New Solid State Forms of the Anti-HIV Drug Efavirenz. Conformational Flexibility and High Z ` Issues

Structural information on the solid forms of efavirenz, a non-nucleoside reverse transcriptase inhibitor, is limited, although various polymorphic forms of this drug have been patented. We report here structural studies of four new crystal forms a pure form, a cyclohexane solvate, and cocrystals with 1,4-cyclohexanedione and 4,4'-bipyridine. Temperature dependent single-crystal to single-crystal phase transitions are observed for the pure form and for the cyclohexane solvate with an increase in the number of symmetry independent molecules, Z', upon a lowering of temperature. Other issues related to these solid forms, such as thermal stability, conformational flexibility, and high Z' occurrences, are addressed by using a combined experimental and computational approach.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

How do heterogametic females survive without gene dosage compensation?

When the male is the heterogametic sex (XX♀-XY♂ or XX♀-XO♂), as inDrosophila, orthopteran insects, mammals andCaenorhabditis elegans, X-linked genes are subject to dosage compensation: the single X in the male is functionally equivalent to the two Xs in the female. However, when the female is heterogametic (ZZ♂-ZW♀), as in birds, butterflies and moths, Z-linked genes are apparently not dosage-compensated. This difference between X-linked and Z-linked genes raises fundamental questions about the role of dosage compensation. It is argued that (i) genes which require dosage compensation are primarily those that control morphogenesis and the prospective body plan; (ii) the products of these genes are required in disomic doses especially during oogenesis and early embryonic development; (iii) heterogametic females synthesize and store during oogenesis itself morphogenetically essential gene products - including those encoded by Z-linked genes — in large quantities; (iv) the abundance of these gene products in the egg and their persistence relatively late into embryogenesis enables heterogametic females to overcome the monosomic state of the Z chromosome in ZW embryos. Female heterogamety is predominant in birds, reptiles and amphibians, all of which have megalecithal eggs containing several thousand times more maternal RNA and other maternal messages than eggs of mammals,Caenorhabditis elegans, orDrosophila. This increase in egg size, yolk content and, concomitantly, the size of the maternal legacy to the embryo, may have facilitated female heterogamety and the absence of dosage compensation.

The C-Terminal Domain of the MutL Homolog from Neisseria gonorrhoeae Forms an Inverted Homodimer

The mismatch repair (MMR) pathway serves to maintain the integrity of the genome by removing mispaired bases from the newly synthesized strand. In E. coli, MutS, MutL and MutH coordinate to discriminate the daughter strand through a mechanism involving lack of methylation on the new strand. This facilitates the creation of a nick by MutH in the daughter strand to initiate mismatch repair. Many bacteria and eukaryotes, including humans, do not possess a homolog of MutH. Although the exact strategy for strand discrimination in these organisms is yet to be ascertained, the required nicking endonuclease activity is resident in the C-terminal domain of MutL. This activity is dependent on the integrity of a conserved metal binding motif. Unlike their eukaryotic counterparts, MutL in bacteria like Neisseria exist in the form of a homodimer. Even though this homodimer would possess two active sites, it still acts a nicking endonuclease. Here, we present the crystal structure of the C-terminal domain (CTD) of the MutL homolog of Neisseria gonorrhoeae (NgoL) determined to a resolution of 2.4 A. The structure shows that the metal binding motif exists in a helical configuration and that four of the six conserved motifs in the MutL family, including the metal binding site, localize together to form a composite active site. NgoL-CTD exists in the form of an elongated inverted homodimer stabilized by a hydrophobic interface rich in leucines. The inverted arrangement places the two composite active sites in each subunit on opposite lateral sides of the homodimer. Such an arrangement raises the possibility that one of the active sites is occluded due to interaction of NgoL with other protein factors involved in MMR. The presentation of only one active site to substrate DNA will ensure that nicking of only one strand occurs to prevent inadvertent and deleterious double stranded cleavage.

Structure of the putative mutarotase YeaD from Salmonella typhimurium in two different forms: in vivo binding of a sugar phosphate

Salmonella typhimurium YeaD (stYeaD), annotated as a putative aldose 1-epimerase, has a very low sequence identity to other well characterized mutarotases. Sequence analysis suggested that the catalytic residues and a few of the substrate-binding residues of galactose mutarotases (GalMs) are conserved in stYeaD. Determination of the crystal structure of stYeaD in an orthorhombic form at 1.9 angstrom resolution and in a monoclinic form at 2.5 angstrom resolution revealed this protein to adopt the beta-sandwich fold similar to GalMs. Structural comparison of stYeaD with GalMs has permitted the identification of residues involved in catalysis and substrate binding. In spite of the similar fold and conservation of catalytic residues, minor but significant differences were observed in the substrate- binding pocket. These analyses pointed out the possible role of Arg74 and Arg99, found only in YeaD-like proteins, in ligand anchoring and suggested that the specificity of stYeaD may be distinct from those of GalMs

Two forms of Pf1 Inovirus: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the asymmetric unit

Inovirus is a helical array of alpha-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Two forms of PF1 INOVIRUS: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the assymetric unit

Inovirus is a helical array of agr-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Structure and conformation of the calcium complex of cyclo(Ala-Leu-Pro-Gly)2 in two crystal forms

Crystal structures of two different forms of the calcium perchlorate complex of cyclo(Ala-Leu-Pro-Gly)2 have been determined and refined using X-ray crystallographic techniques. Orthorhombic form: C32H52N8O8.Ca(ClO4)2.7H2O.2CH3OH, space group C222(1), a = 14.366, b = 18.653, c = 19.824 A, Z = 4, R = 0.068 for 2208 observed reflections. Monoclinic form: C32H52N8O8.Ca(ClO4)2.4H2O, space group C2, a = 21.096, b = 10.182, c = 11.256 A, beta = 103.33 degrees, Z = 2, R = 0.075 for 2165 observed reflections. The cyclic peptide molecule in both the structures has the form of a twofold symmetric, slightly elongated bowl. Type II' beta-turns, involving Gly and Ala at the corners, exist at the two ends of the molecule. The interior of the molecule is substantially hydrophilic, and the external surface of the bowl is largely hydrophobic. The calcium ion is located at the centre of the mouth of the bowl-like molecule. In both crystal forms, four peptide carbonyl oxygens from the cyclic peptide and two solvent oxygens coordinate to the metal ion. The mode of complexation may be described as incomplete encapsulation as, for example, in the case of metal complexes of antamanide. In the crystal structures the complex ions are held together by hydrogen bonds involving perchlorate ions and water molecules. The molecular structure observed in the crystals is entirely consistent with the results of solution studies, which also indicate the conformation of the cyclic peptide in the complex to be similar to that of the uncomplexed molecule.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Proposed role of w chromosome inactivation and the absence of dosage compensation in avian sex determination

Three features of avian sex chromosomes - female heterogamety (ZZ male, ZW female), the apparently inactive state of the W chromosome, and dose-dependent expression of Z-linked genes - are examined in regard to their possible relation to sex determination. It is proposed that the W chromosome is facultatively heterochromatic and that the Z and W chromosomes carry one or more homologous sex-determination genes. The absence of dosage compensation in ZZ embryos, and W inactivation in ZW embryos, would then bring about a 2n(ZZ)-n(ZW) inequality in the effective copy number of such genes. The absence of dosage compensation of Z-linked genes in ZZ embryos is viewed as a means by which two copies of Z-W homologous sex determination genes are kept active to meet the requirements of testis determination. W inactivation may promote ovarian development by reducing the effective copy number of these genes from 2n to n. If there is a W-specific gene for femaleness, spread of heterochromatization to this gene in cells forming the right gonadal primordium may explain the latter's normally undifferentiated state; reversal of heterochromatization may similarly explain the development of the right gonad into a testis following left ovariectomy.

Effective drug dosage design for treatment of infectious diseases using dynamic inversion

A generic nonlinear mathematical model describing the human immunological dynamics is used to design an effective automatic drug administration scheme. Even though the model describes the effects of various drugs on the dynamic system, this work is confined to the drugs that kill the invading pathogen and heal the affected organ. From a system theoretic point of view, the drug inputs can be interpreted as control inputs, which can be designed based on control theoretic concepts. The controller is designed based on the principle of dynamic inversion and is found to be effective in curing the �nominal model patient� by killing the invading microbes and healing the damaged organ. A major advantage of this technique is that it leads to a closed-form state feedback form of control. It is also proved from a rigorous mathematical analysis that the internal dynamics of the system remains stable when the proposed controller is applied. A robustness study is also carried out for testing the effectiveness of the drug administration scheme for parameter uncertainties. It is observed from simulation studies that the technique has adequate robustness for many �realistic model patients� having off-nominal parameter values as well.

Real-time kinetic analysis of hCG-monoclonal antibody interaction using radiolabeled hCG probe: presence of two forms of Ag-mAb complex as revealed by solid phase dissociation studies

Real-time kinetics of ligand-ligate interaction has predominantly been studied by either fluorescence or surface plasmon resonance based methods. Almost all such studies are based on association between the ligand and the ligate. This paper reports our analysis of dissociation data of monoclonal antibody-antigen (hCG) system using radio-iodinated hCG as a probe and nitrocellulose as a solid support to immobilize mAb. The data was analyzed quantitatively for a one-step and a two-step model. The data fits well into the two-step model. We also found that a fraction of what is bound is non-dissociable (tight-binding portion (TBP)). The TBP was neither an artifact of immobilization nor does it interfere with analysis. It was present when the reaction was carried out in homogeneous solution in liquid phase. The rate constants obtained from the two methods were comparable. The work reported here shows that real-time kinetics of other ligand-ligate interaction can be studied using nitrocellulose as a solid support. (C) 2002 Elsevier Science B.V. All rights reserved.