I. H. & Fernández-Recio, J. SKEMPI: a structural kinetic and energetic database of mutant protein interactions and its use in empirical models. Bioinformatics 28, 2600–2607 (2012). source
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The limited performance of the current methods therefore highlights a pressing need for a new generation of ΔΔG predictors that are constructed with entirely new design principles and/or innovative machine learning algorithms.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
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In the paper
“a possible reason is that mutations from a large residue to a small one could lead to a stabilizing effect to the whole system”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation types.
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In the paper
“Persistent homology22–25—a new branch of algebraic topology—is able to bridge geometry and topology, leading to a new efficient approach for the simplification of biological structural complexity26–31; however, it neglects critical chemical/biological information when it is directly applied to complex biomolecular structures.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
What the sources say
- Not checked yetcites [22] Frosini, P. & Landi, C. Size theory as a topological tool for computer vision. Pattern Recognition Image Anal. 9, 596–603 (1999).
- Not checked yetcites [23] Edelsbrunner, H., Letscher, D. & Zomorodian, A. Topological persistence and simplification. Discrete Comput. Geom. 28, 511–533 (2002). source
- Not checked yetcites [24] Zomorodian, A. & Carlsson, G. Computing persistent homology. Discrete Comput. Geom. 33, 249–274 (2005). source
- Not checked yetcites [25] Zomorodian, A. & Carlsson, G. Localized homology. Comput. Geom. 41, 126–148 (2008). source
- Not checked yetcites [26] Xia, K. L. & Wei, G. W. Persistent homology analysis of protein structure, flexibility and folding. Int. J. Numer. Methods Biomed. Eng. 30, 814–844 (2014). source
- Not checked yetcites [27] Gameiro, M. et al. Topological measurement of protein compressibility via persistence diagrams. Japan J. Industr. Appl. Math. 32, 1–17 (2014).
- Not checked yetcites [28] Xia, K. L. & Wei, G. W. Persistent topology for cryo-EM data analysis. Int. J. Numer. Methods Biomed. Eng. 31, e02719 (2015).
- Not checked yetcites [29] Cang, Z. X. et al. A topological approach to protein classification. Mol. Based Math. Biol. 3, 140–162 (2015).
- Not checked yetcites [30] Yao, Y. et al. Topological methods for exploring low-density states in biomolecular folding pathways. J. Chem. Phys. 130, 04B614 (2009).
- Not checked yetcites [31] Kovacev-Nikolic, V., Bubenik, P., Nikolić, D. & Heo, G. Using persistent homology and dynamical distances to analyze protein binding. Stat. Appl. Genet. Mol. Biol. 15, 19–38 (2016). source
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In the paper
“These non-binders could be regarded as outliers in the database and have a strongly negative impact on the prediction model accuracy.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
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In the paper
“A possible reason for these patterns is that different mutation regions vary in their accessibility to water”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation regions.
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Rests on an assumption: In general, surface, interior and rim regions have greater access to water than the core and support regions.
In the paper
“Similar patterns regarding mutation sites and energy changes were reported in the literature49.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation regions.
What the sources say
- Not checked yetcites [49] Petukh, M., Li, M. & Alexov, E. Predicting binding free energy change caused by point mutations with knowledge-modified MM/PBSA method. PLoS Comput. Biol. 11, e1004276 (2015). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“We followed the method of tenfold stratified cross-validation used in mCSM-PPI2 paper for sets S4169 and S833848.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites [48] Rodrigues, C. H. M., Myung, Y., Pires, D. E. V. & Ascher, D. B. mCSM-PPI2: Predicting the effects of mutations on protein–protein interactions. Nucleic Acids Res. 47, W338– W344 (2019). source
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The quote only partly states this claim.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Table 2 shows the Pearson correlation coefficients on tenfold cross-validations.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The quote only partly states this claim.
In the paper
“They filtered only single-point mutations and selected 4,169 variants in 319 different complexes (denoted set S4169).”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
What the sources say
- Not checked yetcites [48] Rodrigues, C. H. M., Myung, Y., Pires, D. E. V. & Ascher, D. B. mCSM-PPI2: Predicting the effects of mutations on protein–protein interactions. Nucleic Acids Res. 47, W338– W344 (2019). source
plain- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Typically, physics-based methods provide mechanistic interpretations but are not designed for handling large and diverse datasets.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We believe that the relative inferior performance for surface mutations is due to its small data size and that the energy disturbance caused by surface mutations is small on average.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different mutation regions.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Models trained on some protein families could extrapolate to other families; for example, the two protein families with the best results, 1KTZ and 2JEL, can reach RP of 0.866 and 0.818, respectively, whereas the two families with the poorest results, 1FFW and 1YY9, have RP values of −0.043 and −0.068, respectively.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Discussion > Prediction result analysis for different protein complexes.
hedgedcorrelationaln = 2- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Topology has recently been shown to be surprisingly effective in simplifying biomolecular structural complexity26,27,29.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Conclusion
What the sources say
- Not checked yetcites [26] Xia, K. L. & Wei, G. W. Persistent homology analysis of protein structure, flexibility and folding. Int. J. Numer. Methods Biomed. Eng. 30, 814–844 (2014). source
- Not checked yetcites [27] Gameiro, M. et al. Topological measurement of protein compressibility via persistence diagrams. Japan J. Industr. Appl. Math. 32, 1–17 (2014).
- Not checked yetcites [29] Cang, Z. X. et al. A topological approach to protein classification. Mol. Based Math. Biol. 3, 140–162 (2015).
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“It has been devised to win worldwide competitions in computer-aided drug design36.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Conclusion
What the sources say
- Not checked yetcites [36] Nguyen, D. D. et al. Mathematical deep learning for pose and binding affinity prediction and ranking in D3R grand challenges. J. Compurt. Aided Mol. Design https://doi.org/10.1007/s10822-018-0146-6 (2018). source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The authors state this as an assumption.
The individual learners in an ensemble are likely to make different mistakes, so summing weak learners reduces overall error.
“It improves the performance on the weak learners with the assumption that the individual learners are likely to make different mistakes and thus summing the weak learners will reduce the overall error.”
The paper relies on this without support.
PPI ΔΔG prediction data are highly complex due to 3D structures, whereas the datasets are relatively small.
“A major challenge in the prediction of binding affinity changes following mutation for PPIs is that the data is highly complex due to 3D structures, whereas the datasets are relatively small.”
The paper relies on this without support.
In general, surface, interior and rim regions have greater access to water than the core and support regions.
“in general, surface, interior and rim regions have greater access to water than the core and support regions.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“TopGBT uses topology-based features to represent the complex, which is not initially designed for representing the interactions between atoms, limiting its predictive power for binding affinity changes upon mutations.”
From Deep geometric representations for modeling effects of mutations on protein-protein binding affinity (2021) · cites this paper as [31]
In the citing paper
“As some complexes in the above benchmark datasets are highly related (S2 and S3 Figs), machine learning methods tend to be overtrained on these datasets, as evidenced by the drops of the prediction performance when machine learning methods meet unseen structures [31].”
From Deep geometric representations for modeling effects of mutations on protein-protein binding affinity (2021) · cites this paper as [31]
In the citing paper
“These datasets have been widely used to test the predictive power of the PPI prediction methods [12, 13, 27–29, 29–35].”
From Deep geometric representations for modeling effects of mutations on protein-protein binding affinity (2021) · cites this paper as [31]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > Abstract
“This database contains 1,101 mutation data entries, including 645 single-point mutations on 32 different antibody–antigen complexes.”
§ A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation > TopNetTree model for PPI binding energy change following mutation prediction > Model performance for PPIs.
“We follow Pires et al.21 by considering only 645 single mutations across 29 antibody–antigen complexes.”
Citations
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Cited by
Sorted by citations
Items 101–200 of 202
Biomolecular Topology: Modelling and Analysis
Liu, J., Xia, K., Wu, J., Yau, S. S. ‐., & Wei, G. (2022) · Acta Mathematica Sinica English Series · doi:10.1007/s10114-022-2326-5 · Cited by 9
“In particular, the TopNetTree model has demonstrated great power in predicting protein-protein binding affinity changes upon mutations [195].”
MethodSelf-citationDecoding the effects of mutation on protein interactions using machine learning
Wang, X., Li, A., Zhao, Y., & Peng, Y. (2025) · Biophysics Reviews · doi:10.1063/5.0249920 · Cited by 7
A Protein Co-Conservation Network Model Characterizes Mutation Effects on SARS-CoV-2 Spike Protein
Zeng, L., Lu, Y., Yan, W., & Yang, Y. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms24043255 · Cited by 6
“The change in binding free energy (∆∆G) upon a single mutation from variants was estimated using TopNetTree [37].”
MethodMuniyappan, S., Rayan, A. X. A., & Varrieth, G. T. (2023) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2023419 · Cited by 6
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“For example, TopGBT [5] employs topology-based features to depict the protein complexes, whereas, this type of features are not initially intended to represent the interatomic interactions, thereby constraining their predictive capacity for the alterations in binding affinity arising from mutations…”
A paired sequence language model for protein-protein interaction modeling
Liu, J., Chen, H., & Zhang, Y. (2026) · Nature Communications · doi:10.1038/s41467-026-70457-5 · Cited by 8
VariBench, new variation benchmark categories and data sets
Shirvanizadeh, N., & Vihinen, M. (2023) · Frontiers in Bioinformatics · doi:10.3389/fbinf.2023.1248732 · Cited by 4
Wang, Y., Shi, X., & Zhou, H. (2023) · IEEE Industrial Electronics Society Annual On-Line Conference (ONCON) · doi:10.1109/oncon60463.2023.10430682 · Cited by 4
“Furthermore, Wang et al.[5] adapted algebraic topology to simplify protein dimers' complex structures and preserve key features in topological invariants.”
BackgroundChen, H., Revennaugh, B., Fu, H., & Ivanov, A. A. (2024) · iScience · doi:10.1016/j.isci.2024.110035 · Cited by 4
“19 To explore cancer-focused PPI networks integrated with cancer genomics, and clinical, pharmacological, and structural data, we have established the OncoPPi Portal.”
Fazekas, Z., Nagy‐Fazekas, D., Shilling-Tóth, B. M., Ecsédi, P., Stráner, P., Nyitray, L., & Perczel, A. (2024) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.4c01023 · Cited by 4
SARS-CoV-2 becoming more infectious as revealed by algebraic topology and deep learning
Chen, J., Wang, R., & Wei, G. (2021) · Communications in Information and Systems · doi:10.4310/cis.2021.v21.n1.a2 · Cited by 4
“The resulting method that integrates the topological representation of complex data and NetTree, called TopNetTree, was about 22% better than the previous best result for the AB-Bind dataset and significantly outperformed the state-of-the-art in the literature on the SKEMPI database [12].”
MethodSelf-citationLuo, X., Tong, F., Zhao, W., Zheng, X., Li, J., Li, J., & Zhao, D. (2023) · mAbs · doi:10.1080/19420862.2023.2285904 · Cited by 4
“For single point mutations, the TopNetTree model, 32 which is based on tertiary structure information, achieved an Rp of 0.65 (SOTA), while our model achieved an Rp of 0.77.”
MethodInfluentialCome la famiglia sostiene il mondo del lavoro
Mazzucchelli, S. (2012) · Cited by 4
Oshik, S., Naik, P., B, K. K. G., Patil, C., & Prakash Goudanavar, S. O. P. (2025) · Journal of Nanoparticle Research · doi:10.1007/s11051-025-06366-3 · Cited by 3
“Likewise, helical and branching nanoparticle ensembles enhance cooperative binding by mimicking biological recognition systems [78].”
Liu, C., Li, M., Tan, Y., Gou, W., Fan, G., & Zhong, B. (2025) · Bioinformatics · doi:10.1093/bioinformatics/btaf446 · Cited by 3
“As observed in Table 2, FoldX’s performance shows fluctuations when different types of structural inputs are used, such as AB645.”
InfluentialZhang, L., Zhou, X., Liang, L., & Lin, J. (2025) · ACS Omega · doi:10.1021/acsomega.5c08777 · Cited by 4
Computational design of protein complexes: influence of binding affinity
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Physics-based machine learning for enhanced drug formulation development
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MAMMAL - Molecular Aligned Multi-Modal Architecture and Language for biomedical discovery
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A New Tool to Study the Binding Behavior of Intrinsically Disordered Proteins
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“in [43] presented a topology-based network tree to predict PPI using convolutional neural networks (CNNs).”
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Integrated Computational Pipeline for the High-Throughput Discovery of Cell Adhesion Peptides
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“A hybrid machine learning algorithm that integrates a CNN and GBT is designed to overcome difficulties, such that partial topologically simplified descriptions are converted into concise features by the CNN module and a GBT module is trained on the whole feature set for a robust predictor with effective control of ove…”
BackgroundMethodInfluentialSelf-citationDeep Local Analysis estimates effects of mutations on protein-protein interactionsPreprint
Behbahani, Y. M., Laine, É., & Carbone, A. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.10.09.511484 · Cited by 3
“Several computational methods have been proposed for estimating mutation-induced binding affinity changes ( ∆∆ G bind ) by exploiting protein sequence and structural information [38, 15, 29, 31, 32, 36, 40, 23].”
BackgroundMethodNapiorkowska, M., Fischer, K., Penner, M., Knyphausen, P., & Hollfelder, F. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.11.20.567881 · Cited by 3
Leveraging Neural Networks to Correct FoldX Free Energy Estimates
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InfluentialWu, J., Sun, J., Liang, T., Zhang, Y., Zhang, H., Zhang, T., Feng, X., Gao, P., Xu, P., & Li, J. (2025) · Chemical Science · doi:10.1039/d5sc08898d · Cited by 2
“20 Among the most advanced models in this category, MT-TopLap integrates persistent Laplacian features with physicochemical descriptors and transformer-based protein language model embeddings, achieving superior performance in predicting binding a ffi nity changes.”
Emerging strategies for computational identification of protein–protein interaction hotspots
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“,46 – 48 Among these tools, we concentrated on two, mmCSM-PPI 22 and TopNetTree, 23,24 of which results on the RBD – ACE2 system were readily available.”
MethodInfluentialTang, J., Hu, R., Liu, Y., Liu, Y., Wang, G., Lv, J., Cheng, L., He, T., Liu, Y., Shao, P., et al. (2024) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2024.108325 · Cited by 2
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“For instance, mmCSM-PPI (Rodrigues et al., 2021), Geo-PPI (Liu et al., 2021), TopNetTree (Wang et al., 2020), and PPI-af fi nity (Romero-Molina et al., 2022) use extra-tree, gradient-boosting trees and support vector machine (SVM) algorithms to achieve a Pearson ’ s correlation coef fi cients (r) of…”
InfluentialLiu, C., Cai, S., Pan, T., Ogata, H., Song, J., & Akutsu, T. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5c00130 · Cited by 2
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“Gradient boosting trees Figure 10: An illustration of the TopNetTree model [74].”
InfluentialSelf-citationEmerging vaccine-breakthrough SARS-CoV-2 variantsPreprint
Wang, R., Chen, J., Hozumi, Y., Yin, C., & Wei, G. (2021) · PubMed · doi:10.48550/arxiv.2109.04509 · Cited by 7
“BFE changes following mutations are predicted by our deep learning model, TopNetTree [32].”
BackgroundSelf-citationChen, C., Boorla, V. S., Chowdhury, R., Nissly, R. H., Gontu, A., Chothe, S. K., LaBella, L. C., Jakka, P., Ramasamy, S., Vandegrift, K. J., et al. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.03.22.485413 · Cited by 2
“accurately reproduce experimentally determined binding free energies (ΔΔGbind).(53,54) As a powerful complement, machine learning algorithms can effectively “learn” highly complex relationships among energy components and the target binding affinity from training samples.”
BackgroundLiu, Y., Armstrong, G., Tam, J. Z., & Chen, B. (2023) · bioRxiv · doi:10.1101/2023.10.26.564257 · Cited by 1
“…mutation benchmark datasets, including single-point mutations in the, non-redundant interface single-point mutations in the SKEMPI dataset (S1131) [ 17 ] , single-point mutations in the SKEMPI2 dataset (S4169) [ 13 ] , and single-point mutations in the SKEMPI2 balanced dataset (s8338) [ 13 ] .”
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Li, M., Yu, H., Fan, G., Zhou, Z., Tan, P., & Hong, L. (2024) · Research Square · doi:10.21203/rs.3.rs-3987561/v1 · Cited by 2
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(2025) · doi:10.1371/journal.pcbi.1013216 · Cited by 4
“Previous binding affinity prediction algorithms that use persistent homology all have computational complexity O(( m + n ) 4.8 ) or worse [34,36–38, 43, 54– 56 ].”
InfluentialClassification 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
“TDA has found applications across diverse fields, such as material science [17], [18], biomolecules [19], [20], on-cology [21], sensor networks [22], and data science [23].”
BackgroundZhu, Y., Xiong, H., Liu, S., Wu, D., Zhang, X., Shi, X., Qu, J. T., Chen, L., Liu, Z., Peng, B., et al. (2023) · Viruses · doi:10.3390/v15071565 · Cited by 1
“Numerous scholars have proposed various methods to forecast the changes in binding free energy (BFE) resulting from mutations, including the TopNetTree model [5], MutaBind2 method [6], SAAMBE-SEQ method [7], SAAMBE-3D method [8], and so on.”
MethodDsouza, N., Sadasivan, S., & Selvaa Kumar, C. (2023) · Proceedings of the Indian National Science Academy · doi:10.1007/s43538-023-00200-x · Cited by 1
“Further, we compared the peripheral amino acid residues in the non-interface region (Wang et al. 2020) in the 5 Å vicini-ties of EFNB2 receptor binding sites.”
BackgroundAn application of topological data analysis in predicting sumoylation sites
Lin, X., Gao, Y., & Lei, F. (2023) · PeerJ · doi:10.7717/peerj.16204 · Cited by 1
“Additional information on TDA and PH can be found in Edelsbrunner, Letscher & Zomorodian (2000) , Zomorodian & Carlsson (2004) , Munkres (2018) , and Wang, Cang & Wei (2020) .”
BackgroundConcept and Development of Algebraic Topological Framework Nucleic Acids
Song, L., Zuo, X., & Li, M. (2024) · ChemPlusChem · doi:10.1002/cplu.202300760 · Cited by 1
Predicting Antibody Affinity Changes upon Mutation Based on Unbound Protein Structures
Chen, Z., He, S., Chi, X., & Bo, X. (2025) · International Journal of Molecular Sciences · doi:10.3390/ijms26031343 · Cited by 1
“The SKEMPI 2.0 dataset and several subsets (e.g., S645 [16], S1131 [27], S4169 [11], M1707 [28]) are widely used in ∆∆ G prediction tasks.”
InfluentialRecent advances in antibody optimization based on deep learning methods
Jin, R., Zhou, R., & Zhang, D. (2025) · Journal of Zhejiang University SCIENCE B · doi:10.1631/jzus.b2400387 · Cited by 1
“Wang et al. (2020) integrated protein crystal struc ‐ ture information and proposed the TopNetTree model to predict changes in binding affinity caused by mu ‐ tations in protein – protein complexes.”
AFToolkit: a framework for molecular modeling of proteins with AlphaFold-derived representations
Sindeeva, M., Telepov, A., Ivanisenko, N. V., Shashkova, T., Khrabrov, K., Tsypin, A., Kadurin, A., & Kardymon, O. L. (2025) · Briefings in Bioinformatics · doi:10.1093/bib/bbaf324 · Cited by 1
Multitask Learning-Based Approaches for Protein Function Prediction
Bahmani, S., Chaudhari, M., Carrier, C., Garrett, S., Pratyush, P., & KC, D. B. (2025) · Methods in molecular biology · doi:10.1007/978-1-0716-4662-5_4 · Cited by 1
Deep learning for affinity prediction and interface prediction in molecular interactions
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Topological descriptors for learning-based, rotation-invariant protein surface classification
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How AI Can Advance Mathematical Biology: Opportunities, Challenges, and Future Directions
Rabiei, K., Rempała, G. A., Laubenbacher, R., & Hao, W. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-026-01744-x · Cited by 1
“In more quantitatively oriented work, data-driven predictors have also been used for the prediction of toxicity, the assessment of protein interactions, and drug screening using engineered molecular descriptors (Wu and Wei 2018; Wang et al. 2020; Feng et al. 2023).”
dos Santos, L. M., de Mendonça, J. G., Lobo, Y. J. G., de Lima, L. H. F., Rocha, G. B., & de Melo-Minardi, R. C. (2024) · Scientific Reports · doi:10.1038/s41598-024-72842-w · Cited by 2
“· ) , corresponding to neutral mutants and variants, and estimated from the TopNetTree application 84,85 .”
BackgroundMethodBehavior Tomographer: Identifying Hidden Cybercrimes by Behavior Interior Structure Modeling
Wang, C., & Zhu, H. (2025) · IEEE Transactions on Services Computing · doi:10.1109/tsc.2025.3539194 · Cited by 1
PLNet : Persistent Laplacian neural network for protein–protein binding free energy prediction
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Self-citationA 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
“Applications of persistent homology to molecular biology has achieved great success in computer aided drug design [63, 79, 80].”
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Self-citationDe novo generation of antibody CDRH3 with a pre-trained generative large language modelPreprint
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Characterizing SARS-CoV-2 mutations in the United StatesPreprint
Wang, R., Chen, J., Gao, K., Hozumi, Y., Yin, C., & Wei, G. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.12692
“The error with the corresponding dataset is given as Pearson correlations coefficient (Rp) of 0.79 and root mean square error (RMSE) of 0.91 kcal/mol from previous work [11].”
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Self-citationTopological AI forecasting of future dominating viral variantsPreprint
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“Right before the pandemic began, researchers developed an ESPH-based deep learning method that offers state-of-the-art predictions of mutation-induced binding affinity changes of protein-protein interactions — including antibody-antigen, interactions [9].”
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A geometric and topological analysis of the binding behavior of Intrinsically Disordered Proteins
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“Menglun et al. in [21] presented a topology-based network tree to predict PPI using convolutional neural networks (CNN).”
BackgroundComputational Prediction Approaches for Predicting Mutation Impact on Protein-Protein Interactions
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Geometric and topological AI for molecular sciences
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Liang, S., Turkeš, R., Li, J., Otter, N., & Montúfar, G. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2310.07073
“PH representations have been used particularly in applications where multiscale homological features can be expected to capture relevant information, such as in the prediction of biomolecular properties (Cang & Wei, 2017; Cang et al., 2018; Wang et al., 2020), quantification of similarity in materials (Lee et al.”
BackgroundMethodAn Antigen Design Method Based on Molecular Dynamics and Deep Learning
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“For comparative analysis, we utilized several computational tools including GeoPPI [38], TopGBT, TopNetTree [39], mCSM-PPI2, MutaBind2 [40], and FoldX.”
Automatic Explanation of Protein-Protein Binding Mechanism: A Preliminary Study
Tam, J. Z., Liu, Y., Jain, D. S., Armstrong, G. A., & Chen, B. Y. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-85435-4_7
Computational Attitudes to Drug Discovery in Autism Spectrum Disorder
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New aspects of analyzing amyloid fibrils
Lin, X., Zi, Y., Li, F., & Li, J. (2025) · Data Analytics and Topology · doi:10.4310/daat.250513010418
“To explore structural or functional properties of proteins in practice, we mostly consider the heavy atoms of residues, the backbone of peptide chain, or the set of C α s [6, 74] to simplify the structure of protein.”
Computational Methods Applied to Drug Discovery of Protein–Protein Interaction Systems
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Behavior Molecule-Level Learning by Behavioral Interior Reconstruction
Wang, C. (2025) · Springer eBooks · doi:10.1007/978-981-95-1013-9_3
Identifying Hidden Cybercrime Behavior by Behavior Tomographer
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SE3Bind: SE(3)-equivariant model for antibody-antigen binding affinity predictionPreprint
Subedy, A., Bhadra-Lobo, S., & Lamoureux, G. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.01.17.700115
“N Validation set N Split R a TopNetTree [34] SKEMPI 1131 [38] 1131 SKEMPI 1131 [38] 1131 Random 0.85 TopNetTree [34] AB-Bind S645 [32] 618 AB-Bind S645 [32] 618 Random 0.68 TopNetTree [34, 35] SKEMPI 1131 [38] 1131 SKEMPI 1131 [38] 1131 Protein ECOD classes 0.38 PerSpect-EL (M3) [39] SKEMPI 1131…”
InfluentialZhang, H., Liu, Y., Yu, L., Wang, Z., Liu, Y., & Guo, M. (2025) · IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · doi:10.1109/bibm66473.2025.11356932
“PCC ↑ RMSE ↓ SAAMBE-SEQ [17] 0.624 - BindProfX [16] 0.738 - TopNetTree [8] 0.850 1.550 PerSpect-EL [9] 0.853 1.303 GeoPPI [10] 0.855 1.298 HCML [19] 0.857 1.279 PTA-SEL [20] 0.866 1.216 PIPR+S2F [21] 0.866 1.210 SFM-Net [11] 0.881 1.142 MFFN 0.911 1.112 The proposed MFFN framework has the best…”
InfluentialDeng, J., Gu, M., Zhang, P., Liu, T., Hu, G., Dong, M., Zhang, Y., Song, Y., Zhang, Y., Liu, M., et al. (2026) · Briefings in Bioinformatics · doi:10.1093/bib/bbag105
“In contrast, topological deep-learning methods, represented by TopNetTree [25], extend beyond pairwise connectivity by integrating convolutional and gradient-boosting models to extract global, high-dimensional topological features.”
Wu, S., Xu, N., Xin, X., Zhang, M., Liu, H., Zhu, H., Wei, Z., Zhao, C., Yu, L., & Feng, W. (2026) · Bioinformatics · doi:10.1093/bioinformatics/btag150
“Data-driven baselines—including GeoPPI, TopGBT, TopNetTree, MpbPPI, DGCddg and MutaBind2—were executed using their official implementations, with identical dataset splits, and evaluation metrics.”
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Layer-Wise Persistent Entropy of CT Scan Point Clouds for Lung Tumor Classification
Jose, C. J., Baiju, A. P., Roy, R., Harikrishnan, A., Sanju, R., Kumar, P., Sherly, K. K., Jacob, R., & Sreekumar, G. (2026) · AppliedMath · doi:10.3390/appliedmath6060095
“TDA-based methods have demonstrated broad utility in biomedical applications, including predicting protein–protein interaction binding affinities [5], classifying biomedical networks [6,7], predicting survival outcomes in cancer patients [8,9], segmenting skin lesions [10], and medical image…”
Zhou, H., Wang, Y., Shi, X., & Ma, Y. (2026) · Journal of Computer-Aided Molecular Design · doi:10.1007/s10822-026-00867-6
The Forgetting-Learning Trade-off: Making Reinforcement Learning Work for Protein Language Models
Cao, H., Zhang, H., Xu, J., Zhang, Z., Shen, L., Sun, M., Liu, G., Xu, J., Li, W.-J., Ni, J., et al. (2026) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3770855.3818895
Sajeev, F., & Roy, S. (2026) · Frontiers in Chemistry · doi:10.3389/fchem.2026.1899937
“This embeds structural information into topological invariants for further machine learning (Wang et al., 2020).”
Han, B., Zhang, Y., Zheng, M., Gong, X., & Xia, K. (2026) · Cell Reports Physical Science · doi:10.1016/j.xcrp.2026.103564
Metadata
- Authors
- Wang, M., Cang, Z., & Wei, G.-W.
- Affiliations
- Michigan State University (US)
- Corresponding author
- Wei, Guo-Wei
- Venue
- Nature Machine Intelligence
- Published
- 2020-02-14
- Volume
- 2
- Issue
- 2
- Pages
- 116-123
- ISSN
- 2522-5839 (ISSN-L)
- PMC
- PMC7223817
- OpenAlex
- W3005822506
- Semantic Scholar
- 544ee14a801abef4019e1962a38e9a1f936ef01a
- Cited by
- 202
- References
- 54
- Citations by year
- 2026: 19 · 2025: 41 · 2024: 39 · 2023: 41 · 2022: 32 · 2021: 22 · 2020: 7
- FWCI
- 8.27
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- Locations
- Nature Machine Intelligence (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation (DMS-1721024, DMS 1761320, DMS-1761320, IIS1900473)
- U.S. Department of Health & Human Services | NIH | National Institute of General Medical Sciences (GM126189)
- Bristol-Myers Squibb
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Machine Learning in Bioinformatics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
- Keywords
- protein-protein interaction, ΔΔG, mutation effects, persistent homology, algebraic topology, protein-protein complex, convolutional neural networks, gradient boosting decision tree, topological invariants
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