Each one teaches one: characterizing active forms of proteins by single molecule force spectroscopy

This Ph.D. candidate thesis collects the research work I conducted under the supervision of Prof.Bruno Samor´ı in 2005,2006 and 2007. Some parts of this work included in the Part III have been begun by myself during my undergraduate thesis in the same laboratory and then completed during the initial part of my Ph.D. thesis: the whole results have been included for the sake of understanding and completeness. During my graduate studies I worked on two very different protein systems. The theorical trait d’union between these studies, at the biological level, is the acknowledgement that protein biophysical and structural studies must, in many cases, take into account the dynamical states of protein conformational equilibria and of local physico-chemical conditions where the system studied actually performs its function. This is introducted in the introductory part in Chapter 2. Two different examples of this are presented: the structural significance deriving from the action of mechanical forces in vivo (Chapter 3) and the complexity of conformational equilibria in intrinsically unstructured proteins and amyloid formation (Chapter 4). My experimental work investigated both these examples by using in both cases the single molecule force spectroscopy technique (described in Chapter 5 and Chapter 6). The work conducted on angiostatin focused on the characterization of the relationships between the mechanochemical properties and the mechanism of action of the angiostatin protein, and most importantly their intertwining with the further layer of complexity due to disulfide redox equilibria (Part III). These studies were accompanied concurrently by the elaboration of a theorical model for a novel signalling pathway that may be relevant in the extracellular space, detailed in Chapter 7.2. The work conducted on -synuclein (Part IV) instead brought a whole new twist to the single molecule force spectroscopy methodology, applying it as a structural technique to elucidate the conformational equilibria present in intrinsically unstructured proteins. These equilibria are of utmost interest from a biophysical point of view, but most importantly because of their direct relationship with amyloid aggregation and, consequently, the aetiology of relevant pathologies like Parkinson’s disease. The work characterized, for the first time, conformational equilibria in an intrinsically unstructured protein at the single molecule level and, again for the first time, identified a monomeric folded conformation that is correlated with conditions leading to -synuclein and, ultimately, Parkinson’s disease. Also, during the research work, I found myself in the need of a generalpurpose data analysis application for single molecule force spectroscopy data analysis that could solve some common logistic and data analysis problems that are common in this technique. I developed an application that addresses some of these problems, herein presented (Part V), and that aims to be publicly released soon.

Expression and cellular localization of Copper transporter 2 (Ctr2) in Mus musculus

The Ctr family is an essential part of the copper homeostasis machinery and its members share sequence homology and structural and functional features. Higher eukaryotes express two members of this family Ctr1 and Ctr2. Numerous structural and functional studies are available for Ctr1, the only high affinity Cu(I) transporter thus far identified. Ctr1 holigotrimers mediate cellular copper uptake and this protein was demonstrated to be essential for embryonic development and to play a crucial role in dietary copper acquisition. Instead very little is known about Ctr2, it bears structural homology to the yeast vacuolar copper transporter, which mediates mobilization of vacuolar copper stores. Recent studies using over-expressed epitope-tagged forms of human Ctr2 suggested a function as a low affinity copper transporter that can mediate either copper uptake from the extracellular environment or mobilization of lysosomal copper stores. Using an antibody that recognizes endogenous mouse Ctr2, we studied the expression and localization of endogenous mouse Ctr2 in cell culture and in mouse models to understand its regulation and function in copper homeostasis. By immunoblot we observed a regulation of mCtr2 protein levels in a copper and Ctr1 dependent way. Our observations in cells and transgenic mice suggest that lack of Ctr1 induces a strong downregulation of Ctr2 probably by a post-translational mechanism. By indirect immunofluorescence we observed an exclusive intracellular localization in a perinuclear compartment and no co-localization with lysosomal markers. Immunofluorescence experiments in Ctr1 null cells, supported by sequence analysis, suggest that lysosomes may play a role in mCtr2 biology not as resident compartment, but as a degradation site. In appendix a LC-mass method for analysis of algal biotoxins belonging to the family of PsP (paralytic shellfish poisoning) is described.

Preparation of new crystal forms via photochemical, mechanochemical and sol-gel methods

This work of thesis involves various aspects of crystal engineering. Chapter 1 focuses on crystals containing crown ether complexes. Aspects such as the possibility of preparing these materials by non-solution methods, i.e. by direct reaction of the solid components, thermal behavior and also isomorphism and interconversion between hydrates are taken into account. In chapter 2 a study is presented aimed to understanding the relationship between hydrogen bonding capability and shape of the building blocks chosen to construct crystals. The focus is on the control exerted by shape on the organization of sandwich cations such as cobalticinium, decamethylcobalticinium and bisbenzenchromium(I) and on the aggregation of monoanions all containing carboxylic and carboxylate groups, into 0-D, 1-D, 2-D and 3-D networks. Reactions conducted in multi-component molecular assemblies or co-crystals have been recognized as a way to control reactivity in the solid state. The [2+2] photodimerization of olefins is a successful demonstration of how templated solid state synthesis can efficiently synthesize unique materials with remarkable stereoselectivity and under environment-friendly conditions. A demonstration of this synthetic strategy is given in chapter 3. The combination of various types of intermolecular linkages, leading to formation of high order aggregation and crystalline materials or to a random aggregation resulting in an amorphous precipitate, may not go to completeness. In such rare cases an aggregation process intermediate between crystalline and amorphous materials is observed, resulting in the formation of a gel, i.e. a viscoelastic solid-like or liquid-like material. In chapter 4 design of new Low Molecular Weight Gelators is presented. Aspects such as the relationships between molecular structure, crystal packing and gelation properties and the application of this kind of gels as a medium for crystal growth of organic molecules, such as APIs, are also discussed.

Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.