(650d) Predicting Anti-HIV-1 Activity of Tibo Compounds by QSAR Approach Using a New Topological Index

The search and development of anti-HIV drugs is currently one of the most urgent tasks of pharmacological studies. The objective of this work was to determine whether a more general HIV-1 inhibitors structure-log(1/IC₅₀)  relationship based solely on one topological index, could be developed through the systematic QSAR approach. A new topological index, a extended distance matrix, was proposed in this work. This new topological index is composed of the distance matrix and the atomic character matrix and applied to build up a positional distributive structure-activity relationship (PDSAR) model for predicting anti-HIV-1 activity of 89 TIBO compounds. The results indicate that our topological index provides very satisfactory results. The overall average absolute difference for log(1/IC₅₀)predictions of 89 TIBO compounds is 0.411693 and R² value is of 0.849292. Comparing with R. Garg et al.’ method, our PDSAR method performed better both in accuracy and generality.

Keywords: Anti-HIV-1 activity; TIBO compounds; QSAR; Positional distributive structure-activity relationship (PDSAR); Topological index

Introduction

Acquired immunodeficiency syndrome (AIDS) is a collection of symptoms and infections resulting from the specific damage to the immune system caused by the human immunodeficiency virus (HIV).^{1-3 In the HIV life cycle, three enzymes are essential for replication of this virus inside host, reverse transcriptase (RT), protease (PR) and integrase (IN). Theoretically, an anti-HIV agent may exert its activity by inhibiting a variety of steps in the life cycle of the virus. Therefore, all of them are considered to be promising targets for the development of anti-HIV drugs. 4-6}

In order to search for anti-HIV drugs with fewer side effects and high efficacy, modeling the biological activity to propose new candidate molecules is an important approach. So, over the last few years, the quantitative structure-activity relationship (QSAR) studies have been carried out for different series of HIV-1 inhibitors, such as HIV-1 RT inhibitors^{1, 7-10}, HIV-1 IN inhibitors^{2, 11-13} and HIV-1 PR inhibitors.^14-15

Nowadays, QSAR models using topological indexes (TIs) generated from molecular graphs have been more frequently used to obtain physicochemical and biological properties. Based on the distance and adjacency matrices, various TIs have been proposed and used in QSAR approaches.^16-20 However, until now no single topological index could be used universally in optimal correlations. Therefore, it is absolutely necessary for the researcher to see if a single set of descriptor, or a single topological index can be used to build a universal model in order to predict good values for all properties.

Recently, authors proposed a universal positional distributive group contribution (PDGC) theory for the prediction of various properties of a diverse set of organics compound.²¹ Our previous works suggests that it is possible to use a totally same universal framework to predict various properties of organic compounds containing various functionalities.

Therefore, the major objectives of this study are: (i) to propose a new topological index, (ii) to develop a more general and robust positional distributive structure-activity relationship (PDSAR) model for biological activity prediction of HIV-1 inhibitors involving various drugs.

Biological data

In this QSAR study, a series of 89 tetrahydroimidazo[4,5,1-jk][1,4]benzodiazepinone (TIBO) compounds were taken under consideration in this study.^1,3 And the logarithm of the inverse of the anti-HIV activity parameter IC₅₀ was used as biological end points (log 1/IC₅₀) in this work.

Method proposed in this work

Based on chemical graphs, a new topological index calculated from a molecular graph was introduced. This newly proposed topological index is a extended distance matrix (MD), from which the extended adjacency matrix(Ma), the extended interval matrix(Mb) and the extended interval jump matrix(Mc) are deduced. In deed, the extended distance matrix(MD) is composed of the distance matrix (D) and the atomic character matrix (Me). Our topological index could quantitatively describe the structural information of molecules, taking into account parameters such as eletronegativity fraction, Van der Waals radius, minimum bond length with adjacent atom except hydrogen, number of adjacent hydrogen atom, and the number of adjacent atom except hydrogen.

Based on the new topological index, our approach is performed with ordinary least squares (OLS) regression. Also, in order to optimization the molecular structure, Gaussian software has been used for optimization the minimum bond length.

In this work, using the new topological index, a positional distributive structure-activity relationship (PDSAR) model for log (1/IC₅₀) prediction is expressed as Eq. (1).

Log(1/IC50)=MD+MA+MB+MC+b1exp(1/N)+b2exp(1/MW)+M0            (1)

 Here,

MD=a_d1·norm(MD,1)+ a_d2·norm(MD,2)+ a_d3·norm(MD, fro)

MA=a_a1·norm(MA,1)+ a_a2·norm(MA,2)+ a_a3·norm(MA, fro)

MB=a_b1·norm(MB,1)+ a_b2·norm(MB,2)+ a_b3·norm(MB, fro)

MC=a_c1·norm(MC,1)+ a_c2·norm(MC,2)+ a_c3·norm(MC, fro)

Where, MD is extended distance matrix, MA is extended adjacency matrix, MB is extended interval matrix,      MC is extended interval jump matrix, norm(MD, 1) means the largest column sum of matrix MD, norm(MD, 2) means the largest singular value of matrix MD, norm(MD, fro) is the frobenius-norm of matrix MD, N for total number of atoms, MW is molecular weight, M₀ is the constant added, and a, b₁, b₂ are regression parameters.

Results and discussion

Results of this work indicate that the predicted log (1/IC₅₀) agree well with the “experimental results”, which demonstrates that the new topological index for predicting log (1/IC₅₀) has good overall accuracy. The average absolute difference (AAD) for log (1/IC₅₀)prediction of 89 TIBO compounds is 0.411693. Also, our high-quality prediction model is evidenced by a R² value of 0.849292 and a PRESS value of 27.32721.

Also, in order to evaluate the performance of our PDSAR model, the log (1/IC₅₀) prediction results with R. Garg et al.’ QSAR method ¹ had been used for comparison. Based on their QSAR model, the AAD for log (1/IC₅₀)prediction is 0.523933. The R² and PRESS values are 0.743363 and 46.5349, respectively. Comparing with R. Garg et al.’ method, our PDSAR method performed better both in accuracy and generality.

In addition, the leave-one-out cross-validation method indicated that the model (eq 1) is significant, robust and has good internal predictability.

Conclusion

A new topological index, calculated directly from molecular structure alone, was proposed and applied to build up a positional distributive structure-activity relationship (PDSAR) model for predicting anti-HIV-1 activity of 89 TIBO compounds in this work. Results indicate that log (1/IC₅₀) was successfully predicted with our PDSAR model. It is evident that the proposed topological index can be used to predict log (1/IC₅₀) with a significant degree of confidence. The overall average absolute difference for log (1/IC₅₀)predictions of 89 TIBO compounds is found to be 0.411693. Comparing with R. Garg et al.’ method,¹ our method performed better both in accuracy and generality.

Acknowledgements. Research reported in this work was supported by the National Natural Science Foundation of China (No. 20976131, and No. u1162104).

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