Predicting Toxicological Activity of Heterocyclic Compounds Using a New Topological Index

Predicting Toxicological Activity of Heterocyclic Compounds Using a New Topological Index

Liping Hu ^a, Qingzhu JIA ^a Qiang WANG ^a*, Xiuping Lu ^a, Peisheng MA ^b, Peng Feng ^a, Pengfei Liu ^a

a. School of Material Science and Chemical Engineering, Tianjin University of Science and Technology, 13St. TEDA, Tianjin, 300457, People's Republic of China

b. School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People's Republic of China

* To whom correspondence should be addressed. E-mail: wang_q@tust.edu.cn  

 

Abstract    

A Quantitative structure-activity relationship (QSAR) study was performed on the aryl hydrocarbon (Ah) receptor(described as pEC₅₀) of dibenzofurans in this article. The objective of this work was to determine whether a more general structure- pEC₅₀ relationship based solely on one topological index, could be developed through the systematic QSAR approach. A new topological index calculated from a molecular graph was introduced and named as WQ index. The results indicate that our topological index provides very satisfactory results. The overall average absolute difference and the relative derivation for pEC₅₀ predictions of 32 dibenzofurans are found to be 0.29 and 5.5 %, respectively. While with the HiQSAR approach, the AAD for pEC₅₀ prediction is 0.45 and the mean absolute relative derivation is 8.7 %. Comparing with the HiQSAR method of Basak SC et al., our method performed better both in accuracy and generality.

Keywords: Dibenzofurans; The aryl hydrocarbon (Ah) receptor (pEC₅₀); QSAR; topological index

Introduction

According to George S. Hammond, the most fundamental and lasting objective of synthesis is not production of new compounds, but production of properties¹. Hence, for the drug discovery process, the aim is at bringing to market new therapeutic agents with desirable pharmacodynamic profile, favorable ADMET (Absorption, Distribution, Metabolism, Elimination and Toxicity) properties. However, the costs and risks associated with this process have become enormous. According to recent Tufts Center for the Study of Drug Development data, drug development, starting from the clinical trials to the final approval, is about 8.5 years long with a cost exceeding $40 billion, and only 21.5% of clinical success rate². Consequently, at the early stage of drug discovery, suitable computational approaches are needed to shorten the time and increase the success rate by deriving in silico models for the prediction of the desirable properties. Quantitative structure-activity relationships (QSARs) or quantitative structure-property relationships (QSPRs) approaches represent probably the most robust well known tools to mathematically analyze the correlation between molecular properties and the corresponding property of interest^2-4.

Heterocyclic molecules play a crucial role in health care and pharmaceutical drug design. As a result, medicinal chemists, drug designers, and toxicologists remain keenly interested in the beneficial and deleterious effects of heterocyclic moieties in molecules. Previous studies have demonstrated that QSAR approach is to be successful in predicting properties, activities, and toxicities including mutagenicity of aromatic and heteroaromatic amines. Specially, With increased computational power and the development of modern QSAR/QSPR approaches, powerful methods for the prediction of heterocyclic compounds' properties have eventually become available^5-7.

However, until now, no single topological index could be used universally in optimal correlations; thus, more than hundreds of topological indices are in existence. In fact, the uniform applicability of topological indices to compounds of wide structural diversity still presents many difficulties. Therefore, it is absolutely necessary for the researcher to see if a single set of descriptor, or a single topological index could be used to build a universal model in order to predict good values for all properties.

Authors recently proposed a universal positional distributive group contribution (PDGC) theory for the prediction of various properties (critical temperature, melting point, vaporization enthalpy and so on.) of a diverse set of organics compound^8,9. Our previous works suggests that it is possible to use a totally same universal framework to predict the critical properties and the thermodynamics properties of organic compounds containing various functionalities.

Therefore, the objective of this work was to determine whether a more general structure-activity relationship based solely on one topological index, could be developed through the systematic QSAR approach.

The aryl hydrocarbon (Ah) receptor data--pEC₅₀

The aryl hydrocarbon (Ah) receptor (described as pEC₅₀) is well documented in the field of toxicology, with the toxicity of certain classes of persistent pollutants, including dibenzofurans, being determined by Ah receptor interaction. So, a set of 32 dibenzofurans compounds with Ah receptor binding potency values obtained from the literature were used for QSAR model development¹⁰.

Method proposed in this work

Based on chemical graphs, a new topological index calculated from a molecular graph was introduced and named as WQ index. This newly proposed topological index is adapted from the distance matrix and the extended distance matrix, from which the extended adjacency matrix, the extended interval matrix and the extended interval jump matrix are deduced. WQ index quantitatively describes the structural information of molecules, taking into account parameters like atom mass,  branching, adjacency pattern, electronegativity, the minimum bond length with adjacent atom, number of hydrogen atom and heteroatom variation etc, which are general but crucial ingredients for modeling thermodynamic properties. Also, the norm(1) and the norm(2) of the above matrixes have be calculated for developing the QSAR model.  

Here, using the WQ index, the QSAR model for pEC₅₀ prediction is expressed as follows:

pEC₅₀=M_D+M_A+M_I+M_IJ+b₁exp(1/N)+b₂exp(1/MV)+M₀

M_D=a₁norm(M_d,1)+ a₂norm(M_d,2)+ a₃norm(M_d,fro)

M_A=a₄norm(M_a,1)+ a₅norm(M_a,2)+ a₆norm(M_a,fro)

M_I=a₇norm(M_i,1)+ a₈norm(M_i,2)+ a₉norm(M_i,fro)

M_IJ=a₁₀norm(M_ij,1)+ a₁₁norm(M_ij,2)+ a₁₂norm(M_ij,fro)

 

M_d extended distance matrix ;   M_a extended adjacency matrix 

M_i extended Interval matrix;    M_ij extended Interval jump matrix

norm(M_d, 1) means the largest column sum of matrix M_d ;

norm(M_d, 2) means the largest singular value of matrix M_d;

norm(M_d, fro)is the frobenius-norm of matrix M_d;

N for total number of atoms, MW is molecular weight, and M₀ is the constant added.

 

Results and discussion

Results of this work indicate that the predicted pEC₅₀ agree well with the "experimental results", which demonstrates that the new topological index for predicting pEC₅₀ has good overall accuracy. The AAD for pEC₅₀ prediction of 32 dibenzofurans compounds is 0.29 and the mean absolute relative derivation is 5.5 %. While, with the HiQSAR approach proposed by Basak SC et al. ⁷, the AAD for pEC₅₀ prediction is 0.45 and the mean absolute relative derivation is 8.7 %. Comparing with the method of Subhash C. Basak et al., our method performed better both in accuracy and generality.

Conclusion

The objective of this work was to develop and evaluate our new topological index for predicting the the Ah receptor prediction of 32 dibenzofurans compounds. Results indicate that pEC₅₀ was successfully predicted. It is evident that the proposed topological index can be used to predict pEC₅₀ for dibenzofurans compounds with a significant degree of confidence. The overall average absolute difference and the relative derivation for pEC₅₀ predictions of 32 dibenzofurans compounds are found to be 0.29 and 5.5 %, respectively. Comparing with the HiQSAR method of Basak SC et al., 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). Also, we would give much thanks to Feng Peng, Liu Pengfei and Fu Dengfeng, who have contributed for valuable advice and discussion.

 

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