Structure Of Variant Research Articles

On integrating the techniques of direct methods with anomalous dispersion. I. The theoretical basis

The recently secured mathematical formalism of direct methods is here generalized to the case that the atomic scattering factors are arbitrary complex numbers, thus including the special case that one or more anomalous scatterers are present. Once again the neighborhood concept plays the central role. Final results from the probabilistic theory of the two- and three-phase structure invariants are briefly summarized. In particular, the conditional probability distribution of the three-phase structure invariant, given the six magnitudes |E| in its first neighborhood, is described. The distribution yields an estimate for the three-phase structure invariant which is particularly good in the favorable case that the variance of the distribution happens to be small (the neighborhood principle). Particularly noteworthy is the fact that, in sharp contrast to all earlier work, the estimate is unique in the whole range 0 to 2π. An example shows that the method is capable of yielding unique estimates for tens of thousands of three-phase structure invariants with unprecedented accuracy, even in the macromolecular case. The clear implication is that the fusion of the traditional techniques of direct methods with anomalous dispersion, which is described here, will facilitate the solution of those crystal structures which contain one or more anomalous scatterers.

On integrating the techniques of direct methods and isomorphous replacement. II. The first applications

With error-free diffraction data from the protein cytochrome c550 from Paracoccus denitrificans, having molecular weight Mr ≃ 14 500, space group P212121, and a single PtCl2-4 derivative, estimates (0 or π) of the three-phase structure invariants are obtained by recently secured direct methods employing the six-magnitude first neighborhood [Hauptman (1982). Acta Cryst. A38, 289-294] and compared with the known values. The comparison shows that these methods are capable of estimating reliably several tens of thousands of those invariants having the extreme values 0 or π, approximately. It is therefore anticipated that direct methods will play an increasingly important role in the determination of macromolecular structures.

Incidence and histological structure of the storiform pattern in benign and malignant fibrous histiocytomas.

A starlike arrangement of cells and fibers, the "storiform pattern", was found to be a typical, but not obligatory, histological feature of benign and malignant fibrous histiocytomas. In 155 benign fibrous histiocytomas storiform structures were missing in 29 cases, chiefly of the fibroblastic type comparable with classical "dermatofibroma". 12 of 70 malignant fibrous histiocytomas did not reveal storiform structures, especially the cellular pleomorphic variant, i.e. the classical pleomorphic sarcoma. Storiform structures were either small and highly cellular with few fibers (collagen type III), or larger, less cellular, but with abundant fibers (collagen type I). There was no sharp demarcation between these two extremes, but many transitional structures or patterns were seen. The histiocytic nature of the cells was demonstrated in both variants of storiform structures by immunhistochemical methods on paraffin embedded material. Alpha 1-antichymotrypsin was especially valuable in this respect.

Prediction of the most biologically active structure of a series of compounds

The contemporary search for biologically active compounds (BAC), such as drugs, herbicides, insecticides, attractants, radioprotectants, etc., is composed to two basic steps. The first step is the chemical synthesis, and the second is the biological testing of the synthesized compounds. Each of these steps is characterized by an excessive number of variants of the prototypical chemical structures. Such a search strategy incurs great expense in time, valuable material, and work in synthesis and biological testing, which is, in the final analysis, only slightly effective. As noted by L. A. Piruzyan [i], "the search for one drug occupies a period of from 5 to i0 years and an economic outlay evaluated at 5-10 million rubles." Actually, from every 3000 substances examined~ only one reaches the stage of clinical testing [2]; from i0,000 synthesized and tested pesticides, only one preparation was brought into production [3].

Application of the three-phase seminvariants to phase determination inP21

Formulas for estimating the values (0 or π) of the enantiomorph-insensitive two- and three-phase structure seminvariants in P21 and for identifying the enantiomorph-sensitive ones (i.e. those having the values ± π/2) have recently been secured. These procedures are here integrated in order to identify still more reliably those seminvariants having the values 0, π or ± π/2. The results are employed in two ways to strengthen direct-methods procedures. The first makes active use of the three-phase structure seminvariants alone and the second relies heavily on the three- and four-phase structure invariants but employs the seminvariant enantiomorph-specific figure of merit CRISEM to select the best of a number of possible solutions. The heavy dependence on the enantiomorph-sensitive seminvariants facilitates the selection and maintenance of the enantiomorph, often a source of difficulty in this space group.

On the theory and estimation of the three-phase structure seminvariant in P1

By embedding the three-phase structure seminvariant T and its three symmetry-related variants in suitable quintets Q (five-phase structure invariants) one obtains the extensions Q of T to which T is related via the space-group symmetries. The neighborhoods of T are then defined in terms of the neighborhoods of its extensions. The conditional probability distribution of T, given the seven magnitudes |E| in its first neighborhood, is derived. The distribution yields a reliable estimate (0 or π) for T in the favorable case that the variance of the distribution happens to be small.

Evidence of a tilted columnar structure for mesomorphic phases of benzene-hexa-n-alkanoates

Optical observations on the mesomorphs of benzene-hexa-n-alkanoates, and their admixtures with benzene, show that the planes of these discotic molecules are not perpendicular to the columns in which they are stacked, as was supposed originally. This evidence comes principally from the occurrence in texture domains of circular bending, between crossed polarizer and analyser, of oblique extinction brushes (i.e., brushes not parallel or perpendicular to polarizer and analyser directions). The obliquity varies from specimen to specimen up to a maximum of about 35°. A tilted stacking, with a tilt angle (for the optic axes of the molecules) of about 35°, will fit all the observations. Four alternative variants of such structures, two with the same tilt axes for all molecules, two with a herring-bone alternation between two orientations of tilt axis, all of which give rectangular pseudo-hexagonal lattices, are discussed. It is shown that the departure from hexagonal axial ratio required by these tilted structures is small enough not to be incompatible with the X-ray diffraction evidence previously interpreted as indicating hexagonal symmetry. These structures allow several different twinning modes, and complex optical features in some domains of circular bending are explicable in terms of these twinnings.

On molecular mechanisms of nucleic acid synthesis. Fidelity aspects: 2. Contribution of protein-nucleotide recognition

Experimental and theoretical data analysis leads to the conclusion that enzymes of nucleic acid synthesis contain a recognition site. The protein-nucleotide recognition in template synthesis of nucleic acids can be provided by interaction of the enzyme recognition site with structure invariants of nucleotide complementary pairs and it is the recognition that enhances the fidelity of replication, repair and transcription. Two possible supplementary molecular mechanisms of such recognition are considered. The first one supposes the formation of hydrogen bonds between recognition portion of the enzyme and invariantly arranged N-3 atom of purine and O-2 of pyrimidine in complementary base pairs. The other molecular mechanism supposes that the enzyme controls the position and conformation of sugarphosphate moiety. The necessary condition for effective function of this mechanism is conformational transition of the enzyme caused by correct position of base pairs. The conception is compared with available experimental data and other viewpoints on the nature of nucleic acid synthesis fidelity.

Application of quartet and quintet invariants in phase determination

Recent derivations of probability expressions for quartet and quintet structure invariants allow the reliable estimation of the phase sums of quartets and quintets in the range 0 to π. A new quartet figure of merit, ENQUAC and a new quintet figure of merit, ENQUIC, based on these estimates are described, which are particularly useful in non-centrosymmetric symmorphic and polar space groups. An adapted tangent-refinement procedure employing selected triplets with a phase sum of 0, together with the quartet and quintet phase estimates, enables enantiomorph-specific phase refinement. The way in which the figures of merit and the refinement technique can be used in various practical procedures is demonstrated and applications to two structures in space group P1 are presented.

The extension concept and its role in the probabilistic theory of the structure seminvariants

By embedding the structure seminvariant T and symmetry-related variants of T in suitable structure invariants Q the values of which, because of the space-group-dependent relations among the phases, are related to T, one reduces the probabilistic theory of the structure seminvariants to that of the structure invariants, which is well developed. The structure invariants Q are said to be extensions of the structure seminvariant T.

The von Mises distribution of the phase of a structure invariant

The main terms in the exponential forms of the phase probability distributions of structure invariants are von Mises distributions P(Φ = [2πI0(k)]-1 exp [k cos (Φ - ϕ)] (a). It is shown that in this formula k and ϕ are given by k exp iϕ = 2 〈F〉 |F|/σ2 (b), where F, a complex variable, is identified with a structure invariant, 〈F〉 is its mean value andσ2 is its variance. From (a) and (b) are obtained, by simple algebraic calculations of 〈F〉 and σ2, the formulae for phase probability distributions of structure invariants, the derivation of which up to now required lengthy calculations via joint probability distributions of many structure factors. A new application is the calculation of the phase probability distribution of a quartet employing both the magnitudes of the cross terms and a priori structural information.

On the conditional probability of quintets

A new expression for the conditional probability distribution of quintet structure invariants is given, which in exponential approximation reduces to the exponential expression of Hauptman & Fortier [Acta Cryst. (1977), A33, 575-580]. In a practical example the expression gave promising results.

The probabilistic theory of the structure invariants φh+ φk+ φl+ φminP\overline{1}

Probability distributions associated with the third, fourth, fifth and sixth neighborhoods of the structure invariant ϕlmϕh + ϕk + ϕl + ϕm are derived. These distributions yield estimates for ϕlm in terms of magnitudes |E| alone which are particularly good in the favorable case that the standard deviations of the distributions are small. The estimates for the ϕlm lead in turn to unique values for the individual phases ϕ even for very complex structures. Conditional distributions of ϕlm given the values of one or more structure invariants ϕpq, ϕrs, ϕtu and appropriate sets of magnitudes |E| are also described.

Problems posed by potential gonococcal vaccines viewed from the vantage point of a control agency.

Progress in the characterisation of Neisseria gonorrhoeae and other bacterial pathogens has suggested that immunoprophylaxis for gonorrhoea may be possible despite the well-known propensity for reinfection. Pili, outer membrane proteins, a capsular polysaccharide, and the lipopolysaccharide may be important gonococcal virulence factors, and immune components (probably antibodies) to more than one of these antigens may be required to confer immunity. A study of antigenic polymorphism of these structures should identify disease isolates more precisely and provide information about the relationship between variants of these gonococcal structures and gonococcal virulence.

Static determination of dynamic properties of generalized type unions

The classical programming languages such as PASCAL or ALGOL 68 do not provide full data type security. Run-time errors are not precluded on basic operations. Type safety necessitates a refinement of the data type notion which allows subtypes. The compiler must also be able to ensure that basic operations are applicable. This verification consists in determining a local subtype of globally declared variables or constants. This may be achieved by improved compiler capabilities to analyze the program properties or by language constructs which permit the expression of these properties. Both approaches are discussed and illustrated by the problems of access to records via pointers, access to variants of record structures, determination of disjoint collections of linked records, and determination of integer subrange. Both approaches are complementary and a balance must be found between what must be specified by the programmer and what must be discovered by the compiler.

Static determination of dynamic properties of generalized type unions

The classical programming languages such as PASCAL or ALGOL 68 do not provide full data type security. Run-time errors are not precluded on basic operations. Type safety necessitates a refinement of the data type notion which allows subtypes. The compiler must also be able to ensure that basic operations are applicable. This verification consists in determining a local subtype of globally declared variables or constants. This may be achieved by improved compiler capabilities to analyze the program properties or by language constructs which permit the expression of these properties. Both approaches are discussed and illustrated by the problems of access to records via pointers, access to variants of record structures, determination of disjoint collections of linked records, and determination of integer subrange. Both approaches are complementary and a balance must be found between what must be specified by the programmer and what must be discovered by the compiler.

Static determination of dynamic properties of generalized type unions

The classical programming languages such as PASCAL or ALGOL 68 do not provide full data type security. Run-time errors are not precluded on basic operations. Type safety necessitates a refinement of the data type notion which allows subtypes. The compiler must also be able to ensure that basic operations are applicable. This verification consists in determining a local subtype of globally declared variables or constants. This may be achieved by improved compiler capabilities to analyze the program properties or by language constructs which permit the expression of these properties. Both approaches are discussed and illustrated by the problems of access to records via pointers, access to variants of record structures, determination of disjoint collections of linked records, and determination of integer subrange. Both approaches are complementary and a balance must be found between what must be specified by the programmer and what must be discovered by the compiler.

Probabilistic theory of the structure invariants: extension to the unequal atom case with application to neutron diffraction

Recent methods in the probabilistic theory of the structure invariants and seminvariants are here generalized to include the case that not all atoms in the unit cell are identical. The presence of unequal atoms, in particular a few heavy atoms, is thus clearly seen to enhance the power of the direct method. Since the method permits the presence of negative scatterers, the application to neutron diffraction is immediate. Only the conditional probability distributions associated with the first neighborhood of the three-phase structure invariant and the first two neighborhoods of the four-phase structure invariant in P1 and P{\bar 1} are treated here. However the methods are clearly sufficiently general to cope with structure invariants and seminvariants in general.

An example of the use of quartet and triplet structure invariants when enantiomorph discrimination is difficult

Problems relating to enantiomorph discrimination in the structure determination of the alborixin antibiotic (C48O14H-84, K+) are studied. To select the starting set, quartet structure invariants are used to define two orthogonal classes of reflexions, and a variation of the tangent formula refinement using the phases of the triplet invariants is described.

A joint probability distribution of seven structure factors inP\overline{1}

For a fixed crystal structure in P{\bar 1}, it is assumed that h, k, l, m are random variables (vectors) uniformly and independently distributed over the subset of reciprocal space defined by h + k + l + m = 0. Then the seven structure factors Eh, Ek, El, Em, Eh + k, Ek + l, El + h, as functions of the primitive random variables h, k, l, m, are themselves random variables, and their joint probability distribution is found. This distribution plays the central role in the theory and estimation of the four-phase structure invariants ϕh + ϕk + ϕl + ϕm.