Computing molecular descriptors of chitosan derivatives and its M-polynomial expressions

V.H., Narendra; A., Usha; M.C., Shanmukha; P., Mahalakshmi; T., Deepika

doi:10.22034/ecc.2023.407945.1669

Document Type : Original Research Article

Authors

¹ Department of Mathematics, Government First Grade College, Holalkere-577526, Karnataka, India

² Department of Mathematics, Alliance School of Applied Mathematics, Alliance University, Bangalure-562106, Karnataka, India

³ Department of Mathematics, Bapuji Institute of Engineering & Technology, Davanagere-577004, India

⁴ Department of Mathematics, School of Engineering, Dayananda Sagar University, Bangalure-560078, India

10.22034/ecc.2023.407945.1669

Abstract

The fundamental topology of the structure of chemical compounds can be better understood by the method of topological indices /numerical descriptors. Topological index depicts the chemical characteristic of a molecule in numerical form. Topological indices are used for modelling of physicochemical, biological, and pharmacokinetic properties of the compounds. It plays vital role in the QSAR/QSPR studies. Descriptor’s ability to extract information typically depends on the type of molecular representation used and the specified algorithm. These numerical values help the researchers in choosing the right compound for the drug design. Chitin and chitosan derivatives act as excellent suppressor of anti-tumour and anticancer activities in living beings. The increasing morbidity and mortality rate worldwide is correlated with two most important diseases viz., obesity and diabetes. To improve health condition and prevention of chronic diseases such as asthma, arthritis, hepatitis, gastritis, atherosclerosis etc, chitin, chitosan and their derivatives play as immune-enhancing anti-inflammatory potential. As chitin and chitosan have remarkable applications discussed above, this work pinpoints on computing a polynomial from which topological indices can be extracted for specific values of the parameters. In this work, the focus is on a type of polynomial known as M-polynomial from which various 11 degree-based TIs are derived for molecular graph of chitosan derivatives such as α, β and γ -chitins.

Graphical Abstract

Keywords

References

[1] M.M Abo Elsoud, E.M. El Kady, Current trends in fungal biosynthesis of chitin and chitosan, Bull. Natl. Res. Cent., 2019, 43, 1-12. [Crossref], [Google Scholar], [Publisher]

[2] S.K. Halder, K.C. Mondal, Microbial valorization of chitinous bioresources for chitin extraction and production of chitooligomers and N-acetylglucosamine: trends, perspectives and prospects, Microbial biotechnology: Application in Food and Pharmacology, 2018, 2, 69-107. [Crossref], [Google Scholar], [Publisher]

[3] A. Anitha, S. Sowmya, P.S. Kumar, S. Deepthi, K.P Chennazhi, H. Ehrlich, M. Tsurkan, R. Jayakumar, Chitin and chitosan in selected biomedical applications, Prog. Polym. Sci., 2014, 39, 1644-1667. [Crossref], [Google Scholar], [Publisher]

[4] W. Wang, Q. Meng, Q. Li, J. Liu, M. Zhou, Z. Jin, K. Zhao, Chitosan derivatives and their application in biomedicine, Int. J. Mol. Sci., 2020, 21, 487. [Crossref], [Google Scholar], [Publisher]

[5] A. Aslam, M.K. Jamil, W. Gao, W. Nazeer, Topological aspects of some dendrimer structures, Nanotechnol Rev, 2018, 7, 123-129. [Crossref], [Google Scholar], [Publisher]

[6] I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer Science & Business Media, 2012. [Google Scholar], [Publisher]

[7] N. Trinajstic, Chemical Graph Theory, 2nd revised CRC Press, Boca. Raton. FL, 1992. [Crossref], [Google Scholar], [Publisher]

[8] R. Todeschini, V. Consonni, Handbook of molecular descriptors, John Wiley & Sons, 2008. [Google Scholar], [Publisher]

[9] E. Estrada, L. Torres, L. Roriguez, I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem., 1998, 37, 849-855. [Google Scholar], [Publisher]

[10] S.A.K. Kirmani, P. Ali, F. Azam, 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, e26594. [Crossref], [Google Scholar], [Publisher]

[11] S. Hayat, M. Imran, J.B. Liu, Correlation between the Estrada index and π - electronic energies for benzenoid hydrocarbons with applications to boron nanotubes, Int. J. Quantum Chem., 2019, 119, e26016. [Crossref], [Google Scholar], [Publisher]

[12] M.C. Shanmukha, N.S. Basavarajappa, K.C. Shilpa, A. Usha, Degreebased topological indices on anticancer drugs with QSPR analysis, Heliyon, 2020, 6, e04235. [Crossref], [Google Scholar], [Publisher]

[13] H. Wiener, Structural determination of paraffin boiling points, J. American Chem. Soc., 1947, 69, 17–20. [Crossref], [Google Scholar], [Publisher]

[14] A.A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta. Appl. Math., 2001, 66, 211-249. [Crossref], [Google Scholar], [Publisher]

[15] M. Randic, On characterization of molecular branching, J. American Chem. Soc., 1975, 97, 6609-6615. [Crossref], [Google Scholar], [Publisher]

[16] M. Randic, Quantitative structure-property relationship. Boiling points of planar benzenoids, New J. Chem., 1996 20, 1001-1009. [Google Scholar], [Publisher]

[17] B. Bollobas & P. Erdos, Graphs of extremal weights, Ars Combinatoria, 1998, 50, 225-233. [Google Scholar], [Publisher]

[18] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals, total π - electron energy of alternant hydrocarbons, Chem. Phys. Lett., 1972, 17, 535-538. [Crossref], [Google Scholar], [Publisher]

[19] A. Milicevic, S. Nikolic & N. Trinajstic, On reformulated Zagreb indices, Mol. Divers., 2004, 8, 393-399. [Crossref], [Google Scholar], [Publisher]

[20] B. Furtula, A. Graovac, D. Vukicevic, Augmented Zagreb index, J. Math. Chem., 2010, 48, 370-380. [Crossref], [Google Scholar], [Publisher]

[21] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 2015, 53, 1184-1190. [Crossref], [Google Scholar], [Publisher]

[22] I. Gutman, E. Milovanovic, I. Milovanovic, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb., 2018, 1-12. [Crossref], [Google Scholar], [Publisher]

[23] M. Ghorbani, M.A. Hosseinzadeh, The third version of Zagreb index, discrete mathematics, Algorithms and Applications, 2013, 5, 1350039. [Crossref], [Google Scholar], [Publisher

[24] S.M. Hosamani, Computing Sanskruti index of certain nanostructures, J. Appl. Math. Comput., 2017, 54, 425-433. [Crossref], [Google Scholar], [Publisher]

[25] M.C. Shanmukha, N.S. Basavarajappa, A. Usha & K.C. Shilpa, Novel neighbourhood redefined first and second Zagreb indices on carborundum structures, J. Appl. Math. Comput., 2020, 1-14. [Crossref], [Google Scholar], [Publisher]

[26] A. Graovac, M. Ghorbani, M.A. Hosseinzadeh, Computing fifth geometric arithmetic index for nanostar dendrimers, J. math. nonosci., 2011, 1, 33-42. [Crossref], [Google Scholar], [Publisher]

[27] S. Mondal, N. De, A. Pal, On some new neighbourhood degree based indices, Acta Chemica Iasi, 2019, 27, 31-46. [Crossref], [Google Scholar], [Publisher]

[28] H. Hosoya, On some counting polynomials in chemistry, Discret. Appl. Math., 1988, 19, 239-257. [Google Scholar], [Publisher]

[29] A.Q. Baig, M. Imran, H. ALI, Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes, Optoelectronics and advanced materials-rapid communications, 2015, 9, 248-255. [Google Scholar], [Publisher]

[30] H.M.A. Siddiqui, Computation of Zagreb indices and Zagreb polynomials of Sierpinski graphs, Hacet. J. Math. Stat., 2020 49, 754-765. [Crossref], [Google Scholar], [Publisher]

[31] M. Nadeem, A. Yousaf, A. Razaq, Certain Polynomials and related topological indices for the series of benzenoid graphs, Scientific Reports, 2019, 1-6. [Crossref], [Google Scholar], [Publisher]

[32] E. Deutsch, S. Klavzar, M-Polynomial and degree − based topological indices, Iran. J. Math. Chem., 2015, 6, 93-102. [Crossref], [Google Scholar], [Publisher]

[33] S. Mondal, M. Kamran, N. De, A. Pal, Topological properties of para-line graph of some convex polytopes using neighborhood M-polynomial, Biointerface Res. Appl. Chem., 2021, 11, 9915-9927. [Crossref], [Google Scholar], [Publisher]

[34] A. Ali, W. Nazeer, M. Munir, S. Min Kang, M-polynomials and topological indices of zigzag and rhombic Benzenoid systems, Open Chem., 2017, 16, 73–78. [Crossref], [Google Scholar], [Publisher]

[35] B. Basavanagoud, A.P. Barangi, M-polynomial of some cactus chains and their topological indices, Open J. Discrete Math., 2019, 2, 59-67. [Google Scholar]

[36] M. Munir, W. Nazeer, S. Rafque, A.R. Nizami, S.M. Kang, M-polynomial and degree-based topological indices of titania nanotubes, Symmetry, 2016, 8, 117. [Crossref], [Google Scholar], [Publisher]

[37] G. Abbas, M. Ibrahim, A. Ahmad, M. Azeem, K. Elahi, M-polynomials of tetra-cyano-benzene transition metal structure, Polycycl. Aromat. Compd., 2021, 1-11. [Crossref], [Google Scholar], [Publisher]

[38] M.C. Shanmukha, A. Usha, K.C. Shilpa, N.S. Basavarajappa, M-polynomial and neighborhood M-polynomial methods for topological indices of porous graphene, Eur. Phys. J. Plus., 2021, 136, 1-16. [Crossref], [Google Scholar], [Publisher]

[39] M.C. Shanmukha, A. Usha, Comparative study of chitosan derivatives through CoM-polynomial, Int. J. Quantum Chem., 2022, e26976. [Crossref], [Google Scholar], [Publisher]

[40] A. Francesko, M.D. Gonz´alez, G.R. Lozano, T. Tzanov, Developments in the processing of chitin, chitosan and bacterial cellulose for textile and other applications, Advances in textile biotechnology, 2010, 288-311. [Crossref], [Google Scholar], [Publisher]

[41] K.B. Rufato, J.P. Galdino, K.S. Ody, A.G. Pereira, E. Corradini, A.F. Martins, E.C. Muniz, Hydrogels based on chitosan and chitosan derivatives for biomedical applications, In Hydrogels-smart materials for biomedical applications. IntechOpen, 2018. [Google Scholar], [Publisher]

[42] Vipin Bansal, Pramod Kumar Sharma, Nitin Sharma, Om Prakash Pal, Rishabha Malviya, Applications of chitosan and chitosan derivatives in drug delivery, Adv. Biol. Res., 2011, 5, 28-37. [Google Scholar], [Publisher]

Eurasian Chemical Communications

Computing molecular descriptors of chitosan derivatives and its M-polynomial expressions

References

References

Volume 5, Issue 10
October 2023
Pages 953-968

Computing molecular descriptors of chitosan derivatives and its M-polynomial expressions

References

References

Volume 5, Issue 10October 2023Pages 953-968

Volume 5, Issue 10
October 2023
Pages 953-968