A bitopological point-free approach to compactifications

This thesis extends the concept of compactifications of topological spaces to a setting where spaces carry a partial order and maps are order-preserving. The main tool is a Stone-type duality between the category of d-frames, which was developed by Jung and Moshier, and bitopological spaces. We demonstrate that the same concept that underlies d-frames can be used to do recover short proofs of well-known facts in domain theory. In particular we treat the upper, lower and double powerdomain constructions in this way. The classification of order-preserving compactifications follows ideas of B. Banaschewski and M. Smyth. Unlike in the categories of spaces or locales, the lattice-theoretic notion of normality plays a central role in this work. It is shown that every compactification factors as a normalisation followed by the maximal compactification, the Stone-Cech compactification. Sample applications are the Fell compactification and a stably compact extension of algebraic domains

KIT Mutation and Loss of 14q May Be Sufficient for the Development of Clinically Symptomatic Very Low-Risk GIST

<div><p>The aim of this study was to determine the minimal set of genetic alterations required for the development of a very low risk clinically symptomatic gastro-intestinal stromal tumour within the stomach wall. We studied the genome of a very low-risk gastric gastro-intestinal stromal tumour by whole-genome sequencing, comparative genomic hybridisation and methylation profiling. The studied tumour harboured two typical genomic lesions: loss of the long arm of chromosome 14 and an activating mutation in exon 11 of KIT. Besides these genetic lesions, only two point mutations that may affect tumour progression were identified: A frame-shift deletion in RNF146 and a missense mutation in a zinc finger of ZNF407. Whilst the frameshift deletion in RNF146 seemed to be restricted to this particular tumour, a similar yet germline mutation in ZNF407 was found in a panel of 52 gastro-intestinal stromal tumours from different anatomical sites and different categories. Germline polymorphisms in the mitotic checkpoint proteins Aurora kinase A and BUB1 kinase B may have furthered tumour growth. The epigenetic profile of the tumour matches that of other KIT-mutant tumours. We have identified mutations in three genes and loss of the long arm of chromosome 14 as the so far minimal set of genetic abnormalities sufficient for the development of a very low risk clinically symptomatic gastric stromal tumour.</p></div

Single nucleotide variations in exon 1 of ZNF407 in a panel of 52 GIST samples.

<p>Abbreviations: NT, nucleotide change in NM_017757; AA, amino acid change in NP_060227; Pred, PolyPhen2 HDIV score; MAF, minor allele frequency 1000 Genomes project; a, Germline mutation; b, Somatic mutation.</p><p>The last column shows in how many of the 52 samples the mutation was found.</p

Potential founding mutations in protein-coding regions.

<p>¹, Fraction of sequenced reads showing the mutation; p, pseudogene; s, confirmed by Sanger sequencing.</p><p>Potential founding mutations in protein-coding regions.</p

Mapping plot of the sequenced GIST sample.

<p>Plotted is the fraction of the genome that is covered to at least a certain depth.</p

Pathological characteristics of a very low-risk GIST.

<p>This H&E staining shows a low (upper picture) and high power view (middle picture) of the GIST that was submitted to whole genome sequencing and how it invades the gut wall. The tumour was also stained with an antibody specific to c-kit (lower picture).</p

Coding mutations in ZNF407 zinc fingers.

<p>^a, The C2H2 zinc finger motif comprises two cysteines and two histidines, shown in capital letters. Positions of amino acid changes are highlighted as [x/x]. Amino acid (AA) positions are internal to protein sequence NP_060227.</p><p>Coding mutations in ZNF407 zinc fingers.</p