Homocysteine, an independent risk factor for cardiovascular disease, is methylated in the liver via the zinc metalloenzyme betaine-homocysteine methyltransferase (BHMT). Established assays for BHMT include a radiochemical assay, a colorometric assay, an HPLC assay and an in vivo microbiological assay. These techniques are either unsuitable for substrate specificity studies, or are unable to give kinetic measurements. BHMT was purified from liver and measured directly and kinetically by a novel ¹H-NMR spectroscopic assay. The disappearance of substrates and the formation of products are monitored simultaneously. Using 2 mM glycine betaine and homocysteine as substrates in 20 mM phosphate buffer (pH = 7.5) and measuring the production of N,N-dimethylglycine the CV is 6.3% (n = 6) and the detection limit is 6 nkatal. An endpoint assay for BHMT activity was also developed and had CV = 5.3%, n = 6, with a detection limit of 2 nkatal. The NMR spectroscopic assay was used to determine the substrate specificity with a library of alternative substrates. Analysis of betaine analogues with different chain length, α-substitution, substitution of the nitrogen and carboxyl moieties demonstrated that BHMT is inactive if there is any steric crowding of the nitrogen or α-carbon positions. BHMT is capable of using group VI heteroatom betaines as methyl donors, with much faster rates than glycine betaine. For glycine betaine the Km was 0.19 ± 0.03 mM with a Vmax of 17 ± 0.7 nMol min-1 mg-1. The same assay was used to detect and partially characterise a BHMT activity from hagfish liver that is similar to that of the mammalian enzyme. NMR spectroscopy was adapted for measurements of glycine betaine in urine, along with other medically significant methylamines. These were shown to be valid for clinical use and in animal studies. A novel metabolite of the sulfonium analogue of glycine betaine (methylsulfinylmethanoate) was identified in rats.

Coherent transient effects are the optical analogs of the many transient phenomena seen in pulsed nuclear magnetic resonance experiments on spin systems. For example, photon-echo and optical nutation are the respective optical equivalents of spin echo and transient nutation of nuclear magnetic resonance. In Stark-switching and frequency-switching techniques the laser field and the molecules are brought into resonance in a sequence of pulses, the rest of the time they remain well off-resonance. So far it has been assumed that the off-resonance field does not have any measureable influence on the experimental results and is utilized to implement a very efficient detection scheme. This work discusses how the off-resonance field affects the coherent transient effects. It is shown here how this field, by inducing changes in the index of refraction as small as 10⁻⁶ produces easily observable effects in photon echo and delayed optical nutation.

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This thesis is concerned with the design of numerical methods for quantum simulation and the development of improved models for quantum relaxation. Analysis is presented for the treatment of quantum systems using the density matrix formalism. This approach has been developed from the early days of quantum mechanics as a tool to describe from a statistical point of view a large number of identical quantum ensembles. Traditional methods are well established and reliable, but they perform poorly for practical simulation as the system size is scaled up. Ad hoc schemes for nuclear spin dynamics appearing in the literature can be shown to fail in certain situations. The challenge is therefore to identify efficient reduction methods for the quantum system which are also based on a rigorous foundation. The method presented in the thesis, for the time–independent Hamiltonian case, combines a quantum density matrix formalism with a procedure based on Chebyshev polynomials; application of the method to Nuclear Magnetic Resonance (NMR) spectroscopy is considered, and it is shown that the new technique outperforms existing alternatives in term of computational costs. The case of a time–dependent Hamiltonian in NMR simulation is studied as well and some splitting methods are presented. To the author’s knowledge this is the first time such methods have been applied within the NMR framework, and the numerical results show a better error–to–cost rate than traditional methods. In a separate strand of research, formulations for open quantum systems are studied and new dynamical systems approaches are considered for this problem. Motivations This thesis work is mainly focused on nuclear spin dynamics. Nuclear spin dynamics constitutes the basis for NMR, which is a very powerful spectroscopy technique that exploits the interaction between nuclear spins and magnetic fields. The same technique is used to reveal the presence of hydrogen atoms in the blood for Magnetic Resonance Imaging (MRI). Within this framework the role of simulations is extremely important, as it provides a benchmark for studies of new materials, and the development of new magnetic fields. The main computational issue is that with current software for NMR simulation it is extremely expensive to deal with systems made of more than few (7–10) spins. There is therefore a strong need to develop new algorithms capable of simulating larger systems. In recent years NMR simulations have been found to be one of the most favorable candidates for quantum computing. There are two reasons for this: nuclear quantum states maintain extremely long coherences, and it is possible to attain a very strong control on the quantum state via the application of sequences of pulses. In order to develop a proper quantum computer it is fundamental to understand how the entangled states lose coherence and relax back to equilibrium by means of external interactions. This process is described as relaxation in an open quantum system. The theory for such systems has been available for 50 years but there are still substantial limitations in the two main approaches. There are also relatively few numerical approaches for the simulation of such systems, for this reason it is important to develop numerical alternatives for the description of open quantum systems. Thesis Outline The thesis is organized as follow: the first two chapters provide background material to familiarize the reader with fundamental concepts of both quantum mechanics and nuclear spin dynamics; in this part of the thesis no new results are presented. The first chapter introduces the concept of quantum systems and the mathematical environment with which we describe those systems. We also present the main equations we need to solve to determine the dynamics of a quantum system in a statistical framework. In the second chapter we introduce the nuclear spin system, that is the physical system that has been the main reference frame in this work, for both tests and practical applications of the new algorithms. We describe how nuclear spin systems are at the basis of very important applications like NMR spectroscopy and MRI. We present in some detail the physical features of the NMR technique and the equations we need to solve to describe the dynamics of a spin system; we also focus on the relevance of numerical simulations for these systems, and consequently which must be the interest in developing new algorithms, and the major obstacles which must be overcome. In the third chapter we investigate the numerical challenges that arise in simulation of quantum systems, we describe some of the methods that have been developed in the literature, focusing on the performances and the computational costs of them, setting the new developments of this thesis in the proper research frame. We discuss one of the major issues: the evaluation of the matrix exponential. We also present the analysis we have done of a recent method called Zero Track Elimination (ZTE) that has been developed specifically for NMR simulations. This analysis shows the limitations of this method but also gives a mathematical explanation of why–and in which cases–it works. In the fourth chapter we present the main result of the thesis, the development of a new method that directly evaluates the expectation values for a quantum simulation via a different application of the well known Chebyshev expansion. We have proved that this new method can provide an excellent boost in terms of performance, with computational costs that can be reduced by a factor ten in common cases. (The results of this chapter and the new method have been presented in international conferences and recently they have been submitted for publication). We also present some attempts we have made in the application of splitting methods for the evolution of the system in a time dependent environment. To our knowledge this is the first time splitting methods have been used for NMR simulations. The results of this approach are as follows: for a particular splitting technique combined with a Lanczos iteration method it is possible to speed up the calculation by a third if compared with a Lanczos type method whilst keeping the error below a critical threshold. This last approach is still a work in progress especially in terms of developing clever ways to split the Hamiltonian. The last chapter of this thesis deals with simulation of quantum systems interacting with an external environment. After presenting the main theoretical approaches for the description of such systems we then survey several the techniques that are currently used for the numerical implementation of such theories. As a work in progress we present a considerably different new approach we have been developing aiming to overcome some of the issues that arise when treating this kind of system within usual frameworks. This is somewhat speculative work that gives rise to some new directions in the development of a numerical description for open quantum systems. We also present some numerical results. (The main core of this chapter has been presented in international conferences).

Factor H (FH) is a key regulator of the complement system, the principal molecular component of innate immunity in humans. The tight regulation of the alternative pathway (AP) of complement by FH occurs on host cells as well as in fluid phase. FH regulation of AP is achieved through its C3b. Bb-decay accelerating activity and cofactor activity for C3b proteolysis by factor I. This study presents evidence that the first three CCP modules, i.e. FH~1-3, constitute the minimal unit with cofactor activity for factor I. The work presented in this thesis describes the recombinant protein expression and NMR-derived structure determination of two overlapping pairs, FH~1-2 and FH~2-3, together with the use of these structures to build a model of the FH~1-3 structure. A structural comparison with other C3bengaging proteins (namely factor B, complement receptor type 1 and decay accelerating factor) is presented and used to devise hypotheses as to the respective roles of the three modules during an encounter with the convertase. This thesis further describes an investigation of the structural effects of two disease-associated sequence variants in the context of FH~1-2: namely the single nucleotide polymorphism V62I linked to age-related macular degeneration, and the R53H mutation linked to atypical haemolytic uraemic syndrome.

Dissertation submitted in partial compliance with the requirements for the Master's Degree in Technology: Homoeopathy, Technikon Natal, 2001. / The purpose of this study was to analyse and compare the NMR spectra ofa homoeopathic remedy (in this case Natrum muriaticum was used for its easy solubility and purity), that was prepared in the classical single vial Hahnemannian method, and also the widely used multi-vial Korsakovian method. Comparison was made in terms of the chemical shift (8) and relative integration values of the CH3, CH2, H20, and OH signals. A control was employed for both methods. The only difference between control and test remedies was the actual inclusion ofNatrum muriaticum in the latter, and the same weight of solvent as solute in the former. Comparison was made between both test methods, between test and control, and between the two controls. It was hypothesized that the method of dilution plays an important part in the potentisation process, and thus becomes part of the remedy's information content. The evolution of distinct physicochemical identities was hypothesized to occur specific to each method in ascending potency levels. Differences were therefore also hypothesized to exist between both methods at parallel potency levels in terms of chemical shift and relative integration values. The experiment was conducted as per the limitations of the scientific method. Both methods and their controls of Natrum muriaticum were potentised to the 9C, 30C, and 200C potency levels. They were prepared in 16ml volumes and transported to the NMR spectroscopy laboratory in Pietermaritzburg for analysis. / M

Dissertation submitted in partial compliance with the requirements for the Master's Degree in Technology: Homoeopathy, Durban Institute of Technology, 2002. / The purpose of this study was to investigate whether frequency strength is a parameter requiring consideration when conducting NMR spectroscopy studies on hornoeopathic potencies. To this end, samples of Sulphur 30CH and a Lactose control were analysed using NMR spectrometers operating at three different frequency strengths of 80MHz, 200.MHz and 500.MHz. It was hypothesized that differences existed in the spectra of respective Sulphur samples, control samples, and between parallel samples of Sulphur and control. It was further hypothesized that differences between parallel samples of Sulphur and control would be more noticeable at the lower frequencies. This hypothesis was based on the assumption that a higher frequency strength would have more intense resonance effects on the structure of the homoeopathic potency, thereby disturbing the micro-structural changes induced during potentisation. The design of the investigation was that of a scientific experiment. Potencies of Sulphur and a lactose-based control were prepared to a 30CH potency each, in 87% ethanol. The final prepared volumes (10ml) of Sulphur and control were blinded by means of colour codes by a third party prior to analysis. The blinded samples were transported to the University of Natal, Pietermaritzburg, where they were subjected to analysis using the following instruments: 1) A Varian FT80A 80.MHz instrument 2) A Varian Gemini 200MHz instrument 3) A Varian Inova 500.MHz instrument At each instrument NMR spectroscopy was conducted on ten (10) samples from each group (Sulphur and control). The samples were prepared in coaxial tubes using acetone as both an external lock and reference, and NMR spectra were recorded for each sample. All the samples were run at a thermostatically controlled temperature of 24\xB0C (\xB1 O,2\xB0C), and the laboratory was maintained at a constant temperature of 22\xB0C. The spectra and data of all the samples were recorded in terms of the chemical shift and integration values of their respective CH2, H20 and OH signals. / M

This thesis is concerned with a systematic study of phosphine-containing transition metal complexes and cluster compounds by high resolution solid state nmr spectroscopy, using the techniques of magic angle spinning and cross polarisation. Previous work has indicated the potential of the solid state nmr technique to investigate a variety of materials: this is considered in the introduction to this thesis, and the reasons for choosing to study transition metal phosphine compounds are discussed. The analysis of spinning sidebands to obtain the principle values of the shielding tensor is examined to determine how well the calculated values represent the true values. Simulations of slow MAS spectra are proposed as a means of testing and refining the calculated tensor components before attempting to correlate the shielding with structural parameters. The results of a study of a series of crystalline phosphine-containing complexes and clusters are presented. The spectra are interpreted on the basis of the known crystal structures: in some cases separate resonances can be resolved in the solid state spectra from the distinct phosphine environments of a cluster framework, and from inequivalent sites in the unit cell. Information is obtained from the isotropic shifts, scalar couplings and the chemical shift anisotropy. Many of the compounds are fluxional in solution, some even at low temperature: whereas a number of these are found to be rigid in the solid state at room temperature, some of the crystalline compounds retain their fluxionality. Investigations of the species formed when transition metal carbonyl clusters are anchored to oxide supports were carried out. These show the presence of several distinct phosphorus-containing species, some of which are not consistent with the simple attachment of the cluster to the surface. The unique importance of the solid state technique is demonstrated in the study of these supported species.