Les protéines sont des molécules flexibles, qui accomplissent une variété de tâches cellulaires à travers des mouvements mécaniques et des changements conformationnels encodés dans leur structure tridimensionnelle. Parmi les approches théoriques qui contribuent à une meilleure compréhension de la relation entre structure, mécanique, dynamique et fonction des protéines, les modèles gros-grains sont un outil très puissant. Ils permettent d’intégrer des informations structurales et dynamiques à un coût computationnel réduit, car le traitement explicite des degrés de liberté moins importants est supprimé. Dans le cadre de cette thèse, des études comparatives rapides de la flexibilité et de la mécanique des protéines ont été menées en se servant du simple modèle gros-grains de Réseau Élastique. La dépendance des résultats de la conformation de départ, ainsi que une liberté dynamique de la chaine principale plutôt limitée, imposée par l’approximation harmonique, nous ont motivé à développer une nouvelle approche, permettant une exploration plus extensive de l’espace conformationnel. Les efforts ont conduit à PaLaCe, modèle gros-grains qui permet des changements majeurs de la structure secondaire, tout en gardant la spécificité de la séquence des acides aminés grâce à une représentation à basse résolution. En utilisant PaLaCe nous avons simulé deux processus impliquant la plasticité protéique: le dépliement du domaine I27 de la protéine musculaire titine et la dynamique à l’équilibre autour de la structure native de deux enzymes homologues adaptées à des températures différentes. Les résultats obtenus concordent avec les données expérimentales et les résultats issus de modèles tout-atom déjà publiés. PaLaCe s’avère donc être un modèle fiable, avec des temps de calcul restreints par rapport aux modèles tout-atome, tout en conservant un bon niveau de détail. Il offre ainsi la possibilité d’effectuer une recherche systématique sur les liens entre mécanique, dynamique et fonction des protéines / Proteins are flexible molecules, which accomplish a variety of cellular tasks through mechanical motions and conformational fluctuations encoded in their three-dimensional structure. Amongst the theoretical approaches contributing to a better understanding of the relationship between protein structure, mechanics, dynamics and function, coarse-grain models are a powerful tool. They can be used to integrate structural and dynamic information over broad time and size scales at a low computational cost, achieved by averaging out the less important degrees of freedom. In this work, fast comparative studies of protein flexibility and mechanics have been performed with the simple coarse-grain Elastic Network Model. However, the dependency of the results on the starting conformation, and the rather constrained backbone dynamics imposed by the harmonic approximation, motivated the development of a new approach, for a more extensive exploration of conformational space. These efforts led to the PaLaCe model, designed to allow significant changes in secondary structure, while maintaining residue specificity despite a lower-level resolution. Using PaLaCe, we were able to reproduce two processes involving protein plasticity: the mechanical unfolding of the I27 domain of the giant muscle protein titin and the near-native dynamics of two homologous enzymes adapted to work at different temperatures. Agreement with experimental data and results from published atomistic models demonstrate that PaLaCe is a reliable, sufficiently accurate, but computationally inexpensive approach. It therefore opens the doors for a systematic investigation of the link between protein dynamics/mechanics and function

Cette thèse est dédiée à l'analyse mathématique et la simulation numérique des équations intervenant dans la modélisation de l’électrophysiologie cardiaque. D'abord, nous donnons une justification mathématique rigoureuse du processus d’homogénéisation périodique à l’aide de la méthode d'éclatement périodique. Nous considérons des conductivités électriques tensorielles qui dépendent de l’espace et des modèles ioniques non linéaires physiologiques et phénoménologiques. Nous montrons l'existence et l'unicité d’une solution du modèle microscopique en utilisant une approche constructive de Faedo- Galerkin suivie par un argument de compacité dans L2. Ensuite, nous montrons la convergence de la suite de solutions du problème microscopique vers la solution du problème macroscopique. À cause des termes non linéaires sur la variété oscillante, nous utilisons l’opérateur d’éclatement sur la surface et un argument de compacité de type Kolmogorov pour les modèles phénoménologiques et de type Minty pour les modèles physiologiques. En outre, nous considérons le modèle monodomaine couplé au modèle physiologique de Beeler-Reuter. Nous proposons un schéma volumes finis et nous analysons sa convergence. D'abord, nous dérivons la formulation variationnelle discrète correspondante et nous montrons l'existence et l'unicité de sa solution. Par compacité, nous obtenons la convergence de la solution discrète. Comme le schéma TPFA (two point flux approximation) est inefficace pour approcher les flux diffusifs avec des tenseurs anisotropes, nous proposons et analysons, ensuite, un schéma combiné non-linéaire qui préserve le principe de maximum. Ce schéma est basé sur l’utilisation d’un flux numérique de Godunov pour le terme de diffusion assurant que les solutions discrètes soient bornées sans restriction sur le maillage du domaine spatial ni sur les coefficients de transmissibilité. Enfin, dans la perspective d'étudier la solvabilité des modèles électromécaniques couplés avec des modèles ioniques physiologiques, nous considérons un modèle avec une description linéarisée de la réponse élastique passive du tissu cardiaque, une linéarisation de la contrainte d'incompressibilité et une approximation tronquée des diffusivités non linéaires intervenant dans les équations du modèle bidomaine. La preuve utilise des approximations par des systèmes non-dégénérés et la méthode Faedo-Galerkin suivie par un argument de compacité. / This thesis is concerned with the mathematical analysis and numerical simulation of cardiac electrophysiology models. We use the unfolding method of homogenization to rigorously derive the macroscopic bidomain equations. We consider tensorial and space dependent conductivities and physiological and simplified ionic models. Using the Faedo-Galerkin approach followed by compactness, we prove the existence and uniqueness of solution to the microscopic bidomain model. The convergence of a sequence of solutions of the microscopic model to the solution of the macroscopic model is then obtained. Due to the nonlinear terms on the oscillating manifold, the boundary unfolding operator is used as well as a Kolmogorov compactness argument for the simplified models and a Minty type argument for the physiological models. Furthermore, we consider the monodomain model coupled to Beeler- Reuter's ionic model. We propose a finite volume scheme and analyze its convergence. First, we show existence and uniqueness of its solution. By compactness, the convergence of the discrete solution is obtained. Since the two-point flux approximation (TPFA) scheme is inefficient in approximating anisotropic diffusion fluxes, we propose and analyze a nonlinear combined scheme that preserves the maximum principle. In this scheme, a Godunov approximation to the diffusion term ensures that the solutions are bounded without any restriction on the transmissibilities or on the mesh. Finally, in view of adressing the solvability of cardiac electromechanics coupled to physiological ionic models, we considered a model with a linearized description of the passive elastic response of cardiac tissue, a linearized incompressibility constraint, and a truncated approximation of the nonlinear diffusivities appearing in the bidomain equations. The existence proof is done using nondegenerate approximation systems and the Faedo-Galerkin method followed by a compactness argument.

Atomic force microscopy (AFM) is a powerful technique that enables to study biological macromolecules and dynamic biological processes at different scales. It is an excellent tool for imaging of biological objects under various conditions at a nanometer resolution. Force mode of AFM, so called single molecule force spectroscopy (SMFS), allows for investigation of the strength of molecular interactions of different origins established between and within biological molecules. In the present work, SMFS was used to detect and locate structurally and functionally important interactions of sodium/glycine betaine transporter BetP of Corynebacterium glutamicum, which serves as a model system for this class of proteins. Mechanical pulling of BetP molecules embedded into the lipid membranes resulted in a step-wise unfolding of the protein and revealed insights into its structural stability. Effect of the lipid environment, N- and C-terminal extensions on inramolecular interactions of BetP as well as protein activation and ligand binding were investigated in great detail. In another part of this work, I demonstrate an application of the AFM based technique that can record unfolding of a protein under force-clamp conditions. This method directly measures the kinetics of the protein unfolding, allowing for the use of simple methods to analyze the data. For the first time the force-clamp technique was used to describe in detail unfolding kinetics of the membrane protein, i. e. Na+/H+-antiporter NhaA from Escherichia coli. Performed here experiments on NhaA in its functionally active and inactive states demonstrated the advantages of examining unfolding kinetics at the single-molecule level. It was possible to observe unfolding events for pH-activated conformation of NhaA that due to the low frequency of occurrence were not represented in the ensemble average of the single-molecule measurements. As mechanical unfolding, similarly to bond rupture, is a force-dependent process, force-clamp technique can allow for a more direct way of probing protein unfolding and is anticipated to be also useful to examine the folding/unfolding kinetics of other membrane proteins.

The neutron plays a central role in numerous fields of physics, a fact that entails a need for methods of measuring neutron energy spectra. In this project, a technique for neutron spectrometry through measurements of neutron-induced radioactivity in activation detectors was developed and tested. The developed technique involves irradiating element samples with neutrons, measuring activation products with a gamma spectrometer, and then performing a neutron spectrum unfolding procedure. The elements indium, iron, magnesium, aluminium, zinc, titanium, and copper were used as activation detectors and irradiated with neutrons from an americium-beryllium (AmBe) neutron source. Subsequent gamma spectrometry was performed with the UGGLA high-purity germanium detector setup at Uppsala University. The GRAVEL unfolding algorithm was implemented in MATLAB and used to unfold neutron spectra based on an initial spectrum guess. The unfolded neutron spectrum agrees well with the expected AmBe spectrum, though some difference between the spectra is attributed to neutron scattering in the irradiation environment. A possible ability to find approximate neutron spectra from inaccurate initial guesses is found, but additional work is needed to understand better how the initial guess affects the result for different neutron sources. Because activation detectors do not require electrical power when measuring neutrons, can be made sensitive to a wide range of neutron energies, and do not detect other types of radiation, future applications could find the developed neutron spectrometry method practical.

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Estudamos singularidades de famílias de matrizes simétricas. O objetivo é classificar as singularidades simples de tais famílias e estudar a geometria de alguns objetos associados a elas / We study the singularities of families of symmetric matrices. The aim of this work is to classify simple singularities of such families and study the geometry of some objects associated to them

Simulações moleculares podem fornecer informações e detalhes mecanísticos que são difíceis de obter de experimentos. No entanto, fenômenos bioquímicos como formação de complexos proteína-ligante e desenovelamento de proteína são lentos e difíceis de amostrar na escala de tempo geralmente atingida por simulações de dinâmica molecular (MD) convencionais. Esses fenômenos moleculares foram estudados aqui pela combinação de simulações de MD com diversos métodos e aproximações para aumentar a amostragem configuracional: método de energia de interação linear (LIE), a aproximação de ensemble ponderado (WE) e dinâmica molecular dirigida (SMD). Uma equação foi parametrizada para prever afinidades entre pequenas moléculas e proteínas baseada na aproximação LIE, que foca a amostragem computacional nos estados complexado e não-complexado do ligante. A flexibilidade proteica foi introduzida usando ensembles de configurações obtidos de simulações de MD. Diferentes esquemas de média foram testados para obter afinidades totais de complexos proteína-ligante, revelando que muitas configurações de complexo contribuem para as afinidades de proteínas flexíveis, enquanto as afinidades de proteínas rígidas são dominadas por uma configuração de complexo. O mutante L99A da lisozima T4 (T4L) é provavelmente a proteína mais frequentemente usada para estudar complexação de ligantes. Estruturas cristalográficas mostram que a cavidade de ligação artificial criada pela mutação é pouco acessível, portanto movimentos proteicos ou uma respiração conformacional são necessários para permitir a entrada e saída de ligantes. Simulações de MD foram combinadas aqui com a aproximação de WE para aumentar a amostragem de eventos infrequentes de saída do benzeno de T4L. Quatro possíveis caminhos foram encontrados e movimentações de alfa-hélices e cadeias laterais envolvidas na saída do ligante foram caracterizadas. Os quatro caminhos correspondem a túneis da proteína previamente observados em simulações de MD longas de T4L apo, sugerindo que a heterogeneidade de caminhos ao longo de túneis intrínsecos é explorada por pequenas moléculas para sair de cavidades de ligação enterradas em proteínas. Experimentos de microscopia de força atômica revelaram informações detalhadas do desenovelamento forçado e da estabilidade mecânica da rubredoxina, uma proteína ferro-enxofre simples. O desenovelamento completo da rubredoxina envolve a ruptura de ligações covalentes. Portanto, o processo de desenovelamento foi simulado aqui por simulações de SMD acopladas a uma descrição clássica da dissociação de ligações. A amostragem de eventos de desenovelamento forçado foi aumentada pelo uso de velocidades rápidas de esticamento. Os resultados foram analisados usando um modelo teórico válido para regimes de desenovelamento forçado lentos e rápidos. As simulações revelaram que mudanças no ponto de aplicação de força ao longo da sequência da rubredoxina levam a diferentes mecanismos de desenovelamento, caracterizados por variáveis graus de rompimento de ligações de hidrogênio e estrutura secundária da proteína. / Molecular simulations may provide information and mechanistic insights that are difficult to obtain from experiments. However, biochemical phenomena such as ligand-protein binding and protein unfolding are slow and hard to sample on the timescales usually reached by conventional molecular dynamics (MD) simulations. These molecular phenomena were studied here by combining MD simulations with several methods or approximations to enhance configurational sampling: linear interaction energy (LIE) method, weighted ensemble (WE) approach and steered molecular dynamics (SMD). An equation was parametrized to predict affinities between small molecules and proteins based on the LIE approximation, which focus computational sampling in ligand bound and unbound states. Protein flexibility was introduced by using ensembles of configurations obtained from MD simulations. Different averaging schemes were tested to obtain overall affinities for ligand-protein complexes, revealing that many bound configurations contribute to affinities for flexible proteins, while affinities for rigid proteins are dominated by one bound configuration. T4 lysozyme (T4L) L99A mutant is probably the protein most often used to study ligand binding. Crystal structures show the artificial binding cavity created by the mutation has low accessibility, so protein movements or conformational breathing are necessary to allow the entry and egress of ligands. MD simulations were combined here with the WE approach to enhance sampling of infrequent benzene unbinding events from T4L. Four possible pathways were found and motions on alpha-helices and side chains involved in ligand egress were characterized. The four pathways correspond to protein tunnels previously observed in long MD simulations of apo T4L, suggesting that pathway heterogeneity along intrinsic tunnels is explored by small molecules to egress from binding cavities buried in proteins. Previous atomic force microscopy experiments revealed detailed information on the forced unfolding and mechanical stability of rubredoxin, a simple iron-sulfur protein. Complete unfolding of rubredoxin involves rupture of covalent bonds. Thus, the unfolding process was simulated here by SMD simulations coupled to a classical description of bond dissociation. Sampling of forced unfolding events was increased by using fast pulling velocities. Results were analyzed using a theoretical model valid for both slow and fast forced unfolding regimes. Simulations revealed that changing the points of force application along the rubredoxin sequence leads to different unfolding mechanisms, characterized by variable degrees of disruption of hydrogen bonds and secondary protein structure.

A qualidade do ambiente das áreas destinadas às florestas é afetada pelos problemas de compactação do solo devido a causas naturais e induzidas pelo tráfego de veículos. O objetivo deste trabalho foi definir as prioridades do preparo mecanizado do solo a partir das exigências das mudas de Eucalyptus spp. A execução do trabalho foi realizada entre dezembro de 2000 a maio de 2001, na Companhia Suzano de Papel e Celulose, município de São Miguel Arcanjo (S.P). O método utilizado teve duas fases: Planejamento da Qualidade, e Avaliação da Qualidade. A primeira fase, consistiu em sistematizar o conceito emitido, por uma equipe especializada na produção florestal, sobre a qualidade do preparo mecanizado do solo para mudas de Eucalyptus spp, utilizando-se do Desdobramento da Função Qualidade (QFD), e a segunda fase, Avaliação da Qualidade, consistiu em verificar as prioridades técnicas através de histograma e carta de controle. Os resultados evidenciaram que os itens da qualidade exigida não possuir limitações físicas, e sem restevas que limitem a mecanização tem respectivamente 19,4% e 15,0% de peso relativo. O requisito técnico profundidade do sulco de plantio relacionou-se fortemente com os itens da qualidade exigida, e apresentou 25,7% de peso relativo. Também, o indicador profundidade do sulco, correlacionou-se fortemente com a largura do sulco e com o tamanho dos torrões, cujos pesos relativos foram iguais a 26,4% e 23,0%. Os fatores operacionais do preparo mecanizado do solo, regulagens do sulcador/implemento e a distribuição da resteva superficial, apresentaram respectivamente 25,6% e 64,0% de pesos relativos, e os graus do custo econômico destes fatores foram respectivamente 1 e 5. As conclusões da pesquisa foram: os itens da qualidade exigida não possuir limitações físicas, e sem restevas que limitem a mecanização são prioritários para as mudas de Eucalyptus spp, sendo que a prioridade técnica foi a profundidade do sulco, tornando-se o indicador da qualidade do preparo mecanizado do solo, o qual será controlado através das regulagens do sulcador/implemento. Nas faixas de galhada, o controle da profundidade do sulco será determinado pela distribuição da resteva superficial. / The quality of the environment of areas destined to artificial forest is reduced by the problems of soil compactation due to natural causes and induced by the traffic of vehicles. The aim of this work was to define the priorities of the mechanized preparation of the soil based on the demands of the Eucalyptus spp seedlings. The work was done during December 2000 to May 2001 at Companhia Suzano de Papel e Celulose, S.P. The method used had two steps: planning of the quality and evaluation of the quality. The first stage consisted of systematizing the concepts about soil preparation emitted by a team of experts in forest production using the Quality Function Deployment (QFD). The second stage, evaluation of the quality, consisted in checking the technical priorities in an experimental area. The results were analized using statistical quality tools mainly histograms and control charts. The results showed that the itens of the demanded quality, not having the physical limitation and without residue that limit the mechanization, have 19.4% and 15.0% respectively of relative weight. The technical requirement, depth of the planting furrow, was strongly related with the itens of demanded quality and it represents 27.5% of relative weight. Also the indicator depth of furrow, was strongly conected with the furrow width and size of soil lumps which the relative weights were 26.4% and 23.0% respectively. The operational factors of soil mechanization, subsoiler adjust and the distribution of the superficial residue, showed respectively 25.6% and 64.0% of the relative weights and the degrees of economical cost of these factors were classified as 1 and 5. The conclusions of the work were: the itens of the demanded quality, not having the physical limitation and without residue that limit the mechanization, are priority for the plants of Eucalyptus; the technical requirement, depth of the planting furrow, becoming the indicator of quality of the soil preparation and it will be controlled through the subsoiler adjustment; in the strips of the wood debris the depth control will be determined by the distribution of the superficial residue.