Conformational analysis by energy embedding

The distance geometry approach to conformational calculation has been shown to be very effective at producing large molecular structures satisfying many given, long-range constraints on the interatomic distances. I now present a significant extension of the method that handles strictly geometric constraints as well as before while also locating conformers of very low energy. The main feature of the algorithm is a projection of the molecule from a low energy conformation in a high dimensional space to three dimensions in such a way as to perturb the energy as little as possible. Tests of the method on very small systems with simple energy functions completely explored by independent means show that the global minimum of energy is sometimes attained. In every case the final energy is very low, and geometric constraints are completely satisfied.     

Conformational sampling by a general linearized embedding algorithm

Linearized embedding is a variant on the usual distance geometry methods for finding atomic Cartesian coordinates given constraints on interatomic distances. Instead of dealing primarily with the matrix of interatomic distances, linearized embedding concentrates on properties of the metric matrix, the matrix of inner products between pairs of vectors defining local coordinate systems within the molecule. We developed a pair of general computer programs that first convert a given arbitrary conformation of any covalent molecule from atomic Cartesian coordinates representation to internal local coordinate systems enforcing rigid valence geometry and then generate a random sampling of conformers in terms of atomic Cartesian coordinates that satisfy the rigid local geometry and a given list of interatomic distance constraints. We studied the sampling properties of this linearized embedding algorithm vs. a standard metric matrix embedding program, DGEOM, on cyclohexane, cycloheptane, and a cyclic pentapeptide. Linearized embedding always produces exactly correct bond lengths, bond angles, planarities, and chiralities; it runs at least two times faster per structure generated, and is successful as much as four times as often at refining these structures to full agreement with the constraints. It samples the full range of allowed conformations broadly, although not perfectly uniformly. Because local geometry is rigid, linearized embedding's sampling in terms of torsion angles is more restricted than that of DGEOM, but it finds in some instances conformations missed by DGEOM. © 1992 by John Wiley & Sons, Inc.     

Global energy minimization by rotational energy embedding

Given a sufficiently good empirical potential function for the internal energy of molecules, prediction of the preferred conformations is nearly impossible for large molecules because of the enormous number of local energy minima. Energy embedding has been a promising method for locating extremely good local minima, if not always the global minimum. The algorithm starts by locating a very good local minimum when the molecule is in a high-dimensional Euclidean space, and then it gradually projects down to three dimensions while allowing the molecule to relax its energy throughout the process. Now we present a variation on the method, called rotational energy embedding, where the descent into three dimensions is carried out by a sequence of internal rotations that are the multidimensional generalization of varying torsion angles in three dimensions. The new method avoids certain kinds of difficulties experienced by ordinary energy embedding and enables us to locate conformations very near the native for avian pancreatic polypeptide and apamin, given only their amino acid sequences and a suitable potential function.     

Determination of an empirical energy function for protein conformational analysis by energy embedding

It is quite easy to propose an empirical potential for conformational analysis such that given crystal structures lie near local minima. What is much more difficult, is to devise a function such that the native structure lies near a relatively deep local minimum, at least in some neighborhood of the native in conformation space. An algorithm is presented for finding such a potential acting on proteins where each amino acid residue is represented by a single point. When the given structure is either an α-helical, β-strand, or hairpin bend segment of pancreatic trypsin inhibitor, the resulting potential function in each case possesses a deep minimum within 0.10 Å of the native conformation. The improved energy embedding algorithm locates a marginally better minimum in each case only 0.1–1.3 Å away from the respective native state. In other words, this potential function guides a conformational search toward structures very close to the native over a wide range of conformation space.     

Conformational energy analysis of substituted diphenylethanes: Part II. Empirical energy calculations on stilbene dihalogenides

The geometry and energy of the stable conformations of the isomeric forms of 1,2-halogeno-1,2-diphenylethanes have been obtained by means of empirical energy functions. A minimization of the conformational energy with respect to the torsion angles and the valence angles around the asymmetrically substituted carbon atoms has been carried out. The evaluated populations of the stable conformations showed good agreement with available experimental data. CNDO/2 calculations on the low-energy conformations of the isomeric forms of 1,2-difluoro-, 1,2-fluorochloro-, and 1,2-dichlorodiphenylethane have been carried out. These yielded improved estimates of the dipole moments for the dichloro isomers.     

Conformational energy penalties of protein-bound ligands

The conformational energies required for ligands to adopt their bioactive conformations were calculated for 33 ligand–protein complexes including 28 different ligands. In order to monitor the force field dependence of the results, two force fields, MM3 and AMBER, were employed for the calculations. Conformational analyses were performed in vacuo and in aqueous solution by using the generalized Born/solvent accessible surface (GB/SA) solvation model. The protein-bound conformations were relaxed by using flat-bottomed Cartesian constraints. For about 70% of the ligand–protein complexes studied, the conformational energies of the bioactive conformations were calculated to be 3 kcal/mol. It is demonstrated that the aqueous conformational ensemble for the unbound ligand must be used as a reference state in this type of calculations. The calculations for the ligand–protein complexes with conformational energy penalties of the ligand calculated to be larger than 3 kcal/mol suffer from uncertainties in the interpretation of the experimental data or limitations of the computational methods. For example, in the case of long-chain flexible ligands (e.g. fatty acids), it is demonstrated that several conformations may be found which are very similar to the conformation determined by X-ray crystallography and which display significantly lower conformational energy penalties for binding than obtained by using the experimental conformation. For strongly polar molecules, e.g. amino acids, the results indicate that further developments of the force fields and of the dielectric continuum solvation model are required for reliable calculations on the conformational properties of this type of compounds.     

Conformational energy surface of 1,2-cyclooctadiene

Boyd's iterative force-field has been used to investigate the conformational energy surface of 1,2-cyclooctadiene. Two energy-minimum conformations with similar strain energies have been found; one has a two-fold axis of symmetry, whereas the other lacks symmetry. The calculated strain-energy barrier for interconversion of the two conformations is 8.8 kcal mol^?1.     

A dimensionally scaled generalization of constrained search energy density functionals

A dimensionally scaled generalization of constrained search density functional theory allows access to some simple model problems. These might be valuable for testing and perhaps improving conventional density functionals. One specific model problem is solved: When extrapolated to infinite numbers of spatial dimensions, the energy density functional for spherically symmetric, two-electron systems can be calculated to arbitrary accuracy. © 1994 John Wiley & Sons, Inc.     

Conformational analysis of lipid molecules by self-organizing maps

The authors have studied the use of the self-organizing map (SOM) in the analysis of lipid conformations produced by atomic-scale molecular dynamics simulations. First, focusing on the methodological aspects, they have systematically studied how the SOM can be employed in the analysis of lipid conformations in a controlled and reliable fashion. For this purpose, they have used a previously reported 50 ns atomistic molecular dynamics simulation of a 1-palmitoyl-2-linoeayl-sn-glycero-3-phosphatidylcholine (PLPC) lipid bilayer and analyzed separately the conformations of the headgroup and the glycerol regions, as well as the diunsaturated fatty acid chain. They have elucidated the effect of training parameters on the quality of the results, as well as the effect of the size of the SOM. It turns out that the main conformational states of each region in the molecule are easily distinguished together with a variety of other typical structural features. As a second topic, the authors applied the SOM to the PLPC data to demonstrate how it can be used in the analysis that goes beyond the standard methods commonly used to study the structure and dynamics of lipid membranes. Overall, the results suggest that the SOM method provides a relatively simple and robust tool for quickly gaining a qualitative understanding of the most important features of the conformations of the system, without a priori knowledge. It seems plausible that the insight given by the SOM could be applied to a variety of biomolecular systems and the design of coarse-grained models for these systems.     

Conformational energy surfaces of triplet-state isomeric methyloxiranes

A conformational study was carried out on the three ring-opened structures of triplet methyloxirane with a minimal Gaussian basis set, within the unrestricted Hartree–Fock framework. For the two structures energy surfaces E(θ₁, θ₂) were generated, where θ₁ measures the methyl rotation and θ₂ is associated with the torsion about the other C? C bond. For the third structure an energy hypersurface E(θ₁, θ₂, θ₃) was generated, where energy was a function of methyl rotation θ₁ and two nonequivalent C? O rotations θ₂ and θ₃. Analysis of the surfaces revealed the locations and relative energies of the critical points (minima, saddle points, and maxima). The overall stereochemical finding was that these ring-opened triplet C₃H₆O species possessed rather flexible structures.     

Conformational energy landscapes of liquid crystal molecules

The conformational energy landscape of the prototypical nematic liquid crystal 4-pentyl-4cyanobiphenyl (5CB) is studied using first principles computer modelling. It is found that the most favourable conformation occurs when the two constituent phenyl rings are inclined at an angle of 31 with respect to each other. Also, the orientation of the alkyl chain is found to have an important influence on the ring-ring torsional potential. We fit the energy surface of these coupled torsions to yield an accurate intramolecular potential for use in empirical modelling. To test the strength of the coupling between the alkyl tail and the phenyl rings and the cyano group, we also calculate potentials for the relative orientation of the phenyl rings in biphenyl and cyanobiphenyl (0CB). Our calculations are performed using density functional theory using pseudo-potentials and the generalized gradient approximation to exchange and correlation. The molecular electronic wavefunction is expanded in terms of a plane wave basis set. We compare our results with recent NMR and Gaussian-based quantum chemistry calculations where available.     

Conformational analysis of cinnamanilides

The conformational analysis of cinnamanilides has been carried out using IR spectroscopy. All the anilides studied were found to exist as equilibrium mixtures ofs-cis ands-trans forms in benzene. Thes-cis form was predominant over thes-trans in all the anilides except in thep-nitro anilide in which thes-trans form was predominant. The relative stabilities of the conformers were found to depend upon the electrostatic repulsions between the anilide nitrogen and the β-carbon atom in thes-trans form and those between the π-electrons of the C=O and C=C bonds in thes-cis form.     

Conformational analysis of tetraarylethanes

NMR evidence establishes that both diastereomers of 1,2-diphenyl-1,2-bis(4-pyridyl)ethane (2), identified by optical resolution of the racemic form, exist predominantly in the anti conformation. Furthermore, empirical force field calculations show that the gauche conformer of 1,1,2,2-tetrakis(2,6-dimethylphenyl)ethane (3) is less stable by ca. 10 $\text{kcal}\text{mol}$ than the anti structure. It thus appears that neither polar effects nor steric congestion are effective in reversing the marked preference of 1,1,2,2-tetraphenylethane (1) and other unclamped tetraarylethanes for an anti ground state. In contrast, as predicted by empirical force field calculations and confirmed by X-ray and NMR evidence, the ground state structure of 9,9'-bifluorenyl (4) is gauche. The conformational behavior of 1–4 is discussed in terms of the intramolecular aryl ring stacking in clamped and unclamped tetraarylethanes.     

Conformational analysis of dimethylmethylphosphonate

The results of a CNDO/2 conformation analysis on dimethylmethylphosphonate are reported. Six stable conformers were found; their relative stabilities can be understood in terms of steric hindrance and gauche effect. Calculated barriers to internal rotation around P—O and O—C bonds are tabulated.     

Conformational analysis of chiral helical perfluoroalkyl chains by VCD

Vibrational circular dichroism (VCD) technique successfully revealed the absolute configuration of the biased helix of perfluoroalkyl chains in solution with the aid of theoretical calculations, which was supported by an X-ray crystallographic study.     

Conformational analysis of colchicine and isocolchicine by molecular mechanics

The structures of isocolchicine ( ) and colchicine ( ) have been calculated using the MMX routine. The low energy conformations for isocolchicine and colchicine fit well with x-ray crystallographic data. The B ring atropisomer of isocolchicine, which can be spectroscopically observed, is calculated to be <1 kcal/mole higher in energy than . The boat-boat inversion conformer of colchicine, which has been predicted to be important in the binding of to tubulin, is also calculated. The B ring geometry of this isomer does not differ to the extent previously predicted.