Molecular mechanisms of cancer predisposition in HNPCC/Lynch syndrome

Hereditary non-polyposis colorectal carcinoma (HNPCC; Lynch syndrome) is among the most common hereditary cancers in man and a model of cancers arising through deficient DNA mismatch repair (MMR). It is inherited in a dominant manner with predisposing germline mutations in the MMR genes, mainly MLH1, MSH2, MSH6 and PMS2. Both copies of the MMR gene need to be inactivated for cancer development. Since Lynch syndrome family members are born with one defective copy of one of the MMR genes in their germline, they only need to acquire a so called second hit to inactivate the MMR gene. Hence, they usually develop cancer at an early age. MMR gene inactivation leads to accumulation of mutations particularly in short repeat tracts, known as microsatellites, causing microsatellite instability (MSI). MSI is the hallmark of Lynch syndrome tumors, but is present in approximately 15% of sporadic tumors as well. There are several possible mechanisms of somatic inactivation (i.e. the second hit ) of MMR genes, for instance deletion of the wild-type copy, leading to loss of heterozygosity (LOH), methylation of promoter regions necessary for gene transcription, or mitotic recombination or gene conversion. In the Lynch syndrome tumors carrying germline mutations in the MMR gene, LOH was found to be the most frequent mechanism of somatic inactivation in the present study. We also studied MLH1/MSH2 deletion carriers and found that somatic mutations identical to the ones in the germline occurred frequently in colorectal cancers and were also present in extracolonic Lynch syndrome-associated tumors. Chromosome-specific marker analysis implied that gene conversion, rather than mitotic recombination or deletion of the respective gene locus accounted for wild-type inactivation. Lynch syndrome patients are predisposed to certain types of cancers, the most common ones being colorectal, endometrial and gastric cancer. Gastric cancer and uroepithelial tumors of bladder and ureter were observed to be true Lynch syndrome tumors with MMR deficiency as the driving force of tumorigenesis. Brain tumors and kidney carcinoma, on the other hand, were mostly MSS, implying the possibility of alternative routes of tumor development. These results present possible implications in clinical cancer surveillance. In about one-third of families suspected of Lynch syndrome, mutations in MMR genes are not found, and we therefore looked for alternative mechanisms of predisposition. According to our results, large genomic deletions, mainly in MSH2, and germline epimutations in MLH1, together explain a significant fraction of point mutation-negative families suspected of Lynch syndrome and are associated with characteristic clinical and family features. Our findings have important implications in the diagnosis and management of Lynch syndrome families.

Noncommutativity and Some of Its Present-Day Developments

This masters thesis explores some of the most recent developments in noncommutative quantum field theory. This old theme, first suggested by Heisenberg in the late 1940s, has had a renaissance during the last decade due to the firmly held belief that space-time becomes noncommutative at small distances and also due to the discovery that string theory in a background field gives rise to noncommutative field theory as an effective low energy limit. This has led to interesting attempts to create a noncommutative standard model, a noncommutative minimal supersymmetric standard model, noncommutative gravity theories etc. This thesis reviews themes and problems like those of UV/IR mixing, charge quantization, how to deal with the non-commutative symmetries, how to solve the Seiberg-Witten map, its connection to fluid mechanics and the problem of constructing general coordinate transformations to obtain a theory of noncommutative gravity. An emphasis has been put on presenting both the group theoretical results and the string theoretical ones, so that a comparison of the two can be made.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.