(193v) 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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