Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Additional binding sites in lysozyme. X-ray analysis of lysozyme complexes with bromophenol red and bromophenol blue

The binding sites in hen egg-white lysozyme for neutral bromophenol red (BPR) and ionized bromophenol blue (BPB) have been characterized at 2 Å resolution. In either case, the dye-bound enzyme is active against the polysaccharide, but not against the cell wall. Both binding sites are outside, but close to, the hexasaccharide binding cleft in the enzyme. The binding site of BPR made up of Arg5, Lys33, Phe34, Asn37, Phe38, Ala122, Trp123 and possibly Arg125, is dose to subsite F while that of BPB made up of Tyr20, Arg21, Asn93, Lys96, Lys97 and Ser100, is close to subsites A and B. The binding sites of the neutral dye and the ionized dye are thus spatially far apart. The peptide component of the bacterial cell wall probably interacts with these cells during enzyme action. Such interactions are perhaps necessary for appropriately positioning the enzyme molecule on the bacterial cell wall.

Purification and characterization of assimilatory nitrite reductase from Candida utilis

Nitrate assimilation in many plants, algae, yeasts and bacteria is mediated by two enzymes, nitrate reductase (EC 1.6.6.2) and nitrite reductase (EC 1.7.7.1). They catalyse the stepwise reduction of nitrate to nitrite and nitrite to ammonia respectively. The nitrite reductase from an industrially important yeast, Candida utilis, has been purified to homogeneity. Purified nitrite reductase is a heterodimer and the molecular masses of the two subunits are 58 and 66 kDa. The native enzyme exhibits a molecular mass of 126 kDa as analysed by gel filtration. The identify of the two subunits of nitrite reductase was confirmed by immunoblotting using antibody for Cucurbita pepo leaf nitrite reductase. The presence of two different sized transcripts coding for the two subunits was confirmed by (a) in vitro translation of mRNA from nitrate-induced C. utilis followed by immunoprecipitation of the in vitro translated products with heterologous nitrite reductase antibody and (b) Northern-blot analysis. The 66 kDa subunit is acidic in nature which is probably due to its phosphorylated status. The enzyme is stable over a range of temperatures. Both subunits can catalyse nitrite reduction, and the reconstituted enzyme, at a higher protein concentration, shows an activity similar to that of the purified enzyme. Each of these subunits has been shown to contain a few unique peptides in addition to a large number of common peptides. Reduced Methyl Viologen has been found to be as effective an electron donor as NADPH in the catalytic process, a phenomenon not commonly seen for nitrite reductases from other systems.

GPRA and the asthma locus on chromosome 7p14-p15

The basis of this work was the identification of a genomic region on chromosome 7p14-p15 that strongly associated with asthma and high serum total immunoglobulin E in a Finnish founder population from Kainuu. Using a hierarchical genotyping approach the linkage region was narrowed down until an evolutionary collectively inherited 133-kb haplotype block was discovered. The results were confirmed in two independent data sets: Asthma families from Quebec and allergy families from North-Karelia. In all the three cohorts studied, single nucleotide polymorphisms tagging seven common gene variants (haplotypes) were identified. Over half of the asthma patients carried three evolutionary closely related susceptibility haplotypes as opposed to approximately one third of the healthy controls. The risk effects of the gene variants varied from 1.4 to 2.5. In the disease-associated region, there was one protein-coding gene named GPRA (G Protein-coupled Receptor for Asthma susceptibility also known as NPSR1) which displayed extensive alternative splicing. Only the two isoforms with distinct intracellular tail sequences, GPRA-A and -B, encoded a full-length G protein-coupled receptor with seven transmembrane regions. Using various techniques, we showed that GPRA is expressed in multiple mucosal surfaces including epithelial cells throughout the respiratory tract. GPRA-A has additional expression in respiratory smooth muscle cells. However, in bronchial biopsies with unknown haplotypes, GPRA-B was upregulated in airways of all patient samples in contrast to the lack of expression in controls. Further support for GPRA as a common mediator of inflammation was obtained from a mouse model of ovalbumin-induced inflammation, where metacholine-induced airway hyperresponsiveness correlated with elevated GPRA mRNA levels in the lung and increased GPRA immunostaining in pulmonary macrophages. A novel GPRA agonist, Neuropeptide S (NPS), stimulated phagocytosis of Esterichia coli bacteria in a mouse macrophage cell line indicating a role for GPRA in the removal of inhaled allergens. The suggested GPRA functions prompted us to study, whether GPRA haplotypes associate with respiratory distress syndrome (RDS) and bronchopulmonary dysplasia (BPD) in infants sharing clinical symptoms with asthma. According to the results, near-term RDS and asthma may also share the same susceptibility and protective GPRA haplotypes. As in asthma, GPRA-B isoform expression was induced in bronchial smooth muscle cells in RDS and BPD suggesting a role for GPRA in bronchial hyperresponsiveness. In conclusion, the results of the present study suggest that the dysregulation of the GPRA/NPS pathway may not only be limited to the individuals carrying the risk variants of the gene but is also involved in the regulation of immune functions of asthma.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

The transfer problem and the intertemporal terms of trade

In this paper the effects of a transfer on the intertemporal terms of trade are examined in the context of a simple two-country, two-period model. When intertemporal trade occurs because the two economies have different rates of time preference, a transfer improves the terms of trade of the paying country. Alternatively, when trade occurs owing to international differences in the endowments of goods over the two periods, the effect of a transfer depends on (a) the relationship between the interest rate and the rates of time preference of the two countries and (b) the relationship between their elasticities of intertemporal consumption substitution.

Positional cloning and pathway analysis of the asthma susceptibility gene, NPSR1

In the present study, we identified a novel asthma susceptibility gene, NPSR1 (neuropeptide S receptor 1) on chromosome 7p14.3 by the positional cloning strategy. An earlier significant linkage mapping result among Finnish Kainuu asthma families was confirmed in two independent cohorts: in asthma families from Quebec, Canada and in allergy families from North Karelia, Finland. The linkage region was narrowed down to a 133-kb segment by a hierarchial genotyping method. The observed 77-kb haplotype block showed 7 haplotypes and a similar risk and nonrisk pattern in all three populations studied. All seven haplotypes occur in all three populations at frequences > 2%. Significant elevated relative risks were detected for elevated total IgE (immunoglobulin E) or asthma. Risk effects of the gene variants varied from 1.4 to 2.5. NPSR1 belongs to the G protein-coupled receptor (GPCR) family with a topology of seven transmembrane domains. NPSR1 has 9 exons, with the two main transcripts, A and B, encoding proteins of 371 and 377 amino acids, respectively. We detected a low but ubiquitous expression level of NPSR1-B in various tissues and endogenous cell lines while NPSR1-A has a more restricted expression pattern. Both isoforms were expressed in the lung epithelium. We observed aberrant expression levels of NPSR1-B in smooth muscle in asthmatic bronchi as compared to healthy. In an experimental mouse model, the induced lung inflammation resulted in elevated Npsr1 levels. Furthermore, we demonstrated that the activation of NPSR1 with its endogenous agonist, neuropeptide S (NPS), resulted in a significant inhibition of the growth of NPSR1-A overexpressing stable cell lines (NPSR1-A cells). To determine which target genes were regulated by the NPS-NPSR1 pathway, NPSR1-A cells were stimulated with NPS, and differentially expressed genes were identified using the Affymetrix HGU133Plus2 GeneChip. A total of 104 genes were found significantly up-regulated and 42 down-regulated 6 h after NPS administration. The up-regulated genes included many neuronal genes and some putative susceptibility genes for respiratory disorders. By Gene Ontology enrichment analysis, the biological process terms, cell proliferation, morphogenesis and immune response were among the most altered. The expression of four up-regulated genes, matrix metallopeptidase 10 (MMP10), INHBA (activin A), interleukin 8 (IL8) and EPH receptor A2 (EPHA2), were verified and confirmed by quantitative reverse-transcriptase-PCR. In conclusion, we identified a novel asthma susceptibility gene, NPSR1, on chromosome 7p14.3. NPS-NPSR1 represents a novel pathway that regulates cell proliferation and immune responses, and thus may have functional relevance in the pathogenesis of asthma.

Two highly unsymmetrical tetradentate (N3O) Schiff base copper(II) complexes: Template synthesis, structural characterization, magnetic and computational studies

Two new copper(II) complexes, [Cu-2(L-1)(2)](ClO4)(2) (1) and [Cu(L-2)(ClO4)] (2), of the highly unsymmetrical tetradentate (N3O) Schiff base ligands HL1 and HL2 (where HL1 = N-(2-hydroxyacetophenone)-bis-3-aminopropylamine and HL2 = N-(salicyldehydine)-bis-3-aminopropylamine) have been synthesised using a template method. Their single crystal X-ray structures show that in complex 1 two independent copper(II) centers are doubly bridged through sphenoxo-O atoms (O1A and O1B) of the two ligands and each copper atom is five-coordinated with a distorted square pyramidal geometry. The asymmetric unit of complex 2 consists of two crystallographically independe N-(salicylidene) bis(aminopropyl)amine-copper(II) molecules, A and B, with similar square pyramidal geometries. Cryomagnetic susceptibility measurements (5-300 K) on complex 1 reveal a distinct antiferromagnetic interaction with J=-23.6 cm(-1), which is substantiated by a DFT calculation (J=-27.6 cm(-1)) using the B3LYP functional. Complex 1, immobilized over highly ordered hexagonal mesoporous silica, shows moderate catalytic activity for the epoxidation of cyclohexene and styrene in the presence of TBHP as an oxidant.

Juggling priorities: Balancing economic and social drivers to address the LLN needs of students in the VET sector

Economic success, and a commitment to the social benefits of inclusive training opportunities are important goals for public vocational education and training (VET). Currently, in Australia, VET policy is a shared responsibility between the Commonwealth and the States and Territories. Priorities for investment are juggled between: a) improving efficiency and responsiveness; and b) providing societal prosperity. Amid recent VET educational reforms and policy directives the authors of this paper undertook a pilot study examining language, literacy and numeracy support and inclusive teaching and learning practices in a Diploma of Nursing course. The data highlighted implications arising from new market driven education reforms. This article reports on identified factors that influenced inclusive learning opportunities, noticeably associated with two recent policy developments: the release of the FSK Foundation Skills Training Package (IBSA 2014); and the Queensland's Higher Skills Program Policy 2014-15.

Determinants of Coronary and Carotid Atherosclerosis in Finnish Patients with Clinically Suspected Coronary Artery Disease. A Quantitative Angiography and Ultrasound Study

Background. Cardiovascular disease (CVD) remains the most serious threat to life and health in industrialized countries. Atherosclerosis is the main underlying pathology associated with CVD, in particular coronary artery disease (CAD), ischaemic stroke, and peripheral arterial disease. Risk factors play an important role in initiating and accelerating the complex process of atherosclerosis. Most studies of risk factors have focused on the presence or absence of clinically defined CVD. Less is known about the determinants of the severity and extent of atherosclerosis in symptomatic patients. Aims. To clarify the association between coronary and carotid artery atherosclerosis, and to study the determinants associated with these abnormalities with special regard to novel cardiovascular risk factors. Subjects and methods. Quantitative coronary angiography (QCA) and B-mode ultrasound were used to assess coronary and carotid artery atherosclerosis in 108 patients with clinically suspected CAD referred for elective coronary angiography. To evaluate anatomic severity and extent of CAD, several QCA parameters were incorporated into indexes. These measurements reflected CAD severity, extent, and overall atheroma burden and were calculated for the entire coronary tree and separately for different coronary segments (i.e., left main, proximal, mid, and distal segments). Maximum and mean intima-media thickness (IMT) values of carotid arteries were measured and expressed as mean aggregate values. Furthermore, the study design included extensive fasting blood samples, oral glucose tolerance test, and an oral fat-load test to be performed in each participant. Results. Maximum and mean IMT values were significantly correlated with CAD severity, extent, and atheroma burden. There was heterogeneity in associations between IMT and CAD indexes according to anatomical location of CAD. Maximum and mean IMT values, respectively, were correlated with QCA indexes for mid and distal segments but not with the proximal segments of coronary vessels. The values of paraoxonase-1 (PON1) activity and concentration, respectively, were lower in subjects with significant CAD and there was a significant relationship between PON1 activity and concentration and coronary atherosclerosis assessed by QCA. PON1 activity was a significant determinant of severity of CAD independently of HDL cholesterol. Neither PON1 activity nor concentration was associated with carotid IMT. The concentration of triglycerides (TGs), triglyceride-rich lipoproteins (TRLs), oxidized LDL (oxLDL), and the cholesterol content of remnant lipoprotein particle (RLP-C) were significantly increased at 6 hours after intake of an oral fatty meal as compared with fasting values. The mean peak size of LDL remained unchanged 6 hours after the test meal. The correlations between total TGs, TRLs, and RLP-C in fasting and postprandial state were highly significant. RLP-C correlated with oxLDL both in fasting and in fed state and inversely with LDL size. In multivariate analysis oxLDL was a determinant of severity and extent of CAD. Neither total TGs, TRLs, oxLDL, nor LDL size were linked to carotid atherosclerosis. Insulin resistance (IR) was associated with an increased severity and extent of coronary atherosclerosis and seemed to be a stronger predictor of coronary atherosclerosis in the distal parts of the coronary tree than in the proximal and mid parts. In the multivariate analysis IR was a significant predictor of the severity of CAD. IR did not correlate with carotid IMT. Maximum and mean carotid IMT were higher in patients with the apoE4 phenotype compared with subjects with the apoE3 phenotype. Likewise, patients with the apoE4 phenotype had a more severe and extensive CAD than individuals with the apoE3 phenotype. Conclusions. 1) There is an association between carotid IMT and the severity and extent of CAD. Carotid IMT seems to be a weaker predictor of coronary atherosclerosis in the proximal parts of the coronary tree than in the mid and distal parts. 2) PON1 activity has an important role in the pathogenesis of coronary atherosclerosis. More importantly, the study illustrates how the protective role of HDL could be modulated by its components such that equivalent serum concentrations of HDL cholesterol may not equate with an equivalent, potential protective capacity. 3) RLP-C in the fasting state is a good marker of postprandial TRLs. Circulating oxLDL increases in CAD patients postprandially. The highly significant positive correlation between postprandial TRLs and postprandial oxLDL suggests that the postprandial state creates oxidative stress. Our findings emphasize the fundamental role of LDL oxidation in the development of atherosclerosis even after inclusion of conventional CAD risk factors. 4) Disturbances in glucose metabolism are crucial in the pathogenesis of coronary atherosclerosis. In fact, subjects with IR are comparable with diabetic subjects in terms of severity and extent of CAD. 5) ApoE polymorphism is involved in the susceptibility to both carotid and coronary atherosclerosis.

Photocytotoxic Oxovanadium(IV) Complexes Showing Light-Induced DNA and Protein Cleavage Activity

Oxovanadium(IV) complexes [VO(L)(B)]Cl-2 (1-3), where L is bis(2-benzimidazolylmethyl)amine and B is 1,10-phenanthroline(phen),dipyrido[3,2-d:2',3'-f]quinoxaline(dpq) or dipyrido[3,2-a:2',3'-c]phenazine (dppz), have been prepared, characterized, and their photo-induced DNA and protein cleavage activity studied. The photocytotoxicity of complex 3 has been studied using adenocarcinoma A549 cells, The phen complex 1, structurally characterized by single-crystal X-ray crystallography, shows the presence of a vanadyl group in six-coordinate VON5 coordination geometry. The ligands L and phen display tridentate and bidentate N-donor chelating binding modes, respectively. The complexes exhibit a d-d band near 740 nm in 15% DMF-Tris-HCl buffer (pH 7.2). The phen and dpq complexes display an irreversible cathodic cyclic voltammetric response near -0.8 V in 20% DMF-Tris-HCl buffer having 0.1 M KCl as supporting electrolyte. The dppz complex 3 exhibits a quasi-reversible voltammogram near -0.6 V (vs SCE) that is assignable to the V(IV)-V(III)couple. The complexes bind to calf thymus DNA giving binding constant values in the range of 6.6 x 10(4)-2.9 x 10(5) M-1. The binding site size, thermal melting and viscosity binding data suggest DNA surface and/or groove binding nature of the complexes. The complexes show poor ``chemical nuclease'' activity in dark in the presence of 3-mercaptopropionic acid or hydrogen peroxide. The dpq and dppz complexes are efficient photocleavers of plasmid DNA in UV-A light of 365 nm via a mechanistic pathway that involves formation of both singlet oxygen and hydroxyl radicals. The complexes show significant photocleavage of DNA in near-IR light (>750 nm) via hydroxyl radical pathway. Among the three complexes, the dppz complex 3 shows significant BSA and lysozyme protein cleavage activity in UV-A light of 365 nm via hydroxyl radical pathway. The dppz complex 3 also exhibits photocytotoxicity in non-small cell lung carcinoma/human lung adenocarcinoma A549 cells giving IC50 value of 17 mu M in visible light(IC50 = 175 mu M in dark).

Understanding solvent effects on structure and reactivity of organic intermediates: a Raman study

The effect of solvent on chemical reactivity has generally been explained on the basis of the dielectric constant and viscosity. However a number of spectroscopic studies, including UV-VIS, IR and Raman, has led to numerous empirical parameters to define solvent effect based on either solvating ability or polarity scale. These parameters include solvent polarizability, dipolarity, Lewis acidity and Lewis basicity, E-T(30), pi*, alpha, beta etc. However, from a structural point of view, we can separate solvation as static and dynamic processes. The static solvation basically relates to stabilization of the molecular structure by the solvent to attain the equilibrium structure, both in the intermediate and ground state. Dynamic solvation relates to solvent reorganization-induced dynamics prior to the structural reorganization to reach the equilibrium state. In this paper, we present (a) structural distortions induced by the solvent due to preferential solvation of the triplet excited state, and (b) the importance of dynamic solvation induced by vibronic coupling (pseudo-Jahn-Teller coupling). The examples include the effect of solvent on structure and reactivity of excited states of 2,2,2-trifluoroacetophenone (TFA). Based on the comparison of time resolved resonance Raman (TR3) data of TFA and other substituted acetophenone systems, it was found that change in solvent polarity indeed results in electronic state switching and structural changes in the excited state, which explains the trend in reactivity. Further, a TR3 study of fluoranil (FA) in the triplet excited state in solvents of varying polarities indicates that the structure of FA in the triplet excited state is determined by vibronic coupling effects and thus distorted structure. These experimental results have been well supported by density functional theoretical computational studies.

Clinical Studies on Epidural and Spinal Postoperative Analgesia : With Special Reference to Continuous Techniques of Administration and Adjuvant Drugs

Continuous epidural analgesia (CEA) and continuous spinal postoperative analgesia (CSPA) provided by a mixture of local anaesthetic and opioid are widely used for postoperative pain relief. E.g., with the introduction of so-called microcatheters, CSPA found its way particularly in orthopaedic surgery. These techniques, however, may be associated with dose-dependent side-effects as hypotension, weakness in the legs, and nausea and vomiting. At times, they may fail to offer sufficient analgesia, e.g., because of a misplaced catheter. The correct position of an epidural catheter might be confirmed by the supposedly easy and reliable epidural stimulation test (EST). The aims of this thesis were to determine a) whether the efficacy, tolerability, and reliability of CEA might be improved by adding the α2-adrenergic agonists adrenaline and clonidine to CEA, and by the repeated use of EST during CEA; and, b) the feasibility of CSPA given through a microcatheter after vascular surgery. Studies I IV were double-blinded, randomized, and controlled trials; Study V was of a diagnostic, prospective nature. Patients underwent arterial bypass surgery of the legs (I, n=50; IV, n=46), total knee arthroplasty (II, n=70; III, n=72), and abdominal surgery or thoracotomy (V, n=30). Postoperative lumbar CEA consisted of regular mixtures of ropivacaine and fentanyl either without or with adrenaline (2 µg/ml (I) and 4 µg/ml (II)) and clonidine (2 µg/ml (III)). CSPA (IV) was given through a microcatheter (28G) and contained either ropivacaine (max. 2 mg/h) or a mixture of ropivacaine (max. 1 mg/h) and morphine (max. 8 µg/h). Epidural catheter tip position (V) was evaluated both by EST at the moment of catheter placement and several times during CEA, and by epidurography as reference diagnostic test. CEA and CSPA were administered for 24 or 48 h. Study parameters included pain scores assessed with a visual analogue scale, requirements of rescue pain medication, vital signs, and side-effects. Adrenaline (I and II) had no beneficial influence as regards the efficacy or tolerability of CEA. The total amounts of epidurally-infused drugs were even increased in the adrenaline group in Study II (p=0.02, RM ANOVA). Clonidine (III) augmented pain relief with lowered amounts of epidurally infused drugs (p=0.01, RM ANOVA) and reduced need for rescue oxycodone given i.m. (p=0.027, MW-U; median difference 3 mg (95% CI 0 7 mg)). Clonidine did not contribute to sedation and its influence on haemodynamics was minimal. CSPA (IV) provided satisfactory pain relief with only limited blockade of the legs (no inter-group differences). EST (V) was often related to technical problems and difficulties of interpretation, e.g., it failed to identify the four patients whose catheters were outside the spinal canal already at the time of catheter placement. As adjuvants to lumbar CEA, clonidine only slightly improved pain relief, while adrenaline did not provide any benefit. The role of EST applied at the time of epidural catheter placement or repeatedly during CEA remains open. The microcatheter CSPA technique appeared effective and reliable, but needs to be compared to routine CEA after peripheral arterial bypass surgery.

Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

Conformation of the flexible bent helix of Leu1-zervamicin in crystal C and a possible gating action for ion passage

The membrane channel-forming polypeptide, Leu(1)-zervamicin, Ac-Leu-Ile-Gln-Iva-Ile(5)-Thr-Aib-Leu-Aib-Hyp(10) -Gln-Aib-Hyp-Aib-Pro(15)-Phol (Aib: alpha-aminoisobutyric acid; Iva: isovaline; Hyp: 4-hydroxyproline; Phol: phenylalininol) has been analyzed by x-ray diffraction in a third crystal form. Although the bent helix is quite similar to the conformations found in crystals A and B, the amount of bending is more severe with a bending angle approximate to 47 degrees, The water channel formed by the convex polar faces of neighboring helices is larger at the mouth than in crystals A and B, and the water sites have become disordered. The channel is interrupted in the middle by a hydrogen bond between the OH of Hyp(10) and the NH2 of the Gln(11) of a neighboring molecule. The side chain of Gln(11) is wrapped around the helix backbone in an unusual fashion in order that it can augment the polar side of the helix. In the present crystal C there appears to be an additional conformation for the Gln(11) side chain (with approximate to 20% occupancy) that opens the channel for possible ion passage. Structure parameters for C85H140N18O22.xH(2)O.C2H5OH are space group P2(1)2(1)2(1), a = 10.337 (2) Angstrom, b = 28.387 (7) Angstrom, c = 39.864 (11) Angstrom, Z = 4, agreement factor R = 12.99% for 3250 data observed > 3 sigma(F), resolution = 1.2 Angstrom. (C) 1994 John Wiley & Sons, Inc.