NMR Spectroscopy of Multi-domain Proteins : Immunoglobulin-like Domains of Human Filamin A

Proteins are complex biomacromolecules playing fundamental roles in the physiological processes of all living organisms. They function as structural units, enzymes, transporters, process regulators, and signal transducers. Defects in protein functions often derive from genetic mutations altering the protein structure, and impairment of essential protein functions manifests itself as pathological conditions. Proteins operate through interactions, and all protein functions depend on protein structure. In order to understand biological mechanisms at the molecular level, one has to know the structures of the proteins involved. This thesis covers structural and functional characterization of human filamins. Filamins are actin-binding and -bundling proteins that have numerous interaction partners. In addition to their actin-organizing functions, filamins are also known to have roles in cell adhesion and locomotion, and to participate in the logistics of cell membrane receptors, and in the coordination of intracellular signaling pathways. Filamin mutations in humans induce severe pathological conditions affecting the brain, bones, limbs, and the cardiovascular system. Filamins are large modular proteins composed of an N-terminal actin-binding domain and 24 consecutive immunoglobulin-like domains (IgFLNs). Nuclear magnetic resonance (NMR) spectroscopy is a versatile method of gaining insight into protein structure, dynamics and interactions. NMR spectroscopy was employed in this thesis to study the atomic structure and interaction mechanisms of C-terminal IgFLNs, which are known to house the majority of the filamin interaction sites. The structures of IgFLN single-domains 17 and 23 and IgFLN domain pairs 16-17 and 18-19 were determined using NMR spectroscopy. The structures of domain pairs 16 17 and 18 19 both revealed novel domain domain interaction modes of IgFLNs. NMR titrations were employed to characterize the interactions of filamins with glycoprotein Ibα, FilGAP, integrin β7 and dopamine receptors. Domain packing of IgFLN domain sextet 16 21 was further characterized using residual dipolar couplings and NMR relaxation analysis. This thesis demonstrates the versatility and potential of NMR spectroscopy in structural and functional studies of multi-domain proteins.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.