Benzoic acid compounds are an important organic chemical raw material that are widely used in food, medicine, cosmetic, antiseptic, insecticide, dyestuff, etc. For example, benzoic acid is a common antiseptic, Aspirin is a famous non-steroid anti-inflammatory drug, Triflusal is a antithrombotic, and Chloramben and Dicamba are common pesticides (see Figure 1). Most benzoic acid compounds are toxic and are hardly degraded by microorganism in the natural environment, which may cause serious public health and environmental problems.

With the development of synthetic chemistry, combinatorial chemistry and pharmaceutical chemistry, millions of new compounds are being synthesized. Classical chemical substance evaluation needs a lot of time and is expensive, and the speed of analyzing the toxicity of compounds is less than the speed of discovery of new compounds. Nowadays, scientists pay more and more attention to the importance of prediction toxicity in the early stage. Quantitative structure-toxicity relationships (QSTR) have been efficiently used for the study of toxicity mechanisms of various compounds [1].

QSTR plays an important role in toxicity forecasting, which is widely used in the modern studying of compounds, since more and more compounds are being found. It is necessary to predict the toxicity of compounds accurately and quickly [2–4]. QSTR of benzoic acid compounds with molecular connectivity index (MCI) in mice via oral LD₅₀ (acute toxicity, half lethal dose) are not reported. The quantitative structure characteristic parameters of 57 benzoic acid compounds were obtained with MCI. Values of LD₅₀ for mice in benzoic acid compounds have been collected from various literature sources. In this work, the QSTR of benzoic acid compounds in mice via oral LD₅₀ was studied and a model was developed to more accurately predict the toxicity of benzoic acid compounds in mice via oral LD₅₀. 39 benzoic acid compounds were used as a training dataset for building the regression model, and 18 other benzoic acid compounds as a forecasting dataset to test the prediction ability of the model. The experimental result analysis showed that ⁰J^A, ¹J^A and cross factor J^B were important factors affecting the toxicity of benzoic acid compounds (although the toxicity mechanism of compounds is not clear yet), where ⁰J^A is zero order connectivity index, ¹J^A is the first order connectivity index and J_B= ⁰J^A × ¹J^A is the cross factor.

In 1975, Milan Randic described a skeletal branching index that correlated with the three physical properties of alkenes [5]. The concept was further developed and applied extensively by Kier and Hall [6–8], which led to the molecular connectivity index (MCI). Eventually, Kier and Hall modified the connectivity indices to discriminate carbon atoms from other heteroatoms, which introduced the valance molecular connectivity index ^mχ^t [9]. The MCI is calculated with the follow formula: (1) m χ t = ∑ Nm j = 1 ( Π m + 1 i   1 / δ i ) 1 / 2^mχ^t is mth-order MCI, t is the type of sub-graph including path (p), cluster (c), path-cluster (pc), N_m is the number of the sub-graph of the same type and order. The abbreviation is δ = σ – h, where σ is the count of electrons in σ orbital and h is the count of bonding hydrogen atoms.

There was no doubt that the MCI was proved to be the one of the most successful and widely used descriptors. The MCI has been introduced and used in many studies [10–13].

From the skeletal branching index of Randic to the connectivity index modified by Kier and Hall, the core is the connectivity of atoms, which is from the connectivity δ_i of upper atom to valence connectivity of δ_iv. The computing method of heteroatom i modified by Kier and Hall is as the following formula: (2) δ iv = ( Z i − h i ) / ( Z − Z i − 1 )

Z and Z_i are the count of extra nuclear electrons and valence electrons, respectively, h_i is the count of hydrogen atoms combining with heteroatom i. Although Kier et al contributed to the computing method of heteroatom i, the method could not discriminate the same heteroatom in different oxidation states. More recently, Yu et al improved the method, and redefined the valence connectivity value δ^h_i using the following formula [14]: (3) δ h i = 2   ×   Z  ( Z i − h i ) [ ( 8 − N i ) 1 / N i ] [ ( 2 n i − 1 ) h i / N i − 1 ] / [ ( m i + L p ) ( 2 n i − 1 ) ]m_i is the count of bonding electrons, Z is the count of extra nuclear electrons, n_i is maximum first quantum number, Z_i is the valence electron number, N_i is the count, L_p is the hybridization style of heteroatom i, the value as following: sp³, L_p = 1; sp², L_p = −1.8; sp, L_p = 2; if that is the atom itself, L_p = 2, m_i = 0.

The program package for calculating the MCI of compounds was compiled by Visual Basic Program Software according to the modified formula. In order to predict the toxicity of benzoic acid compounds and get the prediction model, the molecular structure of 57 benzoic acid compounds was entered into the program package and their MCI were calculated. 39 of them were a training dataset for building the multi variance linear regression model (logarithm of LD₅₀ as dependent variable and MCI as factor), and 18 of them were predicted samples to test the prediction ability of the model using SAS 9.0 Program Software. During the process of building the regression model, the cross factor was considered into the model.

In what follows, we will present the process of computing MCI, choosing factors of the regression model and building the model, as well as testing the model. Firstly, zero order connectivity index ⁰J^A and first order connectivity index ¹J^A were calculated using the program package. The value of LD₅₀ was converted to logarithm in order to make all the data in the same order of magnitude and easier to statistically analysze and compare. Then, the toxicity data was analyzed in the training dataset as regression analysis. Non-intercept stepwise regression was chosen as the statistical method. The influencing factors were as follows: zero order connectivity index ⁰J^A, first order connectivity index ¹J^A and the cross factor J_B= ⁰J^A × ¹J^A. These influencing factors were inspected, and the results were as below:

⁰J^A: R-Square = 0.9542 and C_(p) = 1.0000

The results show that the groups are fine expect (3) and (4), and correlation coefficient (R²) showed that (7) is the best. It was shown that the regression linearity of (7) is better than other groups. Therefore, ⁰J^A, ¹J^A and J^B were chosen as the independent variables of the model (see Table 1).

Comparing the p value in the table, it was shown that ⁰J^A, ¹J^A and J^B had an obvious significant influence, and a regression estimated model was built: LogLD 50 = 1.2399   ×   0 J A   +   2.6911   ×   1 J A − 0.4445   ×   J B   ( R 2 = 0.9860 )

Obeying the principles that the value of correlation coefficient (R²) is approximate to 1 and the p value is less than 0.01, as well as the numbers of the parameters equal to the test coefficient, we found that the linearity of the model is appropriate. The result of residual analysis shows that the fitting of the model was good (see Table 2). The distribution of residual is a normal distribution, since the scatter plots are almost standing on one line (see Figure 2).

From analysis of the model, it was known that ⁰J^A, ¹J^A and cross factor J^B had great influence on the oral toxicity in mice. When ⁰J^A and ¹J^A decrease, the value of LD₅₀ increases. And LD₅₀ decreases as J^B increases. Since increasing LD₅₀ resulted in lower toxicity, therefore, the model showed that ⁰J^A and ¹J^A have a negative correlation to the toxicity of benzoic acid compounds, and J^B has a positive correlation to the toxicity of benzoic acid compounds. The ability of regression model with 18 benzoic acid compounds was also tested, and the result indicates that the prediction ability of the model is good (Table 3). It is shown that these influencing factors indeed had an significant effect on toxicity, and the forecasting accuracy of the model becomes higher when introducing the cross factor (J^B).

LD₅₀ is a common factor for evaluating compound toxicity, which reflects receptivity of test animals, and LD₅₀ values have high reproducibility and stability. In QSTR study, linear regression analysis is a widely useful quantization method [15]. In this work, the quantitative parameters were calculated with MCI and the toxicity prediction model of benzoic acid compounds was obtained as follow. LogLD₅₀=1.2399 × ⁰J^A +2.6911 × ¹J^A – 0.4445 × J^B, R-Square = 0.9860. The model has a good forecasting ability.