<p>Graph theory serves as a powerful mathematical framework for modeling complex systems, including the chemical structures of pharmaceutical compounds. This study employs degree-based topological indices to analyze the chemical structures of 12 commonly prescribed antibiotics for treating kidney infections. These indices represent numerical values derived from a graph, allowing for the prediction of the physicochemical properties of compounds without the need for laboratory experiments. A computer-based technique and algorithm were employed to streamline calculations and data analysis. The degree-based topological indices were calculated using the MATLAB program. A comparison of their topological indices was conducted to predict the physicochemical characteristics of the selected drugs. Additionally, SPSS software was utilized to develop Quantitative Structure–Property Relationship (QSPR) models, which analyze the correlation between topological indicators and the drugs' physicochemical properties. Various regression models were applied to evaluate the effectiveness of the drugs. Effective predictors were identified, and optimal equations were established based on the highest correlation coefficients and Fisher's test. The study found that the power equation is the most effective method for estimating molar refraction (MR) and polarizability (P) using the Randic ( <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_6967_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">${R}_{-1/2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mo>-</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>) index. Conversely, the cubic equation proved the most reliable technique for estimating (MR) and (P) using the second modified Zagreb (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2025_6967_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">${}^{m}{M}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mi>m</mi> </mmultiscripts> <msub> <mi>M</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>) and atomic bond connectivity (ABC) indices. The findings highlight the potential of using degree-based topological indices in predicting the physicochemical characteristics of drugs. Identifying effective predictors and optimal equations contributes to understanding the relationship between chemical structure and properties, paving the way for further research in drug design and development.</p>

Modeling QSPR for pyelonephritis drugs: a topological indices approach using MATLAB

期刊论文
发表日期：

2025年2月10日

查看全文

Mehri Hasani,
Masoud Ghods,
Sourav Mondal,
Muhammad Kamran Siddiqui,
Imran Zulfiqar Cheema

摘要

Graph theory serves as a powerful mathematical framework for modeling complex systems, including the chemical structures of pharmaceutical compounds. This study employs degree-based topological indices to analyze the chemical structures of 12 commonly prescribed antibiotics for treating kidney infections. These indices represent numerical values derived from a graph, allowing for the prediction of the physicochemical properties of compounds without the need for laboratory experiments. A computer-based technique and algorithm were employed to streamline calculations and data analysis. The degree-based topological indices were calculated using the MATLAB program. A comparison of their topological indices was conducted to predict the physicochemical characteristics of the selected drugs. Additionally, SPSS software was utilized to develop Quantitative Structure–Property Relationship (QSPR) models, which analyze the correlation between topological indicators and the drugs' physicochemical properties. Various regression models were applied to evaluate the effectiveness of the drugs. Effective predictors were identified, and optimal equations were established based on the highest correlation coefficients and Fisher's test. The study found that the power equation is the most effective method for estimating molar refraction (MR) and polarizability (P) using the Randic ( ${R}_{-1/2}$ $R_{- 1 / 2}$ ) index. Conversely, the cubic equation proved the most reliable technique for estimating (MR) and (P) using the second modified Zagreb ( ${}^{m}{M}_{2}$ $^{m} M_{2}$ ) and atomic bond connectivity (ABC) indices. The findings highlight the potential of using degree-based topological indices in predicting the physicochemical characteristics of drugs. Identifying effective predictors and optimal equations contributes to understanding the relationship between chemical structure and properties, paving the way for further research in drug design and development.