Quantitative Structure-property Relationship Studies on Amino Acid Conjugates of Jasmonic Acid as Defense Signaling Molecules

Amino acid conjugates of jasmonic acid and their lipophilicity

To obtain the structural requirements for lipophilicity (logP) of amino acid conjugates of jasmonic acid, the structures of 59 amino acid conjugates of jasmonic acid were collected from the literature (Katsin et al. 1977; Bohlmann et al. 1984; Kramell et al. 1988, 1995, 1997, 1999; Schneider et al. 1989; Meyer et al. 1991; Tamogami et al. 1997; Miersch et al. 1999; Jikumaru et al. 2004; Staswick and Tiryaki 2004; Guranowski et al. 2007), and their lipophilicity in the form of n-octanol/water partition coefficient (logP) (Table 1) were automatically calculated in the Cerius² version 4.10, since experimental logP value was unavailable (Liu and So 2001). Some researchers have evaluated the experimental logP and calculated logP of structural dependence in the majority of tested software products and the calculated results were in good correlation with that determined experimentally (Mrkvičková et al. 2008), indicating that logP in this study can represent the actual logP of compounds in some sense.

Table 1. Structures and calculated logP, predicted logP for all molecules based on the best quantitative structure-property relationship (QSPR) models

• ^aMolecules in training set; ^bMolecules in test set; ^cResidual = calculated logP − predicted logP.

Molecules were then rationally divided into a training set and test set (Table 1), maintaining the structure and property diversity in both sets for subsequent QSPR models development. A molecule structurally very similar to the training set molecules will be predicted well because it captures common features.

2D-QSPR models

Different sets of 2D-QSPR equations with several descriptors were generated using the genetic function approximation (GFA) method. A brute force approach was first used to investigate the number of descriptors necessary and adequate for the QSPR equation. As the number of descriptors in the equation increased one by one, the effect of added new terms was evaluated using cross-validated r²(r²_CV) as the limiting factor for the number of descriptors to be used in the model (Chen et al. 2008; Nair and Sobhia 2008; Li et al. 2008c, 2009). As shown in Table 2, adding the number of descriptors in the equation does increase the r²_CV value of the best model, but r²_CV and conventional r² increase a little when the number of descriptors ranges from 4 to 5. Based on our experiments, adding the additional descriptor S_sssCH does not improve the values of Friedman's lack of fit (LOF) and F-Test compared with the model with four descriptors. Thus, the number of descriptors was restricted to four for the final model. The models with varying number of descriptors for amino acid conjugates of jasmonic acid are shown in Table 2. The selection of best model was based on the values of conventional r² (square of the correlation coefficient for the training set of compounds), LOF, F-Test, r²_CV (cross-validated r²), r²_BS (bootstrap correlation coefficient), and predicted sum of deviation squares (PRESS) (Li et al. 2008a).

The statistically significant 2D-QSPR model is shown below. A summary of good GFA method-derived models generated with four descriptors are shown in Table 3.

Model-1

n= 48; LOF = 0.042; r²= 0.990; r²adj = 0.989; F-Test = 1059.542; least square error (LSE) = 0.029; r= 0.995; r²_CV= 0.987; r²_BS= 0.990 +/− 0.000; PRESS = 1.808; r²_pred= 0.789.

The leave-one-out (LOO) test and randomization tests were used to determine reliability and significance of generated models. From the cross-validation test r²_CV of 0.987 indicated that the results obtained were not by chance correlation. The randomization tests (Deswal and Roy 2006; Chen et al. 2008; Li et al. 2008a, 2008c, 2009) were carried out at 90% (nine trials), 95% (19 trials), 98% (49 trials) and 99% (99 trials) confidence levels and carried out by repeatedly permuting the dependent variable set. The results of randomization tests (Table 4) showed that none of the permuted datasets produced the random r comparable to non-random r of 0.995, suggesting that the value obtained for the original GFA method-derived model was significant. The derived best 2D-QSPR model thus was robust and used for predicting the properties of the test set (Table 1). Some compounds in the test set gained poor predicted logP values, partly as a result of the low r²_pred value of the above model. The inter-correlation of the descriptors in the above model was taken into account and the descriptors were found to be reasonably orthogonal (Table 5).

3D-QSPR models

Molecular field analysis (MFA) samples the steric and electrostatic fields surrounding a set of ligands and constructs 3D-QSPR models by correlating the corresponding properties in form of logP with the 3D field values computed using atomic coordinates of binding molecules and interaction energies.

Model-2

n= 48; r²= 0.922; LSE = 0.225; r= 0.960; r²_CV= 0.841; r²_BS= 0.906 +/− 0.003; PRESS = 22.017; r²_pred= 0.905.

The reasonable values of correlation coefficient r² of 0.922 and cross-validated r² of 0.841 indicate that this model could explain satisfactorily the variances of logP. The robust and highly predictive ability of the models was reflected insufficiently only by the cross-validation test; thus, the external predictive power of the model was evaluated with the test set molecules (Equbal et al. 2008). The predictive power of the model is calculated by r²_pred= (SD − PRESS)/SD (Chen et al. 2008; Li et al. 2008c, 2009), where SD is the sum of squared deviations between the logP of each molecule and the mean logP of the molecules in the training set and PRESS is the sum of squared deviations between the predicted and calculated logP values for each molecule in the test set. The high r²_pred value of 0.905 for the test set accounted for good predictive ability, which was also used for predicting logP of the test set (Table 1).

Interpretation of model-1

According to model-1, the calculated logP of amino acid conjugates of jasmonic acid is influenced by structural descriptors (Hond Donor and Density), electronic descriptor (Apol) and E-State-keys (S_ssO), which can also be approved by the usage of descriptors during generation of QSPR models (Figure 1). Among these descriptors, small changes of the molecular density can greatly change logP; thus, Density is an important parameter for amino acid conjugates of jasmonic acid involved in penetration of plant cells. S_ssO is the descriptor of the E-state indices and represents the atomic type of –O– in alkanes or cycloalkanes. The E-state indices encode information about both the topological environment and the electronic interaction of an atom due to all other atoms in the molecule (Hall and Kier 1995). S_ssO with negative coefficient indicates its importance to the lipophilicity (logP) of compounds. The number of hydrogen-bond donors (Hond Donor) with negative coefficient indicates that hydrogen-bonding interactions are important for amino acid conjugates of jasmonic acid to penetrate the plant cells. The sum of atomic polarizabilities (Apol) with small positive coefficient reveals that it contributes less to logP than other descriptors in the model-1, which describes the molecule's ability to polarize in a magnetic field.

Interpretation of model-2

The numbers associated with the descriptors specify their location in the 3D-grid around the aligned molecules is shown in Figure 2. The model-2 explains 92.2% of variances of logP. The good r²_CV and r²_pred values indicate a better predictive credibility compared with the corresponding GFA model. Model-2 contains seven methyl (CH₃) probes and four proton (H⁺) probes. As shown in Figure 2, the appearance of CH₃/573 and CH₃/580 in the region of C7 indicate that bulky substituents are unfavored to the logP. The other probes distributing in the area of C3 indicate that both steric and electrostatic substituents are important to logP.

Molecular modeling

The molecular geometrical structures of 59 amino acid conjugates of jasmonic acid were subjected to an energy minimization procedure of UFF-VALBOND1.1 (Rappe et al. 1992) after structural construction and partial atomic charges were assigned using the Gasteiger method (Gasteiger and Marsili 1980) in the Cerius² Builder option. All of the structures were subsequently energy minimized until a root mean square derivation 0.001 kcal/mol was achieved and used in the present study.

2D-QSPR modeling

The 2D-QSPR analysis was carried out by genetic function approximation (GFA). GFA is a formalism that deals with statistical analysis and correlation between property (biological activity) and selected relevant physicochemical descriptors. It is genetically involved in the combination of Fried machs multivariate adaptive regression splines (MARS) and Holland's genetic algorithm (GA) (Rogers and Hopfinger 1994; Shi et al. 1998; Leonard and Roy 2008). Hundreds of candidate models are created and tested during evolution, but only the superior models survive, and then are used as “parents” for the creation of the next generation of candidate models. And it also provides an error measure called the lack of fit (LOF) score (Nair and Sobhia 2008) that automatically penalizes models with too many features. The length of equation was initially fixed to five terms including a constant for the training set. After some initial runs for observation, GFA crossovers of 5 000 and smoothness value of 1.0 were set (other default settings were maintained) to obtain a reasonable convergence. Cross-validated r²(r²_CV) was calculated using the cross-validated test option. Before generating the 2D-QSPR model, the correlation matrix of about 141 descriptors was considered and the descriptors with value over 0.7 were removed for reducing the crossover on each other and also for improving the correlation with properties. A complete list of remaining descriptors used in subsequent QSPR analysis is shown in Table 6.

3D-QSPR modeling

Molecular field analysis (MFA) was used to derive the 3D-QSPR model in the present study. MFA is an effective method for evaluating the interaction energy between a probe molecule and a set of aligned target molecules at a series of points defined by a rectangular grid, especially for the analysis of datasets with available activity data but unknown 3D receptor site structure (Hirashima et al. 2003; Equbal et al. 2008; Chen et al. 2008; Li et al. 2008b, 2009). The interaction energy values measured for each point of 3D-grids are computed using atomic coordinates of binding molecules and can be used in structure-property relationships.

In the present study, the core substructure search (CSS) method coupled with root mean square (RMS) alignment method (Chen et al. 2008; Li et al. 2008b, 2009) was used to rigidly align all of the structures in the analogous series based on a defined substructure of cyclopentanone. So that common features are discernable from any other random arrangement of orientations and the sum of squares of the distances between all atoms to be superimposed are functionally minimized. The consensus RMS is 0.1781. Stereo-view of aligned molecules in training set and test set is shown in Figure 2.

The molecular fields of the molecules were calculated using CH₃ and H⁺ as probes once they were aligned. The fields were computed at each point of a regularly spaced grid of 2 Å  and were energy truncated ± 30.000 kcal/mol. The total grid points generated were 792 and 10% of all new significant descriptors with highest variance were automatically set as independent X variables for the latter 3D-QSPR modeling. Regression analysis was carried out using the genetic partial least squares (G/PLS) (Chen et al. 2008; Equbal et al. 2008; Li et al. 2008b, 2009) method consisting of over 5 000 generations and a population size of 100. The length of the equation was fixed at 15 terms containing constant. The 3D-QSPR models were done with a cross-validation test by clicking cross-validated test buttons in the validate control panel.

(Handling editor: Dao-Xin Xie)