QSAR of conformationally flexible molecules: Comparative Molecular Field Analysis of protein-tyrosine kinase inhibitors

Summary Comparative Molecular Field Analysis (CoMFA) has been applied to a study of quantitative structureactivity relationships (QSAR) of conformationally flexible molecules. The relationship between three-dimensional structure and activity of 20 styrene derivatives which inhibit protein-tyrosine kinase was determined. A technique was developed that allows accurate prediction of the inhibitory activity of these molecules and identification in each case of the active conformation. The problem of multiple energetically acceptable conformations was approached in an iterative procedure. Use was made of the varying degrees of symmetry among the molecules. First, CoMFA QSAR models were developed using only those compounds that possess a symmetrical substituent pattern on the phenyl ring. These CoMFA models were then used to select the active conformers of the less symmetrical compounds in the set. Allowing multiple conformers for each compound in the dataset yielded higher crossvalidated r² values and better predictivity of the QSAR models. Different probe atoms (C⁺, O^–, neutral C) were explored, the O^– probe atom exhibiting the highest selectivity in the conformer selection process.     

Prediction of geometries and interaction energies of complexes formed by small molecules using semiempirical and ab initio methods

The accuracy of the semiempirical quantum mechanics methods (AM1 and PM3), and the ab initio methods (6-31G^** and MP2/6-31G^**) in predicting intermolecular geometries and interaction energies have been evaluated by detailed studies of 17 bimolecular complexes formed by small molecules. Comparisons between calculated and experimental geometries for 12 complexes are presented. It was found that AM1 gave reasonably good predictions of the geometries of complexes such as CH₄ · CH₄, which have very weak interactions, but it is not as good as other methods in predicting intermolecular geometry for complexes where hydrogen bonding interactions play an important role. This is consistent with its inability to reproduce the charge transfer in the formation of hydrogen bonds in these complexes.

PM3 is able to predict intermolecular geometries for most complexes, including those with hydrogen bonding; its major flaw is its tendency to overestimate the strength of the interactions between hydrogen atoms. Care should be taken therefore in using PM3 to study complicated molecular systems with multiple hydrogen atom interactions and the method's weakness in handling complexes in which electrostatic forces are important should also be noted.

Among ab initio methods, both the 6-31G^** and the MP2/6-31G^** were found to outperform AM1 and PM3 in prediction of intermolecular geometry. Both of these ab initio methods showed excellent consistency in geometry prediction for most of the complexes studied, although MP2/6-31G^** is better than 6-31G^**. It is noted that the MP2/6-31G^** did not produce the correct geometry for the CO₂· HF complex.

For 12 complexes for which experimental geometry data are available, AM1, PM3, 6-31G^**, and MP2/6-31G^** successfully predicted the geometry in 10, 12, 12, and 11 cases, respectively. The average errors given by AM1 in the predicted intermolecular distances were 0.264, 0.272, 0.091, and 0.061 Å, respectively. In comparison to the ab initio methods, AM1 and PM3 commonly underestimated the molecular interaction energy in such complexes by ˜ 1–2 kcal mol⁻¹.     

The structure and conformation of the tryptophanyl diketopiperazines cyclo(Trp–Trp)·C2H6SO and cyclo(Trp–Pro)

The structure and conformation of the cyclic dipeptides [cyclo(L-Trp–L-Trp)·C₂H₆SO] and cyclo(L-Trp–L-Pro) have been investigated with X-ray crystallographic and spectroscopic methods. Cyclo(L-tryptophanyl-L-tryptophanyl)·DMSO solvate crystallized in the space group P2 ₁2₁2₁ with cell dimensions a = 6.193(2), b = 11.545(3), c = 31.117(4) Å. The crystal structure is stabilized by four hydrogen bonds (three intermolecular hydrogen bonds and one intramolecular bond). The first intermolecular bond is between the oxygen of DMSO and the nitrogen of indole ring 2, in contrast to the second intramolecular hydrogen bond between the nitrogen of indole ring 1 and the oxygen of DMSO. The two remaining intermolecular hydrogen bonds are between the nitrogens of the DKP ring and the carbonyl oxygens of the DKP ring. The values of ^1A ₁ (–45.764) and ^1A ₂ (67.437) indicate an extended side chain conformation for Trp residue 1 (E_N) and a folded conformation for Trp residue 2. The DKP ring is more planar than in other cyclic dipeptide compounds (₁ = 11.414, ₁ = –7.516, ₂ = 12.471, and ₂ = –8.256). In cyclo(L-Trp–L-Trp) the C resonance of L-tryptophan (29.88 ppm) is shifted upfield 0.82 ppm when compared with the same resonance in cyclo(L-Trp–L-Gly) (30.7 ppm) and cyclo(L-Leu–L-Trp) (30.7 ppm). Two conformations of cyclo(Trp–Pro) crystallized in the space group P1 with cell dimensions a = 5.422(1), b = 9.902(1), c = 13.443(2) Å, = 80.42(1), = 78.61(1), and = 89.13(1)°. The conformation of the backbone and the orientation of the aromatic side chains for these conformers are very similar. The DKP rings for both conformers adopt a typical boat conformation in contrast to the flattened chair conformation observed for cyclo(Tyr–Pro) and cyclo(Phe–F-Pro). The tryptophan side chains of these conformers are folded towards the diketopiperazine (DKP) ring. The pyrrolidine ring for conformer 1 can be described as an envelope (Cs–C-endo) conformation in contrast to the pyrrolidine ring symmetry for conformer 2 which is an intermediate between C_s and C₂ rather than pure C_s for the proline ring with C-endo and C-exo with respect to C. The two prolyl rings are puckered at the -carbon atoms which deviate from the best planes defined by the four remaining atoms. The crystal structures are stabilized by four intermolecular hydrogens bonds. An intermolecular bond between the nitrogen of the indole ring (conformer 1) and the carbonyl oxygen of the DKP ring (conformer 2) was observed. The second hydrogen bond is between the nitrogen of the indole ring (conformer 2) and the carbonyl oxygen of the DKP ring (conformer 1). The last two hydrogens involve the carbonyl oxygens of the DKP rings and the nitrogens of the DKP rings [carbonyl oxygen of DKP ring (conformer 1)––––nitrogen of DKP ring (conformer 2); nitrogen of DKP ring (conformer 1)––––––carbonyl oxygen of DKP ring (conformer 2)].     

In vivo processing and antibiotic activity of microcin B17 analogs with varying ring content and altered bisheterocyclic sites.

BACKGROUND: The Escherichia coli peptide antibiotic microcin B17 (MccB17) contains four oxazole and four thiazole rings, and inhibits DNA gyrase. The role of individual and tandem pairs of heterocycles in bioactivity has not been determined previously. RESULTS: The two tandem 4,2-bisheterocycles in MccB17 were varied by expression of MccB17 or mutants containing altered sequences at Gly39-Ser40-Cys41 or Gly54-Cys55-Ser56. A mixture of five-nine-ring MccB17 isoforms were separated and quantitated for antibiotic potency. Mutagenesis of the thiazole-oxazole pair significantly affected antibiotic activity compared with the upstream oxazole-thiazole, which might stabilize partially cyclized intermediates against proteolysis. CONCLUSIONS: Enzymatic heterocyclization in native MccB17 occurs distributively. Antibiotic activity correlates with the number of rings and is differentially sensitive to both the location and the identity of the 4,2-tandem heterocycle pairs in MccB17. Such tandem heterocycles might be useful pharmacophores in combinatorial libraries.     

Lefschetz Motives and the Tate Conjecture

A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type implies the Tate conjecture for all Abelian varieties over finite fields, thereby reducing the latter to a problem in complex analysis.     

Rotational motion of the water molecules in the superconductor Na0.28CoO$_{\mathsf{2}} \!\cdot \!{\sf y}$H2O

Quasielastic neutron scattering (QENS) has been used to investigate the dynamical behaviour of H₂O in the superconductor Na_0.28CoO₂ .yH₂O. The measurements were obtained at room temperature for a molar concentration of water, y = 1.3. From the analysis of the Q-dependence of the EISF and the line-width we found that the water dynamics can be well described by rotational motion that likely correspond to re-orientation of the H₂O molecule. We were also able to define a rotational correlation time of τ= 1.85 ps.     

Optical performance of carbon-nanotube electron sources

The figure of merit for the electron optical performance of carbon-nanotube (CNT) electron sources is presented. This figure is given by the relation between the reduced brightness and the energy spread in the region of stable emission. It is shown experimentally that a CNT electron source exhibits a highly stable emission process that follows the Fowler-Nordheim theory for field emission, fixing the relationship among the energy spread, the current, and the radius. The performance of the CNT emitter under realistic operating conditions is compared with state-of-the-art electron point sources. It is demonstrated that the reduced brightness is a function of the tunneling parameter, a measure of the energy spread at low temperatures, only, independent of the geometry of the emitter.     

Diffractive optics implementation of six-wave mixing

Diffractive optics are applied to six-wave mixing processes to provide a single optic approach to attaining the required, relatively complex, phase-matching geometry to discriminate against lower-order nonlinear responses. The diffractive optics were designed specifically for broad-bandwidth operation and passive phase locking of the appropriate pulse pairs for use in femtosecond two-dimensional Raman studies of the dynamic structure of liquids. The fifth-order signal was studied in liquid CS>(2); two different colors were used for the excitation and the probe to reduce background scatter, as were two different phase-matching geometries with different degrees of suppression of cascaded third-order processes.     

Boundary layer development from transition provoking devices

The results of an experimental investigation of four different, incompressible, transitional boundary layer situations are presented. The experiments were carried out in zero pressure gradient conditions and transition was initiated from two- and from three-dimensional provoking agents.

The measurements of transitional intermittency from two-dimensional tripping agents showed a trend consistent with that reported elsewhere in the literature, with the development of mean and fluctuating component velocity profiles and local skin friction coefficient exhibiting approximate similarity through the transition region.

Disturbance frequency and spread angles for turbulent wedge growth behind isolated roughness elements were similar to those reported by others.

Computer predictions using a transition model based on the present correlations show reasonable agreement with the data.     

Mappings of subspaces into subsets

Let V_n(q) denote the n-dimensional vector space over the finite field with q elements, and L_n(q) be the lattice of subspaces of V_n(q). Two rank- and order-preserving maps from L_n(q) onto the lattice of subsets of an n-set are constructed. Three equivalent formulations of these maps are given: an inductive procedure based on an elementary combinatorial interpretation of a well-known pair of difference equations satisfied by the Gaussian coefficients [$\text{n}\text{k}$], a direct set-theoretical definition, and, a direct definition involving a certain pair of modular chains in L_n(q). The direct set-theoretical definition of one of these maps has already been given by Knuth. Knuth's map, however, may be systematically discovered by means of the inductive procedure and the direct lattice-theoretic definition shows how it can be generalized. As a further application of the pair of difference equations satisfied by [$\text{n}\text{k}$], a direct-combinatorial proof of an identity of Carlitz that expands Gaussian coefficients in terms of binomial coefficients has been formulated.