Unique Extension Research Articles

A Unique Dual Activity Amino Acid Hydroxylase in Toxoplasma gondii

The genome of the protozoan parasite Toxoplasma gondii was found to contain two genes encoding tyrosine hydroxylase; that produces l-DOPA. The encoded enzymes metabolize phenylalanine as well as tyrosine with substrate preference for tyrosine. Thus the enzymes catabolize phenylalanine to tyrosine and tyrosine to l-DOPA. The catalytic domain descriptive of this class of enzymes is conserved with the parasite enzyme and exhibits similar kinetic properties to metazoan tyrosine hydroxylases, but contains a unique N-terminal extension with a signal sequence motif. One of the genes, TgAaaH1, is constitutively expressed while the other gene, TgAaaH2, is induced during formation of the bradyzoites of the cyst stages of the life cycle. This is the first description of an aromatic amino acid hydroxylase in an apicomplexan parasite. Extensive searching of apicomplexan genome sequences revealed an ortholog in Neospora caninum but not in Eimeria, Cryptosporidium, Theileria, or Plasmodium. Possible role(s) of these bi-functional enzymes during host infection are discussed.

Defining numbers in some of the Harary graphs

In a given graph G = ( V , E ) , a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G if there exists a unique extension of the colors of S to a c ≥ χ ( G ) coloring of the vertices of G . A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number. In this note, we study the chromatic number, the defining number and the strong defining number in some of the Harary graphs.

On finite 2-groups all of whose subgroups are mutually isomorphic

In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that, we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64.

Human Cardiac Troponin Cross-Linking and the Functional Consequences

Previous structural studies suggested that the cardiac unique N-terminal extension of troponin I interacts with the basic regions near the inhibitory peptide (Howarth et al. (2007) J Mol Biol 373, 706-722). To determine possible interactions, we cross-linked single Cys mutant TnI at either position 5 or 19 in the troponin complex with the hetero-bifunctional cross-linker benzophenone-4-maleimide. Data from SDS-PAGE and reversed phase HPLC indicated intra-molecular and inter-molecular cross-linking with troponin C and T.

Automorphisms of Endomorphism Monoids of 1-Simple Free Algebras

For any set X and any variety 𝒱 of algebras, let 𝒜 = 𝒜 𝒱(X) be the free algebra in 𝒱 with set X of free generators, and let End(𝒜) be the monoid of endomorphisms of 𝒜. We provide a general approach to the description of the automorphism group of End(𝒜), and some subsemigroups of End(𝒜), provided that 𝒜 is 1-simple. We show that every automorphism of End(𝒜) is a unique extension of an automorphism of the monoid of endomorphisms of rank at most 1.

Secretory Trafficking Signal Encoded in the Carboxyl-Terminal Region of the CGβ-Subunit

Although the LHbeta- and chorionic gonadotropin-beta- (CGbeta) subunits share a high degree of sequence identity (>85%) in the first 114 amino acids, there is considerable sequence divergence at their carboxy ends. The CGbeta-subunit terminates with a unique carboxyl-terminal extension (115-145; carboxyl-terminal peptide), which contains four O-linked oligosaccharides, whereas the LHbeta-subunit bears a hydrophobic heptapeptide (115-121) at its carboxy terminus. LH is released through the regulated pathway in the pituitary, whereas CG is secreted constitutively from the placenta. We previously demonstrated in rat somatotroph-derived GH(3) cells that the LH is associated primarily with a regulated routing, and although the majority of CG was released constitutively from the cells, there was a fraction that was segregated through the regulated pathway. Moreover, we showed that the LHbeta heptapeptide is a determinant for the regulated secretion of LH. Given that the primary evolutionary change between LHbeta and CGbeta occurred at the carboxy terminus, these data suggested that the presence of the CGbeta carboxyl-terminal peptide region is responsible for the constitutive secretion of CG. A CG114 mutant (CGDeltaT) was constructed and expressed in GH(3) cells. Steady-state labeling and pulse-chase experiments demonstrated that the CGDeltaT entered the regulated pathway resulting in over 4-fold increase in the intracellular pool. The secretagogue, forskolin, stimulated CGDeltaT release over 3-fold, which was accompanied by a parallel intracellular decrease, and only marginal stimulation of CG was seen. Immunofluorescence demonstrated a unique membrane pattern of staining for CGDeltaT compared with dispersed cytoplasmic puncta for CG. Stimulation with forskolin caused a significant reduction in the relative fluorescence of CGDeltaT cells compared with a minor reduction for CG. These data show that the CGDeltaT analog resembles LH in its intracellular trafficking, further supporting the hypothesis that determinants at the carboxyl-terminal end of the CGbeta-subunit evolved from the LHbeta-subunit primarily to overcome the slow release and intracellular storage of LH resulting in rapid secretion of CG from the placenta.

A note on stochastic integration with respect to optional semimartingales

In this note we discuss the extension of the elementary stochastic Ito-integral w.r.t. an optional semimartingale. The paths of an optional semimartingale possess limits from the left and from the right, but may have double jumps. This leads to quite interesting phenomena in integration theory. <br> We find a mathematically tractable domain of general integrands. The simple integrands are embedded into this domain. Then, we characterize the integral as the unique continuous and linear extension of the elementary integral and show completeness of the space of integrals. Thus our integral possesses desirable properties to model dynamic trading gains in mathematical finance when security price processes follow optional semimartingales.

BV ‐extension of rate independent operators

AbstractRate independent operators naturally arise in the mathematical analysis of hysteresis. Among rate independent operators, the locally monotone ones are those better suited for the study of PDE's with hysteresis. We prove that a rate independent operator R: Lip (0, T) → BV (0, T) ∩ C (0, T) which is locally monotone and continuous with respect to the strict topology of BV admits a unique continuous extension R̃: BV (0, T) → BV (0, T). This general result applies to several concrete hysteresis operators. For many of these operators the existence of a continuous extension was previously known at most to the space BV (0, T) ∩ C (0, T). (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Extensions of p-adic vector measures

For R being a separating algebra of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m: R → E a bounded finitely additive measure, it is shown that: a If m is σ-additive and strongly additive, then m has a unique σ-additive extension m σ on the σ-algebra R σ generated by R. b If m is strongly additive and τ-additive, then m has a unique τ-additive extension m τ on the α-algebra R bo of all τ R -Borel sets, where τ R is the topology having R as a basis. Also, some other results concerning such measures are given.

Structure and Inhibition of the CO 2-Sensing Carbonic Anhydrase Can2 from the Pathogenic Fungus Cryptococcus neoformans

In the pathogenic fungus Cryptococcus neoformans, a CO 2-sensing system is essential for survival in the natural environment (∼ 0.03% CO 2) and mediates the switch to virulent growth in the human host (∼ 5% CO 2). This system is composed of the carbonic anhydrase (CA) Can2, which catalyzes formation of bicarbonate, and the fungal, bicarbonate-stimulated adenylyl cyclase Cac1. The critical role of these enzymes for fungal metabolism and pathogenesis identifies them as targets for antifungal drugs. Here, we prove functional similarity of Can2 to the CA Nce103 from Candida albicans and describe its biochemical and structural characterization. The crystal structure of Can2 reveals that the enzyme belongs to the “plant-type” β-CAs but carries a unique N-terminal extension that can interact with the active-site entrance of the dimer. We further tested a panel of compounds, identifying nanomolar Can2 inhibitors, and present the structure of a Can2 complex with the inhibitor and product analog acetate, revealing insights into interactions with physiological ligands and inhibitors.

Dirac operators on non-compact orbifolds

In this paper we prove that Dirac operators on non-compact almost complex, complete orbifolds which are sufficiently regular at infinity, admit a unique extension. Additonally, we prove a generalized orbifold Stokes’/Divergence theorem.

A Novel Type of Monoheme Cytochrome c: Biochemical and Structural Characterization at 1.23 Å Resolution of Rhodothermus marinus Cytochrome c

Monoheme cytochromes of the C-type are involved in a large number of electron transfer processes, which play an essential role in multiple pathways, such as respiratory chains, either aerobic or anaerobic, and the photosynthetic electron transport chains. This study reports the biochemical characterization and the crystallographic structure, at 1.23 A resolution, of a monoheme cytochrome c from the thermohalophilic bacterium Rhodothermus marinus. In addition to an alpha-helical core folded around the heme, common for this type of cytochrome, the X-ray structure reveals one unusual alpha-helix and a unique N-terminal extension, which wraps around the back of the molecule. Based on a thorough structural and amino acid sequence comparison, we propose R. marinus cytochrome c as the first characterized member of a new class of C-type cytochromes.

Tug-of-war with noise: A game-theoretic view of the p-Laplacian

Fix a bounded domain Ω⊂Rd, a continuous function F:∂Ω→R, and constants ε>0 and 1<p,q<∞ with p−1+q−1=1. For each x∈Ω, let uε(x) be the value for player I of the following two-player, zero-sum game. The initial game position is x. At each stage, a fair coin is tossed, and the player who wins the toss chooses a vector v∈B̲(0,ε) to add to the game position, after which a random noise vector with mean zero and variance (q/p)|v|2 in each orthogonal direction is also added. The game ends when the game position reaches some y∈∂Ω, and player I's payoff is F(y). We show that (for sufficiently regular Ω) as ε tends to zero, the functions uε converge uniformly to the unique p-harmonic extension of F. Using a modified game (in which ε gets smaller as the game position approaches ∂Ω), we prove similar statements for general bounded domains Ω and resolutive functions F. These games and their variants interpolate between the tug-of-war games studied by Peres, Schramm, Sheffield, and Wilson [15], [16] (p=∞) and the motion-by-curvature games introduced by Spencer [17] and studied by Kohn and Serfaty [9] (p=1). They generalize the relationship between Brownian motion and the ordinary Laplacian and yield new results about p-capacity and p-harmonic measure

Regulated Secretion of a Protease Activates Intercellular Signaling during Fruiting Body Formation in M. xanthus

In response to starvation Myxococcus xanthus initiates a developmental program that culminates in fruiting body formation. There are two morphogenetic events in this program, aggregation and sporulation, which are temporally and spatially coordinated by the contact-dependent intercellular C-signal protein (p17). p17 is generated by proteolytic cleavage of the p25 precursor protein, which accumulates in the outer membrane of vegetative and starving cells. However, p17 generation is restricted to starving cells. Here we identify the subtilisin-like protease PopC that is directly responsible for cleavage of p25. PopC accumulates in the cytoplasm of vegetative cells but is selectively secreted during starvation coinciding with the generation of p17. Consequently, p25 and PopC only encounter each other in starving cells. Thus, restriction of p25 cleavage to starving cells occurs by a compartmentalization mechanism that depends on selective secretion of PopC during starvation. Our results provide evidence for regulated proteolysis via regulated secretion.

V-Adic maximal extensions, spectral norms and absolute Galois groups

Let (K, v) be a perfect rank one valued field and let \({(\overline{K_{v}},\overline{v})}\) be the canonical valued field obtained from (K, v) by the unique extension of the valuation \({\widetilde{v}}\) of Kv, the completion of K relative to v, to a fixed algebraic closure \({\overline{K_{v}}}\) of Kv. Let \({\overline{K}}\) be the algebraic closure of K in \({\overline {K_{v}}}\). An algebraic extension L of K, \({L\subset\overline{K}}\), is said to be a v-adic maximal extension, if \({\overline{v}\mid_{L}}\) is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in connection with the v-adic spectral norm on \({\overline{K}}\) and with the absolute Galois groups Gal\({(\overline{K}/K)}\) and Gal\({(\overline{K_{v}} /K_{v})}\). Some other auxiliary results are given, which may be useful for other purposes.

A palindromization map for the free group

We define a self-map Pal : F 2 → F 2 of the free group on two generators a , b , using automorphisms of F 2 that form a group isomorphic to the braid group B 3 . The map Pal restricts to de Luca’s right iterated palindromic closure on the submonoid generated by a , b . We show that Pal is continuous for the profinite topology on F 2 ; it is the unique continuous extension of de Luca’s right iterated palindromic closure to F 2 . The values of Pal are palindromes and coincide with the elements g ∈ F 2 such that a b g and b a g are conjugate.

Effects of training on acquisition of pest management knowledge and skills by small vegetable farmers

Effects of farmer field school (FFS) and the conventional (classroom lectures) training on acquisition of pest management knowledge and skills by small vegetable farmers were studied in Yunnan province, China from 2003 to 2007. There were significant gains of knowledge about vegetable pests, natural enemies, insect and disease ecology and pest management among the FFS farmers, but were no significant improvements of knowledge among the conventional trained farmers. Vegetable FFS enabled farmers to learn simple knowledge as well as complex IPM knowledge. In contrast, the conventional training only improved vegetable farmers' simple knowledge. The potential and limitations of FFS as a unique extension tool to disseminate the complex knowledge of IPM to smallholder farmers were demonstrated.

Extensions of homogeneous polynomials on c 0(l 2i)

Abstract We show that a 2-homogeneous polynomial on the complex Banach space c 0 l 2i) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c 0(l 2i).

A dynamical systems approach to the Kadison–Singer problem

In these notes we develop a link between the Kadison–Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove that if any state corresponding to a minimal idempotent point extends uniquely to the von Neumann algebra of the group, then every state extends uniquely to the von Neumann algebra of the group. We prove that if any state arising in the Kadison–Singer problem has a unique extension, then the injective envelope of a C*-crossed product algebra associated with the state necessarily contains the full von Neumann algebra of the group. We prove that this latter property holds for states arising from rare ultrafilters and δ-stable ultrafilters, independent, of the group action and also for states corresponding to non-recurrent points in the corona of the group.

Irreducible Width 2 Posets of Linear Discrepancy 3

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable in P, then |hL(x) − hL(y)| ≤ k, where hL(x) is the height of x in L. Tannenbaum, Trenk, and Fishburn characterized the posets of linear discrepancy 1 as the semiorders of width 2 and posed the problem for characterizing the posets of linear discrepancy 2. Howard et al. (Order 24:139–153, 2007) showed that this problem is equivalent to finding all posets of linear discrepancy 3 such that the removal of any point reduces the linear discrepancy. In this paper we determine all of these minimal posets of linear discrepancy 3 that have width 2. We do so by showing that, when removing a specific maximal point in a minimal linear discrepancy 3 poset, there is a unique linear extension that witnesses linear discrepancy 2.