QSAR study on the Ah receptor-binding affinities of polyhalogenated dibenzo-p-dioxins using net atomic-charge descriptors and a radial basis neural network

Abstract

A radial basis function neural network (RBFN) has been used to correlate Ah receptor-binding affinities of polychlorinated, polybrominated, and polychlorinated–brominated dibenzo-p-dioxins with molecular weight and eight net atomic charge descriptors. Support vector machine (SVM) and partial least square (PLS) regression models based on the same data set have also been built. Leave-one-out cross-validation was used to train the RBFN, SVM, and PLS models. For predicting Ah receptor-binding affinities, the RBFN model with a squared cross-validation correlation coefficient (q ²) of 0.8818 outperforms the SVM and PLS models and also compares favorably with any other reported quantitative structure–activity relationship model based on the same activity data set. The significance of the RBFN model with net atomic charges as descriptors suggests that electrostatic and dispersion-type interactions play important roles in governing the Ah receptor binding of polychlorinated, polybrominated, and polychlorinated–brominated dibenzo-p-dioxins.

Appendix

• AHH–aryl hydrocarbon hydroxylase

• AhR–Ah receptor

• bHLH–basic helix–loop–helix

• CV–cross-validation

• EROD–7-ethoxyresorufin O-deethylase

• LOO–leave-one-out

• PAS–Per–Arnt–Sim

• PBDD–polybrominated dibenzo-p-dioxin

• PCA–principal components analysis

• PCB–polychlorinated biphenyl

• PCDD–polychlorinated dibenzo-p-dioxin

• PCDF–polychlorinated dibenzofuran

• pEC₅₀–the negative logarithm of the half-maximum effective concentration for assessing AhR-binding affinity of compounds

• PLS–partial least squares regression

• PRESS–predictive residual error sum of squares, ${\text{PRESS}} = {\sum\limits_{i = 1}^n {{\left( {\ifmmode\expandafter\hat\else\expandafter\^\fi{y}_{i} - y_{i} } \right)}^{2} } }$, $\ifmmode\expandafter\hat\else\expandafter\^\fi{y}_{i}$ is the predicted value from cross-validation and y _i is the experimental value.

• PXDD–polychlorinated dibenzo-p-dioxin, polybrominated dibenzo-p-dioxin, or polychlorinated–brominated dibenzo-p-dioxin

• q ²–the square correlation coefficient for cross-validation, ${\text{q}}^{2} = 1 - {{\text{PRESS}}} \mathord{\left/ {\vphantom {{{\text{PRESS}}} {{\sum\limits_{i = 1}^n {{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}^{2} } }}}} \right. \kern-\nulldelimiterspace} {{\sum\limits_{i = 1}^n {{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}^{2} } }}$, $\ifmmode\expandafter\bar\else\expandafter\=\fi{y}$ is the average experimental value

• QSAR–quantitative structure–activity relationship

• QSPR–quantitative structure-property relationship

• R–correlation coefficient,

  $${\text{R}} = {{\sum\limits_{i = 1}^n {{\left( {x_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{x}} \right)}{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}} }} \mathord{\left/ {\vphantom {{{\sum\limits_{i = 1}^n {{\left( {x_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{x}} \right)}{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}} }} {{\sqrt {{\sum\limits_{i = 1}^n {{\left( {x_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{x}} \right)}^{2} {\sum\limits_{i = 1}^n {{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}^{2} } }} }} }}}} \right. \kern-\nulldelimiterspace} {{\sqrt {{\sum\limits_{i = 1}^n {{\left( {x_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{x}} \right)}^{2} {\sum\limits_{i = 1}^n {{\left( {y_{i} - \ifmmode\expandafter\bar\else\expandafter\=\fi{y}} \right)}^{2} } }} }} }}$$

• RBFN–radial basis function neural network

• RE–relative error

• RMSE–root mean square error, ${\text{RMSE}} = {\sqrt {{{\sum\limits_{i = 1}^n {{\left( {\ifmmode\expandafter\hat\else\expandafter\^\fi{y}_{i} - y_{i} } \right)}^{2} } }} \mathord{\left/ {\vphantom {{{\sum\limits_{i = 1}^n {{\left( {\ifmmode\expandafter\hat\else\expandafter\^\fi{y}_{i} - y_{i} } \right)}^{2} } }} n}} \right. \kern-\nulldelimiterspace} n} }$

• SVM–support vector machine