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Open Access Research Article

Study on the molecular structure of hyaluronic acid conjugates using a new class of topological indices

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pp. 1063–1084Vol. 47Issue 3March 2026DOI: 10.47974/JIOS-1876XML
Received:
10 Jul 2024
Published Online:
03 Oct 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1876
Pages:
1063–1084

Abstract

Based on medical experiments, the molecular structure of drugs includes information about their physical-chemical properties. A theoretical descriptor tool for assessing these features is known as a topological index. In this study, the molecular structure of two anticancer drugs hyaluronic acid-Paclitaxel/Curcumin conjugates using an edge-division strategy in graph theory are evaluated. To ensure the correctness of calculations in this study, we use Mathematica and Matlab software. Several new invariants based on the vertex degree are computed for the molecular structures of ayaluronic acid conjugated with curcumin and paclitaxel. We obtain the exact values of these topological indices. The calculation of topological indices for these anticancer drugs provides a more comprehensive understanding of their molecular properties and biological behavior.

Keywords

Subject Classifications

05C9205C0992E10

References

[1] J. Drbohlavova, J. Chomoucka, V. Adam, M. Ryvolova, T. Eckschlager, J. Hubalek, and R. Keizek, “Nanocarriers for anticancer drug-new trends in nanomedicine,” Curr. Drug Metab., vol. 14, pp. 547–564 (2013), doi: 10.2174/1389200211314050005.
[2] L. Lapčík, L. Lapcik, S. De Smedt, J. Demeester, and P. Chabrecek, “Hyaluronan: Preparation, structure, properties, and applications,” Chem. Rev., vol. 98, pp. 2663–2684 (1998).
[3] T. C. Laurent and J. Fraser, “Hyaluronan,” FASEB J., vol. 6, pp. 2397–2404 (1992).
[4] A. Fallacara, E. Baldini, S. Manfredini, and S. Vertuani, “Hyaluronic acid in the third millennium,” Polymers (Basel)., vol. 10, p. 701 (2018).
[5] S. Manju and K. Sreenivasan, “Conjugation of curcumin onto hyaluronic acid enhances its aqueous solubility and stability,” J. Colloid Interface Sci., vol. 359, no. 1, pp. 318–325 (2011).
[6] G. Saravanakumar, V. G. Deepagan, R. Jayakumar, and J. H. Park, “Hyaluronic acid-based conjugates for tumor-targeted drug delivery and imaging,” J. Biomed. Nanotechnol., vol. 10, pp. 17–31 (2014).
[7] H. Lee, K. Lee, and T. G. Park, “Hyaluronic acid-paclitaxel conjugate micelles: synthesis, characterization, and antitumor activity,” Bioconjug. Chem., vol. 19, no. 6, pp. 1319–1325 (2008).
[8] T. M. Mekhail and M. Markman, “Paclitaxel in cancer therapy,” Expert Opin. Pharmacother., vol. 3, pp. 755–766 (2002).
[9] D. Xin, Y. Wang, and J. Xiang, “The use of amino acid linkers in the conjugation of paclitaxel with hyaluronic acid as drug delivery system: Synthesis, self-assembled property, drug release, and in vitro efficiency,” Pharm. Res., vol. 27, pp. 380–389 (2010).
[10] B. B. Aggarwal, A. Kumar, and A. C. Bharti, “Anticancer potential of curcumin: Preclinical and clinical studies,” Anticancer Res., vol. 23, pp. 363–398 (2003).
[11] K. M. Nelson, J. L. Dahlin, J. Bisson, J. Graham, G. F. Pauli, and M. A. Walters, “The essential medicinal chemistry of curcumin,” J. Med. Chem., vol. 60, no. 5, pp. 1620–1637 (2017).
[12] M. Kharat and D. J. McClements, “Recent advances in colloidal delivery systems for nutraceuticals: A case study–Delivery by design of curcumin,” J. Colloid Interface Sci., vol. 557, pp. 506–518 (2019).
[13] D. Bonchev, Chemical Graph Theory: Introduction and Fundamentals, Abacus Press/Gordon & Breach, New York (1991).
[14] T. Hendrik, R. Todeschini, C. Viviana, M. Raimund, and K. Hugo, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim (2002).
[15] J. C. Dearden, “The use of topological indices in QSAR and QSPR modeling,” in Advances in QSAR Modeling, Springer, Berlin, Germany, pp. 57–88 (2017).
[16] A. Mauri, V. Consonni, and R. Todeschini, “Molecular descriptors,” in Handbook of Computational Chemistry, J. Leszczynski, Ed. Springer Netherlands, Dordrecht, Netherlands, pp. 1–29 (2016).
[17] H. Wiener, “Structural determination of paraffin boiling points,” J. Am. Chem. Soc., vol. 69, no. 1, pp. 17–20 (1974).
[18] I. Gutman, E. Milovanovic, and I. Milovanovic, “Beyond the Zagreb indices,” AKCE Int. J. Graphs Combin., vol. 17, no. 1, pp. 74–85 (2018).
[19] M. Imran, A. Q. Baig, H. M. A. Siddiqui, and R. Sarwar, “On molecular topological properties of diamond-like networks,” Can. J. Chem., vol. 95, no. 7, pp. 758–770 (2017).
[20] A. Q. Baig, M. Imran, W. Khalid, and N. Naeem, “Molecular description of carbon graphite and crystal cubic carbon structures,” Can. J. Chem., vol. 95, no. 6, pp. 674–686 (2017).
[21] K. C. Das, I. Gutman, and B. Furtula, “Survey on geometric-arithmetic indices of graphs,” MATCH Commun. Math. Comput. Chem., vol. 65, no. 3, pp. 595–644 (2011).
[22] A. Ali, W. Nazeer, M. Munir, and S. M. Kang, “M-polynomials and topological indices of zigzag and rhombic benzenoid systems,” Open Chem., vol. 16, no. 1, pp. 73–78 (2018).
[23] F. Movahedi, M. H. Akhbari, and H. Kamarulhaili, “On the Hosoya index of some families of graph,” Math. Interdisc. Res., vol. 6, pp. 225–234 (2021).
[24] I. Gutman and K. C. Das, “The first Zagreb index 30 years after,” MATCH Commun. Math. Comput. Chem., vol. 50, no. 1, pp. 83–92 (2004).
[25] M. Riaz, W. Gao, and A. Q. Baig, “M-polynomials and degree-based topological indices of some families of convex polytopes,” Open J. Math. Sci., vol. 2, no. 1, pp. 18–28 (2018).
[26] F. Movahedi, “Matching polynomials for some nanostar dendrimers,” Asian-European J. Math., vol. 14, no. 10, p. 2150188 (2021).
[27] A. Rauf, B. Akram, M. Ishtiaq, and M. K. Siddiqui, “Topological properties of curcumin and hyaluronic acid conjugated molecular structure: An anti-cancer drug,” Polycycl. Aromat. Compd., pp. 1–14 (2021).
[28] P. Ali, S. A. K. Kirmani, O. A. Rugaie, and F. Azam, “Degree-based topological indices and polynomials of hyaluronic acid-curcumin conjugates,” Saudi Pharm. J., vol. 28, no. 9, pp. 1093–1100 (2020).
[29] S. Mondal, N. De, and A. Pal, “Topological indices of some chemical structures applied for the treatment of COVID-19 patients,” Polycycl. Aromat. Compd., vol. 42, no. 4, pp. 1220–1234 (2022).
[30] J. B. Liu, M. Arockiaraj, M. Arulperumjothi, and S. Prabhu, “Distance-based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID-19,” Int. J. Quantum Chem., vol. 121, no. 10, p. e26617 (2021).
[31] S. A. K. Kirmani and P. Ali, “CoM-polynomial and topological coindices of hyaluronic acid conjugates,” Arab. J. Chem., vol. 15, p. 103911 (2022).
[32] S. A. K. Kirmani, P. Ali, and J. Ahmad, “Topological coindices and quantitative structure-property analysis of antiviral drugs investigated in the treatment of COVID-19,” Hindawi J. Chem., vol. 2022, p. 3036655, 15 pages (2022).
[33] I. Gutman, “Geometric approach to degree-based topological indices: Sombor indices,” MATCH Commun. Math. Comput. Chem., vol. 86, pp. 11–16 (2021).
[34] V. R. Kulli and I. Gutman, “Computation of Sombor indices of certain networks,” SSRG Int. J. Appl. Chem., vol. 8, pp. 1–5 (2021).
[35] R. Todeschini and V. Consonni, “New local vertex invariants and molecular descriptors based on functions of the vertex degrees,” MATCH Commun. Math. Comput. Chem., vol. 64, no. 2, pp. 359–372 (2010).
[36] H. Lio, “Multiplicative Sombor index of graphs,” Discrete Math. Lett., vol. 9, pp. 80–85 (2022).
[37] V. R. Kulli, “Multiplicative Sombor indices of certain nanotubes,” Int. J. Math. Arch., vol. 12, no. 3, pp. 1–5 (2021).
[38] I. Radžeporić, “Chemical applicability of Sombor indices,” J. Serb. Chem. Soc., vol. 86, no. 5, pp. 445–457 (2021).
[39] H. Liu, H. Chen, Q. Xiao, X. Fang, and Z. Tang, “More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons,” Int. J. Quantum Chem., vol. 121, no. 17, p. e26689 (2021).
[40] H. Deng, Z. Tang, and R. Wu, “Molecular trees with extremal values of Sombor indices,” Int. J. Quantum Chem., vol. 121, p. e26622 (2021).
[41] H. Liu, L. You, and Y. Huang, “Ordering chemical graphs by Sombor indices and its applications,”  MATCH Commun. Math. Comput. Chem., vol. 87, pp. 5-22 (2022).
[42] F. Movahedi and M. H. Akhbari, “Degree-based topological indices of the molecular structure of hyaluronic acid-methotrexate conjugates in cancer treatment,” Int. J. Quantum Chem., vol. 123, p. e27106 (2023).
[43] S. Alikhani and N. Ghanbari, “Sombor index of polymers,” MATCH Commun. Math. Comput. Chem., vol. 86, pp. 715–728 (2021).
[44] H. Liu, L. You, Z. Tang, and J. B. Liu, “On the reduced Sombor index and its applications,” MATCH Commun. Math. Comput. Chem., vol. 86, pp. 729–753 (2021).
[45] Z. Samiei and F. Movahedi, “Investigating graph invariants for predicting properties of chemical structures of antiviral drugs,” Polycycl. Aromat. Compd., vol. 44, no. 10, pp. 6696-6713 (2023).
[46] Z. Samiei and F. Movahedi, “Some degree-based topological indices of the molecular structure of drugs in the treatment of RNA-viruses,” J. Inf. Optim. Sci., pp. 1-22 (2025). DOI: 10.47974/JIOS-1516.
[47] A. Ahmad, M. F. Nadeem, K. Elahi, and R. Hasni, “Computing topological indices of chemical structures of the conductive 2D MOFs,” J. Inf. Optim. Sci., vol. 42, no. 3, pp. 563–578 (2020). DOI: 10.1080/02522667.2020.1773021.
[48] F. Asif, Z. Zahid, M. N. Husin, M. Cancan, Z. Taş, M. Alaeiyan, and M. R. Farahani, “On Sombor indices of line graph of silicate carbide Si2C3-I[p,q],” J. Discrete Math. Sci. Cryptogr., vol. 25, no. 1, pp. 301–310 (2022). DOI: 10.1080/09720510.2022.2043621.
[49] X. Zhang, F. He, K. Xiang, J. Zhang, M. Xu, P. Long, H. Su, Z. Gan, and Q. Yu, “CD44-targeted facile enzymatic activatable chitosan nanoparticles for efficient antitumor therapy and reversal of multidrug resistance,” Biomacromolecules, vol. 19, no. 3, pp. 883–895 (2018).
[50] F. Dosio, S. Arpicco, B. Stella, and E. Fattal, “Hyaluronic acid for anticancer drug and nucleic acid delivery,” Adv. Drug Deliv. Rev., vol. 97, pp. 204–236 (2016).
[51] E. Kwong, J. Higgins, and A. C. Templeton, “Strategies for bringing drug delivery tools into discovery,” Int. J. Pharm., vol. 412, pp. 1–7 (2011). DOI: 10.1016/j.ijpharm.2011.03.024.
[52] R. Thirumalaisamy, V. Aroulmoji, M. N. Iqbal, S. Saride, M. Bhuvaneswari, M. Deepa, C. Sivasankar, and R. Khan, “Molecular insights of hyaluronic acid-ethambutol and hyaluronic acid-isoniazid drug conjugates act as promising novel drugs for the treatment of tuberculosis,” J. Biomol. Struct. Dyn. (2022).
[53] N. S. Munjal, R. Shukla, and T. Raj Singh, “Physicochemical characterization of paclitaxel prodrugs with cytochrome 3A4 to correlate solubility and bioavailability implementing molecular docking and simulation studies,” J. Biomol. Struct. Dyn., vol. 40, no. 13, pp. 5983–5995, 2022.
[54] Y. Zhong, K. Goltsche, L. Cheng, F. Xie, F. Meng, C. Deng, Z. Zhong, and R. Haag, “Hyaluronic acid-shelled acid-activatable paclitaxel prodrug micelles effectively target and treat CD44-overexpressing human breast tumor xenografts in vivo,” Biomaterials, vol. 84, pp. 250–261 (2016).
[55] C. E. Galer, D. Sano, S. C. Ghosh, J. H. Hah, E. Auzenne, A. N. Hamir, J. N. Myers, and J. Klostergaard, “Hyaluronic acid–paclitaxel conjugate inhibits growth of human squamous cell carcinomas of the head and neck via a hyaluronic acid-mediated mechanism,” Oral Oncol., vol. 47 (2011).
[56] G. Tripodo, A. Trapani, M. L. Torre, G. Giammona, G. Trapani, and D. Mandracchia, “Hyaluronic acid and its derivatives in drug delivery and imaging: recent advances and challenges,” Eur. J. Pharm. Biopharm., vol. 97, pp. 400–416 (2015).
[57] E. Estrada and E. Uriarte, “Recent advances on the role of topological indices in drug discovery research,” Curr. Med. Chem., vol. 8, no. 13, pp. 1573–1588 (2001).

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