Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

An insight into alkali promotion: a density functional theory study of CO dissociation on K/Rh(111)

The important role of alkali additives in heterogeneous catalysis is, to a large extent, related to the high promotion effect they have on many fundamental reactions. The wide application of alkali additives in industry does not, however, reflect a thorough understanding of the mechanism of their promotional abilities. To investigate the physical origin of the alkali promotion effect, we have studied CO dissociation on clean Rh(111) and K-covered Rh(111) surfaces using density functional theory. By varying the position of potassium atoms relative to a dissociating CO, we have mapped out the importance of different K effects on the CO dissociation reactions. The K-induced changes in the reaction pathways and reaction barriers have been determined; in particular, a large reduction of the CO dissociation barrier has been identified. A thorough analysis of this promotion effect allows us to rationalize both the electronic and the geometrical factors that govern alkali promotion effect: (i) The extent of barrier reductions depends strongly on how close K is to the dissociating CO. (ii) Direct K-O bonding that is in a very short range plays a crucial role in reducing the barrier. (iii) K can have a rather long-range effect on the TS structure, which could reduce slightly the barriers.

K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Functional analysis of the large periplasmic loop of the Escherichia coli K-12 WaaL O-antigen ligase

WaaL is a membrane enzyme implicated in ligating undecaprenyl-diphosphate (Und-PP)-linked O antigen to lipid A-core oligosaccharide. We determined the periplasmic location of a large (EL5) and small (EL4) adjacent loops in the Escherichia coli K-12 WaaL. Structural models of the EL5 from the K-12, R1 and R4 E. coli ligases were generated by molecular dynamics. Despite the poor amino acid sequence conservation among these proteins, the models afforded similar folds consisting of two pairs of almost perpendicular alpha-helices. One alpha-helix in each pair contributes a histidine and an arginine facing each other, which are highly conserved in WaaL homologues. Mutations in either residue rendered WaaL non-functional, since mutant proteins were unable to restore O antigen surface expression. Replacements of residues located away from the putative catalytic centre and non-conserved residues within the centre itself did not affect ligation. Furthermore, replacing a highly conserved arginine in EL4 with various amino acids inactivates WaaL function, but functionality reappears when the positive charge is restored by a replacement with lysine. These results lead us to propose that the conserved amino acids in the two adjacent periplasmic loops could interact with Und-PP, which is the common component in all WaaL substrates.

Functional analysis of predicted coiled-coil regions in the Escherichia coli K-12 O-antigen polysaccharide chain length determinant Wzz

Wzz is a membrane protein that determines the chain length distribution of the O-antigen lipopolysaccharide by an unknown mechanism. Wzz proteins consist of two transmembrane helices separated by a large periplasmic loop. The periplasmic loop of Escherichia coli K-12 Wzz (244 amino acids from K65 to A308) was purified and found to be a monomer with an extended conformation, as determined by gel filtration chromatography and analytical ultracentrifugation. Circular dichroism showed that the loop has a 60% helical content. The Wzz periplasmic loop also contains three regions with predicted coiled coils. To probe the function of the predicted coiled coils, we constructed amino acid replacement mutants of the E. coli K-12 Wzz protein, which were designed so that the coiled coils could be separate without compromising the helicity of the individual molecules. Mutations in one of the regions, spanning amino acids 108 to 130 (region I), were associated with a partial defect in O-antigen chain length distribution, while mutants with mutations in the region spanning amino acids 209 to 223 (region III) did not have an apparent functional defect. In contrast, mutations in the region spanning amino acids 153 to 173 (region II) eliminated the Wzz function. This phenotype was associated with protein instability, most likely due to conformational changes caused by the amino acid replacements, which was confirmed by limited trypsin proteolysis. Additional mutagenesis based on a three-dimensional model of region I demonstrated that the amino acids implicated in function are all located at the same face of a predicted alpha-helix, suggesting that a coiled coil actually does not exist in this region. Together, our results suggest that the regions predicted to be coiled coils are important for Wzz function because they maintain the native conformation of the protein, although the existence of coiled coils could not be demonstrated experimentally.

Functional expression of KCNQ (Kv7) channels in guinea-pig bladder smooth muscle and their contribution to spontaneous activity

Background and Purpose: The aim of the study was to determine whether KCNQ channels are functionally expressed in bladder smooth muscle cells (SMC) and to investigate their physiological significance in bladder contractility. 

Experimental Approach: KCNQ channels were examined at the genetic, protein, cellular and tissue level in guinea pig bladder smooth muscle using RT-PCR, immunofluorescence, patch-clamp electrophysiology, calcium imaging, detrusor strip myography, and a panel of KCNQ activators and inhibitors. 

Key Results: KCNQ subtypes 1-5 are expressed in bladder detrusor smooth muscle. Detrusor strips typically displayed TTX-insensitive myogenic spontaneous contractions that were increased in amplitude by the KCNQ channel inhibitors XE991, linopirdine or chromanol 293B. Contractility was inhibited by the KCNQ channel activators flupirtine or meclofenamic acid (MFA). The frequency of Ca2+-oscillations in SMC contained within bladder tissue sheets was increased by XE991. Outward currents in dispersed bladder SMC, recorded under conditions where BK and KATP currents were minimal, were significantly reduced by XE991, linopirdine, or chromanol, and enhanced by flupirtine or MFA. XE991 depolarized the cell membrane and could evoke transient depolarizations in quiescent cells. Flupirtine (20M) hyperpolarized the cell membrane with a simultaneous cessation of any spontaneous electrical activity. 

Conclusions and Implications: These novel findings reveal the role of KCNQ currents in the regulation of the resting membrane potential of detrusor SMC and their important physiological function in the control of spontaneous contractility in the guinea pig bladder.

The fourth extracellular loop of the alpha subunit of Na,K-ATPase. Functional evidence for close proximity with the second extracellular loop.

Na,K-ATPase is the main active transport system that maintains the large gradients of Na(+) and K(+) across the plasma membrane of animal cells. The crystal structure of a K(+)-occluding conformation of this protein has been recently published, but the movements of its different domains allowing for the cation pumping mechanism are not yet known. The structure of many more conformations is known for the related calcium ATPase SERCA, but the reliability of homology modeling is poor for several domains with low sequence identity, in particular the extracellular loops. To better define the structure of the large fourth extracellular loop between the seventh and eighth transmembrane segments of the alpha subunit, we have studied the formation of a disulfide bond between pairs of cysteine residues introduced by site-directed mutagenesis in the second and the fourth extracellular loop. We found a specific pair of cysteine positions (Y308C and D884C) for which extracellular treatment with an oxidizing agent inhibited the Na,K pump function, which could be rapidly restored by a reducing agent. The formation of the disulfide bond occurred preferentially under the E2-P conformation of Na,K-ATPase, in the absence of extracellular cations. Using recently published crystal structure and a distance constraint reproducing the existence of disulfide bond, we performed an extensive conformational space search using simulated annealing and showed that the Tyr(308) and Asp(884) residues can be in close proximity, and simultaneously, the SYGQ motif of the fourth extracellular loop, known to interact with the extracellular domain of the beta subunit, can be exposed to the exterior of the protein and can easily interact with the beta subunit.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Functional studies of the deubiquitinating enzymes USP19, USP4 and UCH-L1

El marcaje de proteínas con ubiquitina, conocido como ubiquitinación, cumple diferentes funciones que incluyen la regulación de varios procesos celulares, tales como: la degradación de proteínas por medio del proteosoma, la reparación del ADN, la señalización mediada por receptores de membrana, y la endocitosis, entre otras (1). Las moléculas de ubiquitina pueden ser removidas de sus sustratos gracias a la acción de un gran grupo de proteasas, llamadas enzimas deubiquitinizantes (DUBs) (2). Las DUBs son esenciales para la manutención de la homeostasis de la ubiquitina y para la regulación del estado de ubiquitinación de diferentes sustratos. El gran número y la diversidad de DUBs descritas refleja tanto su especificidad como su utilización para regular un amplio espectro de sustratos y vías celulares. Aunque muchas DUBs han sido estudiadas a profundidad, actualmente se desconocen los sustratos y las funciones biológicas de la mayoría de ellas. En este trabajo se investigaron las funciones de las DUBs: USP19, USP4 y UCH-L1. Utilizando varias técnicas de biología molecular y celular se encontró que: i) USP19 es regulada por las ubiquitin ligasas SIAH1 y SIAH2 ii) USP19 es importante para regular HIF-1α, un factor de transcripción clave en la respuesta celular a hipoxia, iii) USP4 interactúa con el proteosoma, iv) La quimera mCherry-UCH-L1 reproduce parcialmente los fenotipos que nuestro grupo ha descrito previamente al usar otros constructos de la misma enzima, y v) UCH-L1 promueve la internalización de la bacteria Yersinia pseudotuberculosis.

"Functional Upregulation of Ca2+ -Activated K+ Channels in the Development of Substantia Nigra Dopamine Neurons"

Many connections in the basal ganglia are made around birth when animals are exposed to a host of new affective, cognitive, and sensori-motor stimuli. It is thought that dopamine modulates cortico-striatal synapses that result in the strengthening of those connections that lead to desired outcomes. We propose that there must be a time before which stimuli cannot be processed into functional connections, otherwise it would imply an effective link between stimulus, response, and reward in uterus. Consistent with these ideas, we present evidence that early in development dopamine neurons are electrically immature and do not produce high-frequency firing in response to salient stimuli. We ask first, what makes dopamine neurons immature? and second, what are the implications of this immaturity for the basal ganglia? As an answer to the first question, we find that at birth the outward current is small (3nS-V), insensitive to Ca2z, TEA, BK, and SK blockers. Rapidly after birth, the outward current increases to 15nS-V and becomes sensitive to Ca2z, TEA, BK, and SK blockers. We make a detailed analysis of the kinetics of the components of the outward currents and produce a model for BK and SK channels that we use to reproduce the outward current, and to infer the geometrical arrangement of BK and Ca2z channels in clusters. In the first cluster, T-type Ca2z and BK channels are coupled within distances of *20 nm (200 A˚). The second cluster consists of L-type Ca2z and BK channels that are spread over distances of at least 60 nm. As for the second question, we propose that early in development, the mechanism of action selection is in a ‘‘locked-in’’ state that would prevent dopamine neurons from reinforcing cortico-striatal synapses that do not have a functional experiential- based value.

Functional Upregulation of Ca2+ -Activated K+ Channels in the Development of Substantia Nigra Dopamine Neurons

Many connections in the basal ganglia are made around birth when animals are exposed to a host of new affective, cognitive, and sensori-motor stimuli. It is thought that dopamine modulates cortico-striatal synapses that result in the strengthening of those connections that lead to desired outcomes. We propose that there must be a time before which stimuli cannot be processed into functional connections, otherwise it would imply an effective link between stimulus, response, and reward in uterus. Consistent with these ideas, we present evidence that early in development dopamine neurons are electrically immature and do not produce high-frequency firing in response to salient stimuli. We ask first, what makes dopamine neurons immature? and second, what are the implications of this immaturity for the basal ganglia? As an answer to the first question, we find that at birth the outward current is small (3nS-V), insensitive to Ca2+, TEA, BK, and SK blockers. Rapidly after birth, the outward current increases to 15nS-V and becomes sensitive to Ca2+, TEA, BK, and SK blockers. We make a detailed analysis of the kinetics of the components of the outward currents and produce a model for BK and SK channels that we use to reproduce the outward current, and to infer the geometrical arrangement of BK and Ca2+ channels in clusters. In the first cluster, T-type Ca2+ and BK channels are coupled within distances of similar to 20 nm (200 parallel to). The second cluster consists of L-type Ca2+ and BK channels that are spread over distances of at least 60 nm. As for the second question, we propose that early in development, the mechanism of action selection is in a "locked-in" state that would prevent dopamine neurons from reinforcing cortico-striatal synapses that do not have a functional experiential-based value.

EfeUOB (YcdNOB) is a tripartite, acid-induced and CpxAR-regulated, low-pH Fe2+ transporter that is cryptic in Escherichia coli K-12 but functional in E-coli O157 : H7

Escherichia coli possesses iron transporters specific for either Fe2+ or Fe3+. Although Fe2+ is far more soluble than Fe3+, it rapidly oxidizes aerobically at pH >= 7. Thus, FeoAB, the major Fe2+ transporter of E. coli, operates anaerobically. However, Fe2+ remains stable aerobically under acidic conditions, although a low-pH Fe2+ importer has not been previously identified. Here we show that ycdNOB (efeUOB) specifies the first such transporter. efeUOB is repressed at high pH by CpxAR, and is Fe2+-Fur repressed. EfeU is homologous to the high-affinity iron permease, Ftr1p, of Saccharomyces cerevisiae and other fungi. EfeO is periplasmic with a cupredoxin N-terminal domain; EfeB is also periplasmic and is haem peroxidase-like. All three Efe proteins are required for Efe function. The efeU gene of E. coli K-12 is cryptic due to a frameshift mutation - repair of the single-base-pair deletion generates a functional EfeUOB system. In contrast, the efeUOB operon of the enterohaemorrhagic strain, O157:1147, lacks any frameshift and is functional. A 'wild-type' K-12 strain bearing a functional EfeUOB displays a major growth advantage under aerobic, low-pH, low-iron conditions when a competing metal is provided. Fe-55 transport assays confirm the ferrous iron specificity of EfeUOB.

Declining survival rates in a reintroduced population of the Mauritius kestrel: evidence for non-linear density dependence and environmental stochasticity

1. We studied a reintroduced population of the formerly critically endangered Mauritius kestrel Falco punctatus Temmink from its inception in 1987 until 2002, by which time the population had attained carrying capacity for the study area. Post-1994 the population received minimal management other than the provision of nestboxes. 2. We analysed data collected on survival (1987-2002) using program MARK to explore the influence of density-dependent and independent processes on survival over the course of the population's development. 3.We found evidence for non-linear, threshold density dependence in juvenile survival rates. Juvenile survival was also strongly influenced by climate, with the temporal distribution of rainfall during the cyclone season being the most influential climatic variable. Adult survival remained constant throughout. 4. Our most parsimonious capture-mark-recapture statistical model, which was constrained by density and climate, explained 75.4% of the temporal variation exhibited in juvenile survival rates over the course of the population's development. 5. This study is an example of how data collected as part of a threatened species recovery programme can be used to explore the role and functional form of natural population regulatory processes. With the improvements in conservation management techniques and the resulting success stories, formerly threatened species offer unique opportunities to further our understanding of the fundamental principles of population ecology.