MM3 MODELING OF ALDOPENTOSE PYRANOSE RINGS

MM3 (version 1992, ?=3.0) was used to study the ring conformations of d-xylopyranose, d-lyxopyranose and d-arabinopyranose. The energy surfaces exhibit low-energy regions corresponding to chair and skew forms with high-energy barriers between these regions corresponding to envelope and half-chair forms. The lowest energy conformer is ⁴ C ₁ for α- and β-xylopyranose and α- and β-lyxopyranose, and the lowest energy conformer is ¹ C ₄ for α- and β-arabinopyranose. Only α-lyxopyranose exhibits a secondary low-energy region (¹ C ₄) within 1 kcal/mol of its global minimum. Overall, the results are in good agreement with NMR and crystallographic results. For many of these molecules, skew conformations are found with relatively low energies (2.5 to 4 kcal/mol above lowest energy chair form). The ² S _O and ¹ C ₄ conformers of crystalline benzoyl derivatives of xylopyranose are in secondary low-energy regions on the β-xylopyranose surface, within 3.8 kcal/mol of the global ⁴ C ₁ minimum.     

Monte Carlo sampling algorithm for searching a scale-transformed energy space of polypeptides

A Monte Carlo sampling algorithm for searching a scale-transformed conformational energy space of polypeptides is presented. This algorithm is based on the assumption that energy barriers can be overcome by a uniform sampling of the logarithmically transformed energy space. This algorithm is tested with Met-enkephalin. For comparison, the entropy sampling Monte Carlo (ESMC) simulation is performed. First, the global minimum is easily found by the optimization of a scale-transformed energy space. With a new Monte Carlo sampling, energy barriers of 3000 kcal/mol are frequently overcome, and low-energy conformations are sampled more efficiently than with ESMC simulations. Several thermodynamic quantities are calculated with good accuracy.     

Energy minimization of peptide analogues using genetic algorithms

A genetic algorithm is used to minimize the energy of peptide analogues in the dihedral angle space. It is interfaced to MOPAC, which computes the energy employing the AM1 Hamiltonian. The genetic algorithm identified the global energy minimum of glycine dipeptide analogue, alanine dipeptide analogue, diglycine, and dialanine. It identified three low-energy conformations of tetraalanine, including the reported global minimum, all of which contained three hydrogen bonds. A structure with a lower energy than the reported global minimum has been generated in which one hydrogen bond is replaced by another one. © 1995 John Wiley & Sons, Inc.     

MM3 Modeling of Ribose and 2-Deoxyribose Ring Puckering

ABSTRACT

Conformational energy maps for furanosyl and pyranosyl rings of α- and β-ribose and 2-deoxyribose were generated with the molecular mechanics program MM3. For the furanosyl tautomers, low-energy Northern and Southern minima were found. For the pyranosyl rings, lowest-energy minima corresponded to chair forms. Hydrogen-hydrogen coupling constants for the minimal-energy conformers were calculated based on Karplus equations. Computational and experimental results indicate that several tautomeric forms of ribose and 2-deoxyribose exist in multiple conformations in solution. Ring conformations of related crystal structures have energies within ～2 kcal/mol of the calculated global minima.     

A Conformational Study on Silacyclohexane. Comparison of ab initio (HF,MP2), DFT,and Molecular Mechanics Calculations. Conformational Energy Surface of Silacyclohexane

The structures and relative energies for the basic conformations of silacyclohexane 1 have been calculated using HF, RI‐MP2, RI‐DFT and MM3 methods. All methods predict the chair form to be the dominant conformation and all of them predict structures which are in good agreement with experimental data. The conformational energy surface of 1 has been calculated using MM3. It is found that there are two symmetric lowest energy pathways for the chair‐to‐chair inversion. Each of them consists of two sofa‐like transition states, two twist forms with C₁ symmetry (twist‐C₁), two boat forms with Si in a gunnel position (C₁ symmetry), and one twist form with C₂ symmetry (twist‐C₂). All methods calculate the relative energy to increase in the order chair < twist‐C₂ < twist‐C₁ < boat. At the MP2 level of theory and using TZVP and TZVPP (Si atoms) basis sets the relative energies are calculated to be 3.76, 4.80, and 5.47 kcal mol^–1 for the twist‐C₂, twist‐C₁, and boat conformations, respectively. The energy barrier from the chair to the twisted conformations of 1 is found to be 6.6 and 5.7 kcal mol^–1 from MM3 and RI‐DFT calculations, respectively. The boat form with Si at the prow (C_s symmetry) does not correspond to a local minimum nor a saddle point on the MM3 energy surface, whereas a RI‐DFT optimization under C_s symmetry constraint resulted in a local minimum. In both cases its energy is above that of the chair‐to‐twist‐C₁ transition state, however, and it is clearly not a part of the chair‐to‐chair inversion.     

A theoretical study of the rotational isomers of nitrosomethanol by semiempirical (AM1) and ab initio methods

The conformational potential energy surface as a function of the two internal torsion angles in C-nitrosomethanol has been obtained using the semiempirical AM1 method. Optimized geometries are reported for the local minima on this surface and also for the corresponding points on the HF/6-31G, 6-31G*, and 6-31G** surfaces. All methods predict cis and trans minima which occur in degenerate pairs, each pair being connected by a transition state of C_s symmetry. The AM1 structures are found to compare well with the corresponding ab initio structures. Ab initio HF/6-31G and HF/6-31G* harmonic vibrational frequencies are reported for the cis and trans forms of nitrosomethanol. When scaled appropriately the calculated frequencies are found to compare well with experimental frequencies. The ab initio calculations predict the energy barrier for cis → trans isomerization to be between 5.8 and 6.5 kcal/mol with the trans → cis isomerization barrier lying between 2.3 and 6.5 kcal/mol. The corresponding AM1 energy barriers are around 1 kcal/mol lower in energy. The ab initio calculations predict the barrier to conversion between the two cis rotamers to be very small with the AM1 value being around 1 kcal/mol. Both AM1 and ab initio calculations predict interconversion between trans rotamers to require between 1.2 and 1.4 kcal/mol.     

Efficient search for all low energy conformations of polypeptides by Monte Carlo methods

The Metropolis Monte Carlo method has been added to the program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space. With this extension, different strategies for global minimization of the semiempirical energy function ECEPP/2 by various temperature schedules and restriction of conformational space were tested for locating local minimum conformations with low energy of the pentapeptide Met-enkephalin. In total, 1881 conformations below ?10 kcal/mol were found. These conformations could be represented by 77 nonidentical conformations which were analysed for their pattern of hydrogen bonds, types of tight turn, pairwise root-mean-square-deviation (rmsd), Zimmermann codes and side chain conformations. All low energy conformations below ?10.4 kcal/mol show strong similarity to the global minimum conformation in the backbone structure.     

A conformational analysis of 3′-azido-3′-deoxythymidine

An extensive conformational analysis of 3′-azido-3′-deoxythymidine (AZT) was performed at the semiempirical AM1 level with full relaxation of all geometric parameters and careful consideration of furan puckering and the rotational states of the thymine—furan, furan—azide, furan—methylene, and methylene—hydroxyl bonds. The search located 70 conformers, 21 of which have relative energies within 2.5 kcal/mol of the global minimum. Several geometric features, including various forms of hydrogen bonding, within this selected lowenergy subset were examined in terms of their relative contributions to the conformational states of AZT. Hydrogen bonding of thymine's position 2 carbonyl oxygen atom to the hydroxymethyl group (O₂? ;HO), which until recently has not been mentioned in the literature, is observed in a few low-energy AM1 conformations; however, this form is less favored at the AM1 level than the usually depicted modes involving the thymine moiety with the oxygen atoms of the hydroxyl and furan groups (H₆? ;OH and H₆? O_fur, as observed in the two crystallographically independent structures), as well as that involving the hydroxyl hydrogen and furan oxygen atoms (OH? O_fur, which also has not been mentioned for AZT in the literature until recently). The AM1-optimized geometries agree more closely with nuclear magnetic resonance data than with crystallographic structures and bear little resemblance to molecular mechanics results. The present study shows no evidence of a single dominant conformation or single structural parameter that determines AZT's conformational states. In contrast to our previous analogous study of cGMP, this computational study of AZT does not show strong evidence of a syn conformation with hydrogen bonding involving the base.     

Structures of protonated arginine dimer and bradykinin investigated by density functional theory: further support for stable gas-phase salt bridges

The gas-phase structures and energetics of both protonated arginine dimer and protonated bradykinin were investigated using a combination of molecular mechanics with conformational searching to identify candidate low-energy structures, and density functional theory for subsequent minimization and energy calculations. For protonated arginine dimer, a good correlation (R = 0.88) was obtained between the molecular mechanics and EDF1 6-31+G* energies, indicating that mechanics with MMFF is suitable for finding low-energy conformers. For this ion, the salt-bridge or ion-zwitterion form was found to be 5.7 and 7.2 kcal/mol more stable than the simple protonated or ion-molecule form at the EDF1 6-31++G** and B3LYP 6-311++G** levels. For bradykinin, the correlation between the molecular mechanics and DFT energies was poor (R = 0.28), indicating that many low-energy structures are likely passed over in the mechanics conformational searching. This result suggests that structures of this larger peptide ion obtained using mechanics calculations alone are not necessarily reliable. The lowest energy structure of the salt-bridge form of bradykinin is 10.6 kcal/mol lower in energy (EDF1) than the lowest energy simple protonated form at the 6-311G* level. Similarly, the average energy of all salt-bridge structures investigated is 13.6 kcal/mol lower than the average of all the protonated forms investigated. To the extent that a sufficient number of structures are investigated, these results provide some additional support for the salt-bridge form of bradykinin in the gas phase.     

Conformational properties of permethylcyclohexane as compared to cyclohexane: A force field study

The conformational properties of the recently synthesized highly strained permethylcyclohexane molecule 2 have been studied by empirical force field calculations using three different potentials (CFF, MM2, MM2′) and second-derivative optimization methods. A comparison of the results with the conformational behavior of parent cyclohexane 1 leads to the following conclusions: The best conformation of 2 is a chair minimum whose six-membered ring is flatter than that of 1 , due to the strong H…H repulsions introduced by the methyl groups. The twist minimum of 2 is energetically less favorable than the chair by an amount similar to 1 . A potential energy barrier Δ V^# for the chair inversion of 2 of 15.32 kcal/mol results with the CFF, only about three kcal/mol higher than for 1 . The free energy of activation ΔG^# for this process obtained with the CFF is 16.96 kcal/mol (at 333 K) and agrees well with the experimental value of 16.7(2) kcal/mol.¹ MM2 and MM2′ give substantially lower and higher potential energy inversion barriers Δ V^# of 9.03 and 20.29 kcal/mol, respectively, which is attributed to inappropriate torsional energy terms in these force fields. The characteristic difference in the conformational behavior of 2 and 1 concerns the boat forms which are substantially less favorable in the per-methyl compound than in 1 . Expectedly, strong H…H repulsions between the 1,4 diaxial flagpole–bowsprit methyl groups in 2 are responsible for this difference. The particularly high strain of the boat forms of 2 leads to flexibility differences as compared to 1 which in turn affect the relative entropies of the various statiomers (stationary point conformations); e.g., the chair ring inversion activation entropies of 2 and 1 are predicted by the CFF calculations to have opposite signs (?4.82 and 3.41 cal/mol K, respectively, at 298 K). The twist and half-twist statiomers of 2 are much more rigid than those of 1 , which is a consequence of the substantially larger boat barriers along their pseudorotational interconversion paths. The boat transition state separating two enantiomeric twist minima represents a barrier calculated to be more than tenfold higher for 2 than for 1 (CFF Δ V^# values 11.14 and 0.92 kcal/mol, respectively); likewise the half-boat chair inversion barrier of 2 is calculated 5.07 kcal/mol less favorable than the respective half-twist barrier. These statiomers are practically equienergetic in the case of 1 . Except for the axial flagpole–bowsprit CH₃ substituents of the boat forms, the methyl groups of all the relevant calculated statiomers of 2 are more or less staggered. The rotational barrier of the equatorial methyl groups of the chair minimum of 2 is computationally predicted to be 5.78 kcal/mol (ΔG^#), i.e., unusually high. Interesting vibrational effects are brought about by the strong H…H repulsions in 2 ; thus the chair minimum has a largest C? H stretching frequency estimated to be 3050 cm^?1 and involves several particularly low frequencies which have a substantial influence on its entropy. CFF calculations for the lower homologue permethylcyclopentane 5 indicate that its pseudorotational properties are similar to those of cyclopentane 4 , in contradistinction to the pair 2/1 .     

Mechanisms of conformational chirality inversion in bicyclo[4.2.1]nonan-9-one and bicyclo[4.2.2]decane as studied in two-parametric torsional energy surfaces

With the purpose of deciphering conformational inversion processes of typical mobile bicyclic molecules, torsional energy surfaces near the enantiomers of bicyclo[4.2.1]nonan-9-one ( 1 ) and bicyclo-[4.2.2]decane ( 2 ) were prepared using molecular mechanics with an improved two-bond drive technique. Inversion of 1 takes place most favorably via a C_s transition state with the tetramethylene chain over the ethano bridge [ 1B , ΔH^± 6.1 (calculated) vs. 6.8 (observed) kcal/mol]. An alternative pathway involving a C_s local energy minimum ( 1C ), in which the tetramethylene chain is bent over the carbonyl, has a barrier 2.4 kcal higher than 1B . The global energy minimum conformation of 2 has boat–chair cyclooctane and twist–boat cyclohexane rings (BCTB ), and enantiomerizes into its mirror image (BCTB ') via three intermediates: TCTB , CB , and TCTB '. The highest point in the proposed pathway, a saddlepoint CB , is calculated to lie 8.0 kcal/mol above BCTB (observed ΔH^± 7.8 kcal/mol). The advantage of the two-parametric over the one-parametric torsional energy surface is discussed.     

The effect of aqueous solvation upon alpha-helix formation for polyalanines

The incremental free energies of aqueous solution for acetyl(ala)NNH2 in its extended unfolded and alpha-helical conformations are compared using the SM5.2 solvation method of Cramer and Truhlar. A combination of density functional theory (DFT) at the B3LYP/D95(d,p) and AM1 has been employed using the ONIOM method. The incremental solvation energies of alpha-helical structures are very similar for both ONIOM and AM1 optimized structures as these structures do not significantly change upon solution. However, the conformations of the unfolded peptides change from extended beta-strand to polyproline II conformations upon aqueous solution. The incremental solvation free energy per residue of the polyproline II structure is about 2 kcal/mol/residue greater than that for the alpha-helix, representing an upper limit for the difference between the solvation energies. However, most of this difference disappears when the energy required to distort the optimized gas-phase extended beta-strand structure to the optimized polyproline II solution structure is included in the analysis, leaving an estimated difference in incremental solvation free energy of 0.3-0.5 kcal/mol favoring the unfolded structure. The solution structure sacrifices the stability derived from the intramolecular C5 H-bonds for more favorable interactions with the aqueous solvent.     

Conformational preferences and internal rotation in alkyl- and phenyl-substituted thiourea derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylthiourea, ethylthiourea, isopropylthiourea, tert-butylthiourea, and phenylurea, using the MP2/aug-cc-pVDZ method. Analysis of alkylthioureas shows that conformations, with alkyl groups cis to the sulfur atom, are more stable (by 0.4-1.5 kcal/mol) than the trans forms. All minima adopt anti configurations with respect to nitrogen pyramidalization, whereas syn configurations are not stationary points on the MP2 potential surface. In contrast, analysis of phenylthiourea reveals that a trans isomer in a syn geometry is the global minimum, whereas a cis isomer in an anti geometry is a local minimum with a relative energy of 2.7 kcal/mol. Rotation about the C(sp(2))-N bond in alkyl and phenyl thioureas is slightly more hindered (9.1-10.2 kcal/mol) than the analogous motion in the unsubstituted molecule (8.6 kcal/mol). The maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl substituents are predicted to be 1.2, 8.9, 8.6, 5.3, and 0.9 kcal/mol, respectively. Corresponding PESs are consistent with the experimental dihedral angle distribution observed in crystal structures. The results of the electronic structure calculations are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of selected torsion parameters and one of the van der Waals parameters for sulfur.     

Monte Carlo temperature basin paving with effective fragment potential: an efficient and fast method for finding low-energy structures of water clusters (H2O)20 and (H2O)25

Determining low-energy structures of large water clusters is a challenge for any optimization algorithm. In this work, we have developed a new Monte Carlo (MC)-based method, temperature basin paving (TBP), which is related to the well-known basin hopping method. In the TBP method, the Boltzmann weight factor used in MC methods is dynamically modified based on the history of the simulation. The states that are visited more are given a lower probability by increasing their temperatures and vice versa. This allows faster escapes from the states frequently visited in the simulation. We have used the TBP method to find a large number of low-energy minima of water clusters of size 20 and 25. We have found structures energetically same to the global minimum structures known for these two clusters. We have compared the efficiency of this method to the basin-hopping method and found that it can locate the minima faster. Statistical efficiency of the new method has been investigated by running a large number of trajectories. The new method can locate low-energy structures of both the clusters faster than some of the reported algorithms for water clusters and can switch between high energy and low-energy structures multiple times in a simulation illustrating its efficiency. The large number of minima obtained from the simulations is used to get both general and specific features of the minima. The distribution of minima for these two clusters based on the similarity of their oxygen frames shows that the (H(2)O)(20) can have different variety of structures, but for (H(2)O)(25), low-energy structures are mostly cagelike. Several (H(2)O)(25) structures are found with similar energy but with different cage architectures. Noncage structures of (H(2)O)(25) are also found but they are 6-7 kcal/mol higher in energy from the global minimum. The TBP method is likely to play an important role for exploring the complex energy landscape of large molecules.     

Low-energy tautomers and conformers of neutral and protonated arginine.

The relative stabilities of zwitterionic and canonical forms of neutral arginine and of its protonated derivative were studied by using ab initio electronic structure methods. Trial structures were first identified at the PM3 level of theory with use of a genetic algorithm to systematically vary geometrical parameters. Further geometry optimizations of these structures were performed at the MP2 and B3LYP levels of theory with basis sets of the 6-31++G** quality. The final energies were determined at the CCSD/6-31++G** level and corrected for thermal effects determined at the B3LYP level. Two new nonzwitterionic structures of the neutral were identified, and one of them is the lowest energy structure found so far. The five lowest energy structures of neutral arginine are all nonzwitterionic in nature and are clustered within a narrow energy range of 2.3 kcal/mol. The lowest energy zwitterion structure is less stable than the lowest nonzwitterion structure by 4.0 kcal/mol. For no level of theory is a zwitterion structure suggested to be the global minimum. The calculated proton affinity of 256.3 kcal/mol and gas-phase basicity of 247.8 kcal/mol of arginine are in reasonable agreement with the measured values of 251.2 and 240.6 kcal/mol, respectively. The calculated vibrational characteristics of the low-energy structures of neutral arginine provide an alternative interpretation of the IR-CRLAS spectrum (Chapo et al. J. Am. Chem. Soc. 1998, 120, 12956-12957).     

DFT study of α-maltose: influence of hydroxyl orientations on the glycosidic bond

The result of DFT geometry optimization of 68 unique α-maltose conformers at the B3LYP/6-311++G** level of theory is described. Particular attention is paid to the hydroxyl group rotational positions and their influence on the glycosidic bond dihedral angles. The orientation of lone pair electrons across the bridging hydrogen bonds are implicated in directing the glycosidic dihedral angles with for example, conformers gg-gg and gt-gt, having different minimum energy conformations for the clockwise (c) and the reverse clockwise (r) forms. Conformers tg-gg, gg-tg, tg-tg, gt-gg, and gg-gt were studied, to understand the intermediate glycosidic bond conformations. The conformation, tg-gg-c, was found to be the lowest energy structure. When the hydroxyl groups on each glucose residue were made to point in opposite directions, i.e., c/r and r/c, the optimized structures were found to have high relative energies. Several optimized ‘kink’ structures were found around (, ψ_H) ∼(−40°, −40°), the lowest relative energy conformation being ∼3 kcal/mol. “Kink” conformations are observed in crystalline CA-10 and CA-14mers. Band-flip conformations, also observed in X-ray structures of CA-26 fragments, were studied with the lowest energy α-maltose conformations ∼4.0 kcal/mol above the global energy minimum. Several trends in geometry resulting from hydroxyl rotamer directions are described. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Names are necessary to report factually on available data; however, the USDA neither guarantees nor warrants the standard of the product, and the use of the name by USDA implies no approval of the product to the exclusion of others that may also be suitable.     

Torsion angle preference and energetics of small-molecule ligands bound to proteins

Small organic molecules can assume conformations in the protein-bound state that are significantly different from those in solution. We have analyzed the conformations of 21 common torsion motifs of small molecules extracted from crystal structures of protein-ligand complexes and compared them with their torsion potentials calculated by an ab initio DFT method. We find a good correlation between the potential energy of the torsion motifs and their conformational distribution in the protein-bound state: The most probable conformations of the torsion motifs agree well with the calculated global energy minima, and the lowest torsion-energy state becomes increasingly dominant as the torsion barrier height increases. The torsion motifs can be divided into 3 groups based on torsion barrier heights: high (>4 kcal/mol), medium (2-4 kcal/mol), and low (<2 kcal/mol). The calculated torsion energy profiles are predictive for the most preferred bound conformation for the high and medium barrier groups, the latter group common in druglike molecules. In the high-barrier group of druglike ligands, >95% of conformational torsions occur in the energy region <4 kcal/mol. The conformations of the torsion motifs in the protein-bound state can be modeled by a Boltzmann distribution with a temperature factor much higher than room temperature. This high-temperature factor, derived by fitting the theoretical model to the experimentally observed conformation occurrence of torsions, can be interpreted as the perturbation that proteins inflict on the conformation of the bound ligand. Using this model, it is calculated that the average strain energy of a torsion motif in ligands bound to proteins is approximately 0.6 kcal/mol, a result which can be related to the lower binding efficiency of larger ligands with more rotatable bonds. The above results indicate that torsion potentials play an important role in dictating ligand conformations in both the free and the bound states.     

Conformational analysis of model compounds of vitamin D by theoretical calculations

A conformational analysis of two model compounds of vitamin D was carried out by means of theoretical computations, Ab initio calculations were carried out using the standard 6-31G* basis set at the Hartree–Fock (HF) level of theory. In addition, the Møller–Plesset (MP2) correlation treatment was applied on the simplest model. Semiempirical calculations were also performed using the AM1 Hamiltonian. The results predict stable A-ring twist forms with energies in the order of 4–6 kcal/mol relative to the global minimum, significantly higher than those reported from molecular mechanics calculations. In addition, a folded conformation was found by the HF optimizations; however, its stability is predicted to be very poor. Comparison of the theoretical results with experimental data is discussed. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1647–1655, 1997