Crystallization and preliminary X-ray diffraction studies of FHA domains of Dun1 and Rad53 protein kinases

Forkhead-associated (FHA) domains are modular protein–protein interaction domains of ~130 amino acids present in numerous signalling proteins. FHA-domain-dependent protein interactions are regulated by phosphorylation of target proteins and FHA domains may be multifunctional phosphopeptide-recognition modules. FHA domains of the budding yeast cell-cycle checkpoint protein kinases Dun1p and Rad53p have been crystallized. Crystals of the Dun1-FHA domain exhibit the symmetry of the space group P6122 or P6522, with unit-cell parameters a = b = 127.3, c = 386.3 Å; diffraction data have been collected to 3.1 Å resolution on a synchrotron source. Crystals of the N-terminal FHA domain (FHA1) of Rad53p diffract to 4.0 Å resolution on a laboratory X-ray source and have Laue-group symmetry 4/mmm, with unit-cell parameters a = b = 61.7, c = 104.3 Å.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

Classical and quantum N = 1 super W∞-algebras

We construct higher-spin N = 1 superalgebras as extensions of the super-Virasoro algebra containing generators for all spins s ≥ 3/2. We find two distinct classical (Poisson) algebras on the phase superspace. Our results indicate that only one of them can be consistently quantized.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Learning Methods and Algorithms for Semantic Text Classification across Multiple Domains

Information is nowadays a key resource: machine learning and data mining techniques have been developed to extract high-level information from great amounts of data. As most data comes in form of unstructured text in natural languages, research on text mining is currently very active and dealing with practical problems. Among these, text categorization deals with the automatic organization of large quantities of documents in priorly defined taxonomies of topic categories, possibly arranged in large hierarchies. In commonly proposed machine learning approaches, classifiers are automatically trained from pre-labeled documents: they can perform very accurate classification, but often require a consistent training set and notable computational effort. Methods for cross-domain text categorization have been proposed, allowing to leverage a set of labeled documents of one domain to classify those of another one. Most methods use advanced statistical techniques, usually involving tuning of parameters. A first contribution presented here is a method based on nearest centroid classification, where profiles of categories are generated from the known domain and then iteratively adapted to the unknown one. Despite being conceptually simple and having easily tuned parameters, this method achieves state-of-the-art accuracy in most benchmark datasets with fast running times. A second, deeper contribution involves the design of a domain-independent model to distinguish the degree and type of relatedness between arbitrary documents and topics, inferred from the different types of semantic relationships between respective representative words, identified by specific search algorithms. The application of this model is tested on both flat and hierarchical text categorization, where it potentially allows the efficient addition of new categories during classification. Results show that classification accuracy still requires improvements, but models generated from one domain are shown to be effectively able to be reused in a different one.

The Tabby phenotype is caused by mutation in a mouse homologue of the EDA gene that reveals novel mouse and human exons and encodes a protein (ectodysplasin-A) with collagenous domains

Mouse Tabby (Ta) and X chromosome-linked human EDA share the features of hypoplastic hair, teeth, and eccrine sweat glands. We have cloned the Ta gene and find it to be homologous to the EDA gene. The gene is altered in two Ta alleles with a point mutation or a deletion. The gene is expressed in developing teeth and epidermis; no expression is seen in corresponding tissues from Ta mice. Ta and EDA genes both encode alternatively spliced forms; novel exons now extend the 3′ end of the EDA gene. All transcripts recovered have the same 5′ exon. The longest Ta cDNA encodes a 391-residue transmembrane protein, ectodysplasin-A, containing 19 Gly-Xaa-Yaa repeats. The isoforms of ectodysplasin-A may correlate with differential roles during embryonic development.

Subcellular colocalization of the cellular and scrapie prion proteins in caveolae-like membranous domains

Results of transgenetic studies argue that the scrapie isoform of the prion protein (PrPSc) interacts with the substrate cellular PrP (PrPC) during conversion into nascent PrPSc. While PrPSc appears to accumulate primarily in lysosomes, caveolae-like domains (CLDs) have been suggested to be the site where PrPC is converted into PrPSc. We report herein that CLDs isolated from scrapie-infected neuroblastoma (ScN2a) cells contain PrPC and PrPSc. After lysis of ScN2a cells in ice-cold Triton X-100, both PrP isoforms and an N-terminally truncated form of PrPC (PrPC-II) were found concentrated in detergent-insoluble complexes resembling CLDs that were isolated by flotation in sucrose gradients. Similar results were obtained when CLDs were purified from plasma membranes by sonication and gradient centrifugation; with this procedure no detergents are used, which minimizes artifacts that might arise from redistribution of proteins among subcellular fractions. The caveolar markers ganglioside GM1 and H-ras were found concentrated in the CLD fractions. When plasma membrane proteins were labeled with the impermeant reagent sulfo-N-hydroxysuccinimide-biotin, both PrPC and PrPSc were found biotinylated in CLD fractions. Similar results on the colocalization of PrPC and PrPSc were obtained when CLDs were isolated from Syrian hamster brains. Our findings demonstrate that both PrPC and PrPSc are present in CLDs and, thus, support the hypothesis that the PrPSc formation occurs within this subcellular compartment.

Vps41p Function in the Alkaline Phosphatase Pathway Requires Homo-oligomerization and Interaction with AP-3 through Two Distinct Domains

Transport of proteins through the ALP (alkaline phosphatase) pathway to the vacuole requires the function of the AP-3 adaptor complex and Vps41p. However, unlike other adaptor protein–dependent pathways, the ALP pathway has not been shown to require additional accessory proteins or coat proteins, such as membrane recruitment factors or clathrin. Two independent genetic approaches have been used to identify new mutants that affect transport through the ALP pathway. These screens yielded new mutants in both VPS41 and the four AP-3 subunit genes. Two new VPS41 alleles exhibited phenotypes distinct from null mutants of VPS41, which are defective in vacuolar morphology and protein transport through both the ALP and CPY sorting pathways. The new alleles displayed severe ALP sorting defects, normal vacuolar morphology, and defects in ALP vesicle formation at the Golgi complex. Sequencing analysis of these VPS41 alleles revealed mutations encoding amino acid changes in two distinct domains of Vps41p: a conserved N-terminal domain and a C-terminal clathrin heavy-chain repeat (CHCR) domain. We demonstrate that the N-terminus of Vps41p is required for binding to AP-3, whereas the C-terminal CHCR domain directs homo-oligomerization of Vps41p. These data indicate that a homo-oligomeric form of Vps41p is required for the formation of ALP containing vesicles at the Golgi complex via interactions with AP-3.

Mutational analysis and molecular modeling of the nonapeptide hormone binding domains of the [Arg8]vasotocin receptor.

To identify determinants that form nonapeptide hormone binding domains of the white sucker Catostomus commersoni [Arg8]vasotocin receptor, chimeric constructs encoding parts of the vasotocin receptor and parts of the isotocin receptor have been analyzed by [(3,5-3H)Tyr2, Arg8]vasotocin binding to membranes of human embryonic kidney cells previously transfected with the different cDNA constructs and by functional expression studies in Xenopus laevis oocytes injected with mutant cRNAs. The results indicate that the N terminus and a region spanning the second extracellular loop and its flanking transmembrane segments, which contains a number of amino acid residues that are conserved throughout the nonapeptide receptor family, contribute to the affinity of the receptor for its ligand. Nonapeptide selectivity, however, is mainly defined by transmembrane region VI and the third extracellular loop. These results are complemented by a molecular model of the vasotocin receptor obtained by aligning its sequence with those of other G-protein coupled receptors as well as that of bacteriorhodopsin. The model indicates that amino acid residues of transmembrane regions II-VII that are located close to the extracellular surface also contribute to the binding of vasotocin.

The Berkovits Complex and Semi-free Extensions of Koszul Algebras

Peer reviewed

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are established

Pseudodifferential analysis in Psi*-algebras on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces

The present thesis is a contribution to the theory of algebras of pseudodifferential operators on singular settings. In particular, we focus on the $b$-calculus and the calculus on conformally compact spaces in the sense of Mazzeo and Melrose in connection with the notion of spectral invariant transmission operator algebras. We summarize results given by Gramsch et. al. on the construction of $Psi_0$-and $Psi*$-algebras and the corresponding scales of generalized Sobolev spaces using commutators of certain closed operators and derivations. In the case of a manifold with corners $Z$ we construct a $Psi*$-completion $A_b(Z,{}^bOmega^{1/2})$ of the algebra of zero order $b$-pseudodifferential operators $Psi_{b,cl}(Z, {}^bOmega^{1/2})$ in the corresponding $C*$-closure $B(Z,{}^bOmega^{12})hookrightarrow L(L^2(Z,{}^bOmega^{1/2}))$. The construction will also provide that localised to the (smooth) interior of Z the operators in the $A_b(Z, {}^bOmega^{1/2})$ can be represented as ordinary pseudodifferential operators. In connection with the notion of solvable $C*$-algebras - introduced by Dynin - we calculate the length of the $C*$-closure of $Psi_{b,cl}^0(F,{}^bOmega^{1/2},R^{E(F)})$ in $B(F,{}^bOmega^{1/2}),R^{E(F)})$ by localizing $B(Z, {}^bOmega^{1/2})$ along the boundary face $F$ using the (extended) indical familiy $I^B_{FZ}$. Moreover, we discuss how one can localise a certain solving ideal chain of $B(Z, {}^bOmega^{1/2})$ in neighbourhoods $U_p$ of arbitrary points $pin Z$. This localisation process will recover the singular structure of $U_p$; further, the induced length function $l_p$ is shown to be upper semi-continuous. We give construction methods for $Psi*$- and $C*$-algebras admitting only infinite long solving ideal chains. These algebras will first be realized as unconnected direct sums of (solvable) $C*$-algebras and then refined such that the resulting algebras have arcwise connected spaces of one dimensional representations. In addition, we recall the notion of transmission algebras on manifolds with corners $(Z_i)_{iin N}$ following an idea of Ali Mehmeti, Gramsch et. al. Thereby, we connect the underlying $C^infty$-function spaces using point evaluations in the smooth parts of the $Z_i$ and use generalized Laplacians to generate an appropriate scale of Sobolev spaces. Moreover, it is possible to associate generalized (solving) ideal chains to these algebras, such that to every $ninN$ there exists an ideal chain of length $n$ within the algebra. Finally, we discuss the $K$-theory for algebras of pseudodifferential operators on conformally compact manifolds $X$ and give an index theorem for these operators. In addition, we prove that the Dirac-operator associated to the metric of a conformally compact manifold $X$ is not a Fredholm operator.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.