Main Article Content

Abstract

A large number of medical experiments have confirmed that the features of drugs have a close correlation with their molecular structure. Drug properties can be obtained by studying the molecular structure of corresponding drugs. The calculation of the topological index of a chemical graph enables scientists to have a better understanding of the physical chemistry and biological characteristics of drugs. In this paper, we focus on Hyaluronic Acid-Curcumin/Paclitaxel conjugate which are widely used in the manufacture of anticancer drugs. Therefore in this paper we have computed the Padmakar-Ivan related indices and its polynomial of the Hyaluronic Acid-curcumin/paclitaxel conjugate by using edge partitioning technique.

Keywords

Padmakar-Ivan index Weighted Padmakar-Ivan index Padmakar-Ivan related polynomial Hyaluronic Acid Hyarulonic Acid-Curcumin/Paclitaxel conjugate

Article Details

How to Cite
P.KANDAN, S. SUBRAMANIAN, & P. RAJESH. (2022). Calculating PI Related Indices and Its Polynomial of Hyaluronic Acid and Conjugates. Journal of the Indonesian Mathematical Society, 28(2), 194–214. https://doi.org/10.22342/jims.28.2.1204.194-214

References

  1. Ali .P, Syed .K.K.A , Rugaie .A.O, and Azam .F,Degreebased topological indices and polynomials of hyaluronic acidcurcumin conjugates Saudi Pharmaceutical Journal, 28(9) (2020) 1093 –1100.
  2. Allijn .E.I, Raymond S.M, and Storm .S,Comparison of pharmaceutical nanoformulationsfor curcumin: enhancement of aqueous solubility and carrier retention, InternationalJournal of Pharmaceutics, 506(1-2) (2016) 407-413.
  3. Arpicco .S et al., Hyaluronic Acid Conjugates as Vectors for the Active Targeting of Drugs, Genes and Nanocomposites in Cancer Treatment Molecules, 19 (2014) 3193-3230.
  4. Ashrafiu .A.R, Manoochehrian .B and Azari .H,On the PI polynomial of a graph Utilitas Mathematical, 71 (2006) 97-108.
  5. Ashrafizadeh .M, Zarrabi .A, Hashemi, Farid, Moghadam .R.E and Entezari .M.Curcumin in cancer therapy: A novel adjunct for combination chemotherapy with paclitaxeland alleviation of its adverse effects. Life Sci., 256 (256) PMID 117984
  6. Batra .H, Pawar .S, and Bahl .D,Curcumin in combination with anti-cancer drugs: a nanomedicine review Pharmacological Research, 139 (2019) 91–105.
  7. Balaban .J and Devillers .J,Topological indices and related descriptors in QSAR and QSPAR J. Chem. Inf. Comput. Sci. 42(6) (2002) 1507-1510
  8. Buragohain .J, Deka .J, and Bharali .A,A generalized ISI index of some chemical structures,Journal of Molecular Structure Journal of Molecular Structure, 1208 (2020) Article ID 127843.
  9. C¸ olakˇoglu .O¨,The inverse sum indeg index (ISI) and ISI energy of Hyaluronic Acid-Paclitaxel molecules used in anticancer drugs Open J. Discret. Appl. Math. 4(3) (2021) 72-81.
  10. Dearden J.C. Springer, Berlin,The use of topological indices in QSAR and QSPR modeling in Advances in QSAR Modeling, Germany, 24 (2017) 57-58.
  11. Das .K.C and Y. Shang. Some Extremal Graphs with Respect to Sombor Index, Mathematics 9, (2021), 1202, 1-15
  12. Galer .E.C, Sano .D, Ghosh C.S, Hah .H.J and Auzenne .E, A. N. Hamir, J.N. Myers, 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 Oncology, 47(11) (2011) 1039-1047.
  13. Gopika .C, Geetha .J and Somasundaram .K,Weighted PI index of tensor product and strong product of graphs Discrete Mathematics, Algorithms and Applications, 13(03) (2021) Article ID 2150019.
  14. Ghorbani .M and Jalali .M, The Vertex PI, Szeged and Omega Polynomials of Carbon Nanocones CNC4[n MATCH Commun. Math. Comput. Chem. 62 (2009) 353-362.
  15. Giordano .A and Tommonaro .G,Curcumin and cancer Nutrients, 11(10) (2019) 23-76.
  16. Illiˇc .A and Milosavljevic .N,The weighted vertex PI index Math. Comput. model. 57 (2013) 623–631.
  17. Jahanbani. A, Z. Shao, S.M. Sheikholeslami,Calculating degree based of Hyaluronic acidPaclitaxel conjugates molecular structure in cancer treatment Journal of Biomolecular Structure and Dynamic, 39(1) (2020) 1600-1606.
  18. H. Lee, H. Mok, S. Lee, Y.K. Oh and T. G. Park,Targetspecific intracellular delivery of SiRNA using degradable hyaluronic acid nanogels Journal of Controlled Release, 119(2) (2007) 245–252
  19. Kandan .P and Subramanian .S,Computation of Weighted PI and Szegedindices of Conical graph Advances in Mathematics: Scientific Journal, 10(9) (2021) 3093–3111.
  20. Kharat .M and Mcclement .D.J,Recent advance in colloidal delivery by systems for nutraceutical: Acase study-Delivery by design of curcumin J. Colloid interface Sci. 557 (2019) 506-518.
  21. Khadikar .V.P, Karmarkar .S and Agrawal .V.K, The novel PI index and its application to QSPR/QSAR studies. J. Chem.Inf.Comput.Sci. 41(4) (2001) 934-949.
  22. Mansour .T and Schork .M,The PI index of bridge and chain graphs MATCH Commun. Math. Comput.Chem. 61 (2009) 723-734.
  23. Mansour .T, The vertex PI index and Szeged index of bridge graph Discrete Applied Mthematics, 157 (2009) 1600-1606.
  24. Mirzargar .M,Szeged and Edge Szeged Polynomials of a Dendrimer Nanostar MATCH Commun. Math. Comput. Chem. 62 (2009) 363-370.
  25. Manju .S and Sreenivasan .K,Conjugation of curcumin onto hyaluronic acidenhances its aqueous solubility and stability J. Colloid Interface Sci. 359, (2011) 318–325
  26. Mauri .A, Consonni .V, and Todeschini .R, Leszczynski .J,Molecular descriptors, in Handbook of Computational Chemistry, Springer Netherlands, Dordrecht, Netherlands, (2017) 1–29.
  27. Mondal .S, De .N and Pal .A,Topological Indices of Some Chemical Structures Applied for the Treatment of COVID-19 Patients Polycyclic Aromatic Compounds (2020) 1–15
  28. Pattabiraman .K, and Kandan .P,Weighted szeged indices of some graph operation Transactions on Combinatorics, 5(1) (2016) 25-35.
  29. Pattabiraman .K, and Kandan .P,Weighted PI index of corona product of graphs Discrete Mathematics, Algorithms and Applications, 6(9) (2014) Article ID 1450055.
  30. Rauf .A, Akram .B, Ishtiaq .M and Siddiqui .M.K,M,Topological Properties of Curcumin and Hyaluronic Acid Conjugate Molecular Structure: An Anti-Cancer Drug Polycyclic Aromatic Compounds, 41 (2021) 1-14.
  31. Saravanakumar .G, Deepagan .G.V, Jayakumar .R, and Park .H.J,Hyaluronic acid-based conjugates for tumortargeted drug delivery and imaging Journal of Biomedical Nanotechnology, 10(1) (2014) 17–31.
  32. Shang. Y A remark on the chromatic polynomial of incomparability graphs of posets, International Journal of Pure and Applied Mathematics, 67(2) (2011), 159-164.
  33. Shang .Y , Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs, PLoS ONE 10(3),(2015), e0123426.
  34. Ajaz .S, K. Kirmani .K, Ali .P, Azam .F and Alvi .P.A,Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid-Anticancer Drug Conjugates with QSPR, Hindawi Journal of Chemistry, Article ID 3860856 (2021) 23
  35. Wani .M.C, Taylor .H.L, Wall .M.E, Coggon .P, and Mcphail .A.T,“Plant antitumor agents.VI. Isolation and structure of taxol, a novel antileukemic and antitumor agentfrom Taxus brevifolia, Journal of the American Chemical Society, 93(9), (1971), 2325–2327.
  36. Tripodo .G, Adriana .T, Luisa Torre .M, G. Giammona, G. Trapani, and D. Mandracchia, Hyaluronic acid and its derivatives in drug delivery and imaging: recent advances and challenges European Journal of Pharmaceutics and Biopharmaceutics, 97 (2015) 400–416.
  37. Toole .B.P, Hyaluronan in morphogenesis Seminars in Cell Developmental Biology, 12(2) (2001) 79–87.
  38. Wiener .H, Structural determination of paraffin boiling points J. Am. Chem.Soc. 69 (1987) 17–20.
  39. Wang .J, Wang .Y, Wang .Y and Zheng .L, Computation on the topological indices of hyaluronic acid, J. Appl. Anal. Comput. 10 (2020) 1193–1198.
  40. Wang.K , Guo .C, Xue .D et al.,In vivo evaluation of reduction-responsive alendronatehyaluronan-curcumin polymer-drug conjugates for targeted therapy of bone metastatic breast cancer Molecular Pharmaceutics, 15(7) (2018) 2764–2769.
  41. W.T. Zhu, S.Y. Liu, L. Wu et al.,Delivery of curcumin by directed self-assembled micellesenhances therapeutic treatment of non-small-cell lung cancer International Journal of Nanomedicine, 12 (2017) 2621
  42. Zheng .L , Wang.Y and Gao .W, Topological Indices of Hyaluronic Acid-Paclitaxel Conjugates’ Molecular Structure in Cancer Treatment, Open Chem. 17 (2019) 81–87.
  43. Zhou .B, Trinajsti´c .N, On general sum-connectivity index. J. Math. Chem. 47 (2010) 210–218.
  44. Zhao .S, Ma .L, Cao .C, Yu .Q, Chen .L, and Liu .J,Curcuminloaded redox response of selfassembled micelles for enhancedantitumor and anti-inflammation effi cacy, International Journal of Nanomedicine, 12 (2017) 2489