GRID Molecular Interaction Fields

Molecular interaction fields describe interaction energies between a molecule and a chemical probe positioned in different locations around the molecule. GRID is a widely used program for the calculation of such fields. The chemical probe may be a methyl group, a water molecule, or any of the more than 60 probes provided by GRID. Interaction energies between the molecule and the probe are calculated by inserting the molecule in a box (Figure 3.12). The probe is then moved through a regular 3D array of grid points at positions around the molecule as shown in the figure. The spacing between the grid points is user-defined but normally 0.25- 1A. At each grid point the

FIGURE 3.12 Setup for calculation of molecular interaction fields.

probe-molecule interaction energy (Etot) between the probe and the molecule is calculated by an empirical force-field as a sum of the vdW energy (EvdW), the electrostatic energy (Eel), and the hydrogen bond energy (Ehbond) as shown in Equation 3.1

Etot EV(

The molecular interaction field for each probe may be visualized by calculating and displaying isoenergy contours at a user-defined energy level. Examples of isoenergy contours are shown in Figure 3.13, displaying the results of GRID analyses for the substituted flavone 3.13.

Figure 3.13a shows the GRID results using a water probe. As expected, contours are observed around the carbonyl group and the hydroxy group indicating strong hydrogen bond interactions between the water molecule and 3.13. However, water can donate as well as accept hydrogen bonds but these two modes of interaction cannot be distinguished by the use of a water probe. By choosing an NH+ probe, which can only donate a hydrogen bond, and an O- probe, which can only accept a hydrogen bond, donating and accepting can be distinguished. This is shown in Figure 3.13b, where the blue contour indicates hydrogen bond accepting by the carbonyl group and the red contour hydrogen bond donating by the hydroxy group.

Molecular interaction fields may be used to identify potentially important interactions between a ligand and a protein. The probes are then representing different types of interaction partners in the binding pocket of the protein. However, a more powerful use of molecular interaction fields in ligand-based drug design is the combination of these fields with statistical chemometric methods to develop a 3D-QSAR model for the quantitative prediction of biological activities. The basic idea is


FIGURE 3.13 Isoenergy curves for compound 3.13 and (a) a water probe contoured at -21 kJ/mol and (b) an amine cation (NH+ ) probe contoured at -26 kJ/mol (blue) and a phenolate anion oxygen (O-) probe contoured at -16 kJ/mol (red).

that molecular interaction fields for a series of compounds contain information that can be used for the understanding and prediction of the biological activity of the compounds.

3.7.2 Development of a 3D-QSAR Model for Substituted Flavones

The starting point for the development of a 3D-QSAR model is a series of molecules and their biological activities at a given receptor. To illustrate the methodology, we will use a series of substituted flavones also used in the pharmacophore modeling section earlier.

A crucial first step in a 3D-QSAR analysis is the alignment of the molecules. This is equivalent to the development of a pharmacophore model (see Figure 3.1). For the flavones the alignment has been discussed earlier. Thirty-four substituted flavones were used as a training set for developing the 3D-QSAR model. For each molecule located in a gridbox and aligned according to the pharma-cophore model, the interaction energies with two probes, a methyl probe and a water probe, were calculated by GRID. To find a correlation between the biological activity and the calculated molecular interaction fields, the method of partial least squares projections to latent structures (PLS) in GOLPE is used (for more details see Further Readings). In essence, PLS contracts the original description of each molecule (i.e., the molecular interaction fields) into a few descriptive dimensions/variables that are used for the correlation.

It is essential to validate the 3D-QSAR model. This should optimally be done internally as well as externally. For internal validation, also called cross validation, a portion of the training set compounds are left out and a new model of this reduced training set is built. This model is then used to predict the activities of compounds left out. This procedure is repeated a number of times. The results of the predictions of left out compounds are summarized in terms of a predictive correlation coefficient q2, which should be larger than 0.5 for a high-quality 3D-QSAR model. External validation is performed by predicting the activities of compounds (the test set), which have not been used to build the 3D-QSAR model. The results of this validation may be given as a standard error of prediction (SDEP).

Figure 3.14 displays the results for the series of 34 substituted flavones used as a training set and seven substituted flavones as a test (validation) set. The conventional correlation coefficient r2 is

FIGURE 3.14 Experimental and predicted affinities. The training set is shown as unfilled squares and the test set as filled triangles.

0.90 and q2 is 0.77. The SDEP for the seven test set molecular is 0.51. Thus, the 3D-QSAR model developed is of high quality with high internal as well as external predictivity and may reliably be used for the prediction of the affinities of new compounds.

The results of a 3D-QSAR analysis are usually analyzed by contour maps of the PLS coefficients. Each grid point is associated with two coefficients from the PLS analysis, one coefficient (ck) is related to interactions with the methyl probe, the other one (cl) to interactions with the water probe (Equation 3.2). These coefficients and the corresponding Etot values describe the relative importance of each grid point for explaining the variation in biological activity. The total p^ is a summation over all gridpoints.

pK = - log K = ck Etot (methyl probe) + cl Etot (water probe) (3.2)

A more positive value of p^ means a higher affinity. Thus, a more positive value of Etot (methyl probe) together with a positive value of ck gives a positive contribution to p^i (a higher affinity). A negative sign of ck and a positive value of Etot (methyl probe) give a negative contribution to p^i (a lower affinity). Figure 3.15 displays contour maps of regions of negative and positive PLS coefficients. Such maps may be used as guidelines for the design of new compounds. It should first be noted that there is the absence of contours around the carbonyl group. QSAR relates variation in molecular properties to variation in biological activity and since the carbonyl group is present in all test set molecules there is no (or very small) contributions to the variation in affinity from this group.

In Figure 3.13a the cyan regions correspond to negative PLS coefficients. Substituents that have repulsive vdW interactions with the methyl probe in these regions, i.e., positive Etot values, give a negative contribution to the affinity (a lower affinity). Thus, even small substituents in the 6-, 4'-, and 5'- positions and also very large substituent in the 3'-position are predicted to result in an affinity decrease. Compounds 3.8 and 3.9 in Figure 3.3 are two examples of the effects of substitution in the 4'- and 5'-positions. Furthermore, it has been reported that the 6-isopropyl compound has a 10-fold lower affinity than the 6-bromo compound 3.2 in Figure 3.2.

The yellow regions in Figure 3.15a correspond to positive PLS coefficients. Thus, substituents that have repulsive interactions with the methyl probe in these regions (i.e., significantly positive Etot values) are predicted to give an increase of the affinity. Small substituents in the 6-position and small as well as large substituents in the 3'-position are thus predicted to be favorable for the affinity

FIGURE 3.15 Contour maps of the PLS coefficients for (a) the methyl probe, negative coefficients (-0.002 level) are shown in cyan and positive coefficients (+0.003 level) in yellow (b) the water probe, negative coefficients (-0.006 level) are shown in cyan and positive coefficients (+0.004 level) in yellow. Compound 3.13 is shown to illustrate the size of the regions.

FIGURE 3.15 Contour maps of the PLS coefficients for (a) the methyl probe, negative coefficients (-0.002 level) are shown in cyan and positive coefficients (+0.003 level) in yellow (b) the water probe, negative coefficients (-0.006 level) are shown in cyan and positive coefficients (+0.004 level) in yellow. Compound 3.13 is shown to illustrate the size of the regions.

as exemplified by compounds 3.2 and 3.4 in Figure 3.2. Furthermore, it has been reported that bromo, methyl, or trifluoro methyl substitution in the 3'-position is highly favorable for the affinity.

The interpretation of the contours from the water probe (Figure 3.15b) is less straightforward. As shown in Equation 3.1, interactions with this probe include vdW as well as hydrogen bond and electrostatic interactions. Thus, the water probe as well as the methyl probe displays vdW interactions. Consequently, the regions of interest for the water probe are the regions where the contour plot deviates from the corresponding plot of the methyl probe. The most significant of these regions is encircled in Figure 3.15b. This region has negative PLS coefficients and a negative Etot value, which gives a favorable contribution to the affinity. A hydrogen bond or attractive electrostatic interaction gives a negative interaction energy. Thus, substituents in the 6'- position, which may have such interactions with the water probe, are predicted to give an affinity increase. An example of this is the hydroxy group in compound 3.13.

Contour maps of PLS coefficients can, as demonstrated earlier, provide information for the design of new compounds and the positive and negative regions calculated by GOLPE give a picture of important properties of the binding pocket in the receptor.

In predictions of the affinity of new compounds it should be noted that the test set used to build the 3D-QSAR model should have sufficient structural variation. For instance, if the test set only contains compounds with a methyl group in a particular position, it is not possible to predict the activities of larger alkyl groups in this position.

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