Generic placeholder image

Current Topics in Medicinal Chemistry

Editor-in-Chief

ISSN (Print): 1568-0266
ISSN (Online): 1873-4294

Review Article

Physicochemical Significance of Topological Indices: Importance in Drug Discovery Research

Author(s): Karanpreet Singh Bhatia, Ankit Kumar Gupta and Anil Kumar Saxena*

Volume 23, Issue 29, 2023

Published on: 18 August, 2023

Page: [2735 - 2742] Pages: 8

DOI: 10.2174/1568026623666230731103309

Price: $65

Abstract

Background: Quantitative Structure-Activity Relationship (QSAR) studies describing the correlations between biological activity as dependent parameters and physicochemical and structural descriptors, including topological indices (TIs) as independent parameters, play an important role in drug discovery research. The emergence of graph theory in exploring the structural attributes of the chemical space has led to the evolution of various TIs, which have made their way into drug discovery. The TIs are easy to compute compared to the empirical parameters, but they lack physiochemical interpretation, which is essential in understanding the mechanism of action.

Objectives: Hence, efforts have been made to review the work on the advances in topological indices, their physicochemical significance, and their role in developing QSAR models.

Methods: A literature search has been carried out, and the research article providing evidence of the physicochemical significance of the topological parameters as well as some recent studies utilizing these parameters in the development of QSAR models, have been evaluated.

Result: In this review, the physicochemical significance of TIs have been described through their correlations between empirical parameters in terms of explainable physicochemical properties, along with their application in the development of predictive QSAR models.

Conclusion: Most of these findings suggest a common trend of TIs correlation with MR rather than logP or other parameters; nevertheless, the developed models may be useful in both drug and vaccine development.

Keywords: Topological indices, Physicochemical significance, Molar refractivity, QSAR, QSPR, Drug designing.

Graphical Abstract
[1]
Hughes, J.P.; Rees, S.; Kalindjian, S.B.; Philpott, K.L. Principles of early drug discovery. Br. J. Pharmacol., 2011, 162(6), 1239-1249.
[http://dx.doi.org/10.1111/j.1476-5381.2010.01127.x] [PMID: 21091654]
[2]
Fox, S.; Farr-Jones, S.; Sopchak, L.; Boggs, A.; Nicely, H.W.; Khoury, R.; Biros, M. High-throughput screening: Update on practices and success. SLAS Discov., 2006, 11(7), 864-869.
[http://dx.doi.org/10.1177/1087057106292473] [PMID: 16973922]
[3]
Frearson, J.A.; Collie, I.T. HTS and hit finding in academia: From chemical genomics to drug discovery. Drug Discov. Today, 2009, 14(23-24), 1150-1158.
[http://dx.doi.org/10.1016/j.drudis.2009.09.004] [PMID: 19793546]
[4]
Cherkasov, A.; Muratov, E.N.; Fourches, D.; Varnek, A.; Baskin, I.I.; Cronin, M.; Dearden, J.; Gramatica, P.; Martin, Y.C.; Todeschini, R.; Consonni, V.; Kuz’min, V.E.; Cramer, R.; Benigni, R.; Yang, C.; Rathman, J.; Terfloth, L.; Gasteiger, J.; Richard, A.; Tropsha, A. QSAR modeling: Where have you been? Where are you going to? J. Med. Chem., 2014, 57(12), 4977-5010.
[http://dx.doi.org/10.1021/jm4004285] [PMID: 24351051]
[5]
Hansch, C.; Fujita, T. p -σ-π analysis. a method for the correlation of biological activity and chemical structure. J. Am. Chem. Soc., 1964, 86(8), 1616-1626.
[http://dx.doi.org/10.1021/ja01062a035]
[6]
Dearden, J.C.; Cronin, M.T.D.; Kaiser, K.L.E. How not to develop a quantitative structure–activity or structure–property relationship (QSAR/QSPR). SAR QSAR Environ. Res., 2009, 20(3-4), 241-266.
[http://dx.doi.org/10.1080/10629360902949567] [PMID: 19544191]
[7]
Milne, G.W.A. Mathematics as a basis for chemistry. J. Chem. Inf. Comput. Sci., 1997, 37(4), 639-644.
[http://dx.doi.org/10.1021/ci960165k] [PMID: 9254910]
[8]
Balaban, A.T. Chemical Graphs: Looking back and glimpsing ahead. J. Chem. Inf. Comput. Sci., 1995, 35(3), 339-350.
[http://dx.doi.org/10.1021/ci00025a001]
[9]
Wiener, H. Structural determination of paraffin boiling points. J. Am. Chem. Soc., 1947, 69(1), 17-20.
[http://dx.doi.org/10.1021/ja01193a005] [PMID: 20291038]
[10]
Klopman, G. MULTICASE 1. A hierarchical computer automated structure evaluation program. Quant. Struct.-Act. Relationsh., 1992, 11(2), 176-184.
[http://dx.doi.org/10.1002/qsar.19920110208]
[11]
Gordon, M.; Scantlebury, G.R. Non-random polycondensation: Statistical theory of the substitution effect. Trans. Faraday Soc., 1964, 60(0), 604-621.
[http://dx.doi.org/10.1039/tf9646000604]
[12]
Hosoya, H. Topological Index. a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Japan, 2006, 44(9), 2332-2339.
[http://dx.doi.org/10.1246/bcsj.44.2332]
[13]
Hosoya, H. Topological index as a common tool for quantum chemistry, statistical mechanics, and graph theory. Math. Comput. concepts Chem.Ellis Horwood Ser. Math. Appl., 1986, 110-123.
[14]
Schultz, H.P. Topological organic chemistry. 1. Graph theory and topological indices of alkanes. J. Chem. Inf. Comput. Sci., 1989, 29(3), 227-228.
[http://dx.doi.org/10.1021/ci00063a012]
[15]
Balaban, A.T. Topological indices based on topological distances in molecular graphs. Pure Appl. Chem., 1983, 55(2), 199-206.
[http://dx.doi.org/10.1351/pac198855020199]
[16]
Balaban, A.T. Chemical graphs. Theor. Chim. Acta, 1979, 53(4), 355-375.
[http://dx.doi.org/10.1007/BF00555695]
[17]
Gutman, I. Trinajstić, N. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17(4), 535-538.
[http://dx.doi.org/10.1016/0009-2614(72)85099-1]
[18]
Gutman, I. Ruščić,, B.; Trinajstić, N.; Wilcox, C.F. Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys., 1975, 62(9), 3399-3405.
[http://dx.doi.org/10.1063/1.430994]
[19]
Balaban, A.T.; Motoc, I.; Bonchev, D.; Mekenyan, O. Topological indices for structure-activity correlations.Steric effects in drug design; Springer, 1983, pp. 21-55.
[20]
Todeschini, R.; Consonni, V. Handbook of molecular descriptors; John Wiley & Sons, 2008.
[21]
Randic, M. Characterization of molecular branching. J. Am. Chem. Soc., 1975, 97(23), 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001]
[22]
Fajtlowicz, S. On conjectures of Graffiti-II. Congr. Numer, 1987, 60, 187-197.
[23]
Kier, L.B.; Hall, L.H. Molecular connectivity in structure–activity analysis; Wiley: New York, 1986, p. 262.
[24]
Kier, L.B.; Hall, L.H. Molecular connectivity in chemistry and drug research; Elsevier, 1976, p. 257.
[25]
Kier, L.B. Indexes of molecular shape from chemical graphs. Med. Res. Rev., 1987, 7(4), 417-440.
[http://dx.doi.org/10.1002/med.2610070404] [PMID: 3309506]
[26]
Kier, L.B. Distinguishing atom differences in a molecular graph shape index. Quant. Struct.-Act. Relationsh., 1986, 5(1), 7-12.
[http://dx.doi.org/10.1002/qsar.19860050103]
[27]
Kier, L.B. A shape index from molecular graphs. Quant. Struct.-Act. Relationsh., 1985, 4(3), 109-116.
[http://dx.doi.org/10.1002/qsar.19850040303]
[28]
Balaban, A.T. Highly discriminating distance-based topological index. Chem. Phys. Lett., 1982, 89(5), 399-404.
[http://dx.doi.org/10.1016/0009-2614(82)80009-2]
[29]
Lemont, B. k.; Lowell, h. Molecular structure description: the electrotopological state, 1999, 41 Available at: https://ci.nii.ac.jp/ncid/BA52175441 (Accessed: Feb. 07, 2022)
[30]
Vukičević, D.; Furtula, B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem., 2009, 46(4), 13696-1376.
[http://dx.doi.org/10.1007/s10910-009-9520-x]
[31]
Sharma, V.; Goswami, R.; Madan, A.K. Eccentric connectivity index: A novel highly discriminating topological descriptor for structure- property and structure- activity studies. J. Chem. Inf. Comput. Sci., 1997, 37(2), 273-282.
[http://dx.doi.org/10.1021/ci960049h]
[32]
Gutman, I. The energy of a graph, Ber. Math.—. Statist. Sekt. Forschungsz. Graz., 1978, 103, 1-22.
[33]
Estrada, E. Characterization of 3D molecular structure. Chem. Phys. Lett., 2000, 319(5-6), 713-718.
[http://dx.doi.org/10.1016/S0009-2614(00)00158-5]
[34]
Gutman, I.; Furtula, B.; Zogic, E. Glogić, E. Resolvent energy of graphs Math. Comput. Chem., 2016, 75, 279-290.
[35]
Redžepović, I.; Furtula, B. On degeneracy of a-eigenvalue-based molecular descriptors and r-equienergetic chemical trees. MATCH Commun. Math. Comput. Chem., 2020, 84, 385-397.
[36]
Gutman, I. Milovanović, E.; Milovanović, I. Beyond the zagreb indices. AKCE Int. J.Graph. Comb., 2020, 17(1), 74-85.
[http://dx.doi.org/10.1016/j.akcej.2018.05.002]
[37]
Yap, C.W. PaDEL-descriptor: An open source software to calculate molecular descriptors and fingerprints. J. Comput. Chem., 2011, 32(7), 1466-1474.
[http://dx.doi.org/10.1002/jcc.21707] [PMID: 21425294]
[38]
Dong, J.; Cao, D.S.; Miao, H.Y.; Liu, S.; Deng, B.C.; Yun, Y.H.; Wang, N.N.; Lu, A.P.; Zeng, W.B.; Chen, A.F. ChemDes: an integrated web-based platform for molecular descriptor and fingerprint computation. J. Cheminform., 2015, 7(1), 60.
[http://dx.doi.org/10.1186/s13321-015-0109-z] [PMID: 26664458]
[39]
Deng, H. The largest Hosoya index of (n, n + 1) -graphs. Comput. Math. Appl., 2008, 56(10), 2499-2506.
[http://dx.doi.org/10.1016/j.camwa.2008.05.020]
[40]
Mueller, W.R.; Szymanski, K.; Knop, J.V. Trinajstić, N. Molecular topological index. J. Chem. Inf. Comput. Sci., 1990, 30(2), 160-163.
[http://dx.doi.org/10.1021/ci00066a011]
[41]
Shannon, C. A mathematical theory of communication, ell Syst. Tech. J., 1948, 27, 379-423.
[42]
Zhou, B. Trinajstić, N. On a novel connectivity index. J. Math. Chem., 2008, 46(4), 1252-1270.
[http://dx.doi.org/10.1007/s10910-008-9515-z]
[43]
Shirdel, G.H.; Rezapour, H.; Sayadi, A.A.M. The hyper-zagreb index of graph operations. Iran. J. Math. Chem., 2013, 4(2), 213-220.
[44]
Ranjini, P.S.; Lokesha, V.; Usha, A. Relation between phenylene and hexagonal squeeze using harmonic index. Int. J. Graph Theory, 2013, 1(4), 116-121.
[45]
Vukičević, D.; Gašperov, M. Bond Additive Modeling 1. Adriatic Indices. Croat. Chem. Acta, 2010, 83(3), 243-260.
[46]
Vukičević, D. Bond additive modeling 2. mathematical properties of Max-min rodeg index. Croat. Chem. Acta, 2010, 83(3), 261-273.
[47]
Buragohain, J.; Deka, B.; Bharali, A. A generalized ISI index of some chemical structures. J. Mol. Struct., 2020, 1208, 127843.
[http://dx.doi.org/10.1016/j.molstruc.2020.127843]
[48]
Zheng, L.; Wang, Y.; Gao, W. Topological indices of hyaluronic acid-paclitaxel conjugates’ molecular structure in cancer treatment. Open Chem., 2019, 17(1), 81-87.
[http://dx.doi.org/10.1515/chem-2019-0009]
[49]
Bollobás, B.; Erdös, P. Graphs of extremal weights. Ars Comb., 1998, 50, 225-233.
[50]
Azari, M.; Iranmanesh, A. Generalized Zagreb index of graphs. Stud. Univ. Babes-Bolyai Chem., 2011, 56, 59-70.
[51]
Saxena, A.K. Physicochemical significance of topological parameters, connectivity indices and information content. Part 1: Correlation studies in the sets with aromatic and aliphatic substituents. Quant. Struct.-Act. Relationsh., 1995, 14(1), 31-38.
[http://dx.doi.org/10.1002/qsar.19950140106]
[52]
Saxena, A.K. Physicochemical significance of topological parameters: molecular connectivity index and information content: Part 2. Correlation studies with molar refractivity and lipophylicity. Quant. Struct.-Act. Relationsh., 1995, 14(2), 142-148.
[http://dx.doi.org/10.1002/qsar.19950140206]
[53]
Saxena, A.K. Reply to H. Kubinyi’s Rebuttal. Quant. Struct.-Act. Relationsh., 1995, 14(2), 150.
[http://dx.doi.org/10.1002/qsar.19950140208]
[54]
Kubinyi, H. The physicochemical significance of topological parameters. a rebuttal. Quant. Struct.-Act. Relationsh., 1995, 14(2), 149-150.
[http://dx.doi.org/10.1002/qsar.19950140207]
[55]
García, I.; Fall, Y.; Gómez, G. Using topological indices to predict anti-alzheimer and anti-parasitic gsk-3 inhibitors by multi-target qsar in silico screening. Mol., 2010, 15(8), 5408-5422.
[http://dx.doi.org/10.3390/molecules15085408]
[56]
Shanmukha, M.C.; Basavarajappa, N.S.; Shilpa, K.C.; Usha, A. Degree-based topological indices on anticancer drugs with QSPR analysis. Heliyon, 2020, 6(6), e04235.
[http://dx.doi.org/10.1016/j.heliyon.2020.e04235] [PMID: 32613116]
[57]
Kanabur, R.; Shigehalli, V. QSPR analysis of degree-based topological indices with physical properties of benzenoid hydrocarbons. Gen. Let. Mathem., 2017, 2(3)
[http://dx.doi.org/10.31559/GLM2016.2.3.6]
[58]
Ediz, S. Predicting some physicochemical properties of octane isomers: A topological approach using ev-degree and ve-degree Zagreb indices. arXiv, 2017, 1701, 02859v1. Available at: https://arxiv.org/abs/1701.02859v1 (Accessed: Feb. 10, 2022.)
[59]
Tamilarasi, C.; Simon Raj, F. QSPR analysis of novel indices with priority polycyclic aromatic hydrocarbons(PAHs). Turkish J. Comput. Math. Educ., 2021, 12(10), 3992-3999.
[http://dx.doi.org/10.17762/TURCOMAT.V12I10.5110]
[60]
Odintsov, S.D.; Harriman, A.; Cz Dobrowolski, J.; Wazzan, S.; Saleh, A. New versions of locating indices and their significance in predicting the physicochemical properties of benzenoid hydrocarbons. Symmetry, 2022, 14(5), 1022.
[http://dx.doi.org/10.3390/sym14051022]
[61]
Kirmani, S.A.K.; Ali, P.; Azam, F. Topological indices and QSPR/QSAR analysis of some antiviral drugs being investigated for the treatment of COVID ‐19 patients. Int. J. Quantum Chem., 2021, 121(9), e26594.
[http://dx.doi.org/10.1002/qua.26594] [PMID: 33612855]
[62]
Hosamani, S.M. Quantitative structure property analysis of Anti-Covid-19 drugs. arXiv, 2020, 2008, 07350. Available at: https://arxiv.org/abs/2008.07350v1 (Accessed: Feb. 09, 2022)
[63]
Thakur, A.; Thakur, M.; Kakani, N.; Joshi, A.; Thakur, S.; Gupta, A. Application of topological and physicochemical descriptors: QSAR study of phenylamino-acridine derivatives. ARKIVOC, 2004, 2004(14), 36-43.
[http://dx.doi.org/10.3998/ark.5550190.0005.e03]
[64]
Wang, J.; Land, D.; Ono, K.; Galvez, J.; Zhao, W.; Vempati, P.; Steele, J.W.; Cheng, A.; Yamada, M.; Levine, S.; Mazzola, P.; Pasinetti, G.M. Molecular topology as novel strategy for discovery of drugs with aβ lowering and anti-aggregation dual activities for Alzheimer’s disease. PLoS One, 2014, 9(3), e92750.
[http://dx.doi.org/10.1371/journal.pone.0092750] [PMID: 24671215]
[65]
Roy, K.; Mandal, A.S. Development of linear and nonlinear predictive QSAR models and their external validation using molecular similarity principle for anti-HIV indolyl aryl sulfones. J. Enzyme Inhib. Med. Chem., 2008, 23(6), 980-995.
[http://dx.doi.org/10.1080/14756360701811379] [PMID: 18608761]
[66]
Saxena, A.K.; Prathipati, P. Comparison of MLR, PLS and GA-MLR in QSAR analysis. SAR QSAR Environ. Res., 2003, 14(5-6), 433-445.
[http://dx.doi.org/10.1080/10629360310001624015] [PMID: 14758986]
[67]
Ali, P.; Kirmani, S.A.K.; Al Rugaie, O.; Azam, F. Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates. Saudi Pharm. J., 2020, 28(9), 1093-1100.
[http://dx.doi.org/10.1016/j.jsps.2020.07.010] [PMID: 32922140]
[68]
Gao, W.; Wang, W.; Farahani, M.R. Topological indices study of molecular structure in anticancer drugs. J. Chem., 2016, 2016, 1-8.
[http://dx.doi.org/10.1155/2016/3216327]
[69]
Mondal, S.; De, N.; Pal, A. Topological indices of some chemical structures applied for the treatment of COVID-19 patients. Poly. Arom. Comp., 2020, 42(4), 1220-1234.
[http://dx.doi.org/10.1080/10406638.2020.1770306]
[70]
Shao, Z.; Jahanbani, A.; Sheikholeslami, S.M. Multiplicative topological indices of molecular structure in anticancer drugs. Poly. Arom. Comp., 2020, 42(2), 475-488.
[http://dx.doi.org/10.1080/10406638.2020.1743329]
[71]
Saxena, A.K.; Alam, M. ATP synthase inhibitors as anti-tubercular agents: QSAR studies in novel substituted quinolines. Curr. Top. Med. Chem., 2020, 20(29), 2723-2734.
[http://dx.doi.org/10.2174/1568026620666200903163515] [PMID: 32885753]
[72]
Natarajan, R.; Basak, S.C.; Neumann, T.S. Novel approach for the numerical characterization of molecular chirality. J. Chem. Inf. Model., 2007, 47(3), 771-775.
[http://dx.doi.org/10.1021/ci600542b] [PMID: 17408241]
[73]
Aires-de-Sousa, J.; Gasteiger, J.; Gutman, I. Vidović, D. Chirality codes and molecular structure. J. Chem. Inf. Comput. Sci., 2004, 44(3), 831-836.
[http://dx.doi.org/10.1021/ci030410h] [PMID: 15154747]
[74]
Aires-de-Sousa, J.; Gasteiger, J. New description of molecular chirality and its application to the prediction of the preferred enantiomer in stereoselective reactions. J. Chem. Inf. Comput. Sci., 2001, 41(2), 369-375.
[http://dx.doi.org/10.1021/ci000125n] [PMID: 11277725]
[75]
Fujita, S. Graphs to chemical structures 2. Extended sphericity indices of cycles for stereochemical extension of Pólya’s coronas. Theor. Chem. Acc., 2005, 113(2), 80-86.
[http://dx.doi.org/10.1007/s00214-004-0606-z]
[76]
Fujita, S. Graphs to chemical structures 3. General theorems with the use of different sets of sphericity indices for combinatorial enumeration of nonrigid stereoisomers. Theor. Chem. Acc., 2006, 115(1), 37-53.
[http://dx.doi.org/10.1007/s00214-005-0674-8]
[77]
Randić, M. Graph theoretical descriptors of two-dimensional chirality with possible extension to three-dimensional chirality. J. Chem. Inf. Comput. Sci., 2001, 41(3), 639-649.
[http://dx.doi.org/10.1021/ci000115m] [PMID: 11410041]
[78]
Golbraikh, A.; Bonchev, D.; Tropsha, A. Novel chirality descriptors derived from molecular topology. J. Chem. Inf. Comput. Sci., 2001, 41(1), 147-158.
[http://dx.doi.org/10.1021/ci000082a] [PMID: 11206367]
[79]
Schultz, H.P.; Schultz, E.B.; Schultz, T.P. Topological organic chemistry. 9. graph theory and molecular topological indices of stereoisomeric organic compounds. J. Chem. Inf. Comput. Sci., 1995, 35(5), 864-870.
[http://dx.doi.org/10.1021/ci00027a011]
[80]
Chatterjee, S.; Dey, S.; Nandy, A.; Basak, S.C. A computational search for peptide vaccines using novel mathematical descriptors of sequences of emerging pathogens. Top. Med. Chem., 2020, 37, 195-220.
[http://dx.doi.org/10.1007/7355_2020_108]
[81]
Nandy, A. A New Graphical Representation and Analysis of DNA Sequence Structure: I. Methodology and Application to Globin Genes; ; Current Science Association, 1994, 66, pp. (4)309-31.
[82]
Randić, M.; Vračko, 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]
[83]
Dey, T.; Biswas, S.; Chatterjee, S.; Manna, S.; Nandy, A.; Basak, S. 2D polar co-ordinate representation of amino acid sequences with some applications to ebola virus, SARS and SARS-CoV-2 (COVID-19). MOL2NET, international conference series on multidisciplinary sciences usinews-04: us-in-eu worldwide science workshop series, umn, 11 April 2020Duluth, USA2020.
[84]
Nandy, A.; Ghosh, A.; Nandy, P. Numerical characterization of protein sequences and application to voltage-gated sodium channel α subunit phylogeny. In Silico Biol., 2009, 9(3), 77-87.
[http://dx.doi.org/10.3233/ISB-2009-0389] [PMID: 19795567]

Rights & Permissions Print Cite
© 2024 Bentham Science Publishers | Privacy Policy