A modified standard embedding with jumps in nonlinear optimization

The paper deals with a combination of pathfollowing methods (embedding approach) and feasible descent direction methods (so-called jumps) for solving a non-linear optimization problem with equality and inequality constraints. Since the method that we propose here uses jumps from one connected component to another one, more than one connected component of the solution set of the corresponding one-parametric problem can be followed numerically. It is assumed that the problem under consideration belongs to a generic subset which was introduced by Jongen, Jonker and Twilt. There already exist methods of this type for which each starting point of a jump has to be an endpoint of a branch of local minimizers. In this paper the authors propose a new method by allowing a larger set of starting points for the jumps which can be constructed at bifurcation and turning points of the solution set. The topological properties of those cases where the method is not successful are analyzed and the role of constraint qualifications in this context is discussed. Furthermore,this new method is applied to a so-called modified standard embedding which is a particular construction without equality constraints. Finally, an algorithmic version of this new method as well as computational results are presented

Facile crystallization of Escherichia coli ketol-acid reductoisomerase

Ketol-acid reductoisomerase (EC 1.1.1.86) catalyses the second reaction in the biosynthesis of branched-chain amino acids. The reaction involves an Mg2+-dependent alkyl migration followed by an NADPH-dependent reduction of the 2-keto group. Here, the crystallization of the Escherichia coli enzyme is reported. A form with a C-terminal hexahistidine tag could be crystallized under 18 different conditions in the absence of NADPH or Mg2+ and a further six crystallization conditions were identified with one or both ligands. With the hexahistidine tag on the N-terminus, 20 crystallization conditions were found, some of which required the presence of NADPH, NADP(+), Mg2+ or a combination of ligands. Finally, the selenomethionine-substituted enzyme with the N-terminal tag crystallized under 15 conditions. Thus, the enzyme is remarkably easy to crystallize. Most of the crystals diffract poorly but several data sets were collected at better than 3.2 Angstrom resolution; attempts to phase them are currently in progress

Sensitivity analysis of the proportionate change of a subset of outputs or/and inputs in DEA

Sensitivity analysis in data envelopment analysis (DEA) is studied for the case of the proportionate change of a subset of outputs or/and of a subset of inputs of an efficient decision making unit (DMU) according to the Charnes-Cooper-Rhodes (CCR) ratio model. Sufficient conditions for an efficient DMU to preserve its efficiency under the proportionate changeof a subset of inputs or/and of outputs are obtained. An illustrative numerical example is provided

Crystallization and preliminary X-ray diffraction studies of mammalian purple acid phosphatase

The oxidized form of purple acid phosphatase from pig allantoic fluid has been crystallized in the presence of phosphate using the hanging-drop technique. The crystals belong to the space group P2(1)2(1)2(1) and have unit-cell parameters a = 66.8, b = 70.3, c = 78.7 Angstrom. Diffraction data collected from a cryocooled crystal using a conventional X-ray source extend to 1.55 Angstrom resolution. A knowledge of the three-dimensional structure of mammalian purple acid phosphatase will aid in understanding the substrate specificity of the enzyme and will be important in the rational design of inhibitors, with potential in the treatment of bone diseases

Crystallization and preliminary diffraction studies of native and selenomethionine CcmG (CycY, DsbE)

t Disulfide-bond (Dsb) proteins are a family of redox proteins containing a Cys-X-X-Cys motif. They are essential for disulfide-bond exchange in the bacterial periplasm and are necessary for the correct folding and function of many secreted proteins. CcmG (DsbE) is a reducing Dsb protein required for cytochrome c maturation. Crystals of Bradyrhizobium japonicum CcmG have been obtained that diffract X-rays to 1.14 Angstrom resolution. The crystals are orthorhombic, space group P2(1)2(1)2(1), with unit-cell parameters a = 35.1, b = 48.2, c = 90.2 Angstrom. Selenomethionine CcmG was expressed without using a methionine auxotroph or methionine-pathway inhibition and was purified without reducing agents

Crystallization and preliminary X-ray diffraction data for a purple acid phosphastase from sweet potato

Purple acid phosphatase from sweet potato is a homodimer of 110 kDa. Two forms of the enzyme have been characterized. One contains an Fe-Zn centre similar to that previously reported for red kidney bean purple acid phosphatase. Another isoform, the subject of this work, is the first confirmed example of an Fe-Mn-containing enzyme. Crystals of this protein have been grown from PEG 6000. They have unit-cell parameters a = b = 118.4, c = 287.4 Angstrom and have the symmetry of space group P6(5)22, with one dimer per asymmetric unit. Diffraction data collected using a conventional X-ray source from a cryocooled crystal extend to 2.90 Angstrom resolution. The three-dimensional structure of the enzyme will provide insight into the coordination of this novel binuclear metal centre

Oligomeric state of hypoxanthine-guanine phosphoribosyltransferase from Mycobacterium tuberculosis

Sedimentation equilibrium and size-exclusion chromatography experiments on Mycobacterium tuberculosis hypoxanthine-guanine phosphoribosyltransferase (MtHGPRT) have established the existence of this enzyme as a reversibly associating mixture of dimeric and tetrameric species in 0.1\ua0M Tris-HCl−0.012\ua0M MgCl, pH 7.4. Displacement of the equilibrium position towards the larger oligomer by phosphate signifies the probable existence of MtHGPRT as a tetramer in the biological environment. These data thus add credibility to the relevance of considering enzyme function in the light of a published tetrameric structure deduced from X-ray crystallography. Failure of 5-phospho-α-D-ribosyl-1-pyrophosphate (PRib-PP) to perturb the dimer−tetramer equilibrium position indicates the equivalence and independence of binding for this substrate (the first to bind in an ordered sequential mechanism) to the two oligomers. By virtue of the displacement of the equilibrium position towards dimer that is affected by removing MgCl from the Tris-HCl buffer, it can be concluded that divalent metal ions, as well as phosphate, can affect the oligomerization. These characteristics of MtHGPRT in solution are correlated with published crystal structures of four enzyme−ligand complexes

The structure of the bacterial oxidoreductase enzyme DsbA in complex with a peptide reveals a basis for substrate specificity in the catalytic cycle of DsbA enzymes

Oxidative protein folding in Gram-negative bacteria results in the formation of disulfide bonds between pairs of cysteine residues. This is a multistep process in which the dithiol-disulfide oxidoreductase enzyme, DsbA, plays a central role. The structure of DsbA comprises an all helical domain of unknown function and a thioredoxin domain, where active site cysteines shuttle between an oxidized, substrate-bound, reduced form and a DsbB-bound form, where DsbB is a membrane protein that reoxidizes DsbA. Most DsbA enzymes interact with a wide variety of reduced substrates and show little specificity. However, a number of DsbA enzymes have now been identified that have narrow substrate repertoires and appear to interact specifically with a smaller number of substrates. The transient nature of the DsbA-substrate complex has hampered our understanding of the factors that govern the interaction of DsbA enzymes with their substrates. Here we report the crystal structure of a complex between Escherichia coli DsbA and a peptide with a sequence derived from a substrate. The binding site identified in the DsbA-peptide complex was distinct from that observed for DsbB in the DsbA-DsbB complex. The structure revealed details of the DsbA-peptide interaction and suggested a mechanism by which DsbA can simultaneously show broad specificity for substrates yet exhibit specificity for DsbB. This mode of binding was supported by solution nuclear magnetic resonance data as well as functional data, which demonstrated that the substrate specificity of DsbA could be modified via changes at the binding interface identified in the structure of the comple

High-resolution NMR studies of structure and dynamics of human ERp27 indicate extensive interdomain flexibility

ERp27 (endoplasmic reticulum protein 27.7 kDa) is a homologue of PDI (protein disulfide-isomerase) localized to the endoplasmic reticulum. ERp27 is predicted to consist of two thioredoxinfold domains homologous with the non-catalytic b and b domains of PDI. The structure in solution of the N-terminal blike domain of ERp27 was solved using high-resolution NMR data. The structure confirms that it has the thioredoxin fold and that ERp27 is a member of the PDI family. 15N-NMR relaxation data were obtained and ModelFree analysis highlighted limited exchange contributions and slow internal motions, and indicated that the domain has an average order parameter S 2 of 0.79. Comparison of the single-domain structure determined in the present study with the equivalent domain within fulllength ERp27, determined independently by X-ray diffraction, indicated very close agreement. The domain interface inferred from NMR data in solution was much more extensive than that observed in the X-ray structure, suggesting that the domains flex independently and that crystallization selects one specific interdomain orientation. This led us to apply a new rapid method to simulate the flexibility of the full-length protein, establishing that the domains show considerable freedom to flex (tilt and twist) about the interdomain linker, consistent with the NMR data