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Nuffield Department of Anaesthetics, University of Oxford, John Radcliffe Hospital, Headington, Oxford, UK
Address correspondence to John W. Sear, PhD, FFARCS, Nuffield Department of Anaesthetics, University of Oxford, The John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK. Address e-mail to john.sear{at}nda.ox.ac.uk.
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Abstract |
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Introduction |
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We describe the development of a preliminary CoMFA model for the immobilizing activity of halogenated volatile anesthetics and compare the pharmacophoric maps obtained with those we have previously derived for the nonhalogenated volatile anesthetics (2).
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Methods |
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The anesthetics were randomly divided into training and test sets. The training set was used to formulate the CoMFA activity models, and the test set was used to independently assess the final model's predictive capability. The test set compounds were selected by ranking the anesthetics in order of increasing MAC and dividing the compounds into 17 bins (Table 1). One compound was randomly picked from each bin to form the test set. This ensured that the test set drugs covered the full range of MAC values exhibited by the anesthetics. The most potent anesthetic in the group was excluded from this selection process, as it was used to align the anesthetics for CoMFA.
Details of the modeling procedures used have been described elsewhere (1,2,17). In brief, computer-based models of the anesthetics were constructed using the molecular modeling software SYBYL v.6.7 (Tripos Inc, St. Louis, MO) on a Silicon Graphics O2 R10000 workstation. A random conformational search was performed using the SYBYL molecular mechanics force field to identify the low energy conformers for the flexible anesthetics. The geometry of each conformer was optimized at the semi-empirical level using MOPAC 6 (Quantum Chemistry Program Exchange; Bloomington, IN) with the AM1 Hamiltonian. Atomic partial charges were assigned using the Coulson method.
As the anesthetics have no common substructure, they were aligned for CoMFA using an unbiased molecular similarity approach (18,19) based on the local minimum method (20). In this process, the compounds are orientated so as to maximize their molecular similarity to the most potent drug in the group, the lead structure. The most potent anesthetic present was CF2H-(CF2)3-CH2OH, for which 88 unique low energy conformers were identified. Each conformer of the lead structure was used as a separate alignment template. The conformers of all the anesthetics were pre-aligned by weighted molecular extent and atomic partial charge (using the default ratio of 1:10), before being rotated and translated in a rigid search (30° increments) with Simplex optimization so as to maximize their molecular similarity to the conformer of the lead structure acting as the alignment template. Molecular similarity was calculated as combined shape and electrostatic potential Carbo indices, using an analytical method with the ASP 3.22 software (Automated Similarity Package; Accelrys Inc., Cambridge, UK). The anesthetic conformers and their orientations with the maximum similarity to the lead structure conformer were retained. The process was repeated until all the conformers of the lead structure had a turn at being the alignment template, producing 88 different sets of alignments.
CoMFA models were formulated for each alignment set using SYBYL. The aligned anesthetics were placed in a grid with lattice point spacing of 1Å. As in our previous modeling (1,2), this grid interval was found to provide a good compromise between accuracy and the possible introduction of noise from sampling irrelevant data. The grid extended at least 4Å beyond each molecule and consisted of 3332 lattice points. An sp3 carbon probe with unitary positive charge was placed at each lattice point and the steric and electrostatic interaction energies between the probe and the anesthetics calculated. Steric interaction energies were calculated using a Lennard Jones 6–12 potential, and electrostatic energies were calculated using a Coulomb potential (3,4) with a distance-dependent (
-r) dielectric function. Cutoffs were applied to limit both the steric and electrostatic energies to a maximum of 30 kcal/mol.
The steric and electrostatic interaction energies at each lattice point were block scaled to unit variance and correlated with in vivo potency to formulate activity models. Because of the large number of variables produced and their colinearity, partial least squares (PLS) regression was used for this purpose (21). This procedure derives one or more orthogonal components based on a weighted combination of the interaction energies at each lattice point. The weightings are adjusted so that each component explains as much covariance as possible. A regression-like activity model is formulated by using the orthogonal components as independent variables and in vivo potency as the dependent variable. The number of orthogonal components used was determined using leave-one-out cross-validation, with each additional component having to increase the value of the cross-validated r2 by >0.05 to be included (18).
The intrinsic predictive power of the activity models was assessed using leave-one-out cross-validation (22). In this process, the model is repeatedly reformulated, but one of the training set anesthetics is excluded at each stage. The revised model is used to predict the potency of the excluded drug and the process is repeated until all of the training set anesthetics are excluded once and once only. The CoMFA model with the highest cross-validated r2 values for the training set anesthetics was retained as the final model. The extrinsic predictive power of this final model was determined by predicting the potencies of the randomly excluded test set anesthetics.
Electrostatic and steric pharmacophoric maps were derived for the final CoMFA model by using isocontours to link together lattice points in the CoMFA grid where the standard deviation of the interaction energies multiplied by the PLS weighting coefficients at that point (sd x coeff) exceed a threshold value. The values for the thresholds were chosen to represent the greatest 40% of the individual positive and negative contributions to the activity model in keeping with our previous papers (1,2). The maps for the halogenated drugs were compared with the pharmacophoric maps previously obtained for the nonhalogenated volatile anesthetics (2) using software written with MatLab (Mathworks Inc, Natick, MA) and SYBYL.
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Results |
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The final CoMFA model was based on 4 orthogonal components and explained 94.2% of the variance in the observed activities of the 52 training set anesthetics (F4,47 = 189.314; P < 0.0001). The correlation between observed and predicted activities for the training set drugs is shown in Figure 1. It can be seen that the model is an effective predictor of immobilizing activity over a wide range of anesthetic potencies. The mean ± sem of the residuals [the absolute difference between the -log10 (observed) and -log10 (predicted) MACs] for the training set was 0.265 ± 0.032, with 46% of the compounds having residuals <0.2 and 67% of the compounds residuals <0.3. However, the activities of some compounds were poorly predicted (Table 1). Although there is no clear pattern between absolute residual and the chemical type of the anesthetic, it is interesting to note that the model gave weaker predictions for CF3-CXY-CF3 compounds (where X and Y are different atom types or chemical groups) including CF3-CHOH-CF3 (compound 7), CF3-CBrF-CF3 (compound 45) and CF3-CFH-CF3 (compound 31). The in vivo potency of methylpentafluorobenzene (compound 24) was also poorly predicted.
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Cross-validation experiments indicate that the CoMFA model exhibited adequate intrinsic predictive power for the training set drugs (cross-validated r2 of 0.705). However, a more rigorous test of predictive capability is to use the CoMFA model to predict the potencies of the 17 randomly excluded test set anesthetics (compounds 53 to 69). The model showed a good correlation (r2 = 0.837) between observed and predicted potencies for these compounds (Fig. 2). The mean ± sem of the residuals for the test set was 0.378 ± 0.090, with 47% of the compounds having residuals <0.2 and 53% of the compounds by less than <0.3. However, CH3-CFH-CH3 (compound 64) is a clear outlier, with an absolute residual of 1.462.
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For comparison we also determined the effectiveness of a conventional activity model based on non-polar solubility (olive oil/gas partition coefficients). This model explained 85.7% of the variance in the observed activities of the training set compounds (n = 52, F1,50 = 298.555; P < 0.0001) with a mean ± sem of the residuals of 0.456 ± 0.042, with good intrinsic (cross-validated r2 of 0.844) and extrinsic (test set r2 = 0.876, n = 17, mean ± sem residuals of 0.469 ± 0.060) predictive capability.
The relative contributions of the electrostatic and steric interactions to the CoMFA activity model were 54.4% and 45.6%, respectively. Analysis of the individual PLS regression weightings for each lattice point within the orthogonal components of the model enables the identification of regions where steric and electrostatic interactions are important in determining activity. Pharmacophoric maps showing the spatial distribution of these key regions are derived using isocontour plots that link together lattice points in the CoMFA grid where the standard deviation of the interaction energies multiplied by the PLS weighting coefficients at that point (sd x coeff) exceed a certain value. These plots indicate regions where the differences in either steric or electrostatic interaction energies are strongly associated with changes in anesthetic potency for the training set compounds. The values for the isocontours were chosen using the same strategy as applied in our IV (1) and nonhalogenated volatile general anesthetic (2) CoMFA models, linking lattice points that represent the greatest 40% of the individual positive and negative contributions to the activity model.
The electrostatic and steric pharmacophoric maps for the halogenated anesthetics derived using the final CoMFA model are shown in Figures 3a and 3b, respectively. The electrostatic map has 2 main regions (K and L) colored blue where positive electrostatic potential is favored for high anesthetic potency (sd x coeff > +0.0117) and 2 regions (M and N) colored red where negative potential is favored (sd x coeff < –0.0140). Note that region N is hidden in the view shown. The positioning of the lead structure CF2H-(CF2)3-CH2OH to these regions is shown in Figure 3c. The arrows indicate areas where the electrostatic potential of the molecule qualitatively fits the pharmacophoric map. Thus, the electropositive hydrogen atoms at both ends of the molecule align with the blue positive potential favored regions, and the electronegative fluorine atoms in the middle of the molecule align with the red negative potential favored zone. The crosses indicate areas where the lead structure does not fit the pharmacophore as a result of the electronegative fluorine atoms aligning with a positive potential favored region. This would suggest that substitution of electropositive hydrogen atoms at these points would enhance the in vivo potency of the structure.
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The steric pharmacophoric map is shown in Figure 3b. The orientation and scaling of the map are the same as for the electrostatic equivalent. There are 3 areas (O, P, and Q) colored green where molecular bulk is favored for high anesthetic potency (sd x coeff > +0.0190) and 2 regions (R and S) colored magenta where molecular bulk is disfavored (sd x coeff < –0.0153). If the molecule extends into a disfavored zone, anesthetic potency is reduced. The positioning of hexafluorobenzene with relation to the steric pharmacophore is shown in Figure 3d. Note that the two bulk disfavored zones lie in front and behind the plane of the aromatic ring.
The CoMFA model for the halogenated drugs was compared with the equivalent model we had previously obtained for the nonhalogenated volatile anesthetics (2). For convenience, the pertinent features of the two activity models are summarized in Table 2. Note that the relative contributions of the steric and electrostatic interactions to each activity model differ: for the nonhalogenated volatile anesthetics electrostatic interactions are more important than steric in determining in vivo potency (ratio 2.9:1); whereas for the halogenated drugs electrostatic and steric interactions are of similar importance (ratio 1.2:1).
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The pharmacophoric maps derived from the two models were compared to see whether the spatial distribution of the key steric and electrostatic regions that determine in vivo potency are the same. The maps were simplified to a series of pharmacophore centers representing the position of the lattice points with the greatest sd x coefficient value in each of the key regions. The maps for the nonhalogenated anesthetics were rotated and translated to test all possible combinations of overlap among three or more equivalent pharmacophore centers. The orientation with the lowest root-mean-square distance between equivalent centers was taken as the final match. The best match was obtained using a 3-center fit, producing the orientation of the electrostatic and steric pharmacophoric maps for the nonhalogenated anesthetics shown in Figures 3e and f. The isocontour thresholds for these maps were set using the same 40% contribution criterion as used for the halogenated model, but the absolute values differ (2). The 3-center fit (outlined in red) matched the bulk favored region F and disfavored regions I and J for the nonhalogenated anesthetics to the equivalent centers Q, R, and S on the halogenated anesthetic map. The root-mean square distance ± sd for this 3-center fit was 0.094 ± 0.039Å. In this orientation it is clear that the pharmacophoric maps for the two groups of compounds are not identical. However, combining the nonhalogenated and halogenated volatile anesthetic pharmacophoric maps in their fitted orientation (Figs. 3g and h) shows that the key electrostatic and steric regions superimpose or partially overlap and that there are no significant spatial conflicts.
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Discussion |
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Several compounds were poorly predicted by our CoMFA model. There are a number of possible explanations for these weaker predictions. The most likely explanation is an inappropriate alignment of the drugs within the CoMFA lattice grid. In this study, the anesthetics were aligned using molecular similarity because of their chemical diversity, which precludes alignment by common substructure. Molecular similarity was calculated using Carbo indices based on an average of the shape and electrostatic potential similarity for the whole molecule. However, it should be evident from the pharmacophoric maps derived in this study that not all regions of the molecule are of equal importance in determining anesthetic activity. Hence, inappropriate alignments may have been produced for some anesthetics using the molecular similarity approach. This is the most likely explanation for the poor activity predictions obtained for the CF3-CXY-CF3 compounds in the training set (compounds 7, 31 and 45, Table 1) and CH3-CFH-CH3 (compound 64) in the test set, where a partial alignment to the lead structure focusing on the middle of the molecule may be more appropriate than the alignment currently used. Improved predictions can be achieved for many anesthetics including the CF3-CXY-CF3 drugs and CH3-CFH-CH3 by making slight manual adjustments to their positions in the CoMFA grid. We have avoided this approach because we wish to maintain an unbiased method of molecular alignment and because it is not instantly obvious how some of the more structurally diverse anesthetics should be manually aligned. Alignment by similarity also prevents us from investigating the additive effects of steric and electrostatic interactions with two or more molecules of the smaller anesthetics, as demonstrated in protein-binding models (24).
The predictive capability of the model might also be improved by including additional molecular properties. Of particular interest would be the addition of an explicit polarizability field. However, this requires the use of ab initio quantum mechanics, which is computationally intensive and hence impractical for the range of anesthetic conformers considered in this study. Another aspect is the possibility that the molecular bases of activity for the outliers are different to those of the majority of anesthetic compounds. This issue can only be resolved by modeling these compounds separately.
The pharmacophoric maps derived show the spatial distribution of the key regions where steric and electrostatic interactions are important in determining immobilizing activity. The key dimensions between the different regions are shown in Figure 3. It is of interest that many of these dimensions correspond with those outlined in the hypothesis of Eger et al. (25), in which the authors propose that immobility is produced as a result of the end groups of the anesthetic molecules interacting with 2 sites approximately 5Å apart. Our model represents an alternative interpretation to this hypothesis. Instead of two separate sites, it can be seen that the terminal hydrogen atoms of the lead structure correspond with 2 areas 5.5 Å apart in the positive potential favored region L (Fig. 3c).
We have compared the pharmacophoric maps obtained in this study with those derived in our previously published paper for nonhalogenated drugs. It was necessary to formulate two separate CoMFA models because we found that anesthetics containing multiple halogen atoms would not readily align to a nonhalogenated lead structure using whole molecule similarity and vice versa (2). Qualitative comparison of the maps based on a 3-center fit shows that although they are not identical, they are spatially compatible, with several key steric and electrostatic regions overlapping. Does this imply a common molecular basis for the immobilizing activity of these two groups of anesthetics? At this stage we are unable to answer this question because it is not clear if the differences in the maps are more important than their commonalities. This can only be addressed by the derivation of a second-generation CoMFA model, incorporating both groups of anesthetics aligned using a region-focused approach based on the pharmacophoric maps derived in these studies. It should be noted that a common molecular basis for immobilizing activity does not necessarily imply a common site of action. We anticipate that the region-focused approach will also overcome the alignment problems described earlier, enable us to address the issue of additivity with multiple molecules and also improve predictive capability.
We thank Edmond I Eger II and his colleagues at the University of California, San Francisco, for the anesthetic potency data used in this study. This paper is dedicated to the memory of Michael J. Halsey who was instrumental in the development of our molecular modeling approach.
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Footnotes |
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Accepted for publication October 3, 2005.
Presented, in part, at the annual meeting of the American Society of Anesthesiologists, Orlando, Florida, October 2002 (abstract published in Anesthesiology 2002;96:A117).
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