Ces dernières années, plusieurs modèles d'évolution moléculaire, basés sur l'hypothèse que les séquences des protéines évoluent sous la contrainte d'une structure bien définie et constante au cours de l'évolution, ont été développés. Cependant, un tel modèle repose sur l'expression de la fonction représentant le lien entre la structure et sa séquence. Les potentiels statistiques proposent une solution intéressante, mais parmi l'ensemble des potentiels statistiques existants, lequel serait le plus approprié pour ces modèles d'évolution ? Dans cette thèse est développé un cadre probabiliste d'optimisation de potentiels statistiques, dans le contexte du maximum de vraisemblance, et dans une optique de protein design. Ce cadre intègre différentes méthodes d'optimisation, incluant la prise en compte de structures alternatives pour l'optimisation des potentiels, et fournit un cadre robuste et des tests statistiques (à la fois dans le contexte de l'optimisation des potentiels mais aussi dans le contexte de l'évolution moléculaire) permettant de comparer différentes méthodes d'optimisation de potentiels statistiques pour les modèles soumis à des contraintes structurales. / In the field of molecular evolution, so called Structurally constrained (SC) models have been developped. Expressed at the codon level, they explicitely separe the mutation (applied to the nucleotide sequence) and the selection (applied to the encoded protein sequence) factors. The selection factor is described as a function between the structure and the sequence of the protein, via the use of a statistical potential. However, the whole evolutionary model depends on the expression of this potential, and one can ask wether a potential would be better than another. In this thesis, is developped a probabilistic framework to optimize statistical potentials especially meant for protein design, using a maximum likelihood approach. The statistical potential used in this thesis is composed by a contact potential and a solvent accessibility potential, but the probabilistic framework can easily be generalized to more complex statistical potentials. In a first part, the framework is defined, and then an algorithmical enhancement is proposed, and finally, the framework is modified in order to take into account misfolded structures (decoys). The framework defined in this thesis and in other works allows to compare different optimization methods of statistical potentials for SC models, using cross-validation and Bayes factor comparisons.

Les fonctions d'une molécule d'ARN dans les processus cellulaires sont très étroitement liées à sa structure tridimensionnelle. Il est donc essentiel de pouvoir prédire cette structure pour étudier sa fonction. Le repliement de l'ARN peut être vu comme un processus en deux étapes : le repliement en structure secondaire, grâce à des interactions fortes, puis le repliement en structure tridimensionnelle par des interactions tertiaires. Prédire la structure secondaire a donné lieu à de nombreuses avancées depuis plus de trente ans. Toutefois, la prédiction de la structure tridimensionnelle est un problème bien plus difficile. Nous nous intéressons ici au problème de prédiction de la structure 3D d'ARN sous la forme d'un jeu. Nous représentons la structure secondaire de l'ARN comme un graphe : cela correspond à une modélisation à gros grain de cette structure. Cette modélisation permet de réaliser un jeu de repliement dans l'espace. Notre hypothèse consiste à voir la structure 3D comme un équilibre en théorie des jeux. Pour atteindre cet équilibre, nous utiliserons des algorithmes de minimisation de regret. Nous étudierons aussi différentes formalisations du jeu, basées sur des statistiques biologiques. L'objectif de ce travail est de développer une méthode de repliement d'ARN fonctionnant sur tous les types de molécule d'ARN et obtenant des structures similaires aux molécules réelles. Notre méthode, nommée GARN, a atteint les objectifs attendus et nous a permis d'approfondir l'impact de certains paramètres pour la prédiction de structure à gros grain des molécules. / The functions of RNA molecules in cellular processes are related very closely to its three dimensional structure. It is thus essential to predict the structure for understanding RNA functions. This folding can be seen as a two-step process: the formation of a secondary structure and the formation of three-dimensional structure. This first step is the results of strong interactions between nucleotides, and the second one is obtain by the tertiary interactions. Predicting the secondary structure is well-known and results in numerous advances since thirty years. However, predicting the three-dimensional structure is a more difficult problem due to the high number of possibility. To overcome this problem, we decided to see the folding of the RNA structure as a game. The secondary structure of the RNA is represented as a graph: its corresponds to a coarse-grained modeling of this structure. This modeling allows us to fold the RNA molecule in a discrete space. Our hypothesis is to understand the 3D structure like an equilibrium in game theory. To find this equilibrium, we will use regret minimization algorithms. We also study different formalizations of the game, based on biological statistics. The objective of this work is to develop a method of RNA folding which will work on all types of secondary structures and results more accurate than current approaches. Our method, called GARN, reached the expected objectives and allowed us to deepen the interesting factors for coarse-grained structure prediction on molecules.

Estudos teóricos dos mecanismos moleculares responsáveis pela formação e estabilidade de complexos moleculares vêm ganhando relevância pelas possibilidades práticas que oferecem, por exemplo, na compreensão de diversas doenças e no desenho racional de fármacos. Neste projeto, nossa ênfase está no estudo de complexos de proteínas, extraídos do banco de dados de proteínas (PDB), onde desenvolvemos ferramentas computacionais as quais permitem efetuar análises em duas direções: 1) efetuar previsões básicas, através do emprego de propriedades eletrostáticas de proteínas, em diferentes condições e níveis preditivos e 2) realização de um conjunto de análises estatísticas, como freqüência de contato, em busca de preditores de complexos de proteínas e identificar padrões de interação entre seus aminoácidos em função da distância de separação. Com base nos resultados obtidos por ambos os estudos, objetivamos quantificar as forças físicas envolvidas na formação dos complexos protéicos. O foco do projeto, a longo prazo, é prever o fenômeno da complexação através da fusão dessas duas linhas de estudos: preditor básico de complexos protéicos e análise do potencial estatístico entre os aminoácidos que formam o complexo. O presente projeto é concluído com a construção de portais web que disponibilizarão os resultados obtidos por nossos trabalhos bem como a possibilidade de qualquer usuário, efetuar consultas por propriedades de proteínas e/ou grupo de proteínas. / Theoretical studies of the molecular mechanisms responsible for the formation and stability of molecular complexes are gaining relevance for the practical possibilities that they offer, for example, in the understanding of diverse diseases and rational drug design. In this project, our emphasis is on the study of protein complexes, extracted from protein data bank (PDB). We have developed computational tools which allow to perform analyses in two directions: 1) to make basic complexation forecasts, through the use of electrostatics properties of proteins, in different conditions and predictive levels, and 2) to carry out a set of statistical analyses, as contacts frequency, in order to build up predictor of protein complexes and to identify patters of interactions between the amino acids as a function of their separation distance. Based on the results obtained on both studies, we aim quantify the physical forces involved in the formation of protein complexes. The focus of the project, in the long run, is to foresee the phenomenon of the protein complexes through the fusing of these two study lines: a coarse-grained predictor of protein complexes and analysis of the statistical potentials between the amino acids that form the complex. The present project is concluded with the construction of web services where we make available the results obtained on our works. This server also has the possibility to be used by any computer user, that wishes to perform search on protein and/or protein group properties

Estudos teóricos dos mecanismos moleculares responsáveis pela formação e estabilidade de complexos moleculares vêm ganhando relevância pelas possibilidades práticas que oferecem, por exemplo, na compreensão de diversas doenças e no desenho racional de fármacos. Neste projeto, nossa ênfase está no estudo de complexos de proteínas, extraídos do banco de dados de proteínas (PDB), onde desenvolvemos ferramentas computacionais as quais permitem efetuar análises em duas direções: 1) efetuar previsões básicas, através do emprego de propriedades eletrostáticas de proteínas, em diferentes condições e níveis preditivos e 2) realização de um conjunto de análises estatísticas, como freqüência de contato, em busca de preditores de complexos de proteínas e identificar padrões de interação entre seus aminoácidos em função da distância de separação. Com base nos resultados obtidos por ambos os estudos, objetivamos quantificar as forças físicas envolvidas na formação dos complexos protéicos. O foco do projeto, a longo prazo, é prever o fenômeno da complexação através da fusão dessas duas linhas de estudos: preditor básico de complexos protéicos e análise do potencial estatístico entre os aminoácidos que formam o complexo. O presente projeto é concluído com a construção de portais web que disponibilizarão os resultados obtidos por nossos trabalhos bem como a possibilidade de qualquer usuário, efetuar consultas por propriedades de proteínas e/ou grupo de proteínas. / Theoretical studies of the molecular mechanisms responsible for the formation and stability of molecular complexes are gaining relevance for the practical possibilities that they offer, for example, in the understanding of diverse diseases and rational drug design. In this project, our emphasis is on the study of protein complexes, extracted from protein data bank (PDB). We have developed computational tools which allow to perform analyses in two directions: 1) to make basic complexation forecasts, through the use of electrostatics properties of proteins, in different conditions and predictive levels, and 2) to carry out a set of statistical analyses, as contacts frequency, in order to build up predictor of protein complexes and to identify patters of interactions between the amino acids as a function of their separation distance. Based on the results obtained on both studies, we aim quantify the physical forces involved in the formation of protein complexes. The focus of the project, in the long run, is to foresee the phenomenon of the protein complexes through the fusing of these two study lines: a coarse-grained predictor of protein complexes and analysis of the statistical potentials between the amino acids that form the complex. The present project is concluded with the construction of web services where we make available the results obtained on our works. This server also has the possibility to be used by any computer user, that wishes to perform search on protein and/or protein group properties