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The challenging intricacies of strongly correlated electronic systems necessitate the use of a variety of complementary theoretical approaches. In this thesis, we analyze two distinct aspects of strong correlations and develop further or adapt suitable techniques. First, we discuss magnetization transport in insulating one-dimensional spin rings described by a Heisenberg model in an inhomogeneous magnetic field. Due to quantum mechanical interference of magnon wave functions, persistent magnetization currents are shown to exist in such a geometry in analogy to persistent charge currents in mesoscopic normal metal rings. The second, longer part is dedicated to a new aspect of the functional renormalization group technique for fermions. By decoupling the interaction via a Hubbard-Stratonovich transformation, we introduce collective bosonic variables from the beginning and analyze the hierarchy of flow equations for the coupled field theory. The possibility of a cutoff in the momentum transfer of the interaction leads to a new flow scheme, which we will refer to as the interaction cutoff scheme. Within this approach, Ward identities for forward scattering problems are conserved at every instant of the flow leading to an exact solution of a whole hierarchy of flow equations. This way the known exact result for the single-particle Green's function of the Tomonaga-Luttinger model is recovered.
Colorectal carcinoma (CRC) is a major cause of morbidity and mortality in Western countries. It has so far been molecularly defined mainly by alterations of the Wnt pathway. We show here for the first time that aberrant activities of the signal transducer and activator of transcription STAT3 actively contribute to this malignancy and, thus, are a potential therapeutic target for CRC. Constitutive STAT3 activity was found to be abundant in dedifferentiated cancer cells and infiltrating lymphocytes of CRC samples, but not in non-neoplastic colon epithelium. Cell lines derived from malignant colorectal tumors lost persistent STAT3 activity in culture. However, implantation of colon carcinoma cells into nude mice resulted in restoration of STAT3 activity, suggesting a role of an extracellular stimulus within the tumor microenvironment as a trigger for STAT activation. STAT3 activity in CRC cells triggered through interleukin-6 or through a constitutively active STAT3 mutant promoted cancer cell multiplication, whereas STAT3 inhibition through a dominant-negative variant impaired IL-6-driven proliferation. Blockade of STAT3 activation in CRCderived xenograft tumors slowed down their development, arguing for a contribution of STAT3 to colorectal tumor growth.