Can molecular similarity-activity models for intravenous general anaesthetics help explain their mechanism of action?

J. C. Sewell1 and J. W. Sear*,2

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


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Background. The importance of molecular shape and electrostatic potential in determining the activities of 11 structurally-diverse i.v. general anaesthetics was investigated using computational chemistry techniques.

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: 166–74

Keywords: structure, molecular similarity; anaesthetics, i.v.; theories of anaesthetic action, cellular mechanisms; model; computer simulation


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The molecular mechanism(s) of i.v. general anaesthesia are unknown. Although a range of putative sites of action have been proposed,1 2 the molecular properties that determine anaesthetic potency have not been identified. The situation is complicated for the i.v. anaesthetics by their chemical diversity, ranging from simple alcohols to complex steroids, which excludes the possibility of formulating an activity model based on the spatial arrangement of individual atoms or chemical groups.3 Previous investigations of activity relationships for i.v. general anaesthetics have, therefore, been restricted to either structurally homologous series of compounds (e.g. the steroid anaesthetics),46 or have been based on structurally indiscriminate properties (e.g. their non-polar solubilities).7

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.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Compounds studied
The structures of the 11 chemically diverse i.v. general anaesthetics considered in this study are shown in Figure 1. The compounds include: the steroid hypnotics, minaxolone (2ß-ethoxy, 3{alpha}-hydroxy, 11{alpha}-dimethylamino, 5{alpha}-pregnan 20 one), alphaxalone (5{alpha}-pregnan, 3{alpha}-hydroxy, 11,20 dione), and eltanolone (5ß-pregnanolone); the racemic barbiturates, thiopental, pentobarbital, thiamylal, and methohexital; and a miscellaneous group of propofol, R- and S-ketamine and R-etomidate. Free drug concentrations associated with abolition of the response to a noxious stimulus in 50% of subjects (EC50) were calculated from typical published plasma drug concentration and protein binding data.1232 Where possible, potency data were taken from studies where no other adjuvant drugs were administered up to the time of the stimulus (the initial surgical incision in patient studies). However, for alphaxalone (given as Althesin), minaxolone and R-etomidate, concentration-effect data are only available for infusions of the agents in the presence of 67% nitrous oxide. Adjustment has therefore been made assuming the nitrous oxide to represent 0.6 MAC, and the hypnotic drug concentration 0.4 MAC equivalent.



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Fig 1 Structural diversity of the i.v. general anaesthetics considered in this study. Note that the hydrogen attached to C5 (*) of eltanolone is in the ß configuration (solid line), resulting in a cis junction between the A and B rings.

 
Molecular model construction
Computer-based models of the anaesthetics were constructed using the molecular modelling software SYBYL 6.4 (Tripos Inc, St Louis, USA) on a Silicon Graphics O2 R10000 workstation. All of the compounds were modelled in their un-ionized state. The starting structures were geometry optimized using molecular mechanics minimization, which considers the molecule as a series of spheres (representing the atoms) connected by springs (representing atomic bonds). Potential energy functions, defined in a ‘force field’, describe the optimum bond lengths, bond angles and torsion angles for the atoms of the molecule. During geometry optimization, the above features are adjusted to minimize the total potential energy of the structure. The default Tripos molecular mechanics force field was used, as implemented in SYBYL 6.4. Gasteiger-Huckel partial charges were assigned to each atom, and non-bonded electrostatic interactions calculated using a distance-dependent dielectric function. The latter simulates the electrostatic screening effect of the solvent, without explicitly including the solvent molecules in the calculations.

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 mol–1 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 model’s 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


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Intravenous general anaesthetic potencies
The anaesthetic potencies expressed as plasma drug concentrations associated with no response to a noxious stimulus or surgical incision in 50% of patients (EC50), and octanol/water partition coefficients for the 11 hypnotic agents are summarized in Table 1. These potencies, based on data from the literature, were used for our calculations of equivalent free drug concentrations that abolish a response to the initial surgical stimulus in clinical studies. The potency data were correlated with molecular properties to formulate the anaesthetic activity models.


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Table 1 Non-polar solubilities and typical values for the in vivo potencies of the i.v. general anaesthetics considered in this study. {dagger}Chiral anaesthetic, potency evaluated using racemate. *Calculated octanol/water partition coefficient. {ddagger} Octanol/water partition coefficients based on racemate
 
Octanol/water partition coefficient model
The following bench mark model was obtained using octanol-water partition coefficients (lipophilicity correlation) for the anaesthetic agents (mean variables±95% CI):

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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Fig 2 Correlation between observed anaesthetic potencies and values predicted using octanol/water partition coefficients for steroid, barbiturate and miscellaneous i.v. general anaesthetics. Numbers refer to the compounds listed in Table 1. The model explained 64.7% of the variance in the observed activities (P=0.003). Note that the model is unable to predict the different potencies of the enantiomers of ketamine (8 and 9).

 
Molecular similarity-anaesthetic activity models
Models with greater predictive power were obtained using molecular similarity indices. The conformers of each anaesthetic were aligned so as to maximize their molecular similarity to eltanolone, the most active compound in the group. Three eltanolone conformers were identified, which differed in their torsion angles at the –CO–CH3 side-chain attached to the D ring (Fig. 3). The combined shape and electrostatic potential similarities of all the anaesthetics to the individual eltanolone conformers were calculated using Carbo indices. Table 2 lists the maximum similarity values obtained for each anaesthetic. An example of the optimal alignment of the anaesthetics to one of the eltanolone conformers is illustrated in Figure 4. It can be seen that the chemical groups of the i.v. agents are arranged to correspond to the key electrostatic and steric features of the eltanolone conformer.



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Fig 3 Torsion angles and orientations of the –CO–CH3 side-chain for the three eltanolone conformers identified in this study.

 

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Table 2 Maximum values of Carbo indices describing the combined shape and electrostatic potential similarity of each anaesthetic to the three eltanolone conformers. The data shown were orthogonalized and scaled to mean zero, unit variance for the activity model formulation
 


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Fig 4 (A) The spatial arrangement electrostatic potential (ep) regions for conformer 2 of eltanolone. Areas of negative potential (<–35 kcal mol–1) are shown as purple spheres, and areas of positive potential (>+9 kcal mol–1) as red spheres. The best alignments of thiopental (B) and etomidate (C) that have maximum shape and electrostatic potential similarity to the eltanolone conformer are shown.

 
The best activity correlation was found with a single latent variable model, based on the combined shape and electrostatic potential similarities of the anaesthetics to eltanolone conformers 1 and 2:

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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Fig 5 Correlation between observed and predicted potencies using a model based on the combined shape and electrostatic potential similarities of the i.v. agents to eltanolone conformers 1 and 2. The model explains 82.0% of the variance in the observed activities (P<0.001), and correctly predicts the potency order of the ketamine enantiomers. Note that alphaxalone (1) is an outlier.

 
The influence of the outlier was tested by excluding alphaxalone and repeating the modelling process. A revised single latent variable model obtained, based on the combined shape and electrostatic potential similarities of the agents to eltanolone conformers 2 and 3:

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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Fig 6 Improved activity model obtained with the exclusion of alphaxalone. The model is based on the similarity of the anaesthetics to the electrostatic potentials of eltanolone conformers 2 and 3, and explains 97.2% of the variance in the observed activities of the compounds (P<0.001).

 
Test for chance correlations
The possibility of obtaining chance correlations when using similarity variables was tested by random perturbation of the potency data prior to model formulation. With alphaxalone included, the mean r2 (±95% CI) of the best models over 1000 perturbations was only 0.202±0.011. The standard deviation of the r2 values was 0.169. Unlike the true activity data set, exclusion of alphaxalone did not improve the correlation. Furthermore, the molecular similarity models were very poor predictors of in vivo potency after random perturbation of the activity values, with a mean cross-validated r2 of –0.662±0.036 (n=1000) and standard deviation of 0.584.


    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The results of this study indicate that a common activity model can be formulated for chemically diverse i.v. general anaesthetics, based solely on their similarities in geometric shape and electrostatic potential. Whilst previous similarity studies have demonstrated the importance of these molecular properties in determining the anaesthetic activities of structurally homologous inhalational agents,10 the activity model presented here represents the first similarity model for structurally diverse chiral and non-chiral i.v. anaesthetics. Furthermore, the similarity model is more effective at predicting in vivo potencies than a model based on octanol/water partition coefficients, which do not provide an adequate physico-chemical correlate for i.v. general anaesthetic activity.

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 ml–1, the S(+) isomer 1.4 µg ml–1, and hence the R(–) isomer 4.2 µg ml–1. 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 55–80%. This may be one cause for our apparent over-estimation of the observed plasma EC50 free drug concentration. There are no published concentration–effect data for Althesin under steady state conditions in other mammalian species to validate this observed concentration–effect 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.


    Acknowledgement
 
This work was supported by a project grant from the British Journal of Anaesthesia. We wish to thank Dr Michael J. Halsey (University of Oxford) and Dr Neil H. Spencer (University of Hertfordshire) for their helpful discussions about this paper.


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
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