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The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.

Modelling is a powerful method for understanding complex systems, which works by simplifying them to their most essential components. The choice of the components is driven by the aspects studied. The tool chosen to perform this task will determine what can be modelled, the maximum number of components which can be represented, as well as the analyses which can be performed on the system. Performance Evaluation Process Algebra (PEPA) was initially developed to tackle computer systems issues. Nevertheless, it possesses some interesting properties which could be exploited for the study of epidemiological systems. PEPA's main advantage resides in its capacity to change scale: the assumptions and parameter values describe the behaviour of a single individual, while the resulting model provides information on the population behaviour. Additionally, stochasticity and continuous time have already proven to be useful features in epidemiology. While each of these features is already available in other tools, to find all three combined in a single tool is novel, and PEPA is proposed as a useful addition to the epidemiologist's toolbox. Moreover, an algorithm has been developed which allows converting a PEPA model into a system of Ordinary Differential Equations (ODEs). This provides access to countless additional software and theoretical analysis methods which enable the epidemiologist to gain further insight into the model. Finally, most existing tools require a deep understanding of the logic they are based on and the resulting model can be difficult to read and modify. PEPA's grammar, on the other hand, is easy to understand since it is based on few, yet powerful concepts. This makes it a very accessible formalism for any epidemiologist. The objective of this thesis is to determine precisely PEPA's ability to describe epidemiological systems, as well as extend the formalism when required. This involved modelling two systems: the bubonic plague in prairie dogs, and measles in England and Wales. These models were chosen as they exhibit a good range of typical features, allowing to thoroughly test PEPA. All features required in each of these models have been analysed in detail, and a solution has been provided for representing each of these features. While some of them could be expressed in a straightforward manner, PEPA did not provide the tools to express others. In those cases, we determined methods to approach the desired behaviour, and the limitations of said methods were carefully analysed. In the case of models with a structured population, PEPA was extended to simplify their expression and facilitate the writing process of the PEPA model. The work also required the development of an algorithm to derive ODEs adapted to the type of models encountered. Finally, the PEPAdum software was developed to assist the modeller in the generation and analysis of PEPA models, by simplifying the process of writing a PEPA model with compartments, performing the average of stochastic simulations and deriving and explicitly providing the ODEs using the Stirling Amendment.

Two α-amino acids labelled with 18F, 2-[18F]fluoro-L-tyrosine and 6-[18F]fluoro-L-dopa, are routinely produced at the CRC for PET clinical investigation in oncology and neurology. The first one is a tracer for the in vivo quantitative assessment of cerebral protein synthesis (tumor seeking agent) and the second one is a tracer for in vivo cerebral studies of presynaptic dopaminergic functions. Routine production of these two α-amino acids has been conducted in our laboratory, using a nucleophilic, multistep radiosynthesis approach. The no-carrier-added (nca) [18F]fluoride, which is available in large amounts from proton irradiation of 18O-enriched water in a cyclotron, allows the labelling of benzaldehyde derivatives by the substitution of a good leaving group. The synthesis of [18F]fluorobenzyl bromide derivative by reduction and bromination with gaseous HBr followed by the enantioselective alkylation under Phase Transfer Catalysis (PTC) of a benzophenone imine provides the protected radiopharmaceutical which is hydrolysed and purified by HPLC. Due to the fact that gaseous HBr is quite cumbersome to handle and that its complete automation is difficult, the first goal of our work is to evaluate new methods for the synthesis of the [18F]fluorobenzyl bromide derivatives starting from the labelled benzaldehyde derivatives. In order to propose a radiochemical reaction which can be easily automated, we have evaluated different reactions on solid (and non solid) supported reagents. Five reagents were tested. N-piperidinoaminomethylpolystyrene hydrobromide resin gives the the [18F]fluorobenzyl bromide derivatives as unique products in good yields. In the second part of our work, a new approach for the labelling of peptides from the key intermediate p-[18F]fluorobenzyl bromide has been evaluated using the concept of click chemistry. 1,3-dipolar cycloaddition provides fast access to a large number of five-membered heterocycles. We have used this cycloaddition to label protected p-ethynyl-L-phenylalanine with p-[18F]fluorobenzyl azide. This interesting labelling method will be applied to the labelling of a peptide containing this α-amino acid residue.

The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.

Mon projet de recherche avait pour but de caractériser le rôle de deux protéines, ArgR et PepA, qui agissent en tant que facteurs accessoires de la recombinaison au niveau de deux sites cer du plasmide ColE1 présent dans la bactérie Escherichia coli. Ces deux protéines, couplées aux deux recombinases à tyrosine XerC et XerD, permettent la catalyse de la recombinaison site spécifique au niveau de la séquence cer, convertissant les multimères instables de ColE1 en monomères stables. Cette étude a principalement porté sur la région C-terminale de la protéine ArgR. Cette région de la protéine ArgR possède une séquence en acides-aminés et une structure similaire à celle de la protéine AhrC de Bacillus subtilis. De plus, AhrC, le répresseur de l’arginine de cette bactérie, est capable de complémenter des Escherichia coli mutantes déficientes en ArgR. Les régions C-terminales de ces protéines, montrent une forte similarité. De précédents travaux dans notre laboratoire ont démontré que des mutants d’ArgR comprenant des mutations dans cette région, en particulier les mutants ArgR149, une version tronquée d’ArgR de 149 acides-aminés, et ArgR5aa, une version comprenant une insertion de cinq acides-aminés dans la partie C-terminale, perdaient la capacité de permettre la recombinaison au niveau de deux sites cer présents dans le plasmide pCS210. Malgré cette incapacité à promouvoir la réaction de recombinaison en cer, ces deux mutants étaient toujours capables de se lier spécifiquement à l’ADN et de réprimer une fusion argA :: lacZ. Dans ce travail, les versions mutantes et sauvages d’ArgR furent surexprimées en tant que protéines de fusion 6-histidine. Des analyses crosslinking ont montré que la version sauvage et ArgR5aa pouvaient former des hexamères in-vitro de manière efficace, alors qu’ArgR149 formait des multimères de plus faible poids moléculaire. Des formes tronquées d’ArgR qui comportaient 150 acides-aminés ou plus, étaient encore capables de permettre la recombinaison en cer. Les mutants par substitution ArgRL149A et ArgRL151A ont tous montré que les substitutions d’un seul acide-aminé au sein de cette région avaient peu d’effets sur la recombinaison en cer. Les expériences de crosslinking protéine-à-protéine ont montré que le type sauvage et les formes mutantes d’ArgR étaient capables d’interagir avec la protéine accessoire PepA, également impliquée dans la recombinaison en cer. Les expériences de recombinaison in-vitro utilisant la forme sauvage et les formes mutantes d’ArgR combinées avec les protéines PepA, XerC et XerD purifiées, ont montré que le mutant ArgR149 ne soutenait pas la recombinaison, mais que le mutant ArgR5aa permettait la formation d’une jonction d’Holliday. Des expériences de topologie ont montré que PepA était capable de protéger l’ADN de la topoisomérase 1, et d’empêcher ArgRWt de se lier à l’ADN. Les deux mutants ArgR149 et ArgR5aa protègent aussi l’ADN avec plus de surenroulements. Quand on ajoute PepA, les profils de migration montrent un problème de liaison des deux mutants avec PepA. D’autres expériences impliquant le triplet LEL (leucine-acide glutamique-leucine) et les acides-aminés alentour devraient être réalisés dans le but de connaitre l’existence d’un site de liaison potentiel pour PepA. / My research project involved the role of two proteins, ArgR and PepA, which act as accessory factors in the ColE1 cer recombination system from the gram negative bacteria Escherichia coli. These two proteins, in addition to the tyrosine recombinases XerC and XerD, catalyze a site-specific recombination event at the cer sequence which converts unstable multimeric forms of ColE1 into more stable monomers. Our study mainly focused on the C-terminal end of the ArgR. This region of the ArgR protein possesses a structural and amino acid sequence similarity with the AhrC protein from Bacillus subtilis. Moreover, AhrC, the Arginine repressor of this bacterium, is able to complement Escherichia coli mutants deficient in ArgR. The C-terminal regions of these proteins, display a very high region of similarity. Previous work from our laboratory has shown that ArgR mutants with mutations in this region, especially the mutants ArgR149, a truncated 149 amino acids form of ArgR, and ArgR5aa, a form containing a five amino acid insertion in the C-terminal part, lost the ability to perform a recombination reaction at two cer sites in the plasmid pCS210. Despite this defect in promoting cer recombination, the mutants were still able to bind specifically to DNA, and to repress an argA :: lacZ genetic fusion. In this work, both wild type and mutant ArgR proteins were overexpressed as 6-histidine fusion proteins. Crosslinking analysis showed that both wild type and ArgR5aa efficiently formed hexamers in vitro, while ArgR149 formed lower molecular weight multimers. Truncated forms of ArgR that were 150 amino acids or longer, were able to support cer recombination. The substitution mutants between positions 149 to 151 all showed that single amino acid substitutions at this region had little effect on cer recombination. Protein-protein crosslinking experiments showed that wild type and mutant forms of ArgR, were able to interact with and the other accessory protein involved in cer recombination, PepA. In vitro recombination experiments using wild type and mutant forms of ArgR, combined with purified PepA, XerC and XerD showed that the ArgR149 mutant did not support recombination, but the ArgR5aa mutant did promote Holliday junction formation, raising the possibility that these two mutants interact differently with the Xer recombination machinery. Topology experiments showed that after adding topoisomerase 1, PepA is able to protect DNA from topoisomerase 1, and prevent ArgRWt binding to DNA. The two mutants ArgR149 and ArgR5aa are protecting DNA with more supercoiling. When PepA is added, migration profiles with the two mutants showed a binding problem with PepA. Other experiments involving the LEL triplet (leucine-glutamic acid-leucine) and amino-acids around it should be done in order to know the existence of a possible binding site for PepA.

Mon projet de recherche avait pour but de caractériser le rôle de deux protéines, ArgR et PepA, qui agissent en tant que facteurs accessoires de la recombinaison au niveau de deux sites cer du plasmide ColE1 présent dans la bactérie Escherichia coli. Ces deux protéines, couplées aux deux recombinases à tyrosine XerC et XerD, permettent la catalyse de la recombinaison site spécifique au niveau de la séquence cer, convertissant les multimères instables de ColE1 en monomères stables. Cette étude a principalement porté sur la région C-terminale de la protéine ArgR. Cette région de la protéine ArgR possède une séquence en acides-aminés et une structure similaire à celle de la protéine AhrC de Bacillus subtilis. De plus, AhrC, le répresseur de l’arginine de cette bactérie, est capable de complémenter des Escherichia coli mutantes déficientes en ArgR. Les régions C-terminales de ces protéines, montrent une forte similarité. De précédents travaux dans notre laboratoire ont démontré que des mutants d’ArgR comprenant des mutations dans cette région, en particulier les mutants ArgR149, une version tronquée d’ArgR de 149 acides-aminés, et ArgR5aa, une version comprenant une insertion de cinq acides-aminés dans la partie C-terminale, perdaient la capacité de permettre la recombinaison au niveau de deux sites cer présents dans le plasmide pCS210. Malgré cette incapacité à promouvoir la réaction de recombinaison en cer, ces deux mutants étaient toujours capables de se lier spécifiquement à l’ADN et de réprimer une fusion argA :: lacZ. Dans ce travail, les versions mutantes et sauvages d’ArgR furent surexprimées en tant que protéines de fusion 6-histidine. Des analyses crosslinking ont montré que la version sauvage et ArgR5aa pouvaient former des hexamères in-vitro de manière efficace, alors qu’ArgR149 formait des multimères de plus faible poids moléculaire. Des formes tronquées d’ArgR qui comportaient 150 acides-aminés ou plus, étaient encore capables de permettre la recombinaison en cer. Les mutants par substitution ArgRL149A et ArgRL151A ont tous montré que les substitutions d’un seul acide-aminé au sein de cette région avaient peu d’effets sur la recombinaison en cer. Les expériences de crosslinking protéine-à-protéine ont montré que le type sauvage et les formes mutantes d’ArgR étaient capables d’interagir avec la protéine accessoire PepA, également impliquée dans la recombinaison en cer. Les expériences de recombinaison in-vitro utilisant la forme sauvage et les formes mutantes d’ArgR combinées avec les protéines PepA, XerC et XerD purifiées, ont montré que le mutant ArgR149 ne soutenait pas la recombinaison, mais que le mutant ArgR5aa permettait la formation d’une jonction d’Holliday. Des expériences de topologie ont montré que PepA était capable de protéger l’ADN de la topoisomérase 1, et d’empêcher ArgRWt de se lier à l’ADN. Les deux mutants ArgR149 et ArgR5aa protègent aussi l’ADN avec plus de surenroulements. Quand on ajoute PepA, les profils de migration montrent un problème de liaison des deux mutants avec PepA. D’autres expériences impliquant le triplet LEL (leucine-acide glutamique-leucine) et les acides-aminés alentour devraient être réalisés dans le but de connaitre l’existence d’un site de liaison potentiel pour PepA. / My research project involved the role of two proteins, ArgR and PepA, which act as accessory factors in the ColE1 cer recombination system from the gram negative bacteria Escherichia coli. These two proteins, in addition to the tyrosine recombinases XerC and XerD, catalyze a site-specific recombination event at the cer sequence which converts unstable multimeric forms of ColE1 into more stable monomers. Our study mainly focused on the C-terminal end of the ArgR. This region of the ArgR protein possesses a structural and amino acid sequence similarity with the AhrC protein from Bacillus subtilis. Moreover, AhrC, the Arginine repressor of this bacterium, is able to complement Escherichia coli mutants deficient in ArgR. The C-terminal regions of these proteins, display a very high region of similarity. Previous work from our laboratory has shown that ArgR mutants with mutations in this region, especially the mutants ArgR149, a truncated 149 amino acids form of ArgR, and ArgR5aa, a form containing a five amino acid insertion in the C-terminal part, lost the ability to perform a recombination reaction at two cer sites in the plasmid pCS210. Despite this defect in promoting cer recombination, the mutants were still able to bind specifically to DNA, and to repress an argA :: lacZ genetic fusion. In this work, both wild type and mutant ArgR proteins were overexpressed as 6-histidine fusion proteins. Crosslinking analysis showed that both wild type and ArgR5aa efficiently formed hexamers in vitro, while ArgR149 formed lower molecular weight multimers. Truncated forms of ArgR that were 150 amino acids or longer, were able to support cer recombination. The substitution mutants between positions 149 to 151 all showed that single amino acid substitutions at this region had little effect on cer recombination. Protein-protein crosslinking experiments showed that wild type and mutant forms of ArgR, were able to interact with and the other accessory protein involved in cer recombination, PepA. In vitro recombination experiments using wild type and mutant forms of ArgR, combined with purified PepA, XerC and XerD showed that the ArgR149 mutant did not support recombination, but the ArgR5aa mutant did promote Holliday junction formation, raising the possibility that these two mutants interact differently with the Xer recombination machinery. Topology experiments showed that after adding topoisomerase 1, PepA is able to protect DNA from topoisomerase 1, and prevent ArgRWt binding to DNA. The two mutants ArgR149 and ArgR5aa are protecting DNA with more supercoiling. When PepA is added, migration profiles with the two mutants showed a binding problem with PepA. Other experiments involving the LEL triplet (leucine-glutamic acid-leucine) and amino-acids around it should be done in order to know the existence of a possible binding site for PepA.