As part of the Large Hadron Collider high luminosity upgrade it is proposed to include crab cavities and large aperture niobium tin final focussing magnets in the lattice in order to enhance the luminosity. In this thesis the dynamics of a proposed cavity design were considered in terms of their impact upon the dynamic aperture of the machine. Taylor maps for the cavity were created and used to perform this analysis with a full assessment of their validity. A set of symplectic thin cavity models were also developed and cross checked with the Taylor maps. Finally, dynamic aperture studies were performed using these models in order to determine which components of the crab cavity dynamics are important when considering the long term stability of the beam in the LHC upgrade. It is shown that crab cavities exhibit little impact on the LHC beam stability. For the final focussing magnets a preliminary study was conducted into the importance of including their fringe fields in a model of the LHC upgrade. A technical study was carried out into developing a symplectic model which was compatible with the current magnet models use for dynamic aperture studies. A preliminary dynamic aperture study was performed with the inclusion of fringe fields for the final focussing magnets from which the fringe fields are shown to have a negative impact on the long term beam stability.

Les cavités sont le lieu privilégié des interactions d’une protéine avec ses ligands, et sont donc déterminantes pour sa fonction, elle-même aussi influencée par la dynamique de la protéine. Peu de méthodes permettent d’étudier en détail la dynamique des cavités malgré leur intérêt notamment pour le criblage virtuel. Les cavités d’une protéine définissent un ensemble très labile. Ainsi, suivre une cavité le long d’une trajectoire est ardu car elle peut être sujette à des divisions, fusions, disparitions et apparitions. Je propose une méthode pour résoudre cette question afin d’exploiter la dynamique des cavités de façon systématique et rationnelle, en classifiant les cavités selon les groupes d’atomes les entourant. J’ai identifié les paramètres procurant les meilleurs critères de suivi des cavités. Pour caractériser les évolutions principales de la géométrie des cavités en relation avec la dynamique de la protéine, j’ai développé une méthode basée sur l’Analyse en Composantes Principales. Cette méthode peut être utilisée pour sélectionner ou construire des conformations à partir de la forme de leurs cavités. Deux exemples d’applications sont traitées : la sélection de conformations ayant des cavités de géométries diverses et l’étude de l’évolution des cavités de la myoglobine lors de la diffusion du monoxyde de carbone. Ces deux méthodes ont été utilisées pour trois projets de criblage virtuel ciblant l’ADN-gyrase de M tuberculosis, la subtilisine 1 de P vivax et GLIC, homologue procaryote des récepteurs pentamériques humains. Les molécules sélectionnées à l’aide de ces méthodes ont permis d’identifier une molécule active contre la subtilisine et quatre effecteurs de GLIC. / Cavities are the prime location of the interactions between a protein and its ligands, and thus are crucial for its functions, together with its dynamics. Although cavities have been studied since the seventies, specific studies on their dynamical behavior only appeared recently. Few methods can tackle this aspect, despite its interest for virtual screening and drug design. Protein cavities define an extremely labile ensemble. Following one cavity along a trajectory is therefore an arduous task, because it can be subjected to several events of fusions, divisions, apparitions and disappearances. I propose a method to resolve this question, thus enabling systematic and rational dynamical exploitation of protein cavities. This method classify cavities using the atom groups around them, using algorithms and parameters that I identified as giving best results for cavity tracking. To characterize the main directions of evolution of cavity geometry, and to relate them with the dynamics of the underlying structure, I developed a method based on Principal Component Analysis (PCA). This method can be used to select or build conformations with given cavity shapes. Two examples of applications have been treated: the selection of conformations with diverse cavity geometries, and the analysis of the myoglobin cavity network evolution during the diffusion of carbon monoxide in it. These two methods have been used in three projects involving virtual screening, targeting M. tuberculosis DNA-gyrase, P vivax subtilisin 1 and GLIC, an procaryotic model of human pentameric ligand-gated ion channel. These methods allowed us to identify an inhibitor of subtilisin 1 and four effectors of GLIC.