A python based algorithmic approach to optimize sulfonamide drugs via mathematical modeling

This article explores the structural properties of eleven distinct chemical graphs that represent sulfonamide drugs using topological indices by developing python algorithm. To find significant relationships between the topological characteristics of these networks and the characteristics of the associated sulfonamide drugs. We use quantitative structure-property relationship (QSPR) approaches. In order to model and forecast these correlations and provide insights into the structure-activity relationships that are essential for drug design and optimization, linear regression is a vital tool. A thorough framework for comprehending the molecular characteristics and behavior of sulfonamide drugs is provided by the combination of topological indices, graph theory and statistical models which advances the field of pharmaceutical research and development.


Results and discussion
Chemical graphs representing the molecular structures of sulfonamide drugs shown in Fig. 1 were used to start the QSPR analysis.A systematic representation of the complex connection patterns within each molecule was made possible by this change.The topological indices of these chemical graphs were determined by developing an edge-partitioning-based Python Algorithms.The degree-based topological characteristics that are essential for comprehending the structural subtleties affecting the pharmacological characteristics of sulfonamide drugs were successfully captured by this approach.Linear regression analysis was carried out using the Statistical Package for the Social Sciences (SPSS) to uncover the statistical correlations between the biological activity of the sulfonamide compounds and the computed topological indices.By identifying important links, this stage helped to clarify the essential topological aspects that underlie the biological effects that have been observed.Also, a Python algorithm is developed especially for the comparison section to guarantee the analysis's resilience and dependability.This approach made it possible to thoroughly analyze and validate the linear regression findings, offering a rigorous assessment of the topological indices' predictive power in clarifying the structure-activity relationship of sulfonamide drugs.polymers of sulfonamides.The topological indices for a group of sulfonamide drugs shown in Figs. 2, 3 and 4 have been determined using Algorithm-1 and Algorithm-2 presented in Table 2.
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Regression model
A linear equation in the form of Y = A + BX demonstrates the relationship between the independent variables (X) and the dependent variable (Y) in linear regression.In this case, Y is the dependent variable's predicted or estimated value, X is the independent variable, 'B' denotes the regression line's slope, and ' A' is the y-intercept.'B' and ' A' values that minimize the difference between the expected and actual observed values are the ones that need to be found.As linear regression models enable researchers to investigate and measure the relationships between different molecular parameters and the possible efficacy of treatment candidates, therefore linear regression models are crucial resources for molecular insights into anti-Alzheimer's medications.Below we have computed sevral linear regression models with respect to TIs discussed in Table 2 The physico-chemical properties listed in Table 3 serve as essential descriptors for the desired molecular properties.The development of QSPR model requires these characteristics.In this case, evaluating the dependability and predictive capability of the QSPR model depends significantly on statistical measures like the correlation coefficient (r), standard error (S.E.), F-statistic, and p-value.Tables 4, 5, 6, 7, 8, 9, 10, and 11 provide an overview of these statistical measures that shed light on the strength and importance of the correlations between the topological indices and the reported physico-chemical properties.These statistical parameters guarantee a thorough assessment of the model's performance, allowing scientists to determine how well the model predicts the desired molecular attributes using the topological indices that are specified.
The correlation coefficients between particular topological descriptors and physico-chemical parameters are shown in Table 4. Interestingly, Polarizability has a significant linear relationship with the SS(G) index, as demonstrated by high coefficient of 0.9803.The M 2 (G) index, which measures complexity, shows a strong association with a coefficient of 0.8722.Furthermore, Boiling point (B.P) has a 0.6811 correlation coefficient and significantly aligns with the M 1 (G) index.The RezG 3 index and molecular weight (M.W) have a strong association (coefficient of 0.8809), highlighting the topological descriptor's predictive ability.Furthermore, a good correlation between www.nature.com/scientificreports/Molar Volume (M.V) and the RezG 2 index is indicated by a high coefficient of 0.9588, indicating a dependable link between the two variables.In Table 5, we have shown the statistical parameters employed in the QSPR model with respect to M 2 (G) .color redIn Fig. 5, we have shown the correlation coefficients with respect to TIs.Tables 12, 13, 14, 15, 16 and 17 show the computed values of boiling point , flash point, molar volume, molecular weight, complexity, and polarizability that were compared to their corresponding actual values in order to assess the effectiveness of regression models for predicting different physicochemical properties of sulfonamide drugs.In addition to providing insights into the models' potential utility in forecasting the physicochemical features of sulfonamide drugs and advancing drug development and study, this thorough evaluation is an essential step in demonstrating the models' robustness and reliability.Also graphical comparison shown in Fig. 6.

Conclusion
A Python algorithm is developed to compute degree-based topological indices, which were then used to examine eleven different sulfonamide drugs.This approach has yielded important insights into the chemical features of these drugs.After that, a regression model isused to determine the characteristics of these drugs, and the results showed that Polarizability, Complexity, Molecular Weight, and Molar Volume were significant factors.These results imply that the behavior and characteristics of sulfonamide drugs are substantially influenced by these particular molecular properties.Unexpectedly, the analysis also indicates that the regression model determined that Boiling Point and Flash Point were not significant indicators.This suggests that both of these factors may

Table 2 .
The molecular descriptors for the candidate drugs.

Table 3 .
The properties of drugs related to their Physico-chemical characteristics.

Table 4 .
Correlation coefficients of T.I with respect to different physical characteristics.

Table 5 .
The statistical parameters employed in the QSPR model with respect to M 1 (G).

Table 6 .
The statistical parameters employed in the QSPR model with respect to M 2 (G).

Table 7 .
The statistical parameters employed in the QSPR model with respect to H(G).

Table 8 .
The statistical parameters employed in the QSPR model with respect to F(G).

Table 9 .
The statistical parameters employed in the QSPR model with respect to SS(G).

Table 10 .
The statistical parameters employed in the QSPR model with respect to RezG 2 (G).

Table 11 .
The statistical parameters employed in the QSPR model with respect to RezG 3 (G).

Table 12 .
Comparison of actual and computed values of Polarizability from regression models of TIs.

Table 13 .
Comparison of actual and computed values of Complexity from regression models of TIs.Correlation coefficients with respect to TIs disscused in Table2.

Table 14 .
Comparison of actual and computed values of Boiling Point from regression models of TIs.

Table 15 .
Comparison of actual and computed values of Molecular Weight from regression models of TIs.

Table 16 .
Comparison of actual and computed values of Molecular Volume from regression models of TIs.