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

Abstract

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.

Introduction

Sulfonamide drugs, which contain a sulfonamide functional group, have a significant medical history that dates back to the 1930s when the first synthetic antibacterial agent, Prontosil, was discovered¹. Since then, they have been widely used for their antibacterial qualities, especially in fighting bacterial infections. In addition to their antibacterial properties, sulfonamide drugs also demonstrate effectiveness against specific protozoal infections, making them highly flexible in the treatment of infectious diseases.Sulfonamide drugs have become a vital class of substances with a wide range of therapeutic uses in the field of pharmaceutical research². Sulfonamide’s drugs are also commonly used for the treatment of urinary tract infections, respiratory tract infections, and bacterial meningitis³. They function by limiting the production of folic acid in bacteria, therefore impeding their growth and reproduction. Sulfonamide medications are additionally employed for the treatment of toxoplasmosis and malaria⁴. Sulfonamide’s distinct chemical structure makes them a perfect candidate for optimization in drug development due to their effectiveness against a variety of medical conditions⁵. Customized features of sulfonamide drugs that enhance pharmacological effects require an understanding of their quantitative structure-activity relationship (QSAR)^6,7. Degree-based Topological Indices are essential for understanding the complex relationships among sulfonamide drugs . These indices, which assign numerical values depending on the connectivity of atoms inside the compound, provide a quantitative representation of the molecular structure^8,9,10,11 . More specifically, a molecule’s topological characteristics are mostly determined by the degree or number of bonds that each atom provides^12,13.

Degree-based topological indices that are used in this study presented in Table 1 , which show the spatial arrangement and connectivity of atoms, offer significant novel perspectives on the structural characteristics of sulfonamide drugs that affect their biological behavior¹⁴. The application of these indices is essential in comprehending the complicated relationships between structure and function, particularly with complex molecular structures¹⁵. This aids researchers in designing and refining Sulfonamide compounds in a rational way in order to optimize their pharmacological effects¹⁶. A QSPR analysis is based on the correlation between these indices and the biological activity of sulfonamide drugs. Utilizing mathematical techniques like linear regression makes it possible to systematically examine the structure-activity landscape and identify patterns that inform the optimization of potential sulfonamide drugs candidates. Several researchers have recently made contributions in this domain^17,18,19,20.

A Python program has been developed with the goal of obtaining a thorough understanding and practical application of these relationships. This application streamlines the QSPR analysis process by facilitating the application of mathematical models and the computation of topological indices. Scientists and researchers may quickly optimize sulfonamide medications, find hidden relationships and analyze massive data sets efficiently by incorporating the Python application into their workflow. This integrated strategy which combines Python programming, degree-based topological indices, QSPR analysis and sulfonamide drug research, advances pharmaceutical development and advances the continuous seek for novel and more effective therapeutic agents.

Table 1 Different topological descriptors.

Methodology

We firstly convert chemical structures into molecular graphs and edge partitioning is performed, based on graph connectivity. Secondly, Degree-based topological indices were computed by analyzing the distribution of node degrees within the graph by developing python algorithm. For python program we import necessary library numpy then define different variables for edge-partition and lastly apply for-loop to compute indices. Furthermore we use SPSS software for Regression analysis to assess the connection between the computed indices and experimental characteristics. To evaluate the developed indices ability to predict molecular behavior, a comparison of actual and predicted values was made.

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.

Figure 1

Molecular Graph of Meloxicam and Meticrane.

Figure 2

Molecular structure of Dabrafenib,Famotidine and Dorzolamide.

Figure 3

Molecular structure of Sulfonamide Drugs.

Figure 4

Molecular structure of Daranide, Metahydrin and Sulfadiazine.

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.

Regression models of $M_1(G)$

• Polarizability = 16.5920 + 0.1177 $M_1(G)$

• Complexity = 253.1917 + 2.1931 $M_1(G)$

• Boiling point = 562.5737 + 0.0892 $M_1(G)$

• Molecular weight = 205.7471 + 1.0540 $M_1(G)$

• Molecular volume = 110.2459 + 0.8195 $M_1(G)$

• Flash point = 294.0339 + 0.0539 $M_1(G)$

Regression models of $M_2(G)$

• Polarizability = 7.5184 + 0.1832 $M_2(G)$

• Complexity = 125.5086 + 3.0798 $M_2(G)$

• Boiling point = 510.5981 + 0.5039 $M_2(G)$

• Molecular weight = 113.6467 + 1.7289 $M_2(G)$

• Molecular volume = 31.4493 + 1.4024 $M_2(G)$

• Flash point = 262.5657 + 0.3051 $M_2(G)$

Regression models of H(G)

• Polarizability = 5.0573 + 2.9345 H(G)

• Complexity = 125.4552 + 44.4959 H(G)

• Boiling point = 496.9339 + 8.8771 H(G)

• Molecular weight = 101.2243 + 26.4279 H(G)

• Molecular volume = 24.4009 + 21.0829 H(G)

• Flash point = 254.2942 + 5.3739 H(G)

Regression Models of F(G)

• Polarizability = 5.6774 + 0.0798 F(G)

• Complexity = 85.4367 + 1.3719 F(G)

• Boiling point = 491.9821 + 0.2638 F(G)

• Molecular weight = 88.2033 + 0.7798 F(G)

• Molecular volume = 14.0497 + 0.6219 F(G)

• Flash point = 251.3014 + 0.1597 F(G)

Regression models of SS(G)

• Polarizability = 5.67009 + 1.1078 SS(G)

• Complexity = 115.7992 + 3.2629 SS(G)

• Boiling point = 500.7366 + 3.2629 SS(G)

• Molecular weight = 101.4689 + 10.2152 SS(G)

• Molecular volume = 23.5397 + 8.1969 SS(G)

• Flash point = 256.5959 + 1.9753 SS(G)

Regression models of $Rez G_2(G)$

• Polarizability = 6.6479 + 0.9945 $Rez G_2(G)$

• Complexity = 127.9736 + 15.9940 $Rez G_2(G)$

• Boiling point = 507.9909 + 2.7443 $Rez G_2(G)$

• Molecular weight = 110.4326 + 9.1732 $Rez G_2(G)$

• Molecular volume = 29.1663 + 7.4271 $Rez G_2(G)$

• Flash point = 260.9856 + 1.6614 $Rez G_2(G)$

Regression models of $Rez G_3(G)$

• Polarizability = 9.0849 + 0.0316 $Rez G_3(G)$

• Complexity = 138.6683 + 0.5511 $Rez G_3(G)$

• Boiling point = 517.5597 + 0.0829 $Rez G_3(G)$

• Molecular weight=124.7707 + 0.3038 $Rez G_3(G)$

• Molecular volume = 39.1387 + 0.2484 $Rez G_3(G)$

• Flash point = 266.7802 + 0.0502 $Rez G_3(G)$

Table 2 The molecular descriptors for the candidate drugs.

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

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.

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 $M_1(G)$.

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 its 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 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.

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 $RezG_3(G)$.

Figure 5

Correlation coefficients with respect to TIs disscused in Table 2.

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.

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.

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.

Table 17 Comparison of actual and computed values of Flash Point from regression models of TIs.

Figure 6

Graphical comparison with actual and predicted values.

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 have a limited impact on the observed variances in the sulfonamide drugs under consideration within the framework of this research. Our study improves research processes’ transparency and reproducibility by employing a Python software. Since the software code is publicly available, other researchers can independently validate our findings and repeat our methods. This openness encourages scientific integrity and makes it easier for researchers to work together.