Closed classes of functions, generalized constraints and clusters

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are closed under permutation of variables, addition of dummy variables and composition are characterized in terms of clusters, and a Galois connection is established between operations and clusters.Comment: 21 page

Join-irreducible Boolean functions

This paper is a contribution to the study of a quasi-order on the set $\Omega$ of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the resulting poset $\tilde{\Omega}$. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of $\tilde{\Omega}$ are the -2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of $\tilde{\Omega}$.Comment: The current manuscript constitutes an extension to the paper "Irreducible Boolean Functions" (arXiv:0801.2939v1

Novel applications of shotgun phage display

In a shotgun phage display library, theoretically, the entire proteome of a bacterium is represented. Phages displaying specific polypeptides can be isolated by affinity selection, while the corresponding gene remains physically linked to the gene product. The overall objective of the study in this thesis was to explore the shotgun phage display technique in new areas. Initially, it was used to study interactions between Staphylococcus aureus and an in vivo coated biomaterial. It was shown to be well suited for the identification of bacterial proteins that bind to ex vivo central venous catheters. Several known interactions were detected, but it was also found that β2-glycoprotein I (β2-GPI) is deposited on this type of biomaterial – a finding that is of interest both for the adherence of S. aureus, but perhaps also in view of the occurrence of autoantibodies in certain autoimmune diseases. Further, it is of interest to identify the subset of extracellular proteins in a bacterium since they are involved in important functions like pathogenesis and symbiosis. A method that allows for the rapid and general isolation of extracellular proteins is desirable, and may prove particularly useful when applied to bacteria for which the genome sequences are not known. For this purpose, a specialised phage display method was developed to isolate extracellular proteins by virtue of the presence of signal peptides (SS phage display). It was successfully applied to S. aureus and, on a larger scale, to the symbiotic bacterium Bradyrhizobium japonicum. In elaboration of the SS phage display method, an inducible antisense RNA system was incorporated to enable gene silencing of the isolated genes. A tetracycline-regulated promoter was inserted in such a way, that an antisense RNA covering the cloned gene could be expressed. The new element was shown to be compatible with the properties of SS phage display, and to promote gene expression upon induction on both the transcriptional and translational level. However, screening for clones affected by the induction of antisense RNA transcription was unsuccessful, and further developments of the system are required to improve the efficiency of this attractive application