HIV-1 has evolved with a great deal of functional complexity contained within a very small genome by encoding small, but critical viral proteins within larger viral genes and dividing the replication cycle into early and late phases to differentially produce all proteins leading to efficient replication and virion release. Early replication is restricted by the host spliceosome that processes HIV-1 vRNA transcripts so only the small intragenomic proteins are produced, one of which is Rev (Regulator of Virion Expression). Rev in turn governs the transition from early to late replication by interacting with a highly structured region of vRNA termed the Rev Response Element (RRE). The binding of Rev to the RRE is believed to cause a change in the vRNA tertiary structure and inhibition of splicing of the vRNA. Once, a Rev:RRE complex is formed, a nuclear export signal within Rev facilitates the export of partially spliced and unspliced vRNA to the cytoplasm. During late replication the partially spliced and unspliced vRNA is translated to polyproteins and is packaged into a budding virion where the viral aspartyl protease (HIV-1 PR) autocatalytically excises itself from the larger polyprotein and processes the remaining polyproteins to release all viral structural and functional proteins to form a mature and infectious virion. Since the vRNA salvaged by Rev is translated to the polyproteins containing HIV-1 PR, the inhibition of Rev function will reduce the amount of HIV-1 PR available and thereby reduce the amount of HIV-1 PR therapeutics required to elicit a clinical effect. Therfore a combination approach to HIV-1 treatment using suitably developed therapeutics that inhibit Rev and HIV-1 PR function represents an attractive synergistic approach to treating HIV-1 infection in vivo. The work of this thesis was divided into two parts, the first part was concerned with HIV-1 PR structural biology and addressing problems encountered with inhibitor design. A bicyclic peptide (based on inhibitors of analogous structure) was co-crystallised with active HIV-1 PR to develop an enzyme-product (E-P) complex and with a catalytically inactive mutant HIV-1 PR to provide an analogy to the enzyme-substrate (E-S) complex. Both structures of the E-P and E-S complexes were solved to 1.6Å resolution and were compared to a hydroxyethylamine isostere enzyme-inhibitor complex (E-I), highlighting the similarity of binding mode for all ligands. The inhibitor in the E-I complex was translated towards the S1 - S3 pockets of the substrate binding cleft relative to the substrate in the E-S complex due to the increased length of the hydroxylethylamine isostere compared to the peptide backbone, although the inhibitor "puckered" the isostere linkage and maintains a binding mode similar to the substrate with very little overall differences in the position of the ligands and surrounding protein. The similarity of the E-S, E-I and E-P complexes was attributed to the macrocyclic ligands ordering the surrounding protein environment, especially the protein -strand "flap" structures that form a roof over the ligands in the active site but were not found to close more tightly in any of the trapped catalytic states. The new structures allowed refinement of details of the mechanism of peptide hydrolysis. The mechanism relies on the optimal nucleophilic attack of a water molecule on the scissile amide bond with concerted acid-base catalysis of the active site aspartyl residues intitiated by D125. The alignment and intrinsic position of the N-terminus of the bicyclic substrate was interpreted as being critical to facilitate efficient electron transfer with the bicyclic substrate. An N-terminal cyclic inhibitor, similar to the N-terminal portion of the bicyclic substrate, was used to address a major problem in HIV-1 PR drug design termed "cooperativity," where the sequential optimisation of an inhibitor (or substrate) to individual pockets of the substrate binding cleft, can negatively impact on adjacent and downfield subsites and thereby alter the binding mode of the "optimised" inhibitor. The technique referred to here as "templating" uses the N-terminal cycle to lock the binding mode into a known conformation, probing the S1' and S2' pockets. The structure activity relationship suggested that by viewing the S1' - S3' pockets as a single trough, bulky aromatic groups attached to an N-alkyl sulfonamide could be directed along the line of the trough without adverse interactions with the tops of the S1' and S3' pockets, providing very potent inhibitors. It was also found that specificity and potency of an inhibitor can be maintained with smaller functionalities that carry their bulk low and close to the inhibitor backbone in the S2' pocket, making the P2 functionalities more substrate-like. The second part of the thesis was concerned with establishing suitable surface plasmon resonance assays for testing potential inhibitors of Rev function. Recombinant Rev and its minimal RNA aptamer target (stem loop II of the RRE termed RBE3), were expressed, purified, and used to develop BIAcore-based assays and test potential inhibitors of their interaction. The system was applied to screening of aminoglycoside antibiotics and other small molecules in a competitive assay, and also to quantitative assay of Neomycin and moderate sized analytes: Rev and three peptidic analogues of the high-affinity binding site of Rev - the native peptide, succinylated form of the peptide and a form incorporating a novel helix-inducing cap. The peptide and protein assay was undertaken to test the proposition that helix induction of the high-affinity binding site of Rev can increase affinity for the biologically important RNA target and thereby form the basis of a new class of inhibitors. The screen of small molecule antagonists found that Neomycin was the best inhibitor of the Rev:RBE3 interaction and that efficacy of other aminoglycosides was due to the neamine-base structure presenting charge to bind to the RNA and blocking interaction with Rev. The quantitative assay was optimised to reduce non-specific interactions of Rev protein to allow reliable studies of the analytes with RBE3 by the sytematic testing of buffers and modifiers. It was found that mutliple analytes bound to the RBE3 aptamer and a comparison of the KD values found that the native and capped peptides had similar affinity for RBE3 RNA (native slightly greater at 21 ± 7nM cf capped 41 ± 10nM) that was greater than the Rev protein (101 ± 19nM), however the succinylated peptide exhibited stronger binding with a KD ≤8nM and Neomycin had the lowest affinity (KD 13 ± 3M). The similarity of the native and capped peptides may be due to the high concentration of salt in the assay buffers and was necessary for the stability of the Rev protein, but is sufficient to influence secondary structure of the peptides. Therefore, it could not be stated that the helix-inducing cap increased the affinity of the native peptide for the biologically important therapeutic target. The work conducted in this thesis firmly establishes foundations for the continued development of inhibitors against both Rev and HIV-1 PR that play key roles in the HIV-1 replication strategy. It is envisaged this work could lead to a novel synergistic therapeutic approach to treating HIV-1 infection.

Nous nous intéressons, dans cette thèse, à l'étude des méthodes d'extrapolation polynômiales et à l'application de ces méthodes dans l'accélération de méthodes de points fixes pour des problèmes donnés. L'avantage de ces méthodes d'extrapolation est qu'elles utilisent uniquement une suite de vecteurs qui n'est pas forcément convergente, ou qui converge très lentement pour créer une nouvelle suite pouvant admettreune convergence quadratique. Le développement de méthodes cycliques permet, deplus, de limiter le coût de calculs et de stockage. Nous appliquons ces méthodes à la résolution des équations de Navier-Stokes stationnaires et incompressibles, à la résolution de la formulation Kohn-Sham de l'équation de Schrödinger et à la résolution d'équations elliptiques utilisant des méthodes multigrilles. Dans tous les cas, l'efficacité des méthodes d'extrapolation a été montrée.Nous montrons que lorsqu'elles sont appliquées à la résolution de systèmes linéaires, les méthodes d'extrapolation sont comparables aux méthodes de sous espaces de Krylov. En particulier, nous montrons l'équivalence entre la méthode MMPE et CMRH. Nous nous intéressons enfin, à la parallélisation de la méthode CMRH sur des processeurs à mémoire distribuée et à la recherche de préconditionneurs efficaces pour cette même méthode. / In this thesis, we study polynomial extrapolation methods. We discuss the design and implementation of these methods for computing solutions of fixed point methods. Extrapolation methods transform the original sequance into another sequence that converges to the same limit faster than the original one without having explicit knowledge of the sequence generator. Restarted methods permit to keep the storage requirement and the average of computational cost low. We apply these methods for computing steady state solutions of incompressible flow problems modelled by the Navier-Stokes equations, for solving the Schrödinger equation using the Kohn-Sham formulation and for solving elliptic equations using multigrid methods. In all cases, vector extrapolation methods have a useful role to play. We show that, when applied to linearly generated vector sequences, extrapolation methods are related to Krylov subspace methods. For example, we show that the MMPE approach is mathematically equivalent to CMRH method. We present an implementation of the CMRH iterative method suitable for parallel architectures with distributed memory. Finally, we present a preconditioned CMRH method.

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