On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Immune response to insulin and changes in the gut immune system in children with or at risk for type 1 diabetes

Type 1 diabetes (T1D) is considered to be an autoimmune disease. The cause of T1D is the destruction of insulin-producing β-cells in the pancreatic islets. The autoimmune nature of T1D is characterized by the presence of autoreactive T-cells and autoantibodies against β-cell molecules. Insulin is the only β-cell-specific autoantigen associated with T1D but the insulin autoantibodies (IAAs) are difficult to measure with proper sensitivity. T-cell assays for detection of autoreactive T-cells, such as insulin-specific T-cells, have also proven to be difficult to perform. The genetic risk of T1D is associated with the HLA gene region but the environmental factors also play an important role. The most studied environmental risk factors of T1D are enteroviruses and cow's milk which both affect the immune system through the gut. One hypothesis is that the insulin-specific immune response develops against bovine insulin in cow's milk during early infancy and later spreads to include human insulin. The aims of this study were to determine whether the separation of immunoglobulin (Ig)G from plasma would improve the sensitivity of the IAA assay and how insulin treatment affects the cellular immune response to insulin in newly diagnosed patients. Furthermore, the effect of insulin concentration in mother's breast milk on the development of antibodies to dietary insulin in the child was examined. Small intestinal biopsies were also obtained from children with T1D to characterize any immunological changes associated with T1D in the gut. The isolation of the IgG fraction from the plasma of T1D patients negative for plasma IAA led to detectable IAA levels that exceeded those in the control children. Thus the isolation of IgG may improve the sensitivity of the IAA assay. The effect of insulin treatment on insulin-specific T-cells was studied by culturing peripheral blood mononuclear cells with insulin. The insulin stimulation induced increased expression of regulatory T-cell markers, such as Foxp3, in those patients treated with insulin than in patients examined before initiating insulin treatment. This finding suggests that insulin treatment in patients with T1D stimulates regulatory T-cells in vivo and this may partly explain the difficulties in measuring autoantigen-specific T-cell responses in recently diagnosed patients. The stimulation of regulatory T-cells by insulin treatment may also explain the remission period often seen after initiating insulin treatment. In the third study we showed that insulin concentration in mother's breast milk correlates inversely with the levels of bovine insulin-specific antibodies in those infants who were exposed to cow's milk proteins in their diet, suggesting that human insulin in breast milk induces tolerance to dietary bovine insulin. However, in infants who later developed T1D-associated autoantibodies, the insulin concentration in their mother's breast milk was increased. This finding may indicate that in those children prone to β-cell autoimmunity, breast milk insulin does not promote tolerance to insulin. In the small intestinal biopsies the presence of several immunological markers were quantified with the RT-PCR. From these markers the expression of the interleukin (IL)-18 cytokine was significantly increased in the gut in patients with T1D compared with children with celiac disease or control children. The increased IL-18 expression lends further support for the hypothesis that the gut immune system is involved in the pathogenesis of T1D.

U12-type Spliceosome: Localization and Effects of Splicing Efficiency on Gene Expression

The removal of non-coding sequences, introns, is an essential part of messenger RNA processing. In most metazoan organisms, the U12-type spliceosome processes a subset of introns containing highly conserved recognition sequences. U12-type introns constitute less than 0,5% of all introns and reside preferentially in genes related to information processing functions, as opposed to genes encoding for metabolic enzymes. It has previously been shown that the excision of U12-type introns is inefficient compared to that of U2-type introns, supporting the model that these introns could provide a rate-limiting control for gene expression. The low efficiency of U12-type splicing is believed to have important consequences to gene expression by limiting the production of mature mRNAs from genes containing U12-type introns. The inefficiency of U12-type splicing has been attributed to the low abundance of the components of the U12-type spliceosome in cells, but this hypothesis has not been proven. The aim of the first part of this work was to study the effect of the abundance of the spliceosomal snRNA components on splicing. Cells with a low abundance of the U12-type spliceosome were found to inefficiently process U12-type introns encoded by a transfected construct, but the expression levels of endogenous genes were not found to be affected by the abundance of the U12-type spliceosome. However, significant levels of endogenous unspliced U12-type intron-containing pre-mRNAs were detected in cells. Together these results support the idea that U12-type splicing may limit gene expression in some situations. The inefficiency of U12-type splicing has also promoted the idea that the U12-type spliceosome may control gene expression, limiting the mRNA levels of some U12-type intron-containing genes. While the identities of the primary target genes that contain U12-type introns are relatively well known, little has previously been known about the downstream genes and pathways potentially affected by the efficiency of U12-type intron processing. Here, the effects of U12-type splicing efficiency on a whole organism were studied in a Drosophila line with a mutation in an essential U12-type spliceosome component. Genes containing U12-type introns showed variable gene-specific responses to the splicing defect, which points to variation in the susceptibility of different genes to changes in splicing efficiency. Surprisingly, microarray screening revealed that metabolic genes were enriched among downstream effects, and that the phenotype could largely be attributed to one U12-type intron-containing mitochondrial gene. Gene expression control by the U12-type spliceosome could thus have widespread effects on metabolic functions in the organism. The subcellular localization of the U12-type spliceosome components was studied as a response to a recent dispute on the localization of the U12-type spliceosome. All components studied were found to be nuclear indicating that the processing of U12-type introns occurs within the nucleus, thus clarifying a question central to the field. The results suggest that the U12-type spliceosome can limit the expression of genes that contain U12-type introns in a gene-specific manner. Through its limiting role in pre-mRNA processing, the U12-type splicing activity can affect specific genetic pathways, which in the case of Drosophila are involved in metabolic functions.

Type III Secretion System of Phytopathogenic Bacterium Pseudomonas syringae:From Gene to Function

The type III secretion system (T3SS) is an essential requirement for the virulence of many Gram-negative bacteria which infect plants, animals and men. Pathogens use the T3SS to deliver effector proteins from the bacterial cytoplasm to the eukaryotic host cells, where the effectors subvert host defenses. The best candidates for directing effector protein traffic are the bacterial type III-associated appendages, called needles or pili. In plant pathogenic bacteria, the best characterized example of a T3SS-associated appendage is the HrpA pilus of the plant pathogen Pseudomonas syringae pv. tomato DC3000. The components of the T3SS in plant pathogens are encoded by a cluster of hrp (hypersensitive reaction and pathogenicity) genes. Two major classes of T3SS-secreted proteins are: harpin proteins such as HrpZ which are exported into extracellular space, and avirulence (Avr) proteins such as AvrPto which are translocated directly to the plant cytoplasm. This study deals with the structural and functional characterization of the T3SS-associated HrpA pilus and the T3SS-secreted harpins. By insertional mutagenesis analysis of HrpA, we located the optimal epitope insertion site in the amino-terminus of HrpA, and revealed the potential application of the HrpA pilus as a carrier of antigenic determinants for vaccination. By pulse-expression of proteins combined with immuno-electron microscopy, we discovered the Hrp pilus assembly strategy as addition of HrpA subunits to the distal end of the growing pilus, and we showed for the first time that secretion of HrpZ occurs at the tip of the pilus. The pilus thus functions as a conduit delivering proteins to the extracellular milieu. By using phage-display and scanning-insertion mutagenesis methods we identified a conserved HrpZ-binding peptide and localized the peptide-binding site to the central domain of HrpZ. We also found that the HrpZ specifically interacts with a host bean protein. Taken together, the current results provide deeper insight into the molecular mechanism of T3SS-associated pilus assembly and effector protein translocation, which will be helpful for further studies on the pathogenic mechanisms of Gram-negative bacteria and for developing new strategies to prevent bacterial infection.