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Nuffield Department of Anaesthetics, University of Oxford, John Radcliffe Hospital, Headington, Oxford, United Kingdom
Address correspondence to John W. Sear, PhD, FFARCS, Nuffield Department of Anesthetics, University of Oxford, The John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK. Address e-mail to john.sear{at}nda.ox.ac.uk Reprints will not be available from the authors.
| Abstract |
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IMPLICATIONS: We have derived an activity model for a group of structurally diverse nonhalogenated volatile anesthetics that correlates in vivo potency (minimum alveolar anesthetic concentration) with the spatial distribution of their molecular bulk and electrostatic potential. Our results suggest that there is a common molecular basis for the immobilizing activity of the anesthetics.
| Introduction |
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An alternative approach to investigating the molecular basis of activity is to focus on the anesthetic molecules themselves. The aims of such ligand-oriented approaches are to identify the molecular properties that determine activity and to formulate a model that correlates the magnitude of these properties with potency. One example of a ligand-oriented modeling technique is comparative molecular field analysis (CoMFA), a computer-aided drug design method frequently used when the detailed structure of a receptor is unknown (5). In CoMFA, the ligand compounds are aligned and placed in a grid consisting of regularly spaced lattice points. The steric and electrostatic interaction energies between the ligands and a charged probe atom are calculated at each point and correlated with potency to formulate an activity model. By identifying which lattice points make the greatest contribution to the model, three-dimensional pharmacophoric maps of the key steric and electrostatic features of the ligands that determine activity can be derived.
One of the major obstacles in applying CoMFA and related modeling approaches to general anesthetics is the structural diversity of the compounds, which precludes aligning them in the lattice grid by a common substructure. We have recently described how chemically diverse IV anesthetics can be aligned on the basis of similarities in their molecular shapes and electrostatic potentials (6,7), which overcomes this fundamental difficulty. In this study, we developed the molecular similarity approach to formulate a preliminary CoMFA activity model for a wide range of structurally diverse nonhalogenated volatile general anesthetics. We investigated the molecular basis for their immobilizing activity by using CoMFA to correlate in vivo potency with the spatial distribution of the molecules steric and electrostatic features.
| Methods |
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Full details of the modeling procedures have been described elsewhere (6,7). In brief, computer-based models of the anesthetics in the gas phase were constructed by using the molecular modeling software SYBYL 6.7 (Tripos Inc., St. Louis, MO) on a Silicon Graphics O2 R10000 workstation. The structures were geometry-optimized by using molecular mechanics minimization with the default SYBYL force field (6). This process considers the molecules as a series of spheres (representing the atoms) connected by springs (representing atomic bonds). Potential energy functions defined in the force field describe the optimum bond lengths, bond angles, and torsion angles for the atoms of the molecule. These molecular features are adjusted during geometry optimization to minimize the total potential energy of the structure.
Most of the anesthetics are flexible structures that exist as an ensemble of interchangeable configurations called conformers. This flexibility was incorporated in the model by deriving a set of low-energy conformers for the anesthetics by using a random search procedure in SYBYL (6). The torsion angles of the molecules were randomly perturbed, and the resultant structures were subjected to full molecular mechanics geometry optimization. The optimized conformers with a potential energy within +4 kcal/mol of the lowest-energy conformer for a given anesthetic were retained. This limit ensured that only conformers with realistic geometries were used in the subsequent analyses. The process was repeated until each anesthetic had undergone 10,000 random perturbations or until each conformer had been found at least 12 times. The geometries of the conformers were further optimized by using quantum mechanics, in which a mathematical description of molecular structure is formed in terms of the nuclei and electron distribution. This provides a more accurate representation of molecular geometry but is computationally more intensive. The computation time was reduced by using semiempirical quantum mechanics, in which only the valence electrons are explicitly considered and in which experimentally derived variables are used to represent the nuclei and inner-shell electrons. Geometry optimization was performed with MOPAC 6 (Quantum Chemistry Program Exchange, IN) with the AM1 Hamiltonian. Atomic partial charges were assigned by using the Coulson method (6). After optimization, duplicate conformers (defined as conformers with a root-mean-square difference of <0.2 Å) were removed. A total of 625 conformers were retained for the 38 anesthetics.
The chemical diversity of the anesthetics precludes their alignment by a common substructure. Suitable alignments were obtained by using an unbiased molecular similarity approach (15) based on the local minimum method (16,17). In this process, the compounds are oriented to maximize their molecular similarity to the most potent drug in the group, the lead structure. Inspection of the potency data showed that the most active anesthetic was hexanol, which had 66 conformers. Each conformer of the lead structure was used as a separate alignment template.
Molecular similarity was calculated as combined shape and electrostatic potential Carbo indices, which range from 0 (totally dissimilar shapes and electrostatic potentials) to 1 (totally identical). The anesthetic conformers were prealigned by weighted molecular extent and atomic partial charge (by using the default weighting ratio of 1:10) before being translated and rotated in a rigid search (30° increments) with Simplex optimization to maximize their molecular similarity to the lead structure conformer acting as the alignment template. Carbo indices were calculated with an analytical method (18) by using ASP 3.22 software (Automated Similarity Package; Accelrys Inc., Cambridge, UK). The anesthetic conformers and alignments with the maximum similarity to the lead structure conformer were retained (7). The process was repeated until all the conformers of the lead structure had been used as the alignment template, producing 66 different sets of alignments for the anesthetics.
Separate CoMFA activity models were formulated for each alignment set by using the standard SYBYL variables for steric and electrostatic fields (see Ref. 19 for a description of these variables and their significance). The aligned anesthetics were placed in a rectangular grid consisting of lattice points at 1-Å intervals. This grid interval provides a good compromise between accuracy and the possible introduction of noise from sampling irrelevant data. The grid extended at least 4 Å beyond the surface of all the molecules and consisted of 3600 lattice points. An sp3 carbon probe atom with a unitary positive charge was placed at each lattice point, and the steric and electrostatic interaction energies between the probe and the anesthetic molecules were calculated (5,19). Steric energies were calculated by using Lennard-Jones potentials, which describe both the attraction between molecules due to van der Waals forces (dispersion, dipole-induced dipole, and dipole-dipole interactions) and the repulsion as a result of steric clashes. The electrostatic energies were calculated by using Coulomb potentials with a distance-dependent dielectric function. Cutoffs were applied to both the steric and electrostatic energies at 30 kcal/mol (5,19).
The 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 (3600 steric and 3600 electrostatic) and their colinearity, partial least squares (PLS) regression was used for this purpose (20). This process 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 anesthetic activity as the dependent variable. The number of orthogonal components used was determined by leave-one-out cross-validation (see below), with each additional component having to increase the value of the cross-validated r2 by >0.05 to be included (15).
The intrinsic predictive power of the activity models was assessed by using leave-one-out cross-validation (21). In this process, the model was repeatedly reformulated, but one of the training-set anesthetics was excluded at each stage. The revised model was used to predict the potency of the excluded anesthetic, and the process was repeated until all of the anesthetics had been excluded once and once only. The CoMFA model with the greatest cross-validated r2 was retained as the final model. The extrinsic predictive power of this final model was evaluated by predicting the potencies of the randomly excluded test-set anesthetics.
The possibility of a chance correlation occurring was evaluated by randomly reassigning the observed anesthetic potencies of the training-set anesthetics and repeating the CoMFA analysis. A total of 100 random perturbation cycles were used, and the intrinsic and extrinsic predictive powers of the distorted data sets were evaluated.
| Results |
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An equivalent procedure for halogenated volatile anesthetics (22) showed that their electrostatic potentials differ significantly from that of the lead structure, hexanol (Table 2). The Carbo electrostatic similarity index was only 0.178 ± 0.019 (mean ± SEM) (n = 58) for the halogenated anesthetics, compared with 0.682 ± 0.023 (n = 38) for nonhalogenated anesthetics. Hence, hexanol is not a suitable alignment template for halogenated anesthetics, and these drugs will be considered elsewhere.
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For comparison, we also determined the effectiveness of a conventional activity model based on nonpolar solubility (olive oil/gas partition coefficients). This model explained only 73.2% of the variance in the observed activities of the training-set compounds (F1,26 = 71.138; P < 0.0001), with mean ± SEM residuals of 0.494 ± 0.087 (n = 28). The predictive capability of the nonpolar solubility model was also less than that of the CoMFA model for both the training-set (cross-validated r2 = 0.693) and test-set (r2 = 0.705) anesthetics.
The relative contributions of the electrostatic and steric interactions to the activity model were 74.4% and 25.6%, respectively. Analysis of the individual PLS weightings for each grid point within the orthogonal components of the model enables the identification of regions where steric and electrostatic interaction energies are important in determining activity. Pharmacophoric maps showing the spatial distribution of these regions can be derived by using isocontour plots. These plots were obtained by linking 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. Hence, the plots indicate the regions where the differences in either steric or electrostatic interaction energies are strongly associated with changes in anesthetic potency. We have used the same strategy for assigning the isocontour thresholds as described in our article for the IV anesthetics (7), linking lattice points that represent the greatest 40% of the individual positive and negative contributions to the activity model.
The pharmacophores derived from the final CoMFA model are shown in Figure 3. It can be seen from the electrostatic map (Fig. 3a) that there are two areas (A and B) where positive electrostatic potential is favored for high anesthetic potency (SD x coeff > +0.004) and two main areas where negative potential is favored (C and D; SD x coeff < 0.020). The positioning of these areas in relation to the lead compound hexanol is shown in Figure 3b. The arrows indicate areas where the electrostatic potential of the molecule qualitatively fits the pharmacophoric map. Thus, the electronegative oxygen atom of the hydroxyl group aligns with the red negative potential favored region (D), and most of the electropositive hydrogen atoms align with the blue positive potential favored regions. However, it is evident that there are areas where the electrostatic potential of hexanol does not match the pharmacophoric template. These regions, marked with crosses, correspond with the alignment of the hydrogen atoms with the negative potential favored area (C). On this basis, we speculate that substitution of these hydrogen atoms with more electronegative substituents (e.g., fluorine atoms) would result in a molecule with increased potency.
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| Discussion |
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Halogenated volatile anesthetics were not considered because the electrostatic profiles of these drugs differ substantially from that of the lead structure, hexanol. The Carbo electrostatic similarity is only 0.178 ± 0.019 (mean ± SEM) (n = 58), compared with 0.682 ± 0.023 (n = 38) for nonhalogenated anesthetics. Hence, it is not possible to derive a suitable alignment for halogenated anesthetics by using hexanol as a template (22). Although this practical difficulty necessitates the separate modeling of nonhalogenated and halogenated anesthetics, it does not imply that the molecular basis of their immobilizing activity is different. This question can be addressed only when the independently derived pharmacophores for the two groups of anesthetics are quantitatively compared. Although the putative sites of anesthetic action are not considered in our ligand-oriented model at this stage, it is interesting to note that different receptor specificities have been proposed for nonhalogenated and halogenated volatile anesthetics (24).
How valid is the modeling approach for such a group of structurally diverse anesthetics? The predicted log(MAC) values for 71% of the training-set anesthetics and 60% of the test-set anesthetics were within 0.3 of the observed values. This error is consistent with other published CoMFA models for structurally diverse systems (17,25) and a 4D-QSAR model for structurally homologous propofol analogs (26). Furthermore, the model is a good predictor of potency for unknown excluded test-set anesthetics (r2 = 0.921). It is unlikely that the predictive power of the model is due to a chance correlation, because random perturbation of the potency data resulted in models with no predictive capability. However, the CoMFA model poorly predicts the activities of some anestheticsnotably, the smaller molecules such as ethanol, acetylene, and cyclopropane. There may be some benefit in deriving a separate activity model for these compounds.
In general, the error associated with MAC estimations is <10%. Our activity model is not yet able to predict potency at this level of accuracy, hence its preliminary designation. The weaker predictions for some anesthetics are most likely due to an inappropriate alignment within the CoMFA lattice grid. The anesthetics were aligned by molecular similarity because of their structural diversity. However, this similarity was calculated by using whole-molecule Carbo indices based on an average of the shape and electrostatic potential similarities. This process assumes not only that the steric and electrostatic interactions are of equal importance in determining activity, but also that all regions of the molecules are of significance. However, our results indicate that the electrostatic interactions make a threefold greater contribution to the CoMFA model compared with steric interactions and that not all of the steric and electrostatic features of the anesthetic molecules are important for activity. We anticipate that improved MAC predictions will be obtained by using the preliminary pharmacophores presented in this article as alignment templates for the next-generation model.
Predictive capability might also be improved by allowing the geometries of the molecules to be flexible in the alignment process (thereby allowing a better fit to either the lead structure or pharmacophore templates) or by incorporating additional molecular properties in the activity model. Of particular interest would be the inclusion of an explicit polarizability field. This would enable anesthetics that do not exhibit molecular electrostatic potentials (nitrogen and inert gases) to be incorporated into the model. However, calculation of polarizability fields requires ab initio quantum mechanics, which is computationally intensive and would be impractical for the 625 anesthetic conformers considered in this study.
What does this study contribute to our understanding of the molecular mechanisms of volatile anesthetic action? Our results for the nonhalogenated anesthetics support the findings of previous studies that have shown that steric and electrostatic interactions are important in determining anesthetic activity (27,28). We have now developed this concept and derived a CoMFA model that has characterized the molecular basis of immobilizing activity in terms of the magnitude and spatial distribution of these steric and electrostatic interactions. The pharmacophoric maps illustrate the three-dimensional relationship of the key regions where such interactions are important in determining MAC. The predictive capability of the activity model demonstrates that these maps are applicable to a structurally diverse range of nonhalogenated volatile anesthetics. This raises the possibility that there might be a common molecular basis for the immobilizing activity of the anesthetics considered. However, it is important to note that a common molecular basis for immobilizing activity does not imply a common site of action. Further studies are required to establish whether the molecular basis of anesthetic specificity for various receptor systems (determined by using CoMFA with receptor-binding data as dependent variables) differs from the molecular basis of the immobilizing activity we have described.
| Acknowledgments |
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We thank Edmond I Eger II and his colleagues at the University of California, San Francisco, for the anesthetic potency data and for helpful discussions concerning our modeling approach.
| Footnotes |
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| References |
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