The Taxol molecule is a complex diterpenoid with a conformationally immobile core consisting of the fused A-D rings. Side chains critical for bioactivity of the molecule and analogs are those emanating from the core at C2, C4 and C13. To evaluate the energetic performance of various computational schemes, seven Taxol conformations derived from experimental data with differing torsional angles in the C13 fragment were examined. The diversity of C3' side chain orientations is illustrated in Figure 2, in which the diterpenoid core A-C rings have been superimposed, and amplified with reference to specific torsions in Table 1. The first five are those with the highest estimated populations (4 to 35%) with a ΔG range of 0.0–1.3 kcal/mol from an NMR/NAMFIS analysis in CDC1₃ solution. 1112 Structure 1 corresponds to the non-polar conformation observed as the predominant species in CDC1₃ or CD₂Cl₂ as depicted in Figure 3. Characteristic of the form is the "hydrophobic collapse" 13 of the benzamido phenyl at C3' and the benzoyl phenyl at C2. The point is illustrated by the short 5.4 Å distance between the centers of the corresponding phenyl rings. Conformer 2 experiences a similar collapse with a somewhat shorter ring-to-ring distance derived from an alternative set of torsions along the C13 side chain (Table 1). With respect to the close approach between pendant hydrophobic centers, 1 and 2 resemble the semisynthetic analog of Taxol, Taxotere (docitaxel). The latter compound differs constitutionally from Taxol in that the C10 acetate becomes an OH and the NHC(=O)Ph benzamido group is replaced by NHC(=O)O-t-Bu. The single crystal X-ray structure14 and the 2-D NMR (CDCl₃) 6d of Taxotere likewise demonstrate hydrophobic association, in this case between the tert-butyl and the C2 phenyl group. Structure 5 is the polar form frequently found in DMSO-d₆/D₂O. It too exhibits hydrophobic collapse, but between the Taxol phenyl ring attached directly to C3' and the C2-benzoyl ring (Figure 2). Isomers 3 and 4 are extended rotamers in which the C2 benzoyl phenyl ring is distant from both C3' terminal rings. Rotamer 4 corresponds to the recently proposed bioactive conformation of Taxol bound to β-tubulin.9 The perspective given as 4' illustrates the "T" relationship between the three phenyl rings of the molecule (Figure 2). The final two Taxol conformers included in our dataset, 6 and 7, appear together in the unit cell of an X-ray crystal structure determination.15 The latter is a C13 side chain extended structure, while hydrophobically collapsed 6 is very similar to 5. Table 1 complements Figure 3 in providing a selected set of dihedral angles to illustrate explicitly the conformational variation among the seven Taxol torsional isomers.

For Taxol, application of commonly applied force fields as well as the semiempirical methods AM1 and PM3 results in an ordering of conformational energies that is method dependent and mostly inconsistent with experimental data. In an attempt to understand this behavior within the force field framework, we examined the various energy contributions for each conformation and method. In most cases the overwhelming factor is the electrostatic term, a component that is seriously amplified by incorporating ESP charges. The point is likewise illustrated by damping rather than magnifying intramolecular electrostatics. Taxol includes ten polar functionalities: five 3-atom units (four esters, one amide) and five 1- or 2-atom units (three OHs, one ether, one C9 carbonyl). In one set of calculations, the latter five groups were converted to the hydrocarbon analogs (CH₃, CH₂ and C=CH₂, respectively). The optimized structures (Table 5) are very similar to those cited in Tables 2 and 3, but the individual global minima are shifted to different conformers. When the five C(=O)-X units are converted to trans butene moieties, now removing all heteroatoms and most of the electrostatics in the molecule, the energy minima shift once again and the average energy spread between high and low unconstrained energy conformations (i.e. 1-5) diminishes to an average of 2.8 kcal/mol (Table 5). The latter is to be compared with an average of 7.5 and 57.6 kcal/mol for the fully optimized structures of Tables 2 and 3, respectively.

The molecular mechanics results might be ascribed to the presence of "low quality"17 parameters in the force fields employed. Indeed MM3* and MMFF involve 74 and 62 such interactions out of a total of 439 and 555 (17 and 11%), respectively. However, MM2* and AMBER* incorporate only 2 and 6% such parameters, respectively, yet their ability to accurately predict the purported experimental forms is not improved. The two semiempirical methods each locate 2–6 conformations with energies no more than 2.5 kcal/mol above the lowest, but none of the calculations selects the same set of low energy conformers.

Modern force fields with stretch, bend, torsional, hydrogen bond and cross-terms are parameterized primarily within three-bond units (A-B-X-Y). Of the two additional key terms, the van der Waals component operates with a very short range force and essentially prevents atom-atom interpenetration. In the absence of damping, the single long-range interaction that persists from one end of the molecule to the other is the electrostatic contribution. While individual bond dipoles are characteristic of the Allinger MM family of force fields, other molecular mechanics methods employ atomic charges. In either case, no general scheme for parameterizing the electrostatic interaction among multiple polar groups in three-space in terms of conformational energies has yet emerged.

Similarly, within a quantum chemical semiempirical framework, charge polarization notwithstanding, conformational energies are sensitive to method and charge distribution. Inspection of Table 4 reveals that, unlike the force-field results described in Tables 2 and 3, all four semiempirical recipes predict polar conformers 5 and 6 to be the low and "global" minimum energy forms, respectively, when the aqueous solvation continuum model is employed. The one exception, AM1//AM1 suggests both polar and nonpolar forms 6 and 2 to be equally populated. This limited success is negated, however, by the incorrect prediction that the same polar species are also the low energy forms in the gas phase and in the CHCl₃ solvation model. In no instance do the semiempirical calculations predict either nonpolar forms 1 or 2 to be dominant in CHCl₃. As mentioned above, the AM1//AM1 calculations posit equal populations for 2 and 6 within the latter regime, but they simultaneously relegate nonpolar 1 to a higher energy. The remaining semiempirical methods predict the empirically verified nonplar conformers 1 and 2 to be unobservable in the chlorocarbon solvent with energies ranging from 3.8 to 6.9 kcal/mol above the polar collapsed conformation. It might be concluded that the water model is robust, while the chloroform model is ill-parameterized, although the AMSOL literature on solvation18 gives little basis for this contention. Alternatively, the few inerrant predictions for 6, combining both structure and continuum aqueous solvation energies, might well be fortuitous. The likelihood that this is correct is accentuated by the fact that Taxol conformational analysis by NMR has never been performed in pure water, but always as a mixture of DMSO-d₆ and D₂O.5 In addition, in anhydrous methanol, a solvent with a high dielectric and the capacity for explicit hydrogen bonding as in water, the polar form goes undetected. 5b

For the unsuspecting organic or medicinal chemist, however, either interpretation is equally unfortunate. Faced with a large, poly-polar organic structure and a solvation-equipped semiempirical package, the user is limited by the proposition that the aqueous solvation model might provide the correct global minimum, but that other conformers may or may not be assigned an appropriate relative energy. In less polar chlorocarbon solvents, the Taxol structure and other molecules with similar complexity do not appear to be capable of even qualitative ranking by the various methods with respect to energy. An interesting but fortuitous outcome in this respect is that conformer 4, the T or butterfly conformer of Taxol, is predicted to be the dominant conformation by MMFF, AMBER* and MM2* under various protocols (Table 2). Semiempirical models likewise predict it to be of low energy, though not the most stable (Table 4). This conformer was assigned a low population in the multi-conformational analysis of Taxol in chloroform12, used in the fitting of the electron crystallographic density of the β-tubulin/Taxol complex in zinc-stabilized sheets, and ultimately assessed as the binding conformation for Taxol in this structure. 9. A unique, but difficulty observed conformer, computational methodology overestimates its stability and might have led to its discovery by misrepresentation. While the operation of serendipity is much to be desired in the drug seeking process, errant methodology is the least desired path to discovery.

The study was conducted by employing four popular force fields in MacroModel6.5 (MM2*, MM3*, AMBER* and MMFF).2 Each was used in the "gas phase" with two continuum solvation models (CHCl₃, H₂O) 2b with default MacroModel atomic charges (Table 2). To provide a comparison with MacroModel, we also tested solvated MM3(96) and polarization enhanced MM3(2000).21 In addition, the seven AMBER* conformations were fitted with MNDO electrostatic potential (ESP) charges scaled to the 6-31G* level2223 and the calculations repeated (Table 3). The structures were also fully optimized with the AM1 and PM3 semiempirical methods22 and supplemented by AMSOL SM5.4a solvation energies (Table 4). 24