A joint optimization QSAR model of fathead minnow acute toxicity based on a radial basis function neural network and its consensus modeling

Acute toxicity of the fathead minnow (Pimephales promelas) is an important indicator to evaluate the hazards and risks of compounds in aquatic environments. The aim of our study is to explore the predictive power of the quantitative structure–activity relationship (QSAR) model based on a radial basis function (RBF) neural network with the joint optimization method to study the acute toxicity mechanism, and to develop a potential acute toxicity prediction model, for fathead minnow. To ensure the symmetry and fairness of the data splitting and to generate multiple chemically diverse training and validation sets, we used a self-organizing mapping (SOM) neural network to split the modeling dataset (containing 955 compounds) characterized by PaDEL-descriptors. After preliminary selection of descriptors via the mean decrease impurity method, a hybrid quantum particle swarm optimization (HQPSO) algorithm was used to jointly optimize the parameters of RBF and select the key descriptors. We established 20 RBF-based QSAR models, and the statistical results showed that the 10-fold cross-validation results (Rcᵥ₁₀²) and the adjusted coefficients of determination (Rₐdⱼ²) were all great than 0.7 and 0.8, respectively. The Qₑₓₜ² of these models was between 0.6480 and 0.7317, and the Rₑₓₜ² was between 0.6563 and 0.7318. Combined with the frequency and importance of the descriptors used in RBF-based models, and the correlation between the descriptors and acute toxicity, we concluded that the water distribution coefficient, molar refractivity, and first ionization potential are important factors affecting the acute toxicity of fathead minnow. A consensus QSAR model with RBF-based models was established; this model showed good performance with R² = 0.9118, Rcᵥ₁₀² = 0.7632, and Qₑₓₜ² = 0.7430. A frequency weighted and distance (FWD)-based application domain (AD) definition method was proposed, and the outliers were analyzed carefully. Compared with previous studies the method proposed in this paper has obvious advantages and its robustness and external predictive power are also better than Xgboost-based model. It is an effective QSAR modeling method.