Molecular conformation–activity relationship of decamethonium congeners

British Journal of Anaesthesia 88 (5): 692±9 (2002)

Molecular conformation±activity relationship of decamethonium congeners C. Lee1* and T. Jones2 1

Department of Anesthesiology, Harbor-UCLA Medical Center, Torrance, CA 90509, USA. 2 Tripos, Inc., St Louis, MO, USA *Corresponding author Background. Of the polymethylene bismethonium congeners (C5±C12 and C18), decamethonium (C10) is the most potent neuromuscular blocking agent. We tested the hypothesis that these congeners act as straight molecules and will not bend easily in spite of the ¯exible connecting chain between the methonium heads. For congeners higher than C10, we also hypothesized that the relative dif®culty with which the molecules to bend to conform to the interonium distance of C10 proportionately reduces their neuromuscular blocking potency. Methods. Each congener was modelled and subjected to computer searches for representative low-energy molecular conformers. The conformation±potency 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 AÊ and a total molecular length of 20.10 AÊ. 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 kg±1) 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 AÊ should best ®t the space available to neuromuscular blocking agents between the two receptive sites of the endplate acetylcholine receptor. Br J Anaesth 2002; 88: 692±9 Keywords: structure, molecular conformation±activity relationship; structure, molecular structure±activity relationship; neuromuscular block, decamethonium congeners Accepted for publication: January 4, 2002

Of the polymethylene bismethonium series of compounds, C5±C12 and C18, congener C10 (decamethonium) has an optimal neuromuscular blocking action1 and was once brought to clinical use as neuromuscular blocking drug for anaesthetized humans undergoing surgery.2 3 Other congeners, longer and shorter alike, are less potent. Instead of having neuromuscular blocking properties, C5 and C6 are potent ganglion blockers.1 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 pro®le of the series of congeners. Consequentially, one can assume that at one point congener C10 optimally ®ts into an available space between the two receptive sites of the skeletal muscle endplate acetylcholine receptor.4±7 Furthermore, one can also hypothesize that the relative dif®culty with which other congeners to ®t 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 ¯exible, 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

Ó The Board of Management and Trustees of the British Journal of Anaesthesia 2002

Molecular conformation of decamethonium congeners

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 conformation±activity 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,4±7 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 pro®le for theoretical explorations of their conformation±activity 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

Methods The study was performed on an SGI R10000 workstation using the Sybyl (version 6.7) molecular modelling software package (Tripos, St Louis, MO, USA). Molecules of C5 to C18 were ®rst constructed in a straight-chain conformation. Their total energy was minimized. Each molecule was then subjected to extensive searches for a collection of representative low-energy conformers, by a method of conformational searching using a genetic algorithm (GA search; for description, see Appendix).11 For each congener, we programmed the computer to identify up to 70 lowenergy conformers and store them in a database. In a subsequent operation, all conformers in the entire database were energy-minimized thoroughly, to converge at Ê ±1 using the MMFF94s force ®eld,12 and 0.05 kcal mol±1 A

conformers considered duplicates of others were deleted. The MMFF94s takes into consideration the following components of total energy: bond stretch, angle bending, torsional, stretch-bending interaction, out of plane bending, 1±4 van der Waals, van der Waals, 1±4 electrostatic, and electrostatic. The interonium distance of each conformer was measured from the centre of one N atom to the other (N±N distance). The van der Waals extensions of the terminal H atoms were computed. These extensions de®ne 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 N±N 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 N±N distance and the total energy penalty required to conform to certain N±N 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 identi®ed 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 C5±C12 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 kg±1 to mmol kg±1 and expressed as log(ED95 mmol kg±1) where appropriate. As bonds do not stretch under ordinary conditions, the energy penalty determined by linear extrapolation for Ê shorter molecules (C5±C9) to conform to N±N = 14.03 A (the N±N 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 C10±C12 and C18, whose neuromuscular blocking ED95 values in log(mmol kg±1) were regressed on their N±N distance differentials from Ê , and again on the total energy penalty required to 14.03 A accommodate the difference differentials. The values were also ranked. For C6±C10, the ED95 values in log(mmol kg±1) and the N±N distance differentials were examined by ranking. As C5 and C6 were inferior neuromuscular blockers1 and their ED95 values were available only as >40 mg kg±1, C5 was excluded from the ranking.

Results The lowest-energy conformer of all congeners, as expected, was the straight-chain conformer. Figure 1 shows the

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Ê respectively and the Fig 1 The lowest-energy straight-chain conformers of C9, C10 and C11. Their interonium distances are 12.76, 14.03 and 15.29 A Ê , including the van der Waals extensions of the terminal H atoms, shown as dotted corresponding total molecular lengths are 18.83, 20.10 and 21.36 A half-circles.

Table 1 Decamethonium congeners' relationships between N±N distance and energy, among conformers. dE=energy penalty; N±N distance=distance from centre of one N to the other; global minimum=conformer with lowest energy, also shortest N±N distance, of each congener; minimum dE=least energy increment from global minimum Congener

C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18

Global minimum N±N Ê) distance (A

Global minimum energy (kcal mol±1)

7.71 8.99 10.23 11.51 12.76 14.03 15.28 16.55 17.82 19.07 20.32 21.60 22.86 24.12

80.50 74.27 69.63 65.90 62.91 60.39 58.30 56.42 54.84 53.39 52.13 50.96 49.93 48.96

Linear regression (energy on N±N distance) dE slope Ê ±1) (kcal mol±1 A

r2

P<

n

12.36 9.14 5.44 4.57 3.76 2.83 2.62 2.15 2.12 1.92 1.80 1.47 1.20 1.22

0.64 0.71 0.71 0.89 0.91 0.90 0.95 0.91 0.88 0.85 0.80 0.82 0.92 0.81

0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

16 31 37 45 45 55 54 54 61 69 65 63 62 67

lowest-energy straight-chain conformers of C9, C10 and Ê C11. Their N±N distances were 12.76, 14.03 and 15.29 A respectively and their computed total molecular lengths, including the van der Waals extensions of the terminal H Ê , in that order. atoms, were 18.83, 20.10 and 21.36 A Table 1 lists the N±N distance and energy of the lowestenergy straight-chain conformer of each congener from C5 to C18. Also shown are the linear regression data. Reduction of the N±N distance (by bending) invariably increased the energy linearly. Each congener demonstrated good linear ®t between the energy and the N±N distance of its conformers. Of C5±C18, the lower congeners (with shorter separation of the methonium heads) were less ¯exible, as indicated by a steeper slope of the energy penalty required to bend unit

Minimum dE (kcal mol±1)

4.32 3.41 3.11 2.56 2.41 2.07 1.95 1.79 1.68 1.59 1.54 1.42 1.39 1.34

length (Table 1, dE slope). Figure 2 shows the representative regression line for the 55 conformers of C10. Inspection of the geometry of the conformers in each database showed that bending of one methylene bond was the least conformational change observed and that the torsion of the terminal methylene bond was more energycostly to twist than other methylene bonds. The differences in energy between the two lowest-energy conformers of all congeners (C5±C18) are also shown in Table 1, as minimum dE. This value increased rapidly towards the lower congeners, and was 2.07 kcal mol±1 in the case of C10. Corresponding to the large minimum dE, the scatter plot of Figure 2 shows clear separation of the lowest-energy conformer (global minimum) from the second lowest.

694

Molecular conformation of decamethonium congeners

Fig 2 Linear relationship between energy and N±N distance of the 55 conformers of C10. The lowest-energy conformer (global minimum) is Ê . It is the straight-chain conformer with an N±N distance of 14.03 A clearly separated from the rest. Of the two conformers of next shortest N±N distances, the high-energy outlier (H) results from rotation of one bond closest to the methonium head. The other (L), from rotation of one non-terminal bond, represents minimum changes in N±N distance and energy (2.07 kcal mol±1).

This clear separation was observed in all congeners (C5±C18). Among congeners, the minimum dE is another indicator of the relative dif®culty with which the congeners change conformation, and again shows that the shorter the congener, the harder it is to bend. The conformation±activity 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 C10±C12 and Ê was obtained C18 to conform to an N±N distance of 14.03 A by multiplying the energy penalty slope by the distance Ê . In both the C10 and higher and differential from 14.03 A the C10 and lower category, the ED95 values, the energy Ê penalty and the N±N distance differentials from 14.03 A showed identical rank order with no exceptions. Figure 3 shows the relationship between the ED95 (mmol kg±1) values of the C10 and higher congeners and the energy Ê penalties required to conform to the N±N distance of 14.03 A (Fig. 3, upper left) and the relationship between the ED95 (mmol kg±1) values and the N±N distance differentials from Ê (Fig. 3, upper right). Upon logarithmic transform14.03 A ation of the dose requirements, the relationships become linear (Fig. 3, lower left and lower right).

Discussion The genetic algorithm validated for the search for lowenergy molecular conformations (GA search) is a practical version of the general optimization theory11 (see Appendix).

The MMFF94s force ®eld used in this study to minimize the total energy of each conformer is a version of a reliable force ®eld for small molecules and proteins.12 As the number of possible conformers of a molecule increases geometrically with the number of rotatable bonds, it is theoretically impracticable to ascertain the discovery of the least-energy conformer of molecules with many rotatable bonds. Hence, a GA search is particularly useful for our purpose, because, unlike the random search, for which computer time increases geometrically with the number of bonds, the GA search uses an algorithm for which the computer time required increases arithmetically.11 Brie¯y, the GA search is a `global minimizer' that optimizes the population by improving the average ®tness of its individuals. It effectively searches the entire conformational space of a molecule for a collection of ®t samples, without detailed re®nement of each sample during the search. To re®ne 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 ®nal 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 ®rst ef®ciently sample a wide conformational space and then reliably re®ne the samples. For the present study, we used the combination of steps not only to ®nd 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 (C5±C18) 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 ¯exibility and reduce mutual repulsion between the methonium heads. Also readily understandable is the ®nding 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

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Lee and Jones Table 2 Neuromuscular blocking dose requirements of C10 congeners and related factors. ED95 values are from Paton and Zaimis.1 dE=energy penalty Ê (*see text); dN±N=N±N distance difference from 14.03 A Ê (see text concerning C5±C9); dE and dN±N required to conform to the N±N distance of 14.03 A computations were based on the global minimum of each congener. **Excluded from ranking (see text) Congener

C5 C6 C7 C8 C9 C10 C11 C12 C18

ED95 (mg kg±1)

Molecular weight

ED95 (mmol kg±1)

dE (kcal mol±1)

dN±N Ê) (A

>40 >40 1.900 0.160 0.036 0.030 0.060 0.100 1.500

188.36 202.39 216.41 230.44 244.47 258.49 272.52 286.55 370.71

>0.21236 >0.19764 0.00878 0.00069 0.00015 0.00012 0.00022 0.00035 0.00405

* * * * *

6.32 5.04 3.80 2.52 1.27 0.00 1.25 2.52 10.09

0.00 3.28 5.42 12.27

Dreiding13) have permitted crude measurement of the dimensions of molecules and tactile estimation of their ¯exibility. 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 structure±activity relationship to the conformation±activity 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 con®guration 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 mol±1.8 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 Ê of the N±N distance of C10, can decrease from 13 to 11 A without linearly increasing the energy penalty. By contrast, it will take 5±7 kcal mol±1 for C10 to do so. The minimum energy penalty to twist one bond is 0.84 kcal mol±1 for the hypothetical compound vs 2.07 kcal mol±1 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 mol±1 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 mol±1

Rank order ED95, dE, dN±N C10±C12, C18

1 2 3 4

ED95, dN±N C6±C10 ** 5 4 3 2 1

means a 72-to-28 chance in favour of the straight conformer.8 By the same principle, our ®nding 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 mol±1 indicates that C5 will only vibrate around its global minimum, with little chance of assuming a bent conformation. Our data on the conformation±activity 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 signi®cant 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 intersite space of the muscle endplate acetylcholine receptor available to neuromuscular blocking agents at one point of the drug±receptor 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 ®rst 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 acid±base status of the

696

Molecular conformation of decamethonium congeners

Fig 3 The relationship between the neuromuscular blocking dose requirements of C10±C12 and C18 (in the tibialis anterior muscle of the cat, from Ê (left) and the relationship between the dose Paton and Zaimis1) and the energy penalties required to conform to an N±N distance of 14.03 A Ê (right). The non-linear distributions (upper panels) become linear (lower panels) upon requirements and the N±N distance differentials from 14.03 A transformation of the ED95 values from mmol kg±1 to log(mmol kg±1).

biological ¯uid 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 structure±activity studies to the conformation±activity 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 ®t, 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 ®nd and the search results consistent. Geometry at the level of the receptive sites is important in determining how the muscle relaxant molecule may ®t the receptor. Experiments in vitro have shown a distance of Ê between the inner borders of the receptive sites about 30 A 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 Ê (the molecular length of C10) measures close to 20 A between the anionic centres of the receptive sites. The Ê and 20 A Ê is explainable by the discrepancy between 30 A space unavailable to muscle relaxants, different receptors and experimental techniques, treatment artefacts in vitro, the state of receptor desensitization and imprecision in

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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 ®t 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 ®t 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.

Appendix A GA search for molecular conformations, in general terms, starts with the creation of an initial population of conformers by randomly changing the torsion angles of designated rotatable bonds of the molecule to be searched. Each conformer is considered an `individual' with `genes' contained in a `chromosome'. In this instance, each gene represents the torsion angle of a rotatable bond. The population of conformers then evolves, generation after generation, towards a population of higher and higher `®tness' by `selection', `crossover breeding', `mutation' and `elitism'. In this case, ®tness of the individuals means low energy of the conformers. Selection means that individuals of high ®tness are added preferentially to the next generation to participate in further evolution. Selection is done by a `roulette wheel pseudorandom' method in which individuals of greater ®tness are assigned a larger arc in the wheel, which means a greater chance of being selected `randomly' into the `mating pool'. Crossover breeding means crossing of conformers to exchange bonds. Elitism means that the best conformer of each generation is guaranteed a place in the next generation and is protected from mutation. Mutation means random twisting of bonds. Each product of crossover breeding and/or mutation is subjected to partial re®nement by abbreviated energy minimization. All conformers (newly created and pre-existing) are then compared and, keeping the population size constant, un®t conformers are left out while ®t conformers enter the next generation. Generation after generation, the entire population then becomes a collection of conformers of lower and lower average energy. As a result, a GA search ef®ciently samples all available conformational space and produces a

representative collection of ®t conformers for further re®nement. Re®nement means thorough minimization of energy. For large molecules, each search and minimization run of the database may take hours, depending on the computer and the programs. According to the general algorithm, we speci®ed 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 ®t conformers were saved, as long as each had energy within 5 kcal mol±1 per rotatable bond of the ®ttest. For the linear regression, we aimed at producing 30±50 evenly distributed discrete conformers for each congener, all within a range of 10 kcal mol±1 fully minimized. A large energy allowance during the search prevented premature elimination of ®t conformers before ®nal minimization. Preliminary experiments had shown that these parameters would allow a thorough search and yield satisfactory results for all congeners, C5±C18 alike. We used the MMFF94s force ®eld12 in the minimization of the conformers in the database, allowing an unlimited number of iterations for each conformer to converge at a Ê ±1 gradient between iterations. All 0.05 kcal mol±1 A 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 Ê or less from any other inter-atom distance of 0.1 A conformer was considered a duplicate and was deleted.

References

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