1Department of Anesthesiology, Harbor-UCLA Medical Center, Torrance, CA 90509, USA. 2Tripos, Inc., St Louis, MO, USA*Corresponding author
Accepted for publication: January 4, 2002
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Abstract |
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Methods. Each congener was modelled and subjected to computer searches for representative low-energy molecular conformers. The conformationpotency relationship of the congeners was examined.
Results. For all congeners, we found that the lowest energy conformer (the global minimum) has a straight-chain conformation. Reduction of the interonium distance (by bending) incurs a steep energy penalty linearly related to the distance reduced. The global minimum of C10 has an interonium distance of 14.03 Å and a total molecular length of 20.10 Å. For other congeners, the interonium distance differential from that of C10 and the energy penalty required to conform to the interonium distance of C10 (where applicable) correlate with the reported logarithmic (mmol kg1) dose requirement for neuromuscular block.
Conclusions. The C10 congeners strongly prefer a straight conformation. Their molecular length and resistance to bending is key to their neuromuscular blocking potency. A molecular length of approximately 20 Å should best fit the space available to neuromuscular blocking agents between the two receptive sites of the endplate acetylcholine receptor.
Br J Anaesth 2002; 88: 6929
Keywords: structure, molecular conformationactivity relationship; structure, molecular structureactivity relationship; neuromuscular block, decamethonium congeners
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Introduction |
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In the literature, the molecules of these congeners are generally presented in straight-chain conformation. Each congener differs from its neighbour only by one methylene group in the polymethylene chain that connects the two terminal methonium heads. Besides molecular length and a slight increment in lipophilicity with each additional methylene group, no known chemical factors may plausibly explain the neuromuscular blocking profile of the series of congeners. Consequentially, one can assume that at one point congener C10 optimally fits into an available space between the two receptive sites of the skeletal muscle endplate acetylcholine receptor.47 Furthermore, one can also hypothesize that the relative difficulty with which other congeners to fit into this inter-site space may explain their relative lack of neuromuscular blocking potency. However, because the polymethylene chain connecting the terminal methonium heads is flexible, the molecule of each congener might adopt a shorter (bent) conformation with relative ease. If this were true, the molecular length of these congeners would become less meaningful and the superior neuromuscular blocking potency of C10 would no longer be explainable.
To test the hypothesis that the polymethylene bismethonium congeners probably exist as straight-chain molecules, we searched for their low-energy conformations and computed the energy penalty that hinders them from reducing their interonium distance. The basic assumption is that low-energy conformers are stable and preferentially populated.8 Only low-energy conformers, especially the global minimum, may represent the molecule in conformationactivity relationship studies.
To test the hypothesis that the molecular length of these congeners determines their neuromuscular blocking potency, we also investigated the relationships between the neuromuscular blocking dose requirement, the interonium distance and the energy penalty required to change the interonium distance of these congeners. In this series of congeners, the interonium distance parallels the molecular length because they all have the same methonium head. These relationships are of interest not only in medicinal chemistry but also for the assessment of the distance between the two receptive sites of the endplate acetylcholine receptor in vivo. Although the morphology of the nicotinic acetylcholine receptor of the electric organ has been studied very extensively in vitro,47 few studies have given an indication of the inter-receptive site distance of the endplate acetylcholine receptor in vivo. Because of their simple molecular structure, the conformation of the C10 congeners depends on few forces other than the torsion of the methylene bonds and the hindrance and mutual repulsion of the two charged methonium heads. This increases the chance that their molecular conformation can be determined accurately. Once their conformation is determined, one can exploit their well-established pharmacological profile for theoretical explorations of their conformationactivity relationship.9 An abbreviated account of the conformation of C9, C10 and C11 has been presented10 and preliminary results of the present report have been cited in a recent review.9
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Methods |
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The interonium distance of each conformer was measured from the centre of one N atom to the other (NN distance). The van der Waals extensions of the terminal H atoms were computed. These extensions define the outer boundaries of the H atoms and were included in the determination of the total molecular length. For each congener, the relationship between the NN distance and the energy of the conformers was examined by linear regression. The linear regression also yielded the slope of energy penalty required to change the NN distance and the total energy penalty required to conform to certain NN distances. When it became certain that the lowest energy conformer of each congener had a straight-chain conformation, these global minima of the entire series were identified and all further analyses, including examination of the relationship between molecular length and neuromuscular blocking dose requirement, were based on these straight-chain conformers, as follows.
The neuromuscular blocking dose requirements of C5C12 and C18 were established by the work of Paton and Zaimis.1 For the present study, we adopted, without bias, their ED95 (dose requirement to block neuromuscular transmission by 95%) values for the tibialis anterior muscle of the cat in vivo. The ED95 values were converted from mg kg1 to mmol kg1 and expressed as log(ED95 mmol kg1) where appropriate.
As bonds do not stretch under ordinary conditions, the energy penalty determined by linear extrapolation for shorter molecules (C5C9) to conform to NN = 14.03 Å (the NN distance of C10) has uncertain meaning. For some studies, we therefore separated the congeners into two categories, namely C10 and higher and C10 and lower, and recognized that in each category the effect of molecular length on the neuromuscular blocking potency, if any, may need a different explanation. Accordingly, linear regressions were performed only on C10C12 and C18, whose neuromuscular blocking ED95 values in log(mmol kg1) were regressed on their NN distance differentials from 14.03 Å, and again on the total energy penalty required to accommodate the difference differentials. The values were also ranked. For C6C10, the ED95 values in log(mmol kg1) and the NN distance differentials were examined by ranking. As C5 and C6 were inferior neuromuscular blockers1 and their ED95 values were available only as >40 mg kg1, C5 was excluded from the ranking.
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Results |
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The conformationactivity relationship concerning the neuromuscular blocking potency of the congeners is presented in Table 2 and Figure 3, using the lowest-energy straight-chain conformer as representative of each congener and the neuromuscular blocking ED95 values adopted from Paton and Zaimis1. The energy penalty for C10C12 and C18 to conform to an NN distance of 14.03 Å was obtained by multiplying the energy penalty slope by the distance differential from 14.03 Å. In both the C10 and higher and the C10 and lower category, the ED95 values, the energy penalty and the NN distance differentials from 14.03 Å showed identical rank order with no exceptions. Figure 3 shows the relationship between the ED95 (mmol kg1) values of the C10 and higher congeners and the energy penalties required to conform to the NN distance of 14.03 Å (Fig. 3, upper left) and the relationship between the ED95 (mmol kg1) values and the NN distance differentials from 14.03 Å (Fig. 3, upper right). Upon logarithmic transformation of the dose requirements, the relationships become linear (Fig. 3, lower left and lower right).
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Discussion |
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Briefly, the GA search is a global minimizer that optimizes the population by improving the average fitness of its individuals. It effectively searches the entire conformational space of a molecule for a collection of fit samples, without detailed refinement of each sample during the search. To refine the samples, a GA conformational search is generally followed by an energy minimization that fully minimizes the individual conformers harvested previously. An energy minimizer improves the inter-atom relationship of a conformer and joggles among all components of energy to reduce the total to a minimum. While allowing components of energy to increase (if needed towards that goal), an energy minimizer must reduce the total energy iteration after iteration. It may not allow the total energy to increase at any step, even if such an intermediate step may lead to a better final outcome, because allowing both the total energy and its components to increase will make the entire process open-ended and endless. An energy minimizer is therefore a local minimizer, bound to what is possible within the limit of its starting geometry. The two minimizers are thereby mutually complementary and interdependent processes. Combined, they first efficiently sample a wide conformational space and then reliably refine the samples. For the present study, we used the combination of steps not only to find the global minima for correlation with neuromuscular blocking potency among congeners but also to collect local minima for linear regression of the energy penalty required to bend each congener.
The observation that the global minimum of every congener (C5C18) has the straight-chain geometry is not unexpected.8 Nor is the observation that the higher congeners have gentler slopes of energy penalty to bend, because long connecting chains increase conformational flexibility and reduce mutual repulsion between the methonium heads. Also readily understandable is the finding that among the methylene bonds in the connecting chain the terminal methylene bond is the hardest to twist, because rotation of this bond directly involves the bulk and the charge of the methonium head. Rather, it is the large energy barrier in favour of the straight conformation and the close relationship between the conformational features and the neuromuscular blocking dose requirement of the congeners that are interesting. Before computer modelling became available, stereomodels (such as the model of Dreiding13) have permitted crude measurement of the dimensions of molecules and tactile estimation of their flexibility. However, these models are at best semiquantitative and they give only a snapshot of a local minimum. They cannot search conformational space, minimize total energy, compute electrostatic or other components of energy, or quantify the slope of changes. They are hard to assemble in the case of large rigid cubic structures. Since the conclusion of the present project, we have extended our studies to neuromuscular blocking agents of greater structural complexity, and have likewise obtained useful preliminary information to extend their structureactivity relationship to the conformationactivity relationship.10 It should be noted that, as a rule, the geometry of muscle relaxant molecules is grossly inaccurate until computed thoroughly.
Like all alkanes, the methylene bonds of these congeners have lower torsional energy when their neighbouring bonds are staggered anti and the molecule is straight.8 For example, when the configuration of butane is changed from anti to gauche, by a twist of one bond, the four-carbon chain bends and shortens and the energy of the molecule increases by about 0.9 kcal mol1.8 For another comparison, we replaced the N atoms of C10 with C atoms and subjected the hypothetical compound to the same study. This hypothetical compound, 2,2,13,13-tetramethyl tetradecane, or (CH3)3C(CH2)10C(CH3)3, also has a straight-chain conformer as its global minimum. It has no charged atoms. The distance between its carbon 2 and carbon 13, the equivalent of the NN distance of C10, can decrease from 13 to 11 Å without linearly increasing the energy penalty. By contrast, it will take 57 kcal mol1 for C10 to do so. The minimum energy penalty to twist one bond is 0.84 kcal mol1 for the hypothetical compound vs 2.07 kcal mol1 for C10 (Table 1, C10). Viewed from these perspectives, our results indicate the large extent to which the C10 congeners resist bending.
As molecules stabilize at low energy, a difference in energy of 1.4 kcal mol1 would mean a 10-to-1 ratio for the lower-energy conformer to be populated preferentially.6 In the example of butane, an energy barrier of 0.9 kcal mol1 means a 72-to-28 chance in favour of the straight conformer.8 By the same principle, our finding of a large energy penalty required to bend would indicate the large extent to which the straight conformers of the C10 congeners would prevail. In the case of C5, the minimum dE of 4.32 kcal mol1 indicates that C5 will only vibrate around its global minimum, with little chance of assuming a bent conformation.
Our data on the conformationactivity relationship support the hypothesis that the molecular length determines the neuromuscular blocking dose requirement of the C10 congeners. The lipophilicity of the molecule is a factor in the neuromuscular blocking potency of a series of aminosteroid neuromuscular blocking agents.14 However, increments in lipophilicity are unlikely to be large enough to play a significant role in the neuromuscular blocking potency of the C10 congeners; otherwise, the neuromuscular blocking potency of the congeners would not show a biphasic distribution to peak at C10. In agreement with this hypothesis, the slope of conformational energy penalty changed in tandem with the decrease in neuromuscular blocking potency. Both showed reduced inter-congener decrement towards the higher end of the series.
From the above, it appears that C10 is a credible molecular yardstick to measure, in vivo, the inner inter-site space of the muscle endplate acetylcholine receptor available to neuromuscular blocking agents at one point of the drugreceptor interaction. One can also argue that the long congeners act by conforming to the receptive sites by bending, and that the shorter congeners have different mechanisms of action. However, some caveats, which follow, must first be observed. These caveats should not qualitatively nullify our conclusions.
First, all conformational searches can be criticized for not taking into consideration the effects of the milieu in which the molecules actually exist and act. For example, polar solvents such as water tend to orient their molecules in a coordinated manner so as to reduce the effect of the electric charges on the conformation of the dissolved molecules. Furthermore, electrolytes and the acidbase status of the biological fluid will further complicate the issue. Modelling the congeners in the presence of solvent may alter the results in quantitative terms. However, we are not aware of any validation of the solvation method or of the application of other advanced molecular modelling techniques to the study of quaternary neuromuscular blocking drugs. Meanwhile, conformational search and minimization appear encouraging as an affordable step in the right direction to extend traditional structureactivity studies to the conformationactivity relationship.
Another caveat concerns the thoroughness of the conformational search. Inadequate searches will produce samples of greater scatter in energy and will miss the best possible product. Increased scatter will increase the slope if the point of lowest energy alone has no scatter, which is the case with the global minima here. Furthermore, congeners with a greater number of rotatable bonds have a greater chance of being searched inadequately. If this happens, the inter-congener relationship will be skewed. To minimize technical errors, we used large populations, many generations and much computer time. We also adjusted these parameters according to the chain length, based on repeated preliminary test runs (see Appendix). As a result, our data in Table 1 show consistency, high goodness of linear fit, and smooth and logical transition between congeners, in agreement with basic thermodynamic predictions. The simple molecular structure of the congeners has rendered their global minima relatively easy to find and the search results consistent.
Geometry at the level of the receptive sites is important in determining how the muscle relaxant molecule may fit the receptor. Experiments in vitro have shown a distance of about 30 Å between the inner borders of the receptive sites of the nicotinic acetylcholine receptor.6 Using C10 as a molecular yardstick, our data would suggest that the space actually available to the neuromuscular blocking agents measures close to 20 Å (the molecular length of C10) between the anionic centres of the receptive sites. The discrepancy between 30 Å and 20 Å is explainable by the space unavailable to muscle relaxants, different receptors and experimental techniques, treatment artefacts in vitro, the state of receptor desensitization and imprecision in measuring the receptor macromolecule.5 7 15 It is possible that our argument may apply only to the cat tibialis anterior muscle preparation in vivo, as used by Paton and Zaimis.1
Higher and lower congeners require different explanations of why they are both weaker neuromuscular blockers than C10. Higher congeners may act by bringing their methonium heads to fit the available inter-site space of the receptor. The loss of potency will depend on the energy penalty, which is proportional to the distance of the required accommodation and the slope. As molecules do not stretch, lower congeners will not span both receptive sites. Instead, they may use two molecules acting simultaneously, one at each site, as does succinylcholine, with a loss of potency.16 If the receptor changes its local conformation during the interaction to fit the congeners, the energy penalty will likewise depend on the distance that has to be accommodated. If Figure 3 were extrapolated to include the lower congeners, as if they were stretchable, linearity of correlation would still exist (personal observation). In any case, molecular length and how strongly the congeners prefer a straight conformation determine their neuromuscular blocking potency.
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Appendix |
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According to the general algorithm, we specified the following parameters for the present study. All methylene (CC) bonds were designated as rotatable. The size of the population equalled 100 individuals for each rotatable bond. For example, C10 has nine rotatable bonds and therefore 900 individuals in the evolving population. Likewise, C15 has 14 bonds and a population of 1400 individuals. The number of generations each population evolved through was set to 10 times the number of individuals in the population. Thus, C10 evolved through 9000 generations and C18 through 17 000 generations. At the end of each search, up to 70 fit conformers were saved, as long as each had energy within 5 kcal mol1 per rotatable bond of the fittest. For the linear regression, we aimed at producing 3050 evenly distributed discrete conformers for each congener, all within a range of 10 kcal mol1 fully minimized. A large energy allowance during the search prevented premature elimination of fit conformers before final minimization. Preliminary experiments had shown that these parameters would allow a thorough search and yield satisfactory results for all congeners, C5C18 alike.
We used the MMFF94s force field12 in the minimization of the conformers in the database, allowing an unlimited number of iterations for each conformer to converge at a 0.05 kcal mol1 Å1 gradient between iterations. All minimized conformers in the database were also compared, by matching each conformer with all other conformers atom for atom. Any conformer matching with a root mean square inter-atom distance of 0.1 Å or less from any other conformer was considered a duplicate and was deleted.
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References |
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2 Karis JH, Katz RL, Gissen AJ, DeJong RH, Freund FG. Neuromuscular block with succinylcholine and decamethonium. Anesthesiology 1968; 29: 1667[ISI][Medline]
3 Payne JP. In pursuit of relaxation. Anaesthesia 1986; 41: 95060[ISI][Medline]
4
Pedersen SE, Cohen JB. D-Tubocurarine binding sites are located at
and
subunit interfaces of the nicotinic acetylcholine receptor. Proc Natl Acad Sci USA 1990; 87: 27859[Abstract]
5 Unwin N. The nicotinic acetylcholine receptor of the torpedo electric ray. J Struct Biol 1998; 121: 18190[ISI][Medline]
6 Taylor P, Insel P. Molecular basis of pharmacologic selectivity. In: Pratt WB, Taylor Palmer, eds. Principles of Drug Action: The Basis of Pharmacology. Philadelphia: Churchill Livingstone, 1990; 1102
7 Unwin N, Toyoshima C, Kubalek E. Arrangement of the acetylcholine receptor subunits in the resting and desensitized states, determined by cryoelectron microscopy of crystallized torpedo postsynaptic membranes. J Cell Biol 1988; 107: 112338[Abstract]
8 Streitwieser A, Heathcock CH, Kosower EM. Alkanes. In: Streitwieser A, Heathcock CH, Kosower EM, eds. Introduction to Organic Chemistry. New York: MacMillan, 1992; 7499
9
Lee C. Structure, conformation, and action of neuromuscular blocking drugs. Br J Anaesth 2001; 87: 75569
10 Lee C, Jones T. Conformations of nona-, deca- and undecamethonium [abstract]. In: 12th World Congress of Anaesthesiologists, June 49, 2000, Montreal, Canada. 7.4.27
11 Judson R. Genetic algorithms and their use in chemistry. In: Lipkowitz KB, Boyd DB, eds. Review in Computational Chemistry, Vol. 10. New York: VCH Publishers, 1997; 173
12 Gundertofte K, Liljefors T, Norrby P-O, Pettersson I. A comparison of conformational energies calculated by several molecular mechanics methods. J Comput Chem 1996; 17: 42949[ISI]
13 Streitwieser A, Heathcock CH, Kosower EM. Organic structures. In: Streitwieser A, Heathcock CH, Kosower EM, eds. Introduction to Organic Chemistry. New York: MacMillan, 1992; 3254
14 Wierda JM, Proost JH. Structure-pharmacodynamic-pharmacokinetic relationships of steroidal neuromuscular blocking agents. Eur J Anaesthesiol Suppl 1995; 11: 4554[Medline]
15 Dilger JP. Structure and function of the nicotinic acetylcholine receptor. In: Yaksh TL, Lynch C III, Zapol WM, Maze M, Biebuyck JF, Saidman LJ, eds. Anesthesia: Biologic Foundations. Philadelphia: Lippincott-Raven, 1998; 22137
16 Marshall CG, Ogden DC, Colquhoun D. The actions of suxamethonium (succinyldicholine) as an agonist and channel blocker at the nicotinic receptor of frog muscle [published erratum appears in J Physiol (Lond) 1991; 435: 6456]. J Physiol (Lond) 1990; 428: 15574[ISI]