On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR

Abstract

The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msubsup><a:mrow><a:mtext>ISI</a:mtext></a:mrow><a:mrow><a:mfenced open="(" close=")" separators="|"><a:mrow><a:mi>α</a:mi><a:mo>,</a:mo><a:mi>β</a:mi></a:mrow></a:mfenced></a:mrow><a:mrow><a:mtext>ve</a:mtext></a:mrow></a:msubsup><a:mfenced open="(" close=")" separators="|"><a:mrow><a:mi>G</a:mi></a:mrow></a:mfenced></a:math> and general ve-Zagreb index <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M2"><i:msubsup><i:mi>M</i:mi><i:mi>α</i:mi><i:mrow><i:mtext>ve</i:mtext></i:mrow></i:msubsup><i:mfenced open="(" close=")" separators="|"><i:mrow><i:mi>G</i:mi></i:mrow></i:mfenced></i:math> of graph <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" id="M3"><n:mi>G</n:mi></n:math> and compute <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M4"><p:msubsup><p:mrow><p:mtext>ISI</p:mtext></p:mrow><p:mrow><p:mfenced open="(" close=")" separators="|"><p:mrow><p:mi>α</p:mi><p:mo>,</p:mo><p:mi>β</p:mi></p:mrow></p:mfenced></p:mrow><p:mrow><p:mtext>ve</p:mtext></p:mrow></p:msubsup><p:mfenced open="(" close=")" separators="|"><p:mrow><p:mi>G</p:mi></p:mrow></p:mfenced><p:mo>,</p:mo><p:msubsup><p:mi>M</p:mi><p:mi>α</p:mi><p:mrow><p:mtext>ve</p:mtext></p:mrow></p:msubsup><p:mfenced open="(" close=")" separators="|"><p:mrow><p:mi>G</p:mi></p:mrow></p:mfenced></p:math> , and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" id="M5"><ab:msubsup><ab:mi>M</ab:mi><ab:mi>α</ab:mi><ab:mrow><ab:mtext>ev</ab:mtext></ab:mrow></ab:msubsup><ab:mfenced open="(" close=")" separators="|"><ab:mrow><ab:mi>G</ab:mi></ab:mrow></ab:mfenced></ab:math> (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" id="M6"><fb:msubsup><fb:mrow><fb:mtext>ISI</fb:mtext></fb:mrow><fb:mrow><fb:mfenced open="(" close=")" separators="|"><fb:mrow><fb:mi>α</fb:mi><fb:mo>,</fb:mo><fb:mi>β</fb:mi></fb:mrow></fb:mfenced></fb:mrow><fb:mrow><fb:mtext>ve</fb:mtext></fb:mrow></fb:msubsup><fb:mfenced open="(" close=")" separators="|"><fb:mrow><fb:mi>G</fb:mi></fb:mrow></fb:mfenced><fb:mo>,</fb:mo><fb:msubsup><fb:mi>M</fb:mi><fb:mi>α</fb:mi><fb:mrow><fb:mtext>ve</fb:mtext></fb:mrow></fb:msubsup><fb:mfenced open="(" close=")" separators="|"><fb:mrow><fb:mi>G</fb:mi></fb:mrow></fb:mfenced></fb:math> , and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" id="M7"><qb:msubsup><qb:mi>M</qb:mi><qb:mi>α</qb:mi><qb:mrow><qb:mtext>ev</qb:mtext></qb:mrow></qb:msubsup><qb:mfenced open="(" close=")" separators="|"><qb:mrow><qb:mi>G</qb:mi></qb:mrow></qb:mfenced></qb:math> . Furthermore, QSPR analysis of <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" id="M8"><vb:msubsup><vb:mrow><vb:mtext>ISI</vb:mtext></vb:mrow><vb:mrow><vb:mfenced open="(" close=")" separators="|"><vb:mrow><vb:mi>α</vb:mi><vb:mo>,</vb:mo><vb:mi>β</vb:mi></vb:mrow></vb:mfenced></vb:mrow><vb:mrow><vb:mtext>ve</vb:mtext></vb:mrow></vb:msubsup><vb:mfenced open="(" close=")" separators="|"><vb:mrow><vb:mi>G</vb:mi></vb:mrow></vb:mfenced><vb:mo>,</vb:mo><vb:msubsup><vb:mi>M</vb:mi><vb:mi>α</vb:mi><vb:mrow><vb:mtext>ve</vb:mtext></vb:mrow></vb:msubsup><vb:mfenced open="(" close=")" separators="|"><vb:mrow><vb:mi>G</vb:mi></vb:mrow></vb:mfenced></vb:math> , and <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" id="M9"><gc:msubsup><gc:mi>M</gc:mi><gc:mi>α</gc:mi><gc:mrow><gc:mtext>ev</gc:mtext></gc:mrow></gc:msubsup><gc:mfenced open="(" close=")" separators="|"><gc:mrow><gc:mi>G</gc:mi></gc:mrow></gc:mfenced></gc:math> for particular values of <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" id="M10"><lc:mi>α</lc:mi></lc:math> and <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" id="M11"><nc:mi>β</nc:mi></nc:math> is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.

Topics & Concepts