Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions

Krishnan       Balasubramanian; Satya    P.    Gupta
Abstract

Background: Protein-protein interactions (PPIs) are becoming increasingly important as PPIs form the basis of multiple aggregation-related diseases such as cancer, Creutzfeldt-Jakob, and Alzheimer’s diseases. This mini-review presents hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies facilitate the discovery of some PPI inhibitors of therapeutic importance.
Objective: The objective of this review is to present hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies enable the discovery of some PPI inhibitors of therapeutic importance.
Methods: This article presents a detailed survey of hybrid quantum dynamics that combines classical and quantum MD for PPIs. The article also surveys various developments pertinent to topological, graph theoretical, group theoretical and docking studies of PPIs and highlight how the methods facilitate the discovery of some PPI inhibitors of therapeutic importance.
Results: It is shown that it is important to include higher-level quantum chemical computations for accurate computations of free energies and electrostatics of PPIs and Drugs with PPIs, and thus techniques that combine classical MD tools with quantum MD are preferred choices. Topological, graph theoretical and group theoretical techniques are shown to be important in studying large network of PPIs comprised of over 100,000 proteins where quantum chemical and other techniques are not feasible. Hence, multiple techniques are needed for PPIs.
Conclusion: Drug discovery and our understanding of complex PPIs require multifaceted techniques that involve several disciplines such as quantum chemistry, topology, graph theory, knot theory and group theory, thus demonstrating a compelling need for a multi-disciplinary approach to the problem.
Keywords: Protein-protein interactions, Molecular dynamics, Topological techniques, Graph-Theoretical methods, Grouptheoretical methods, Docking, Knot theory.
Graphical Abstract

[1] 
Gupta, M.; Chauhan, R.; Prasad, Y.; Wadhwa, G.; Jain, C.K. Protein-protein interaction and molecular dynamics analysis for identification of novel inhibitors in Burkholderia cepacia GG4. Comput. Biol. Chem.,  2016, 65, 80-90.
[http://dx.doi.org/10.1016/j.compbiolchem.2016.10.003] [PMID:  27776248] 
[2] 
Rakers, C.; Bermudez, M.; Keller, B.G.; Mortier, J.; Wolber, G. Computational close up on protein–protein interactions: How to unravel the invisible using molecular dynamics simulations? Wiley Interdiscip. Rev. Comput. Mol. Sci.,  2015, 5(5), 345-359.
[http://dx.doi.org/10.1002/wcms.1222] 
[3] 
Haberl, F.; Othersen, O.; Seidel, U.; Lanig, H.; Clark, T. Investigating protein-protein and protein-ligand interactions by molecular dynamics simulations; High Performance Computing in Science and Engineering: Garching, Munich, 2009, pp. 153-164.
[http://dx.doi.org/10.1007/978-3-540-69182-2_12] 
[4] 
Cau, Y.; Fiorillo, A.; Mori, M.; Ilari, A.; Botta, M.; Lalle, M. Molecular dynamics simulations and structural analysis of Giardia duodenalis 14-3-3 protein-protein interactions. J. Chem. Inf. Model.,  2015, 55(12), 2611-2622.
[http://dx.doi.org/10.1021/acs.jcim.5b00452] [PMID:  26551337] 
[5] 
Jones, M.R.; Liu, C.; Wilson, A.K. Molecular dynamics studies of the protein-protein interactions in inhibitor of κB kinase-β. J. Chem. Inf. Model.,  2014, 54(2), 562-572.
[http://dx.doi.org/ 10.1021/ci400720n] [PMID:  24437505] 
[6] 
Elcock, A.H.; Sept, D.; McCammon, J.A. Computer simulation of protein−protein interactions. J. Phys. Chem. B,  2001, 105, 1504-1518.
[http://dx.doi.org/10.1021/jp003602d] 
[7] 
Plattner, N.; Doerr, S.; De Fabritiis, G.; Noé, F. Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling. Nat. Chem.,  2017, 9(10), 1005-1011.
[http://dx.doi.org/10.1038/nchem.2785] [PMID:  28937668] 
[8] 
Neumann, J. Molecular dynamics simulations of protein-protein interactions and THz driving of molecular rotors on gold (Doctoral dissertation, lmu). 2011.
[9] 
Sun, Z.; Yan, Y.N.; Yang, M.; Zhang, J.Z. Interaction entropy for protein-protein binding. J. Chem. Phys.,  2017, 146(12), 124124.
[http://dx.doi.org/10.1063/1.4978893] [PMID:  28388125] 
[10] 
Sivakamavalli, J.; Selvaraj, C.; Singh, S.K.; Vaseeharan, B. Exploration of protein-protein interaction effects on α-2-macroglobulin in an inhibition of serine protease through gene expression and molecular simulations studies. J. Biomol. Struct. Dyn.,  2014, 32(11), 1841-1854.
[http://dx.doi.org/10.1080/07391102.2013.838909] [PMID:  24124927] 
[11] 
Lu, M.C.; Yuan, Z.W.; Jiang, Y.L.; Chen, Z.Y.; You, Q.D.; Jiang, Z.Y. A systematic molecular dynamics approach to the study of peptide Keap1-Nrf2 protein-protein interaction inhibitors and its application to p62 peptides. Mol. Biosyst.,  2016, 12(4), 1378-1387.
[http://dx.doi.org/10.1039/C6MB00030D] [PMID:  26935067] 
[12] 
Delaforge, E.; Milles, S.; Huang, J.R.; Bouvier, D.; Jensen, M.R.; Sattler, M.; Hart, D.J.; Blackledge, M. Investigating the role of large-scale domain dynamics in protein-protein interactions. Front. Mol. Biosci.,  2016, 3, 54.
[http://dx.doi.org/10.3389/fmolb.2016. 00054] [PMID:  27679800] 
[13] 
Cole, D.J.; Skylaris, C.K.; Rajendra, E.; Venkitaraman, A.R.; Payne, M.C. Protein-protein interactions from linear-scaling first-principles quantum-mechanical calculations. EPL Europhys. Lett.,  2010, 91(3), 37004.
[http://dx.doi.org/10.1209/0295-5075/91/37004] 
[14] 
Demissie, T.B.; Garabato, B.D.; Ruud, K.; Kozlowski, P.M. Mercury methylation by cobalt corrinoids: Relativistic effects dictate the reaction mechanism. Angew. Chem. Int. Ed. Engl.,  2016, 55(38), 11503-11506.
[http://dx.doi.org/10.1002/anie.201606001] [PMID:  27510509] 
[15] 
Tenderholt; A. L.; Szilagyi; R. K.; Holm; R. H.; Hodgson; K. O.; Hedman; B.; Solomon; E. I. Sulfur K-edge XAS of WVO vs. MoVObis (dithiolene) complexes: Contributions of relativistic effects to electronic structure and reactivity of tungsten enzymes. J. Inorg. Biochem.,  2007, 101(11-12), 1594-1600.
[http://dx.doi.org/10. 1016/j.jinorgbio.2007.07.011] [PMID:  17720249] 
[16] 
Balasubramanian, K. Spectroscopic constants and potential energy curves of tungsten carbide. J. Chem. Phys.,  2000, 112(17), 7425-7436.
[http://dx.doi.org/10.1063/1.481373] 
[17] 
Balasubramanian, K.; Liao, D.W. Spectroscopic properties of low-lying electronic states of rhodium dimer. J. Phys. Chem.,  1989, 93(10), 3989-3992.
[http://dx.doi.org/10.1021/j100347a025] 
[18] 
Balasubramanian, K. Relativistic Effects in Chemistry, Part A:
Theory & Techniques Wiley-Interscience, New York. , 1997; p. 327.
[19] 
Balasubramanian, K. Relativity and chemical bonding. J. Phys. Chem. A,  1989, 93, 6585-6596.
[http://dx.doi.org/10.1021/j100355a005] 
[20] 
(a)Balasubramanian, K. Relativistic calculations of electronic states and potential energy surfaces of Sn3. J. Chem. Phys.,  1996, 85, 3401-3406.
(b)Balasubramanian, K. CASSCF/CI calculations on Si4 and Si4+. Chem. Phys. Lett.,  1987, 135(3), 283-287.
(c)Balasubramanian, K.; Sumathi, K.; Dai, D. Group V trimers and their positive ions: The electronic structure and potential energy surfaces. J. Chem. Phys.,  1991, 95(5), 3494-3505.
[http://dx.doi.org/ 10.1063/1.460852] 
[21] 
Majumdar, D.; Balasubramanian, K.; Nitsche, H. A comparative theoretical study of bonding in UO2++, UO2+, UO2, UO2−, OUCO, O2U(CO)2 and UO2CO3. Chem. Phys. Lett.,  2002, 361, 143-151.
[http://dx.doi.org/10.1016/S0009-2614(02)00899-0] 
[22] 
Benavides-Garcia, M.G.; Balasubramanian, K. Structural insights into the binding of uranyl with human serum protein apotransferrin structure and spectra of protein-uranyl interactions. Chem. Res. Toxicol.,  2009, 22(9), 1613-1621.
[http://dx.doi.org/10.1021/tx900184r] [PMID:  19678663] 
[23] 
Balasubramanian, K. Applications of combinatorics and graph theory to spectroscopy and quantum chemistry. Chem. Rev.,  1985, 85(6), 599-618.
[http://dx.doi.org/10.1021/cr00070a005] 
[24] 
Bu, D.; Zhao, Y.; Cai, L.; Xue, H.; Zhu, X.; Lu, H.; Zhang, J.; Sun, S.; Ling, L.; Zhang, N.; Li, G.; Chen, R. Topological structure analysis of the protein-protein interaction network in budding yeast. Nucleic Acids Res.,  2003, 31(9), 2443-2450.
[http://dx.doi.org/10.1093/nar/gkg340] [PMID:  12711690] 
[25] 
Balasubramanian, K. Spectra of chemical trees. Int. J. Quantum Chem.,  1982, 21(3), 581-590.
[http://dx.doi.org/10.1002/qua. 560210306] 
[26] 
Balasubramanian, K.; Randić, M. Spectral polynomials of systems with general interactions. Int. J. Quantum Chem.,  1985, 28(4), 481-498.
[http://dx.doi.org/10.1002/qua.560280406] 
[27] 
Balasubramanian, K.; Randić, M. The characteristic polynomials of structures with pending bonds. Theor. Chim. Acta,  1982, 61(4), 307-323.
[http://dx.doi.org/10.1007/BF00550410] 
[28] 
Balasubramanian, K. Tree pruning and lattice statistics on Bethe lattices. J. Math. Chem.,  1988, 2(1), 69-82.
[http://dx.doi.org/ 10.1007/BF01166469] 
[29] 
Balasubramanian, K. Recent developments in tree-pruning methods and polynomials for cactus graphs and trees. J. Math. Chem.,  1990, 4(1), 89-102.
[http://dx.doi.org/10.1007/BF01170006] 
[30] 
Balasubramanian, K. The use of Frame’s method for the characteristic polynomials of chemical graphs. Theor. Chim. Acta,  1984, 65(1), 49-58.
[http://dx.doi.org/10.1007/BF00552298] 
[31] 
Balasubramanian, K. Computer generation of the characteristic polynomials of chemical graphs. J. Comput. Chem.,  1984, 5(4), 387-394.
[http://dx.doi.org/10.1002/jcc.540050417] 
[32] 
Balasubramanian, K. Computer generation of distance polynomials of graphs. J. Comput. Chem.,  1990, 11(7), 829-836.
[http://dx.doi.org/10.1002/jcc.540110706] 
[33] 
Balasubramanian, K. Computer generation of characteristic polynomials of edge‐weighted graphs, heterographs, and directed graphs. J. Comput. Chem.,  1988, 9(3), 204-211.
[http://dx.doi.org/10.1002/jcc.540090304] 
[34] 
Balasubramanian, K. Symmetry and spectra of graphs and their chemical applications; Chemical Applications of Topology and Graph Theory, 1983. 
[35] 
Balasubramanian, K. Characteristic polynomials of organic polymers and periodic structures. J. Comput. Chem.,  1985, 6(6), 656-661.
[http://dx.doi.org/10.1002/jcc.540060620] 
[36] 
Balasubramanian, K.; Basak, S.C. Characterization of isospectral graphs using graph invariants and derived orthogonal parameters. J. Chem. Inf. Comput. Sci. J.,  1985, 38(3), 367-373.
[http://dx.doi.org/10.1021/ci970052g] 
[37] 
Balasubramanian, K.; Khokhani, K.; Basak, S.C. Complex graph matrix representations and characterizations of proteomic maps and chemically induced changes to proteomes. J. Proteome Res.,  2006, 5(5), 1133-1142.
[http://dx.doi.org/10.1021/pr050445s] [PMID:  16674102] 
[38] 
Khokhani, K.; Basak, S.; Balasubramanian, K. Complex graph matrix representations and characterizations of proteomic maps and chemically induced changes to proteomes. J. Proteome Res.,  2006, 5(5), 1133-1142.
[http://dx.doi.org/10.1021/pr0504455] 
[39] 
Bajzer, Z.; Randić, M.; Plavsić, D.; Basak, S.C. Novel map descriptors for characterization of toxic effects in proteomics maps. J. Mol. Graph. Model.,  2003, 22(1), 1-9.
[http://dx.doi.org/10.1016/S1093-3263(02)00186-9] [PMID:  12798386] 
[40] 
Randić, M.; Lerš, N.; Plavić, D.; Basak, S.C. On invariants of a 2-D proteome map derived from neighborhood graphs. J. Proteome Res.,  2004, 3(4), 778-785.
[http://dx.doi.org/10.1021/pr049957h] [PMID:  15359731] 
[41] 
Randić, M.; Witzmann, F.; Vračko, M.; Basak, S.C. On characterization of proteomics maps and chemically induced changes in proteomes using matrix invariants: Application to peroxisome proliferators. Med. Chem. Res.,  2001, 10(7-8), 456-479.
[42] 
Vračko, M.; Basak, S.C. Similarity study of proteomic maps. Chemom. Intell. Lab. Syst.,  2004, 70(1), 33-38.
[http://dx.doi.org/ 10.1016/j.chemolab.2003.09.005] 
[43] 
Guo, X.; Randic´, M.; Basak, S.C. A novel 2-D graphical representation of DNA sequences of low degeneracy. Chem. Phys. Lett.,  2001, 350(1-2), 106-112.
[http://dx.doi.org/10.1016/S0009-2614(01)01246-5] 
[44] 
Basak, S.C.; Gute, B.D.; Witzmann, F. Information-theoretic biodescriptors for proteomics maps: Development and applications in predictive toxicology. Complexity,  2005, 1, 2.
[45] 
Vračko, M.; Basak, S.C.; Witzmann, F. Chemometrical analysis of proteomics data obtained from three cell types treated with multi-walled carbon nanotubes and TiO2 nanobelts$. SAR QSAR Environ. Res.,  2018, 29(8), 567-577.
[http://dx.doi.org/10.1080/1062936X.2018.1498015] [PMID:  30052065] 
[46] 
Randić, M.; Novic, M.; Vracko, M. Novel characterization of proteomics maps by sequential neighborhoods of protein spots. J. Chem. Inf. Model.,  2005, 45(5), 1205-1213.
[http://dx.doi.org/ 10.1021/ci0497612] [PMID:  16180897] 
[47] 
Randić, M.; Zupan, J.; Balaban, A.T. Unique graphical representation of protein sequences based on nucleotide triplet codons. Chem. Phys. Lett.,  2004, 397(1-3), 247-252.
[http://dx.doi.org/ 10.1016/j.cplett.2004.08.118] 
[48] 
Randić, M.; Vracko, M.; Nandy, A.; Basak, S.C. On 3-D graphical representation of DNA primary sequences and their numerical characterization. J. Chem. Inf. Comput. Sci.,  2000, 40(5), 1235-1244.
[http://dx.doi.org/10.1021/ci000034q] [PMID:  11045819] 
[49] 
Davis, D.; Yaveroğlu, Ö.N.; Malod-Dognin, N.; Stojmirovic, A.; Pržulj, N. Topology-function conservation in protein-protein interaction networks. Bioinformatics,  2015, 31(10), 1632-1639.
[http://dx.doi.org/10.1093/bioinformatics/btv026] [PMID:  25609797] 
[50] 
Birlutiu, A.; Heskes, T. Using topology information for proteinprotein
interaction prediction.Pattern Recognition in Bioinformatics.
(LNCS, volume 8626); , 2014, pp. 10-22.
[51] 
Singh, B. Topological characterization of protein-protein interaction
networks in human and mouse. Nature Proceedings, 2011.http://hdl.handle.net/10101/npre 2011.6126.1
[52] 
Holland, D.O.; Shapiro, B.H.; Xue, P.; Johnson, M.E. Protein-protein binding selectivity and network topology constrain global and local properties of interface binding networks. Sci. Rep.,  2017, 7(1), 5631.
[http://dx.doi.org/10.1038/s41598-017-05686-2] [PMID:  28717235] 
[53] 
Susymary, J.; Lawrance, R. Graph theory analysis of protein-protein interaction network and graph based clustering of proteins linked with zika virus using MCL algorithm. 2017International Conference on,  , pp. 1-7.
[http://dx.doi.org/10.1109/ICCPCT.2017.8074381] 
[54] 
Basak, S.C.; Grunwald, G.D.; Gute, B.D.; Balasubramanian, K.; Opitz, D. Use of statistical and neural net approaches in predicting toxicity of chemicals. J. Chem. Inf. Comput. Sci.,  2000, 40(4), 885-890.
[http://dx.doi.org/10.1021/ci9901136] [PMID:  10955514] 
[55] 
Wallace, R. Spontaneous symmetry breaking in a non-rigid molecule approach to intrinsically disordered proteins. Mol. Biosyst.,  2012, 8(1), 374-377.
[http://dx.doi.org/10.1039/C1MB05256J] [PMID:  21904747] 
[56] 
Wallace, R. Multifunction moonlighting and intrinsically disordered proteins: information catalysis, non-rigid molecule symmetries and the ‘logic gate’spectrum. C. R. Chim.,  2011, 14(12), 1117-1121.
[http://dx.doi.org/10.1016/j.crci.2011.10.003] 
[57] 
Wallace, R. Extending Swerdlow’s hypothesis: statistical models of mitochondrial deterioration and aging. J. Math. Chem.,  2014, 52(10), 2663-2679.
[http://dx.doi.org/10.1007/s10910-014-0418-x] 
[58] 
Wallace, R. Tools for the future: Hidden symmetries. Comput.
Psychiatry,  2017, 153-165.
[http://dx.doi.org/10.1007/978-3-319- 53910-2_7] 
[59] 
Balasubramanian, K. The symmetry groups of nonrigid molecules as generalized wreath products and their representations. J. Chem. Phys.,  1980, 72(1), 665-677.
[http://dx.doi.org/10.1063/1.438963] 
[60] 
Balasubramanian, K. Group theory of non-rigid molecules and its applications. Studies Phys. Theor. Chem,  1983, 23, 149-168.
[61] 
Balasubramanian, K. Symmetry groups of chemical graphs. Int. J. Quantum Chem.,  1982, 21(2), 411-418.
[http://dx.doi.org/ 10.1002/qua.560210206] 
[62] 
Balasubramanian, K. A generalized wreath product method for the enumeration of stereo and position isomers of polysubstituted organic compounds. Theor. Chim. Acta,  1979, 51(1), 37-54.
[http://dx.doi.org/10.1007/BF02399129] 
[63] 
Balasubramanian, K. Generators of the character tables of generalized wreath product groups. Theor. Chim. Acta,  1990, 78(1), 31-43.
[http://dx.doi.org/10.1007/BF01112351] 
[64] 
Balasubramanian, K. Nested wreath groups and their applications to phylogeny in biology and Cayley trees in chemistry and physics. J. Math. Chem.,  2017, 55(1), 195-222.
[http://dx.doi.org/ 10.1007/s10910-016-0680-1] 
[65] 
Balasubramanian, K. Character tables of n-dimensional hyperoctahedral groups and their applications. Mol. Phys.,  2016, 114(10), 1619-1633.
[http://dx.doi.org/10.1080/00268976.2016.1142129] 
[66] 
Liang, C.; Mislow, K. Knots in proteins. J. Am. Chem. Soc.,  1994, 116(24), 11189-11190.
[http://dx.doi.org/10.1021/ja00103a057] 
[67] 
Taylor, W.R. A deeply knotted protein structure and how it might fold. Nature,  2000, 406(6798), 916-919.
[http://dx.doi.org/10.1038/35022623] [PMID:  10972297] 
[68] 
Long, J.A.; Moan, E.I.; Medford, J.I.; Barton, M.K. A member of the KNOTTED class of homeodomain proteins encoded by the STM gene of Arabidopsis. Nature,  1996, 379(6560), 66-69.
[http://dx.doi.org/10.1038/379066a0] [PMID:  8538741] 
[69] 
Erdmann, M.A. Protein similarity from knot theory: Geometric convolution and line weavings. J. Comput. Biol.,  2005, 12(6), 609-637.
[http://dx.doi.org/10.1089/cmb.2005.12.609] [PMID:  16108707] 
[70] 
Lua, R.C.; Grosberg, A.Y. Statistics of knots, geometry of conformations, and evolution of proteins. PLOS Comput. Biol.,  2006, 2(5), e45.
[http://dx.doi.org/10.1371/journal.pcbi.0020045] [PMID:  16710448] 
[71] 
Emmert-Streib, F. Algorithmic computation of knot polynomials of secondary structure elements of proteins. J. Comput. Biol.,  2006, 13(8), 1503-1512.
[http://dx.doi.org/10.1089/cmb.2006.13.1503] [PMID:  17061925] 
[72] 
Yeates, T.O.; Norcross, T.S.; King, N.P. Knotted and topologically complex proteins as models for studying folding and stability. Curr. Opin. Chem. Biol.,  2007, 11(6), 595-603.
[http://dx.doi.org/ 10.1016/j.cbpa.2007.10.002] [PMID:  17967433] 
[73] 
Sumners, D.W. Knot theory and DNA. Proceedings of Symposia in Applied Mathematics,  1992, 45, 45-72.
[http://dx.doi.org/ 10.1090/psapm/045/1196715] 
[74] 
Qiu, W.Y. Knot theory, DNA topology, and molecular symmetry breaking. Chemical Topology-Applications and Techniques. Mathematical Chemistry Series,  2006, 6, 175-237.
[75] 
Sumners, D.W. The role of knot theory in DNA research. Geom. Topol.,  1987, 297-318.
[76] 
Balasubramanian, K. Molecular orbitals and Hadamard matrices. Chem. Phys. Lett.,  1993, 210(1-3), 216-222.
[http://dx.doi.org/ 10.1016/0009-2614(93)89126-3] 
[77] 
Balasubramanian, K. Computer generation of Hadamard matrices. J. Comput. Chem.,  1993, 14(5), 603-619.
[http://dx.doi.org/ 10.1002/jcc.540140513] 
[78] 
MacWilliams, F.J.; Sloane, N.J.A. The theory of error-correcting codes, 1st ed; Elsevier, 1977, Vol. 16, p. 782.
[79] 
Petoukhov, S.V. Hadamard matrices and quint matrices in matrix presentations of molecular genetic systems. Symmetry Cult. Sci.,  2005, 16(3), 247-266.
[80] 
Petoukhov, S.V. Symmetries of the genetic code, Walsh functions and the theory of genetic logical holography. Symmetry Cult. Sci,  2016, 27, 95-98.
[81] 
Mallion, R.B.; Rouvray, D.H. The Golden Jubilee of the Coulson-Rushbrooke Pairing Theorem. J. Math. Chem.,  1990, 5(1), 1-21.
[http://dx.doi.org/10.1007/BF01166272] 
[82] 
Bonchev, D.; Rouvary, D.H. omplexity in chemistry: Introduction
& fundamentals 2003, 203.
[83] 
Kier, L.B.; Hall, L.H. Molecular connectivity in drug research; , 1976, p. 256.
[84] 
Randić, M. Characterization of molecular branching. J. Am. Chem. Soc.,  1975, 97(23), 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001] 
[85] 
Hosoya, H. The topological index Z before and after 1971. Internet Electron. J. Mol. Des.,  2002, 1, 428-442.
[86] 
Devilliers, J.; Balaban, A.T. Topological Indices & Related Descriptors in QSAR and QSPR; , 1999, p. 815.
[87] 
Estrada, E.; Uriarte, E. Recent advances on the role of topological indices in drug discovery research. Curr. Med. Chem.,  2001, 8(13), 1573-1588.
[http://dx.doi.org/10.2174/0929867013371923] [PMID:  11562286] 
[88] 
Arockiaraj, M.; Kavitha, S.R.J.; Balasubramanian, K.; Gutman, I. Hyper-Wiener and Wiener polarity indices of silicate and oxide frameworks. J. Math. Chem.,  2018, 56, 1493.
[http://dx.doi.org/ 10.1007/s10910-018-0881-x] 
[89] 
Arockiyaraj, M.; Clement, J.; Balasubramanian, K. Analytical expressions for topological properties of polycyclic benzenoid networks. J. Chem.,  2016, 30, 682-697.
[http://dx.doi.org/ 10.1002/cem.2851] 
[90] 
Arockiyaraj, M.; Clement, J.; Balasubramanian, K. Topological indices and their applications to circumcised donut benzenoid systems, kekulenes and drugs. Polycycl. Aromat. Compd., 2017.
[http://dx.doi.org/10.1080/10406638.2017.1411958] 
[91] 
Arockiaraj, M.; Klavžar, S.; Mushtaq, S.; Balasubramanian, K. Distance-based topological indices of nanosheets, nanotubes and nanotori of SiO2. J. Math. Chem.,  2018, 2018, 1-27.
[http://dx.doi.org/10.1007/s1091] 
[92] 
Arockiaraj, M.; Ruth Julie Kavitha, S.; Balasubramanian, K.; Rajasingh, I.; Clement, J. Topological characterization of coronoid polycyclic aromatic hydrocarbons. Polycycl. Aromat. Compd.,  2018, 1-19.
[http://dx.doi.org/10.1080/10406638.2018.1484778] 
[93] 
Arockiaraj, M.; Kavitha, S.R.J.; Balasubramanian, K.; Gutman, I. Hyper-Wiener and Wiener polarity indices of silicate and oxide frameworks. J. Math. Chem.,  2018, 56(5), 1493-1510.
[http://dx.doi.org/10.1007/s10910-018-0881-x] 
[94] 
Sable, R.; Jois, S. Surfing the protein-protein interaction surface using docking methods: Application to the design of PPI inhibitors. Molecules,  2015, 20(6), 11569-11603.
[http://dx.doi.org/10.3390/molecules200611569] [PMID:  26111183] 
[95] 
Cheng, A.C.; Coleman, R.G.; Smyth, K.T.; Cao, Q.; Soulard, P.; Caffrey, D.R.; Salzberg, A.C.; Huang, E.S. Structure-based maximal affinity model predicts small-molecule druggability. Nat. Biotechnol.,  2007, 25(1), 71-75.
[http://dx.doi.org/10.1038/nbt1273] [PMID:  17211405] 
[96] 
Wells, J.A.; McClendon, C.L. Reaching for high-hanging fruit in drug discovery at protein-protein interfaces. Nature,  2007, 450(7172), 1001-1009.
[http://dx.doi.org/10.1038/nature06526] [PMID:  18075579] 
[97] 
Fuller, J.C.; Burgoyne, N.J.; Jackson, R.M. Predicting druggable binding sites at the protein-protein interface. Drug Discov. Today,  2009, 14(3-4), 155-161.
[http://dx.doi.org/10.1016/j.drudis. 2008.10.009] [PMID:  19041415] 
[98] 
Wishart, D.S.; Knox, C.; Guo, A.C.; Cheng, D.; Shrivastava, S.; Tzur, D.; Gautam, B.; Hassanali, M. DrugBank: A knowledgebase for drugs, drug actions and drug targets. Nucleic Acids Res.,  2008, 36(Database issue), D901-D906.
[http://dx.doi.org/10.1093/nar/gkm958] [PMID:  18048412] 
[99] 
Xu, G.G.; Guo, J.; Wu, Y. Chemokine receptor CCR5 antagonist maraviroc: Medicinal chemistry and clinical applications. Curr. Top. Med. Chem.,  2014, 14(13), 1504-1514.
[http://dx.doi.org/ 10.2174/1568026614666140827143745] [PMID:  25159165] 
[100] 
Dömling, A. Small molecular weight protein-protein interaction antagonists: an insurmountable challenge? Curr. Opin. Chem. Biol.,  2008, 12(3), 281-291.
[http://dx.doi.org/10.1016/j.cbpa.2008. 04.603] [PMID:  18501203] 
[101] 
Bogan, A.A.; Thorn, K.S. Anatomy of hot spots in protein interfaces. J. Mol. Biol.,  1998, 280(1), 1-9.
[http://dx.doi.org/10.1006/jmbi.1998.1843] [PMID:  9653027] 
[102] 
Fischer, G.; Rossmann, M.; Hyvönen, M. Alternative modulation of protein-protein interactions by small molecules. Curr. Opin. Biotechnol.,  2015, 35, 78-85.
[http://dx.doi.org/10.1016/j.copbio. 2015.04.006] [PMID:  25935873] 
[103] 
Dias, D.M.; Van Molle, I.; Baud, M.G.; Galdeano, C.; Geraldes, C.F.; Ciulli, A. Is nmr Fragment screening fine-tuned to assess druggability of protein-protein interactions? ACS Med. Chem. Lett.,  2014, 5(1), 23-28.
[http://dx.doi.org/10.1021/ml400296c] [PMID:  24436777] 
[104] 
Kuenemann, M.A.; Sperandio, O.; Labbé, C.M.; Lagorce, D.; Miteva, M.A.; Villoutreix, B.O. In silico design of low molecular weight protein-protein interaction inhibitors: Overall concept and recent advances. Prog. Biophys. Mol. Biol.,  2015, 119(1), 20-32.
[http://dx.doi.org/10.1016/j.pbiomolbio.2015.02.006] [PMID:  25748546] 
[105] 
Jubb, H.; Blundell, T.L.; Ascher, D.B. Flexibility and small pockets at protein-protein interfaces: New insights into druggability. Prog. Biophys. Mol. Biol.,  2015, 119(1), 2-9.
[http://dx.doi.org/10.1016/j.pbiomolbio.2015.01.009] [PMID:  25662442] 
[106] 
Zhao, Y.; Aguilar, A.; Bernard, D.; Wang, S. Small-molecule inhibitors of the MDM2-p53 protein-protein interaction (MDM2 Inhibitors) in clinical trials for cancer treatment. J. Med. Chem.,  2015, 58(3), 1038-1052.
[http://dx.doi.org/10.1021/jm501092z] [PMID:  25396320] 
[107] 
Cierpicki, T.; Grembecka, J. Challenges and opportunities in targeting the menin-MLL interaction. Future Med. Chem.,  2014, 6(4), 447-462.
[http://dx.doi.org/10.4155/fmc.13.214] [PMID:  24635524] 
[108] 
Falchi, F.; Caporuscio, F.; Recanatini, M. Structure-based design of small-molecule protein-protein interaction modulators: the story so far. Future Med. Chem.,  2014, 6(3), 343-357.
[http://dx.doi.org/10. 4155/fmc.13.204] [PMID:  24575969] 
[109] 
Mori, M.; Vignaroli, G.; Botta, M. Small molecules modulation of 14-3-3 protein-protein interactions. Drug Discov. Today. Technol.,  2013, 10(4), e541-e547.
[http://dx.doi.org/10.1016/j.ddtec.2012. 10.001] [PMID:  24451646] 
[110] 
Silvian, L.; Enyedy, I.; Kumaravel, G. Inhibitors of protein-protein interactions: New methodologies to tackle this challenge. Drug Discov. Today. Technol.,  2013, 10(4), e509-e515.
[http://dx.doi.org/10.1016/j.ddtec.2012.10.004] [PMID:  24451642] 
[111] 
Jin, L.; Wang, W.; Fang, G. Targeting protein-protein interaction by small molecules. Annu. Rev. Pharmacol. Toxicol.,  2014, 54, 435-456.
[http://dx.doi.org/10.1146/annurev-pharmtox-011613-140028] [PMID:  24160698] 
[112] 
Coelho, E.D.; Arrais, J.P.; Oliveira, J.L. From protein-protein interactions to rational drug design: are computational methods up to the challenge? Curr. Top. Med. Chem.,  2013, 13(5), 602-618.
[http://dx.doi.org/10.2174/1568026611313050005] [PMID:  23548023] 
[113] 
Morris, G.M.; Huey, R.; Lindstrom, W.; Sanner, M.F.; Belew, R.K.; Goodsell, D.S.; Olson, A.J. AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility. J. Comput. Chem.,  2009, 30(16), 2785-2791.
[http://dx.doi.org/ 10.1002/jcc.21256] [PMID:  19399780] 
[114] 
Ewing, T.J.; Makino, S.; Skillman, A.G.; Kuntz, I.D. DOCK 4.0: Search strategies for automated molecular docking of flexible molecule databases. J. Comput. Aided Mol. Des.,  2001, 15(5), 411-428.
[http://dx.doi.org/10.1023/A:1011115820450] [PMID:  11394736] 
[115] 
Friesner, R.A.; Banks, J.L.; Murphy, R.B.; Halgren, T.A.; Klicic, J.J.; Mainz, D.T.; Repasky, M.P.; Knoll, E.H.; Shelley, M.; Perry, J.K.; Shaw, D.E.; Francis, P.; Shenkin, P.S. Glide: A new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy. J. Med. Chem.,  2004, 47(7), 1739-1749.
[http://dx.doi.org/10.1021/jm0306430] [PMID:  15027865] 
[116] 
Grinter, S.Z.; Zou, X. Challenges, applications, and recent advances of protein-ligand docking in structure-based drug design. Molecules,  2014, 19(7), 10150-10176.
[http://dx.doi.org/10.3390/molecules190710150] [PMID:  25019558] 
[117] 
Cross, J.B.; Thompson, D.C.; Rai, B.K.; Baber, J.C.; Fan, K.Y.; Hu, Y.; Humblet, C. Comparison of several molecular docking programs: pose prediction and virtual screening accuracy. J. Chem. Inf. Model.,  2009, 49(6), 1455-1474.
[http://dx.doi.org/ 10.1021/ci900056c] [PMID:  19476350] 
[118] 
Cao, J.; Kaneko, O.; Thongkukiatkul, A.; Tachibana, M.; Otsuki, H.; Gao, Q.; Tsuboi, T.; Torii, M. Rhoptry neck protein RON2 forms a complex with microneme protein AMA1 in Plasmodium falciparum merozoites. Parasitol. Int.,  2009, 58(1), 29-35.
[http://dx.doi.org/10.1016/j.parint.2008.09.005] [PMID:  18952195] 
[119] 
Srinivasan, P.; Beatty, W.L.; Diouf, A.; Herrera, R.; Ambroggio, X.; Moch, J.K.; Tyler, J.S.; Narum, D.L.; Pierce, S.K.; Boothroyd, J.C.; Haynes, J.D.; Miller, L.H. Binding of Plasmodium merozoite proteins RON2 and AMA1 triggers commitment to invasion. Proc. Natl. Acad. Sci. USA,  2011, 108(32), 13275-13280.
[http://dx.doi.org/10.1073/pnas.1110303108] [PMID:  21788485] 
[120] 
Pihan, E.; Delgadillo, R.F.; Tonkin, M.L.; Pugnière, M.; Lebrun, M.; Boulanger, M.J.; Douguet, D. Computational and biophysical approaches to protein-protein interaction inhibition of Plasmodium falciparum AMA1/RON2 complex. J. Comput. Aided Mol. Des.,  2015, 29(6), 525-539.
[http://dx.doi.org/10.1007/s10822-015-9842-7] [PMID:  25822046] 
[121] 
Chen, L.; Flies, D.B. Molecular mechanisms of T cell co-stimulation and co-inhibition. Nat. Rev. Immunol.,  2013, 13(4), 227-242.
[http://dx.doi.org/10.1038/nri3405] [PMID:  23470321] 
[122] 
Davis, S.J.; Ikemizu, S.; Evans, E.J.; Fugger, L.; Bakker, T.R.; van der Merwe, P.A. The nature of molecular recognition by T cells. Nat. Immunol.,  2003, 4(3), 217-224.
[http://dx.doi.org/10.1038/ni0303-217] [PMID:  12605231] 
[123] 
Satyanarayanajois, S.D. Cell adhesion molecules: structure, function, drug design, and biomaterials. Curr. Pharm. Des.,  2008, 14(22), 2126-2127.
[http://dx.doi.org/10.2174/13816120878 5740144] [PMID:  18781966] 
[124] 
Giddu, S.; Subramanian, V.; Yoon, H.S.; Satyanarayanajois, S.D. Design of β-hairpin peptides for modulation of cell adhesion by β-turn constraint. J. Med. Chem.,  2009, 52(3), 726-736.
[http://dx.doi.org/10.1021/jm8008212] [PMID:  19123855] 
[125] 
Gokhale, A.; Kanthala, S.; Latendresse, J.; Taneja, V.; Satyanarayanajois, S. Immunosuppression by co-stimulatory molecules: Inhibition of CD2-CD48/CD58 interaction by peptides from CD2 to suppress progression of collagen-induced arthritis in mice. Chem. Biol. Drug Des.,  2013, 82(1), 106-118.
[http://dx.doi.org/10.1111/cbdd.12138] [PMID:  23530775] 
[126] 
Gokhale, A.; Weldeghiorghis, T.K.; Taneja, V.; Satyanarayanajois, S.D. Conformationally constrained peptides from CD2 to modulate protein-protein interactions between CD2 and CD58. J. Med. Chem.,  2011, 54(15), 5307-5319.
[http://dx.doi.org/10.1021/jm200004e] [PMID:  21755948] 
[127] 
Satyanarayanajois, S.D.; Büyüktimkin, B.; Gokhale, A.; Ronald, S.; Siahaan, T.J.; Latendresse, J.R. A peptide from the β-strand region of CD2 protein that inhibits cell adhesion and suppresses arthritis in a mouse model. Chem. Biol. Drug Des.,  2010, 76(3), 234-244.
[PMID:  20572813] 
[128] 
Ferguson, K.M. Structure-based view of epidermal growth factor receptor regulation. Annu. Rev. Biophys.,  2008, 37, 353-373.
[http://dx.doi.org/10.1146/annurev.biophys.37.032807.125829] [PMID:  18573086] 
[129] 
Wang, J.H.; Smolyar, A.; Tan, K.; Liu, J.H.; Kim, M.; Sun, Z.Y.; Wagner, G.; Reinherz, E.L. Structure of a heterophilic adhesion complex between the human CD2 and CD58 (LFA-3) counterreceptors. Cell,  1999, 97(6), 791-803.
[http://dx.doi.org/10.1016/S0092-8674(00)80790-4] [PMID:  10380930] 
[130] 
Arkin, M.R.; Tang, Y.; Wells, J.A. Small-molecule inhibitors of protein-protein interactions: progressing toward the reality. Chem. Biol.,  2014, 21(9), 1102-1114.
[http://dx.doi.org/10.1016/j.chembiol.2014.09.001] [PMID:  25237857] 
[131] 
Bakail, M.; Ochsenbein, F. Targeting protein-protein interactions,
A wide open field for drug design C.R. Chimie,  2016, 19, 19e27.
[http://dx.doi.org/10.1016/j.crci.2015.12.004] 
[132] 
Blaszczyk, M.; Kurcinski, M.; Kouza, M.; Wieteska, L.; Debinski, A.; Kolinski, A.; Kmiecik, S. Modeling of protein-peptide interactions using the CABS-dock web server for binding site search and flexible docking. Methods,  2016, 93, 72-83.
[http://dx.doi.org/ 10.1016/j.ymeth.2015.07.004] [PMID:  26165956] 
[133] 
Laraia, L.; McKenzie, G.; Spring, D.R.; Venkitaraman, A.R.; Huggins, D.J.; Huggins, D.J. Overcoming chemical, biological, and computational challenges in the development of inhibitors targeting protein-protein interactions. Chem. Biol.,  2015, 22(6), 689-703.
[http://dx.doi.org/10.1016/j.chembiol.2015.04.019] [PMID:  26091166] 
[134] 
Jubb, H.; Higueruelo, A.P.; Winter, A.; Blundell, T.L. Structural biology and drug discovery for protein-protein interactions. Trends Pharmacol. Sci.,  2012, 33(5), 241-248.
[http://dx.doi.org/10.1016/j.tips.2012.03.006] [PMID:  22503442] 
[135] 
Barradas-Bautista, D.; Rosell, M.; Pallara, C.; Fernández-Recio, J. Structural prediction of protein-protein interactions by docking: Application to biomedical problems. Adv. Protein Chem. Struct. Biol.,  2018, 110, 203-249.
[http://dx.doi.org/10.1016/bs.apcsb.2017.06.003] [PMID:  29412997] 
[136] 
Moreira, I.S.; Fernandes, P.A.; Ramos, M.J. Hot spots--A review of the protein-protein interface determinant amino-acid residues. Proteins,  2007, 68(4), 803-812.
[http://dx.doi.org/10.1002/prot.21396] [PMID:  17546660] 
[137] 
Blundell, T.L.; Sibanda, B.L.; Montalvão, R.W.; Brewerton, S.; Chelliah, V.; Worth, C.L.; Harmer, N.J.; Davies, O.; Burke, D. Structural biology and bioinformatics in drug design: Opportunities and challenges for target identification and lead discovery. Philos. Trans. R. Soc. Lond. B Biol. Sci.,  2006, 361(1467), 413-423.
[http://dx.doi.org/10.1098/rstb.2005.1800] [PMID:  16524830] 
[138] 
Noble, R.L.; Gout, P.W.; Wijcik, L.L.; Hebden, H.F.; Beer, C.T. The distribution of [3H]vinblastine in tumor and host tissues of Nb rats bearting a transplantable lymphoma which is highly sensitive to the alkaloid. Cancer Res.,  1977, 37(5), 1455-1460.
[PMID:  856464] 
[139] 
Ahern, M.J.; Reid, C.; Gordon, T.P.; McCredie, M.; Brooks, P.M.; Jones, M. Does colchicine work? The results of the first controlled study in acute gout. Aust. N. Z. J. Med.,  1987, 17(3), 301-304.
[http://dx.doi.org/10.1111/j.1445-5994.1987.tb01232.x] [PMID:  3314832] 
[140] 
Tse, C.; Shoemaker, A.R.; Adickes, J.; Anderson, M.G.; Chen, J.; Jin, S.; Johnson, E.F.; Marsh, K.C.; Mitten, M.J.; Nimmer, P.; Roberts, L.; Tahir, S.K.; Xiao, Y.; Yang, X.; Zhang, H.; Fesik, S.; Rosenberg, S.H.; Elmore, S.W. ABT-263: A potent and orally bioavailable Bcl-2 family inhibitor. Cancer Res.,  2008, 68(9), 3421-3428.
[http://dx.doi.org/10.1158/0008-5472.CAN-07-5836] [PMID:  18451170] 
[141] 
Zhong, M.; Gadek, T.R.; Bui, M.; Shen, W.; Burnier, J.; Barr, K.J.; Hanan, E.J.; Oslob, J.D.; Yu, C.H.; Zhu, J.; Arkin, M.R.; Evanchik, M.J.; Flanagan, W.M.; Hoch, U.; Hyde, J.; Prabhu, S.; Silverman, J.A.; Wright, J. Discovery and development of potent LFA-1/ICAM-1 antagonist SAR 1118 as an ophthalmic solution for treating dry eye. ACS Med. Chem. Lett.,  2012, 3(3), 203-206.
[http://dx.doi.org/10.1021/ml2002482] [PMID:  24900456] 
[142] 
Vu, B.; Wovkulich, P.; Pizzolato, G.; Lovey, A.; Ding, Q.; Jiang, N.; Liu, J-J.; Zhao, C.; Glenn, K.; Wen, Y.; Tovar, C.; Packman, K.; Vassilev, L.; Graves, B. Discovery of RG7112: a small-molecule MDM2 inhibitor in clinical development. ACS Med. Chem. Lett.,  2013, 4(5), 466-469.
[http://dx.doi.org/ 10.1021/ml4000657] [PMID:  24900694] 
[143] 
Fader, L.D.; Malenfant, E.; Parisien, M.; Carson, R.; Bilodeau, F.; Landry, S.; Pesant, M.; Brochu, C.; Morin, S.; Chabot, C.; Halmos, T.; Bousquet, Y.; Bailey, M.D.; Kawai, S.H.; Coulombe, R.; LaPlante, S.; Jakalian, A.; Bhardwaj, P.K.; Wernic, D.; Schroeder, P.; Amad, M.; Edwards, P.; Garneau, M.; Duan, J.; Cordingley, M.; Bethell, R.; Mason, S.W.; Bös, M.; Bonneau, P.; Poupart, M.A.; Faucher, A.M.; Simoneau, B.; Fenwick, C.; Yoakim, C.; Tsantrizos, Y. Discovery of BI 224436, A Noncatalytic Site Integrase Inhibitor (NCINI) of HIV-1. ACS Med. Chem. Lett.,  2014, 5(4), 422-427.
[http://dx.doi.org/10.1021/ml500002n] [PMID:  24900852] 
Cite As
Current Topics in Medicinal Chemistry

Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions

Abstract

Graphical Abstract
