Distinction and Quantification of Noncovalent Dispersive and Hydrophobic Effects

The possibilities of comparing computational results of noncovalent interactions with experimental data are discussed, first with respect to intramolecular interactions. For these a variety of experimental data such as heats of formation, crystal sublimation heats, comparison with energy minimized structures, and spectroscopic data are available, but until now largely have not found widespread application. Early force field and QM/MP2 calculations have already shown that the sublimation heats of hydrocarbons can be predicted with an accuracy of ±1%. Intermolecular interactions in solution or the gas phase are always accompanied by difficult to compute entropic contributions, like all associations between molecules. Experimentally observed T∆S values contribute 10% to 80% of the total ∆G, depending on interaction mechanisms within the complexes, such as, e.g., hydrogen bonding and ion pairing. Free energies ∆G derived from equilibrium measurements in solution allow us to define binding increments ∆∆G, which are additive and transferable to a variety of supramolecular complexes. Data from more than 90 equilibrium measurements of porphyrin receptors in water indicate that small alkanes do not bind to the hydrophobic flat surfaces within a measuring limit of ∆G = ±0.5 kJ/mol, and that 20 functions bearing heteroatoms show associations by dispersive interactions with up to ∆G = 8 kJ/mol, roughly as a function of their polarizability. Aromatic systems display size-dependent affinities ∆G as a linear function of the number of π-electrons.

Molecular mechanics (MM4) study of amines

The MM4 force field has been extended to include aliphatic amines. About 20 amines have been examined to obtain a set of useful molecular mechanics parameters for this class. The vibrational spectra of seven amines (172 frequencies) calculated by MM4 have an overall rms error of 27 cm(-1), compared with corresponding MM4 value of 24 cm(-1) for alkanes. The rms and signed average errors of the moments of inertia of nine simple amines compared with the experimental data were 0.18% and -0.004%, respectively. The heats of formation of 30 amines were also studied. The MM4 weighted standard deviation is 0.41 kcal/mol, compared with experiment. Electronegativity effects occur in the hydrocarbon portion of an amine from the nitrogen, and are accounted for by including electronegativity induced changes in bond lengths and angles, and induced dipole-dipole interactions in the molecule. Negative hyperconjugation results from the presence of the lone pair of electrons on nitrogen, and leads to the Bohlmann bands in the infrared, and also to strong and unusual geometric changes in the molecules (Bohlmann effect), all of which are fairly well accounted for. The conformational energies in amines appear to be less straightforward than those for most other classes of molecules, apparently because of the Bohlmann effect, and these are probably not yet completely understood. In general, the agreement between the MM4 calculated results and the available data is reasonably good.

Origin of Co-Conformational Selectivity in a [3]rotaxane

Co-conformational selectivity and structure-energy relationships in a [3]rotaxane are investigated with a recently developed multiple-sampling and statistical analysis procedure for modeling interlocked molecules and mechanical molecular devices. The results presented confirm the experimentally observed co-conformational selectivity. The theoretical calculations reveal that ring-ring interactions are very small and ring-shaft inter-component interactions decide the co-conformational preference. In particular, it is found that stronger ring binding at the central binding station on the shaft than at either of the two terminal binding stations gives rise to the observed co-conformational preference. Analysis of radius of gyration data shows that co-conformational isomerism is not strongly correlated to coiling of the shaft.

Molecular Mechanics (MM4) Study of Fluorinated Hydrocarbons

A molecular mechanics study of small saturated hydrocarbons (up to C-6) substituted by up to six fluorines has been carried out with the MM4 force field. A parameter set has been developed for use in the calculation of bond lengths, bond angles, torsion angles, conformational energies, barriers to rotation, dipole moments, moments of inertia, and vibrational frequencies for these compounds. The results are mostly in fair to good agreement with experiment and ab initio calculations. The high electronegativity of fluorine leads to serious geometric consequences in these compounds, but these consequences can be dealt with adequately by suitable cross-terms in the force constant matrix, and by recognizing that some of the reference bond lengths and angles (l(0), theta(0)) and the corresponding stretching and bending constant parameters (k(s), k(theta)) that are usually thought of as constants must in fact be treated as functions of the electronegativity of the substituents. Additionally, the heavy mass of the fluorine (relative to the mass of hydrogen in alkanes) leads to large values for other cross-terms that were found to be unimportant in hydrocarbons. Conformational equilibria for polyfluorinated compounds are affected by the delta-two effect well-known in carbohydrates. A few larger fluorinated and polyfluorinated alkanes, including perfluoropropane, perfluorobutane, and Teflon, have also been studied.

Alcohols, ethers, carbohydrates, and related compounds. IV. Carbohydrates

Ab initio calculations [B3LYP/6-311++G(2d,2p)] have been carried out on 84 conformations of 12 different sugars (hexoses), in both pyranose and furanose forms, with the idea of generating a data base for carbohydrate structural energies that may be used for developing the predictive value of molecular mechanics calculations for carbohydrates. The average value for the apparent gas phase anomeric effect for a series of 31 pairs of pyranose conformations was found to be 1.83 kcal/mol (vs. 2.67 kcal/mol with a smaller basis set used in earlier calculations). In developing MM4 to reproduce these data, it was necessary first to have good energies for simple alcohols and ethers, together with an adequate treatment of hydrogen bonding, and then to include the anomeric effect, and the ethylene glycol type system, as was previously recognized. It was also found that the so-called delta-2 effect, long recognized in carbohydrates, must be explicitly included, in order to obtain acceptable results. When a force field that included all of these items as developed from the small molecules based on the MM4 hydrocarbon force field was applied without any parameter adjustment to the set of hexopyranose and furanose conformations mentioned earlier, the E(beta) - E(alpha) was found to have an average value of 1.88 kcal/mol, versus 1.74 for the quantum calculations. The signed average and RMS deviations of the MM4 from the QM results were +0.15 and 0.87 kcal/mol.

Alcohols, ethers, carbohydrates, and related compounds. I. The MM4 force field for simple compounds

Simple alcohols and ethers have been studied with the MM4 force field. The structures of 13 molecules have been well fit using the MM4 force field. Moments of inertia have been fit with rms percentage errors as indicated: 18 moments for ethers, 0.28%; 21 moments for alcohols, 0.22%. Rotational barriers and conformational equilibria have also been examined, and the experimental and ab initio results are reproduced substantially better with MM4 than they were with MM3. Much of the improvement comes from the use of additional interaction terms in the force constant matrix, of which the torsion-bend and torsion-torsion are particularly important. Induced dipoles are included in the calculation, and dipole moments are reasonably well fit. It has been possible for the first time to fit conformational energetic data for both open chain and cyclic alcohols (e.g., propanol and cyclohexanol) with the same parameter set. For vibrational spectra, over a total of 82 frequencies, the rms error is 27 cm(-1), as opposed to 38 cm(-1) with MM3. Both the alpha and beta bond shortening resulting from the presence of the electronegative oxygen atom in the molecule are well reproduced. The electronegativity of the oxygen is sufficient that one must also include not only the alpha and beta electronegativity effects on bond lengths, but also on angle distortions, if structures are to be well reproduced. The heats of formation of 32 alcohols and ethers were fit overall to within experimental error (weighted standard deviation error 0.26 kcal/mol).

ICFF: a new method to incorporate implicit flexibility into an internal coordinate force field

We introduce a new method to accurately "project" a Cartesian force field onto an internal coordinate molecular model with fixed-bond geometry. The algorithm automatically generates the Internal Coordinate Force Field (ICFF), which is a close approximation of the "source" Cartesian force field. The ICFF method reduces the number of free variables in a model by at least 10-fold and facilitates the fast convergence of geometry optimizations, an advantage that is critical for many applications such as the docking of flexible ligands or conformational modeling of macromolecules. Although covalent geometry is fixed in an ICFF model, implicit flexibility is incorporated into the force field parameters in the following two ways. First, we formulate an empirical torsion energy term in ICFF as a sixfold Fourier series and develop a procedure to calculate the Fourier coefficients from the conformational energy profiles of the fully flexible Cartesian model. The ICFF torsion parameters thus represent not only torsion component of the source force field, but also bond bending, bond stretching, and "1-4" van der Waals interactions. Second, we use a soft polynomial repulsion function for "1-5" and "1-6" interactions to mimic the flexibility of bonds, connecting these atoms. Also, we suggest a way to use a local part of the Cartesian force field to automatically generate fixed covalent geometries, compatible with the ICFF energy function. Here, we present an implementation of the ICFF algorithm, which employs the MMFF94s Cartesian force field as a "source." Extensive benchmarking of ICFF with a representative set of organic molecules demonstrates that the implicit flexibility model accurately reproduces MMFF94s equilibrium conformational energy differences (RMSD approximately 0.64 kcal) and, most importantly, detailed torsion energy profiles (RMSD approximately 0.37 kcal). This accuracy is characteristic of the method, because all the ICFF parameters (except one scaling factor in the "1-5,1-6" repulsion term) are derived directly from the source Cartesian force field and do not depend on any particular molecular set. In contrast, the rigid geometry model with the MMFF94s energy function yields highly biased estimations in this test with the RMSD exceeding 1.2 kcal for the equilibrium energy comparisons and approximately 3.4 kcal for the torsion energy profiles.

Molecular modelling in structural biology

Molecular modelling is a powerful methodology for analysing the three dimensional structure of biological macromolecules. There are many ways in which molecular modelling methods have been used to address problems in structural biology. It is not widely appreciated that modelling methods are often an integral component of structure determination by NMR spectroscopy and X-ray crystallography. In this review we consider some of the numerous ways in which modelling can be used to interpret and rationalise experimental data and in constructing hypotheses that can be tested by experiment. Genome sequencing projects are producing a vast wealth of data describing the protein coding regions of the genome under study. However, only a minority of the protein sequences thus identified will have a clear sequence homology to a known protein. In such cases valuable three-dimensional models of the protein coding sequence can be constructed by homology modelling methods. Threading methods, which used specialised schemes to relate protein sequences to a library of known structures, have been shown to be able to identify the likely protein fold even in cases where there is no clear sequence homology. The number of protein sequences that cannot be assigned to a structural class by homology or threading methods, simply because they belong to a previously unidentified protein folding class, will decrease in the future as collaborative efforts in systematic structure determination begin to develop. For this reason, modelling methods are likely to become increasingly useful in the near future. The role of the blind prediction contests, such as the Critical Assessment of techniques for protein Structure Prediction (CASP), will be briefly discussed. Methods for modelling protein-ligand and protein-protein complexes are also described and examples of their applications given.

An orthorhombic crystal form of cyclohexaicosaose, CA26.32.59 H(2)O: comparison with the triclinic form

Cycloamylose containing 26 glucose residues (cyclohexaicosaose, CA26) crystallized from water and 30% (v/v) polyethyleneglycol 400 in the orthorhombic space group P2(1)2(1)2(1) in the highly hydrated form CA26.32.59 H(2)O. X-ray analysis of the crystals at 0.85 A resolution shows that the macrocycle of CA26 is folded into two short left-handed V-amylose helices in antiparallel arrangement and related by a twofold rotational pseudosymmetry as reported recently for the (CA26)(2).76.75 H(2)O triclinic crystal form [Gessler, K. et al. Proc. Natl. Acad. Sci. USA 1999, 96, 4246-4251]. In the orthorhombic crystal form, CA26 molecules are packed in motifs reminiscent of V-amylose in hydrated and anhydrous forms. The intramolecular interface between the V-helices in CA26 is dictated by formation of an extended network of interhelical C-H...O hydrogen bonds; a comparable molecular arrangement is also evident for the intermolecular packing, suggesting that it is a characteristic feature of V-amylose interaction. The hydrophobic channels of CA26 are filled with disordered water molecules arranged in chains and held in position by multiple C-H...O hydrogen bonds. In the orthorhombic and triclinic crystal forms, the structures of CA26 molecules are equivalent but the positions of the individual water molecules are different, suggesting that the patterns of water chains are perturbed even by small structural changes associated with differences in packing arrangements in the two crystal lattices rather than with differences in the CA26 geometry.