Kinetic aspects of macromolecular crystallization.
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Biomedical subjects
Publications and source records attributed to G T DeTitta.
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Eliminating the N atomic position vectors rj, j = 1, 2, ..., N, from the system of equations defining the normalized structure factors EH yields a system of identities that the EH's must satisfy, provided that the set of EH's is sufficiently large. Clearly, for fixed N and specified space group, this system of identities depends only on the set [H], consisting of n reciprocal-lattice vectors H, and is independent of the crystal structure, which is assumed for simplicity to consist of N identical atoms per unit cell. However, for a fixed crystal structure, the magnitudes magnitude of /EH/ are uniquely determined so that a system of identities is obtained among the corresponding phases psi H alone, which depends on the presumed known magnitudes magnitude of /EH/ and which must of necessity be satisfied. The known conditional probability distributions of triplets and quartets, given the values of certain magnitudes magnitude of /E/, lead to a function R(psi) of phases, uniquely determined by magnitudes magnitude of /E/ and having the property that RT < 1/2 < RR, where RT is the value of R(psi) when the phases are equal to their true values, no matter what the choice of origin and enantiomorph, and RR is the value of R(psi) when the phases are chosen at random. The following conjecture is therefore plausible: the global minimum of R(psi), where the phases are constrained to satisfy all identities among them that are known to exist, is attained when the phases are equal to their true values and is thus equal to RT.(ABSTRACT TRUNCATED AT 250 WORDS)
The minimal function, R(psi), has been used to provide the basis for a new computer-intensive direct-methods procedure that shows potential for providing fully automatic routine solutions for structures in the 200-400 atom range. This procedure, which has been called shake-and-bake, is an iterative process in which real-space filtering is alternated with phase refinement using a technique that reduces the value of R(psi). It has been successfully tested using experimental data for a dozen known structures ranging in size from 25 to 317 atoms and crystallizing in a variety of space groups. The details of this procedure, the parameters used and the results of these applications are described.
The Shake-and-Bake method of structure determination is a new direct methods phasing algorithm based on a minimum-variance, phase invariant residual, which is referred to as the minimal principle. Previously, the algorithm had been applied only to known structures. This algorithm has now been applied to two previously unknown structures that contain 105 and 110 non-hydrogen atoms, respectively. This report focuses on (i) algorithmic and parametric optimizations of Shake-and-Bake and (ii) the determination of two previously unknown structures. Traditional tangent formula phasing techniques were unable to unravel these two new structures.
Biotin is a coenzyme that fixes CO2 for transfer in a family of carboxylase, decarboxylase, and transcarboxylase enzymes. Their enzyme reactions involve two basic steps during which a carboxybiotinyl intermediate forms at one site and translocates to a second (distinct) site for CO2 transfer. Our diffraction studies of biotin and its vitamers suggest that translocation involves rotation about one, or at most two, bonds in biotin's valeryl chain. The rotations are energetically economical gauche in equilibrium trans rotations about the two valeryl bonds nearest the biotin bicyclic ring. They move a carbon atom of a CO2 moiety bound at N-1' approximately 7 A, a distance in accord with spectroscopic measurements of one of the biotin enzymes. From our studies we infer that sulfur in biotin imparts to the valeryl chain a conformational variability necessary for bond rotation and, hence, translocation between catalytic sites.
The crystal structure of N1'-methoxycarbonylbiotin methyl ester, a model for N1'-carboxybiotin, has been determined. The ureido carbonyl bond has more double bond (keto) character than does the corresponding bound in free biotin, which has single bond (enolate) character. In addition, there is an interesting intermolecular interaction between the ureido carbonyl oxygen and a methyl group. Comparison of the molecular structure and crystal packing with those of free biotin suggests that the coenzyme may have evolved with the incorporation of the ureido moiety because the electronic configuration of this region of the molecule is sensitive to N1' carboxylation. On decarboxylation, the ureido carbonyl bond becomes more polarized (C-O-), thereby facilitating the deprotonation of N1' and increasing its nucleophilicity. As a result, carboxylation can occur readily. On carboxylation, the carbonyl bond is depolarized (C = O), allowing the carboxylated coenzyme to interact with nonpolar groups and carboxylate them. Thus, the carboxylation and decarboxylation of biotin appear to act as a mechanistic switch, turning off and on the polarization of the ureido carbonyl bond as well as modulating the nucleophilicity of N1'.
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The hairpin conformational hypothesis has been proposed to rationalise much of the structure-activity and receptor-binding data which have accumulated for the prostaglandin (PG) hormones. The hairpin conformation, thought to be necessary for PG activity, requires that the alpha- and omega-chains of the molecule be extended and in parallel alignment, separated by a van der Waals contact distance for the full length of the chains, with the ends of the chains approximately 5.5 A apart. The similarity between the structures of the thromboxanes (TXs) and the PGs suggests that the profile of activity of TXs, like that of PGs, centres on subtle conformational variation of the hairpin geometry. Thromboxane B2 (TXB2) is a stable hydrolysis product of a highly reactive, short-lived intermediate, thromboxane A2 (TXA2), which is formed from the prostaglandin endoperoxide (PGH2) as indicated in Fig. 1. An examination of molecular models of TXA2 and TXB2 suggests that the structural differences between the ring moieties may have much less influence in altering the side-chain conformation of TXs than do substitutents on the relatively more flexible cyclopentane ring of a PG molecule. We report here the first diffraction analysis of a thromboxane structure and note that the molecular conformation is not hairpin shaped.
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The conformation of prostaglandin F 2alpha (PGF 2alpha) has been determined by x-ray diffraction techniques. Two independent conformers of PGF 2alpha, studied as the tris(hydroxymethyl)methylamine salt, are observed to adopt the familiar "hairpin" conformation with the alpha and omega chains aligned roughly parallel. The conformers differ in ring conformation and at the C(17)-C(18) bond, one adopting a C(9) envelope ring conformation and a trans geometry at the C(17)-C(18) bond, while the other adopts a C(8) envelope ring conformation and a novel gauche geometry about C(17)-C(18). Comparison of the conformation of PGF 2alpha with that of prostaglandin E2 suggests a recognition mechanism which would permit PGF 2alpha and prostaglandin E receptors to distinguish between the two potent prostaglandins. The recognition model explains much of the binding data for the PGF 2alpha receptor in the corpus luteum and predicts the existence of an interesting PGF 2alpha analog.
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The crystal and molecular structure of prostaglandin B1( PGB1) has been determined. The conformation is L-shaped, with the alpha and omega side chains roughly perpendicular to one another. This arrangement differs from the "hairpin" or approximately parallel disposition of side chains observed for other prostaglandins. The omega chain, which normally turns at the 15-hydroxyl back toward the alpha chain, is fully extended. The conformation is stabilized by the conjugation of the dienone chromophore. The 15-hydroxyl, which is normally directed away from the centroid of the prostaglandin in the hairpin model, is turned inward in L-shaped PGB1. The low biological activity of PGB1 in many systems and especially its inhibition of the metabolizing enzyme 15-hydroxyprostaglandin dehydrogenase may be attributable directly to the observed L-shape conformation.
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The molecular conformation of the monoclinic crystalline polymorph of prostaglandin A1 has been determined by X-ray diffraction techniques. The space group is P21 with a = 13.637(2), b = 7.567(1), c = 10.576(2) A, beta = 107.37(3) degrees; Dc = 1.073 g.cm-3 for Z = 2. The molecular conformation is characterized by the nearly parallel arrangement of the C1-C7 and C13-C20 side chains, with a general flattening of the overall structure when compared with the orthorhombic polymorph. The cyclopentenone moiety assumes a C8 envelope conformation with C8 and O9 displaced +0.29 A and -0.18 A from the C9-C10=C11-C12 plane respectively. Concerted, small varations of the torsion angles, primarily about the C8-C12, C14-C15 and C16-C17 bonds, bring the monoclinic and orthorhombic conformations into coincidence.
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