1Department of Biosciences, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB and 2Nuffield Department of Anaesthetics, University of Oxford, John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK*Corresponding author
Accepted for publication: October 8, 2001
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Abstract |
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Methods. The free plasma anaesthetic concentrations that abolished the response to noxious stimulation were obtained from the literature. The similarities in the molecular shapes and electrostatic potentials of the agents to eltanolone (the most potent anaesthetic agent in the group) were calculated using Carbo indices, and correlated with in vivo potency.
Results. The best model obtained was based on the similarities of the anaesthetics to two eltanolone conformers (r2=0.820). This model correctly predicted the potencies of the R- and S-enantiomers of ketamine, but identified alphaxalone as an outlier. Exclusion of alphaxalone substantially improved the activity correlation (r2=0.972). A bench mark model based on octanol/water partition coefficients (r2=0.647) failed to predict the potency order of the ketamine enantiomers.
Conclusions. The results demonstrate that a single activity model can be formulated for chiral and non-chiral i.v. anaesthetic agents using molecular similarity indices.
Br J Anaesth 2002; 88: 16674
Keywords: structure, molecular similarity; anaesthetics, i.v.; theories of anaesthetic action, cellular mechanisms; model; computer simulation
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Introduction |
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Computer-modelling techniques have recently been developed that give the potential to formulate a single activity model for chemically diverse agents. Such approaches ignore the individual atomic arrangements of the compounds, but consider the three-dimensional molecular properties that are determined by the atomic structure.8 Such properties include the geometric shapes of the molecules and their electrostatic potentials (a measure of the distribution of charge around the molecule). These molecular properties can be numerically compared by the calculation of similarity indices, and correlated with in vivo potencies to formulate activity models.9 We have previously applied the similarity approach to demonstrate that molecular shape is important in determining the in vivo potencies of halogenated ether and ethane volatile anaesthetics.10
Preliminary models for i.v. general anaesthetics demonstrate the importance of electrostatic potential in determining in vivo activity. A model based on electrostatic potential similarity explains 87% of the variance in observed potencies of i.v. general anaesthetics.11 This represents a substantial improvement compared with a conventional activity model based on the octanol/water partition coefficients of the compounds, which explained only 66% of the variance in observed activity. However, these preliminary investigations did not take into account the effects of chirality of the various agents. The present study is an extension of this earlier work (previously reported to the Anaesthetic Research Society),11 to develop an improved activity model for the i.v. agents that can address this shortcoming.
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Methods |
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Although the i.v. general anaesthetics consist of relatively rigid ring systems, the side chain groups are capable of free rotation. The anaesthetics, therefore, exist as an ensemble of interchangeable configurations, referred to as conformers. The lower the potential energy of a conformer, the more frequently that configuration will occur in solution (based on the Boltzmann distribution). This flexibility was considered in our model by deriving a set of low energy conformers for each of the anaesthetics, using a SYBYL random search. In this process, the torsion angles of the molecules are randomly perturbed, and the resultant structures are subjected to molecular mechanics geometry optimization. Only the optimized conformers with a potential energy within +4 kcal mol1 of the lowest energy conformer for a given anaesthetic were retained. The process was repeated until each anaesthetic had been subjected to 10 000 random structure perturbations, or until each of the low energy conformers had been found at least 12 times. A total of 1308 conformers were produced for the 11 anaesthetics at this stage.
The geometries of the 1308 conformers were further refined 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 considered explicitly and experimentally derived variables are used to represent the nuclei and inner-shell electrons. The geometry optimization was performed in vacuo using the MOPAC 6 software package (Quantum Chemistry Program Exchange, Indiana, USA) with the AM1 Hamiltonian. Atomic partial charges were assigned using the Coulson method. After geometry optimization, duplicate conformers (defined as conformers with an RMS difference of <0.2 Å) were removed. The final set consisted of 621 unique conformers for the 11 anaesthetics.
Similarity indices
Alignment of the structurally diverse general anaesthetics was based on the local minimum method,33 34 in which the structures are aligned so as to maximize their molecular similarity with the conformers of the most active agent in the group. Thus, the anaesthetic conformers were rotated and translated in a SIMPLEX optimization to maximize their similarity with the conformers of eltanolone. Molecular similarity was quantified by the calculation of Carbo indices,9 which range from 0 (totally dissimilar molecular shapes and electrostatic potentials) to 1 (totally identical). Combined shape and electrostatic potential Carbo indices were calculated using an analytical method9 with the ASP 3.22 software (Automated Similarity Package, Accelrys Inc., Cambridge, UK). The conformers of each anaesthetic with the maximum similarity to the eltanolone conformers were retained.
Activity model formulation
Activity models were formulated by correlating the molecular similarity variables with the in vivo potencies of the anaesthetics. However, the high co-linearity of the similarity variables prevents the application of standard multiple regression techniques. Hence, the latent variable procedure35 of partial least squares (PLS) regression was applied, using the PLS Toolbox 2.1.1 (Eigenvector Research, Manson, USA) for MatLab 5 (The MathWorks Inc., Natick, USA). Models using all possible combinations of two similarity variables were considered. In each case, the second similarity variable in the model was orthogonalized to the first using the Gram-Schmidt procedure.36 This process identifies the information which is common to both variables, and removes this common factor from the second variable, so that the latter contains only unique data (i.e. it is orthogonal to the first variable). The variables were subsequently scaled to mean zero and unit variance, so that they have the same numerical range for the PLS analyses. The number of latent variables included in each PLS model, and the models predictive capability, were determined by leave-one-out cross-validation.37 In this process, each model was repeatedly reformulated, but with one of the anaesthetics excluded at each stage. The revised model was used to predict the in vivo potency of the excluded agent, and the process repeated until all of the compounds had been excluded once and once only. In effect, cross-validation is testing the ability of the models to predict the activities of an unknown agent. The model with the minimum number of latent variables and best cross-validated r2 was retained. Confidence intervals (95%) for the final model variables were estimated using bootstrapping37 over 100 iterations, and statistical significance determined by an analysis of variance (F statistic) using SYBYL.
The possibility of obtaining a chance correlation was tested by randomly re-assigning the observed potency data to different anaesthetics, and repeating the modelling process. A total of 1000 cycles of random perturbations were used, and the mean r2 and cross-validated r2 for this distorted data set calculated. For benchmark purposes, a conventional activity model based on non-polar solubility was also formulated for the anaesthetics, using published octanol/water partition coefficients.38
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Results |
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Predicted log(EC50)=
(0.995±0.043xoctanol/water partition coeff.)+2.535±0.116
This model explained only 64.7% of the variance in the observed activities of the compounds (F(1,9)=16.531, P=0.003, n=11). A plot of the predicted anaesthetic potencies (Fig. 2) shows that the model failed to predict the potency order for the enantiomers of the chiral anaesthetic, ketamine. Furthermore, the model had a low predictive power, with a cross-validated r2 of 0.418.
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Predicted log(EC50) =
(0.358 ± 0.024 x C1) (0.447 ± 0.013 x C2) + 5.377 ± 0.024
where:
C1=Scaled combined similarity to eltanolone conformer 1
C2=Scaled combined similarity to eltanolone conformer 2, orthogonalized to C1
This model explained 82.0% of the variance in the observed activities of the anaesthetics (F(1,9)=41.094, P<0.001, n=11). The model was also a good predictor of in vivo potency (cross-validated r2 of 0.755), and correctly predicted the relative activities of the ketamine enantiomers (Fig. 5). However, alphaxalone (the main active component of the steroid Althesin) was identified as an outlier, being less potent than would be predicted from its molecular similarity to the eltanolone conformers.
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Predicted log(EC50) =
(0.607 ± 0.047 x C2) + (0.376 ± 0.034xC3)+5.392±0.027
where:
C2=Scaled combined similarity to eltanolone conformer 2
C3=Scaled combined similarity to eltanolone conformer 3, orthogonalized to C2
The exclusion of alphaxalone improved the model considerably (Fig. 6), explaining 97.2% of the variance in the observed activities of the compounds (F(1,8)=278.836, P<0.001, n=10). The predictive power of the model was also increased (cross-validated r2 of 0.950).
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Discussion |
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There are several factors that could influence the effectiveness of our activity model. One of the key factors is the EC50 calculations of in vivo anaesthetic potency. The endpoint used in this paper for the potency of Althesin (as alphaxalone), minaxolone, methohexital, thiopental, propofol, eltanolone, R-etomidate and the isomers of ketamine has been the plasma drug concentration during infusion anaesthesia associated with suppression of a noxious stimulus (initial surgical incision) in 50% patients (or the equivalent endpoint in animals). The data shown in Table 1 are typical values of the derived kinetic variables. For pentobarbital and thiamylal, the concentration values cited are the best approximation to those in the blood at the time of the surgical incision following single bolus doses to patients. Because of the long elimination half-lives of these barbiturates, the decline in the plasma drug concentration (and hence the brain concentration) will be slow after the initial redistribution phase, and we have therefore assumed that pseudo-steady state conditions exist. However, the potency of an i.v. anaesthetic is related to its brain:effect-site concentration rather than the plasma concentration. Based on the known kinetics of our 11 hypnotic agents and their blood:brain uptake times, we have assumed that for all agents there is approximate blood:brain equilibration.
The effects of stereochemistry on hypnotic potency have been described for the isomers of etomidate,39 40 the barbiturates,41 ketamine,42 43 and some of the steroid anaesthetics.4446 In the case of ketamine, there are kinetic and dynamic data available for both enantiomers as well as the racemate.42 43 47 Although there are comparative data for the dynamics of the two enantiomers following i.v. bolus dosing,48 there are fewer data for infusions of ketamine and none for the R() isomer. Clinical studies with infusions of ketamine show the anaesthetic potency of the S(+) enantiomer to be twice that of the racemate,48 with the potency ratio for S(+) to R() being 3 to 4:1.43 Based on the infusion data of Adams and colleagues48 and Idvall and colleagues,49 we have assumed the Cp50 (plasma drug concentration associated with no response in 50% of patients receiving ketamine alone) for racemic ketamine to be 2.5 to 3.0 µg ml1, the S(+) isomer 1.4 µg ml1, and hence the R() isomer 4.2 µg ml1. Differences in potency have been demonstrated in vitro for the stereoisomers of etomidate 39, but in vivo only the R(+) isomer is present in the clinically available formulation.
There are, however, no mammalian data examining the dynamics of the various enantiomers of the barbiturates, although stereo-kinetics have been determined for several of the drugs (particularly thiopental, pentobarbital and thiamylal) which reveal subtle and possibly important differences in disposition which might affect the concentration effect relationships for different enantiomers.5052 We have, therefore, based our potency calculations for the barbiturates on racemate concentrations.
It is difficult to offer firm reasons for alphaxalone being an outlier in our similarity model. Alphaxalone is the major hypnotic steroid in Althesin, with alphadolone acetate being present to increase lipid solubility. Richards and White53 showed additivity between alphaxalone and alphadolone in rodents; but there are no comparable data for man. Our studies to determine the anaesthetic or immobilizing concentration of Althesin only measured plasma alphaxalone concentrations.30 However, when the kinetics of the two steroids are studied, the observed plasma concentrations show the expected 3:1 concentration ratio with similar disposition profiles.54 The only available reported estimate for alphaxalone plasma protein binding is 40%.31 This binding estimate appears to be low and not in keeping with other pregnane steroids, where plasma protein binding is often concentration dependent, and of the order of 5580%. This may be one cause for our apparent over-estimation of the observed plasma EC50 free drug concentration. There are no published concentrationeffect data for Althesin under steady state conditions in other mammalian species to validate this observed concentrationeffect relationship.
What does this study indicate about the mechanism of anaesthetic action? The fact that a common activity model can be formulated for structurally diverse i.v. general anaesthetics suggests two features.
(i) First, that there is a common molecular basis for the mechanism of general anaesthesia. This does not necessarily imply that there is a common site of action: indeed, in vitro studies indicate that GABAA, neuronal nicotinic acetylcholine and NMDA receptors are all sensitive to the wide range of i.v. anaesthetic agents at clinically relevant concentrations,1 55 56 although the involvement of these ligand-gated ion channels in inducing general anaesthesia in vivo is less clear.57 58 Rather, our studies suggest that certain molecular features involved in determining anaesthetic activity are common to all the 11 hypnotic agents.
(ii) Second, that molecular shape and electrostatic potential are key in determining the in vivo potencies of chiral and non-chiral i.v. general anaesthetics. This opens the possibility of deriving a non-structural pharmacophore for general anaesthetics, based on their three-dimensional steric and electrostatic features.
Whether the molecular shape characteristics in silico of a novel putative hypnotic agent can be used to predict its subsequent in vivo potency remains to be determined. However, identification of a three-dimensional pharmacophore will clearly be the first stage in this process.
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Acknowledgement |
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