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The study of three-dimensional protein structure is essential to understanding the myriad of functions of these important biomolecules and the complexes they form. Viruses are entities that exploit their protein machinery with a high degree of efficacy and economy and the structural characterisation of virus proteins is vital to discovering new ways to combat disease. No single biophysical technique can provide a complete picture of protein architecture, so a range of complementary approaches is required. This thesis presents the use of noncovalent mass spectrometry (MS) techniques for the study of a diverse range of viral structural proteins, including human, animal, and bacterial viruses. Noncovalent MS and travelling-wave ion mobility spectrometry-MS (TWIMS-MS) were used successfully to analyse the dynamic behaviour of the assembly domain (CP149) of the capsid protein of hepatitis B virus (HBV), and, along with limited proteolysis, locate these dynamics to the C-terminus of a half-dimer. The C-terminus is crucial for virus particle assembly and such direct conformational analysis is • difficult with more established techniques. Following this, investigations were made into the effects of an anti-HBV small molecule, HAP-l, on the behaviour of CP149. The molecule had no observable effect on CP149 conformation but interestingly, induced the formation of oligomers which were found by TWIMS-MS to have a globular structure, i.e. not 'sheet-like' as may be expected for assembly intermediates. The small molecule also promoted the formation of large flat particles observed by electron microscopy (EM). The formation of these two rather different classes of particle possibly reflects two facets of the activity of the HAP class of compounds in cells. The technique of collision-induced unfolding (ClU) was studied to investigate whether this can be used to characterise and differentiate between CP149 mutants. Although valuable insights into the unfolding pathway were revealed, together with a number of distinct conformational families, it was found that ClU could not distinguish between the mutations. This is thought to be a result of the substitution of only hydrophobic residues, which may not influence gas-phase structure due to the absence of the hydrophobic effect. MS, TWIMS-MS, EM and coarse-grained structural modelling were utilised to study the oligomerisation processes of the nucleocapsid (N) proteins of Bunyamwera and Schmallenberg viruses from the Bunyaviridae family, a topical and increasingly important class of viruses, for which there is currently no high resolution structural information. The N proteins were shown to oligomerise on binding to RNA to form a range of well-defined but different oligomers. The MS and EM data suggest the shapes of the oligomers to be based on ring structures rather than possible tetramer-based arrangements. These data represent the first insights into the assembly pathways of these important viruses, and the first such MS assembly study of a non-spherical virus class. Noncovalent MS and TWIMS-MS were used to study the baseplate complexes of bacteriophages known to infect the bacterium lactococcus lactis, which is important to the dairy industry. The phages p2 and TP901-1 have multiprotein organelles termed baseplates that mediate cell attachment and genome release and are critical for infection. The complexes, of 0.8 and 1.8 MDa, respectively, were characterised in terms of their mass, and stoichiometry as were several subcomplexes likely to be important in assembly. The studies, in conjunction with published EM and X-ray crystallography data, highlighted the importance of the distal tail protein as a central hub to control baseplate assembly and showed that valuable structural information can be gained in the absence of high resolution crystallography data. In summary, MS and TWIMS-MS were found to be valuable tools with which to study protein dynamics, structure and assembly, which makes them vital for the advancement of biophysical characterisation of viral systems.

This thesis covers a number of related topics in the foundations of set theory. Section 1 contains an analysis of the paradoxes which suggests a way of looking at the axioms of any formalised set theory as to a certain extent legislating how 'is a member of' and 'set' are to be used. In section 2, two other points of view are examined and rejected. There are doubtless other views which directly contradict the view put forward in section 1, but clearly one cannot examine all the different solutions of the paradoxes in any one thesis. The positions examined in section 2 seem to represent views that are most opposed to the general tendency of this thesis. Section 3 consists of a critical examination of Tarski's work on the semantic conception of truth for a formalised calculus of classes. This section has two aspects. The first is a defence of Tarski against some of his critics; the second an attack on certain of Tarski's conclusions. Section 4 begins where section 3 leaves off. it examines Tarski's conclusions about a definition of truth for set theory. It contains an analysis of Godel's results on the incompleteness of formal systems and is particularly concerned with the transference of certain inferences made from Godel's theorem for a formalised arithmetic to a formalised set theory. The conclusion of section 4 returns to the theme of section 1 and utilises certain metatheorems recently proved about formalised set theories. Throughout the thesis no one axiom system of set theory is presupposed though reference will be made to several. The discussion is of a general nature and can be taken to be about any axiom system of set theory rather than some particular one.

Studies have been made of the extraction from aqueous solution of nitric and hydrofluoric acids, alone and in the presence of each other and, where relevant of hydrochloric acid, into di-(2-ethyl hexyl)phosphate, tri-n-butyl phosphate and tri-n-octylamine. Also, similar studies have been made of the extraction of uranium in the presence of hydrofluoric and nitric acids into the same acidic, neutral and basic organic solvents. In all cases, the practical work has taken the form of equilibrium experiments made under carefully controlled conditions and analysis of the resulting aqueous and organic phases. The organic solvents have been used either alone or as solutions in various inert diluents such as kerosene, benzene or xylene and the aqueous solutions have covered a very wide range of concentrations. From the results of these experiments, deductions have been made regarding the mechanisms of the extraction processes and the nature of the species taken up into the organic media. Equilibrium constants are given and, where sufficient data is available, stability constants have been calculated. The extraction of the mineral acids into di-(2-ethyl hexyl)phosphate and tributyl phosphate is found to be similar. With dilute aquwous solutions, one mole of acid is taken up per mole of extractant and the acid is probably hydrogen bonded to the phosphoryl oxygen. At higher aqueous concentrations, more acid is extracted and possible explanations of this are offered. With tri-octylamine, the acids are extracted as the amine salts R3NH. NO3 or R3NH. HF2 but again more acid than expected is taken up from concentrated aqueous solutions. Uranium is extracted into tributyl phosphate in the presence of nitric or hydrochloric acids but not at all in the presence of hydrofluoric acid and possible explanations are offered for this. With di-(2-ethyl hexyl)phosphate and tri-n-octylamine uranium is extracted in the presence of all acids and it would appear from the results that this is a simple ion exchange process, UO2 2+ exchanging with H+ in the former case and UO2F3 - exchanging with the anion in the latter case.