Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

DEVELOPMENTAL AND CELLULAR FUNCTIONS OF DELTA-CATENIN

Catenins have diverse and powerful roles in embryogenesis, homeostasis or disease progression, as best exemplified by the well-known beta-catenin. The less studied delta-catenin likewise contains a central Armadillo-domain. In common with other p120 sub-class members, it acts in a variety of intracellular compartments and modulates cadherin stability, small GTPase activities and gene transcription. In mammals, delta-catenin exhibits neural specific expression, with its knock-out in mice correspondingly producing cognitive defects and synaptic dysfunctions. My work instead employed the amphibian, Xenopus laevis, to explore delta-catenin’s physiological functions in a distinct vertebrate system. Initial isolation and characterization indicated delta-catenin’s expression in Xenopus. Unlike the pattern observed for mammals, delta-catenin was detected in most adult Xenopus tissues, although enriched in embryonic structures of neural fate as visualized using RNA in-situ hybridization. To determine delta-catenin’s requirement in amphibian development, I employed anti-sense morpholinos to knock-down gene products, finding that delta-catenin depletion results in developmental defects in gastrulation, neural crest migration and kidney tubulogenesis, phenotypes that were specific based upon rescue experiments. In biochemical and cellular assays, delta-catenin knock-down reduced cadherin levels and cell adhesion, and impaired activation of RhoA and Rac1, small GTPases that regulate actin dynamics and morphogenetic movements. Indeed, exogenous C-cadherin, or dominant-negative RhoA or dominant-active Rac1, significantly rescued delta-catenin depletion. Thus, my results indicate delta-catenin’s essential roles in Xenopus development, with contributing functional links to cadherins and Rho family small G proteins. In examining delta-catenin’s nuclear roles, I identified delta-catenin as an interacting partner and substrate of the caspase-3 protease, which plays critical roles in apoptotic as well as non-apoptotic processes. Delta-catenin’s interaction with and sensitivity to caspase-3 was confirmed using assays involving its cleavage in vitro, as well as within Xenopus apoptotic extracts or mammalian cell lines. The cleavage site, a highly conserved caspase consensus motif (DELD) within Armadillo-repeat 6 of delta-catenin, was identified through peptide sequencing. Cleavage thus generates an amino- (1-816) and carboxyl-terminal (817-1314) fragment each containing about half of the central Armadillo-domain. I found that cleavage of delta-catenin both abolishes its association with cadherins, and impairs its ability to modulate small GTPases. Interestingly, the carboxyl-terminal fragment (817-1314) possesses a conserved putative nuclear localization signal that I found is needed to facilitate delta-catenin’s nuclear targeting. To probe for novel nuclear roles of delta-catenin, I performed yeast two-hybrid screening of a mouse brain cDNA library, resolving and then validating its interaction with an uncharacterized KRAB family zinc finger protein I named ZIFCAT. My results indicate that ZIFCAT is nuclear, and suggest that it may associate with DNA as a transcriptional repressor. I further determined that other p120 sub-class catenins are similarly cleaved by caspase-3, and likewise bind ZIFCAT. These findings potentially reveal a simple yet novel signaling pathway based upon caspase-3 cleavage of p120 sub-family members, facilitating the coordinate modulation of cadherins, small GTPases and nuclear functions. Together, my work suggested delta-catenin’s essential roles in Xenopus development, and has revealed its novel contributions to cell junctions (via cadherins), cytoskeleton (via small G proteins), and nucleus (via ZIFCAT). Future questions include the larger role and gene targets of delta-catenin in nucleus, and identification of upstream signaling events controlling delta-catenin’s activities in development or disease progression.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

The anterior determinant bicoid of Drosophila is a derived Hox class 3 gene

The Drosophila gene bicoid functions as the anterior body pattern organizer of Drosophila. Embryos lacking maternally expressed bicoid fail to develop anterior segments including head and thorax. In wild-type eggs, bicoid mRNA is localized in the anterior pole region and the bicoid protein forms an anterior-to-posterior concentration gradient. bicoid activity is required for transcriptional activation of zygotic segmentation genes and the translational suppression of uniformly distributed maternal caudal mRNA in the anterior region of the embryo. caudal genes as well as other homeobox genes or members of the Drosophila segmentation gene cascade have been found to be conserved in animal evolution. In contrast, bicoid homologs have been identified only in close relatives of the schizophoran fly Drosophila. This poses the question of how the bicoid gene evolved and adopted its unique function in organizing anterior–posterior polarity. We have cloned bicoid from a basal cyclorrhaphan fly, Megaselia abdita (Phoridae, Aschiza), and show that the gene originated from a recent duplication of the direct homolog of the vertebrate gene Hox3, termed zerknüllt, which specifies extraembryonic tissues in insects.

DRC1, DNA replication and checkpoint protein 1, functions with DPB11 to control DNA replication and the S-phase checkpoint in Saccharomyces cerevisiae

In addition to DNA polymerase complexes, DNA replication requires the coordinate action of a series of proteins, including regulators Cdc28/Clb and Dbf4/Cdc7 kinases, Orcs, Mcms, Cdc6, Cdc45, and Dpb11. Of these, Dpb11, an essential BRCT repeat protein, has remained particularly enigmatic. The Schizosaccharomyces pombe homolog of DPB11, cut5, has been implicated in the DNA replication checkpoint as has the POL2 gene with which DPB11 genetically interacts. Here we describe a gene, DRC1, isolated as a dosage suppressor of dpb11–1. DRC1 is an essential cell cycle-regulated gene required for DNA replication. We show that both Dpb11 and Drc1 are required for the S-phase checkpoint, including the proper activation of the Rad53 kinase in response to DNA damage and replication blocks. Dpb11 is the second BRCT-repeat protein shown to control Rad53 function, possibly indicating a general function for this class of proteins. DRC1 and DPB11 show synthetic lethality and reciprocal dosage suppression. The Drc1 and Dpb11 proteins physically associate and function together to coordinate DNA replication and the cell cycle.

HLA class I and II antigens are partially co-clustered in the plasma membrane of human lymphoblastoid cells

Major histocompatibility complex (MHC) class II molecules displayed clustered patterns at the surfaces of T (HUT-102B2) and B (JY) lymphoma cells characterized by interreceptor distances in the micrometer range as detected by scanning force microscopy of immunogold-labeled antigens. Electron microscopy revealed that a fraction of the MHC class II molecules was also heteroclustered with MHC class I antigens at the same hierarchical level as described by the scanning force microscopy data, after specifically and sequentially labeling the antigens with 30- and 15-nm immunogold beads. On JY cells the estimated fraction of co-clustered HLA II was 0.61, whereas that of the HLA I was 0.24. Clusterization of the antigens was detected by the deviation of their spatial distribution from the Poissonian distribution representing the random case. Fluorescence resonance energy transfer measurements also confirmed partial co-clustering of the HLA class I and II molecules at another hierarchical level characterized by the 2- to 10-nm Förster distance range and providing fine details of the molecular organization of receptors. The larger-scale topological organization of the MHC class I and II antigens may reflect underlying membrane lipid domains and may fulfill significant functions in cell-to-cell contacts and signal transduction.

The Export of Major Histocompatibility Complex Class I Molecules from the Endoplasmic Reticulum of Rat Brown Adipose Cells Is Acutely Stimulated by Insulin

Major histocompatibility complex class I (MHC-I) molecules have been implicated in several nonimmunological functions including the regulation and intracellular trafficking of the insulin-responsive glucose transporter GLUT4. We have used confocal microscopy to compare the effects of insulin on the intracellular trafficking of MHC-I and GLUT4 in freshly isolated rat brown adipose cells. We also used a recombinant vaccinia virus (rVV) to express influenza virus hemagglutinin (HA) as a generic integral membrane glycoprotein to distinguish global versus specific enhancement of protein export from the endoplasmic reticulum (ER) in response to insulin. In the absence of insulin, MHC-I molecules largely colocalize with the ER-resident protein calnexin and remain distinct from intracellular pools of GLUT4. Surprisingly, insulin induces the rapid export of MHC-I molecules from the ER with a concomitant approximately three-fold increase in their level on the cell surface. This ER export is blocked by brefeldin A and wortmannin but is unaffected by cytochalasin D, indicating that insulin stimulates the rapid transport of MHC-I molecules from the ER to the plasma membrane via the Golgi complex in a phosphatidyl-inositol 3-kinase–dependent and actin-independent manner. We further show that the effect of insulin on MHC-I molecules is selective, because insulin does not affect the intracellular distribution or cell-surface localization of rVV-expressed HA. These results demonstrate that in rat brown adipose cells MHC-I molecule export from the ER is stimulated by insulin and provide the first evidence that the trafficking of MHC-I molecules is acutely regulated by a hormone.

Considerations of transcriptional control mechanisms: Do TFIID–core promoter complexes recapitulate nucleosome-like functions?

The general transcription initiation factor TFIID was originally identified, purified, and characterized with a biochemical assay in which accurate transcription initiation is reconstituted with multiple, chromatographically separable activities. Biochemical analyses have demonstrated that TFIID is a multiprotein complex that directs preinitiation complex assembly on both TATA box-containing and TATA-less promoters, and some TFIID subunits have been shown to be molecular targets for activation domains in DNA-binding regulatory proteins. These findings have most commonly been interpreted to support the view that transcriptional activation by upstream factors is the result of enhanced TFIID recruitment to the core promoter. Recent insights into the architecture and cell-cycle regulation of the multiprotein TFIID complex prompt both a reassessment of the functional role of TFIID in gene activation and a review of some of the less well-appreciated literature on TFIID. We present a speculative model for diverse functional roles of TFIID in the cell, explore the merits of the model in the context of published data, and suggest experimental approaches to resolve unanswered questions. Finally, we point out how the proposed functional roles of TFIID in eukaryotic class II transcription fit into a model for promoter recognition and activation that applies to both eubacteria and eukaryotes.

Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.

Distinct functions and cooperative interaction of the subunits of the transporter associated with antigen processing (TAP)

The ATP-binding cassette (ABC) transporter TAP translocates peptides from the cytosol to awaiting MHC class I molecules in the endoplasmic reticulum. TAP is made up of the TAP1 and TAP2 polypeptides, which each possess a nucleotide binding domain (NBD). However, the role of ATP in peptide binding and translocation is poorly understood. We present biochemical and functional evidence that the NBDs of TAP1 and TAP2 are non-equivalent. Photolabeling experiments with 8-azido-ATP demonstrate a cooperative interaction between the two NBDs that can be stimulated by peptide. The substitution of key lysine residues in the Walker A motifs of TAP1 and TAP2 suggests that TAP1-mediated ATP hydrolysis is not essential for peptide translocation but that TAP2-mediated ATP hydrolysis is critical, not only for translocation, but for peptide binding.

Human CD8+ T lymphocyte subsets that express HLA class I-specific inhibitory receptors represent oligoclonally or monoclonally expanded cell populations.

A small percentage of human T lymphocytes, predominantly CD8+ T cells, express receptors for HLA class 1 molecules of natural killer type (NK-R) that are inhibitory for T-cell antigen receptor (TCR)-mediated functions. In the present study, it is demonstrated that the various NK-R molecules typically expressed by NK cells are also expressed on periheral blood T lymphocytes. These CD3+ NK-R+ cells have a cell surface phenotype typical of memory cells as indicated by the expression of CD45RO and CD29 and by the lack of CD28 and CD45RA. Furthermore, by the combined use of anti-TCR V beta-specific antibodies and a semiquantitative polymerase chain reaction assay, the TCR repertoire in this CD3+ NK-R+ cell subset was found to be skewed; in fact, one or two V beta families were largely represented, and most of the other V beta s were barely detected. In addition, analysis of recombinant clones of the largely represented V beta families demonstrated that these V beta s were oligoclonally or monoclonally expanded.

N-methyl-D-aspartate receptor-induced proteolytic conversion of postsynaptic class C L-type calcium channels in hippocampal neurons.

Ca2+ influx controls multiple neuronal functions including neurotransmitter release, protein phosphorylation, gene expression, and synaptic plasticity. Brain L-type Ca2+ channels, which contain either alpha 1C or alpha 1D as their pore-forming subunits, are an important source of calcium entry into neurons. Alpha 1C exists in long and short forms, which are differentially phosphorylated, and C-terminal truncation of alpha 1C increases its activity approximately 4-fold in heterologous expression systems. Although most L-type calcium channels in brain are localized in the cell body and proximal dendrites, alpha 1C subunits in the hippocampus are also present in clusters along the dendrites of neurons. Examination by electron microscopy shows that these clusters of alpha 1C are localized in the postsynaptic membrane of excitatory synapses, which are known to contain glutamate receptors. Activation of N-methyl-D-aspartate (NMDA)-specific glutamate receptors induced the conversion of the long form of alpha 1C into the short form by proteolytic removal of the C terminus. Other classes of Ca2+ channel alpha1 subunits were unaffected. This proteolytic processing reaction required extracellular calcium and was blocked by inhibitors of the calcium-activated protease calpain, indicating that calcium entry through NMDA receptors activated proteolysis of alpha1C by calpain. Purified calpain catalyzed conversion of the long form of immunopurified alpha 1C to the short form in vitro, consistent with the hypothesis that calpain is responsible for processing of alpha 1C in hippocampal neurons. Our results suggest that NMDA receptor-induced processing of the postsynaptic class C L-type Ca2+ channel may persistently increase Ca2+ influx following intense synaptic activity and may influence Ca2+-dependent processes such as protein phosphorylation, synaptic plasticity, and gene expression.

A class of single-stranded telomeric DNA-binding proteins required for Rap1p localization in yeast nuclei.

We have identified a class of proteins that bind single-stranded telomeric DNA and are required for the nuclear organization of telomeres and/or telomere-associated proteins. Rlf6p was identified by its sequence similarity to Gbp1p, a single-stranded telomeric DNA-binding protein from Chlamydomonas reinhardtii. Rlf6p and Gbp1p bind yeast single-stranded G-strand telomeric DNA. Both proteins include at least two RNA recognition motifs, which are found in many proteins that interact with single-stranded nucleic acids. Disruption of RLF6 alters the distribution of repressor/activator protein 1 (Rap1p), a telomere-associated protein. In wild-type yeast cells, Rap1p localizes to a small number of perinuclear spots, while in rlf6 cells Rap1p appears diffuse and nuclear. Interestingly, telomere position effect and telomere length control, which require RAP1, are unaffected by rlf6 mutations, demonstrating that Rap1p localization can be uncoupled from other Rap1p-dependent telomere functions. In addition, expression of Chlamydomonas GBP1 restores perinuclear, punctate Rap1p localization in rlf6 mutant cells. The functional complementation of a fungal gene by an algal gene suggests that Rlf6p and Gbp1p are members of a conserved class of single-stranded telomeric DNA-binding proteins that influence nuclear organization. Furthermore, it demonstrates that, despite their unusual codon bias, C. reinhardtii genes can be efficiently translated in Saccharomyces cerevisiae cells.

Expression cloning of dSR-CI, a class C macrophage-specific scavenger receptor from Drosophila melanogaster.

Mammalian class A macrophage-specific scavenger receptors (SR-A) exhibit unusually broad binding specificity for a wide variety of polyanionic ligands. The properties of these receptors suggest that they may be involved in atherosclerosis and host defense. We have previously observed a similar receptor activity in Drosophila melanogaster embryonic macrophages and in the Drosophila macrophage-like Schneider L2 cell line. Expression cloning was used to isolate from L2 cells a cDNA that encodes a third class (class C) of scavenger receptor, Drosophila SR-CI (dSR-CI). dSR-CI expression was restricted to macrophages/hemocytes during embryonic development. When expressed in mammalian cells, dSR-CI exhibited high affinity and saturable binding of 125I-labeled acetylated low density lipoprotein and mediated its chloroquine-dependent, presumably lysosomal, degradation. Although the broad polyanionic ligand-binding specificity of dSR-CI was similar to that of SR-A, their predicted protein sequences are not similar. dSR-CI is a 609-residue type I integral membrane protein containing several well-known sequence motifs, including two complement control protein (CCP) domains and somatomedin B, MAM, and mucin-like domains. Macrophage scavenger receptors apparently mediate important, well-conserved functions and may be pattern-recognition receptors that arose early in the evolution of host-defense mechanisms. Genetic and physiologic analysis of dSR-CI function in Drosophila should provide further insights into the roles played by scavenger receptors in host defense and development.

On the uniform approximation of Cauchy continuous functions

In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.