Serine/threonine protein kinases (STKs) are extremely ancient and ubiquitous signaling enzymes; despite their common name “eukaryotic protein kinases”, these protein domains are also present in archaea and bacteria suggesting their presence in the last universal common ancestor 3-4 billion years ago. It is known that tyrosine kinases (TKs) descended from this lineage much later, just prior to the emergence of the first metazoans. TKs share a great deal of structural homology with even the most distantly related STKs, however their ability to phosphorylate Tyr instead of Ser and Thr along with their unique domain organizations sets them apart from STKs in both sequence and function. This thesis explores the distinct conformational “landscapes” of these two important protein families, dealing with a ~20 residue long “activation loop” which has multiple inactive conformations but only one active conformation. By employing a statistical energy Potts Hamiltonian model of protein sequences and using molecular dynamics free-energy simulations, major sequence features of the catalytic domain were determined which control the shape of the free-energy landscape i.e., the relative depths of the “active” and “inactive” basins, a quantity termed the reorganization free-energy ΔG_reorg. A key finding from this approach is the marked divergence in the conformational landscapes of TKs from STKs that is encoded in the sequences of extant family members, which was detected by threading their Potts sequence energies over the active “DFG-in” (catalytic “Asp-Phe-Gly motif oriented “in”) basin relative to an inactive “DFG-out” basin where the activation loop is “folded up” by ~20 Å. This free-energy basin autoinhibits the kinase because the activation loop behaves as a pseudo-substrate in cis. The Potts couplings threaded over the active and inactive basins suggest that TKs evolved to have a smaller free-energy difference between the active and inactive basins compared with STKs, by 4-6 kcal/mol. The sequence and structural basis for this effect was explored in detail by decomposing the threaded Potts Hamiltonian into pairwise interactions and analyzing the statistical energy effects of natural sequence variation at evolutionary divergent positions in the sequence. These effects were then verified by performing mutations of amino acid sidechains using FEP (Free Energy Perturbation) molecular dynamics simulations in both the active and inactive conformational states and comparing the results with analogous sequence-based calculations by making mutations in the Potts model. The results are highly consistent (Pearson correlation of 0.81) suggesting that the Potts model is comparable to FEP in its ability to capture the physical free-energy balance of amino acid sidechain interactions between two different conformational basins and validates the Potts model-predicted evolutionary divergent landscapes of TKs and STKs. This divergence can in part be attributed to autoinhibitory pseudo-substrate interactions involving the activation loop; the evolved peptide-substrate specificity of TKs compared with STKs, and the functional surfaces that have been evolutionarily molded to complement Tyr vs Ser/Thr-containing peptides, appear to have energetic feedback with the propensity of the kinase’s own activation loop to “fold” against these surfaces when the DFG is flipped from “in” to “out”, and TKs have evolved to exploit this as a means of regulation. / Chemistry

Ce travail concerne l'imagerie micro-onde en vue d'application à l'imagerie biomédicale. Cette technique d'imagerie a pour objectif de retrouver la distribution des propriétés diélectriques internes (permittivité diélectrique et conductivité) d'un objet inconnu illuminé par une onde interrogatrice connue à partir des mesures du champ électrique dit diffracté résultant de leur interaction. Un tel problème constitue un problème dit inverse par opposition au problème direct associé qui consiste à calculer le champ diffracté, l'onde interrogatrice et l'objet étant alors connus.La résolution du problème inverse nécessite la construction préalable du modèle direct associé. Celui-ci est ici basé sur une représentation intégrale de domaine des champs électriques donnant naissance à deux équations intégrales couplées dont les contreparties discrètes sont obtenues à l'aide de la méthode des moments. En ce qui concerne le problème inverse, hormis le fait que les équations physiques qui interviennent dans sa modélisation directe le rendent non-linéaire, il est également mathématiquement mal posé au sens de Hadamard, ce qui signifie que les conditions d'existence, d'unicité et de stabilité de la solution ne sont pas simultanément garanties. La résolution d'un tel problème nécessite sa régularisation préalable qui consiste généralement en l'introduction d'information a priori sur la solution recherchée. Cette résolution est effectuée, ici, dans un cadre probabiliste bayésien où l'on introduit une connaissance a priori adaptée à l'objet sous test et qui consiste à considérer ce dernier comme étant composé d'un nombre fini de matériaux homogènes distribués dans des régions compactes. Cet information est introduite par le biais d'un modèle de « Gauss-Markov-Potts ». De plus, le calcul bayésien nous donne la distribution a posteriori de toutes les inconnues connaissant l'a priori et l'objet. On s'attache ensuite à déterminer les estimateurs a posteriori via des méthodes d'approximation variationnelles et à reconstruire ainsi l'image de l'objet recherché. Les principales contributions de ce travail sont d'ordre méthodologique et algorithmique. Elles sont illustrées par une application de l'imagerie micro-onde à la détection du cancer du sein. Cette dernière constitue en soi un point très important et original de la thèse. En effet, la détection du cancer su sein en imagerie micro-onde est une alternative très intéressante à la mammographie par rayons X, mais n'en est encore qu'à un stade exploratoire. / This work concerns the problem of microwave tomography for application to biomedical imaging. The aim is to retreive both permittivity and conductivity of an unknown object from measurements of the scattered field that results from its interaction with a known interrogating wave. Such a problem is said to be inverse opposed to the associated forward problem that consists in calculating the scattered field while the interrogating wave and the object are known. The resolution of the inverse problem requires the prior construction of the associated forward model. This latter is based on an integral representation of the electric field resulting in two coupled integral equations whose discrete counterparts are obtained by means of the method of moments.Regarding the inverse problem, in addition to the fact that the physical equations involved in the forward modeling make it nonlinear, it is also mathematically ill-posed in the sense of Hadamard, which means that the conditions of existence, uniqueness and stability of the solution are not simultaneously guaranteed. Hence, solving this problem requires its prior regularization which usually involves the introduction of a priori information on the sought solution. This resolution is done here in a Bayesian probabilistic framework where we introduced a priori knowledge appropriate to the sought object by considering it to be composed of a finite number of homogeneous materials distributed in compact and homogeneous regions. This information is introduced through a "Gauss-Markov-Potts" model. In addition, the Bayesian computation gives the posterior distribution of all the unknowns, knowing the a priori and the object. We proceed then to identify the posterior estimators via variational approximation methods and thereby to reconstruct the image of the desired object.The main contributions of this work are methodological and algorithmic. They are illustrated by an application of microwave imaging to breast cancer detection. The latter is in itself a very important and original aspect of the thesis. Indeed, the detection of breast cancer using microwave imaging is a very interesting alternative to X-ray mammography, but it is still at an exploratory stage.

La cartographie du risque en épidémiologie permet de mettre en évidence des régionshomogènes en terme du risque afin de mieux comprendre l’étiologie des maladies. Nousabordons la cartographie automatique d’unités géographiques en classes de risque commeun problème de classification à l’aide de modèles de Markov cachés discrets et de modèlesde mélange de Poisson. Le modèle de Markov caché proposé est une variante du modèle dePotts, où le paramètre d’interaction dépend des classes de risque.Afin d’estimer les paramètres du modèle, nous utilisons l’algorithme EM combiné à une approche variationnelle champ-moyen. Cette approche nous permet d’appliquer l’algorithmeEM dans un cadre spatial et présente une alternative efficace aux méthodes d’estimation deMonte Carlo par chaîne de Markov (MCMC).Nous abordons également les problèmes d’initialisation, spécialement quand les taux de risquesont petits (cas des maladies animales). Nous proposons une nouvelle stratégie d’initialisationappropriée aux modèles de mélange de Poisson quand les classes sont mal séparées. Pourillustrer ces solutions proposées, nous présentons des résultats d’application sur des jeux dedonnées épidémiologiques animales fournis par l’INRA. / The analysis of the geographical variations of a disease and their representation on a mapis an important step in epidemiology. The goal is to identify homogeneous regions in termsof disease risk and to gain better insights into the mechanisms underlying the spread of thedisease. We recast the disease mapping issue of automatically classifying geographical unitsinto risk classes as a clustering task using a discrete hidden Markov model and Poisson classdependent distributions. The designed hidden Markov prior is non standard and consists of avariation of the Potts model where the interaction parameter can depend on the risk classes.The model parameters are estimated using an EM algorithm and the mean field approximation. This provides a way to face the intractability of the standard EM in this spatial context,with a computationally efficient alternative to more intensive simulation based Monte CarloMarkov Chain (MCMC) procedures.We then focus on the issue of dealing with very low risk values and small numbers of observedcases and population sizes. We address the problem of finding good initial parameter values inthis context and develop a new initialization strategy appropriate for spatial Poisson mixturesin the case of not so well separated classes as encountered in animal disease risk analysis.We illustrate the performance of the proposed methodology on some animal epidemiologicaldatasets provided by INRA.

Les méthodes de Monte Carlo par chaines de Markov MCMC sont des outils mathématiques utilisés pour simuler des mesures de probabilités π définies sur des espaces de grandes dimensions. Une des questions les plus importantes dans ce contexte est de savoir à quelle vitesse converge la chaine de Markov P vers la mesure invariante π. Pour mesurer la vitesse de convergence de la chaine de Markov P vers sa mesure invariante π nous utilisons la distance de la variation totale. Il est bien connu que la vitesse de convergence d’une chaine de Markov réversible P dépend de la deuxième plus grande valeur propre en valeur absolue de la matrice P notée β!. Une partie importante dans l’estimation de β! consiste à estimer la deuxième plus grande valeur propre de la matrice P, qui est notée β1. Diaconis et Stroock (1991) ont introduit une méthode basée sur l’inégalité de Poincaré pour estimer β1 pour le cas général des chaines de Markov réversibles avec un nombre fini d'état. Dans cette thèse, nous utilisons la méthode de Shiu et Chen (2015) pour étudier le cas de l'algorithme de l'échantillonneur de Gibbs pour le modèle d'Ising unidimensionnel avec trois états ou plus appelé aussi modèle de Potts. Puis, nous généralisons le résultat de Shiu et Chen au cas du modèle d’Ising deux- dimensionnel avec deux états. Les résultats obtenus minorent ceux introduits par Ingrassia (1994). Puis nous avons pensé à perturber l'échantillonneur de Gibbs afin d’améliorer sa vitesse de convergence vers l'équilibre. / Monte Carlo Markov chain methods MCMC are mathematical tools used to simulate probability measures π defined on state spaces of high dimensions. The speed of convergence of this Markov chain X to its invariant state π is a natural question to study in this context.To measure the convergence rate of a Markov chain we use the total variation distance. It is well known that the convergence rate of a reversible Markov chain depends on its second largest eigenvalue in absolute value denoted by β!. An important part in the estimation of β! is the estimation of the second largest eigenvalue which is denoted by β1.Diaconis and Stroock (1991) introduced a method based on Poincaré inequality to obtain a bound for β1 for general finite state reversible Markov chains.In this thesis we use the Chen and Shiu approach to study the case of the Gibbs sampler for the 1−D Ising model with three and more states which is also called Potts model. Then, we generalize the result of Shiu and Chen (2015) to the case of the 2−D Ising model with two states.The results we obtain improve the ones obtained by Ingrassia (1994). Then, we introduce some method to disrupt the Gibbs sampler in order to improve its convergence rate to equilibrium.

Le thème de cette thèse est l’utilisation de méthodes probabilistes (plus spécifiquement de technique venant de la théorie de la percolation) pour mener une analyse non-perturbative de plusieurs modèles de physique statistique. La thèse est centrée sur les systèmes de spins et les modèles de percolation. Cette famille de modèle comprend le modèle d’Ising, le modèle de Potts, la percolation de Bernoulli, la percolation de Fortuin-Kasteleyn et les modèles de percolation continue. L’objectif principal de la thèse est de démontrer la décroissance exponentielle des corrélations au-dessus de la température critique et d’étudier les états de Gibbs des modèles en dessus. / The underlying theme of this thesis is using probabilistic methods and especially techniques of percolation theory to carry on a non-perturbative analysis of several models of statistical physics. The focus of this thesis is set on spin systems and percolation models including the Ising model, the Potts model, the Bernoulli percolation, the random-cluster model, and the continuum percolation models. The main objective of the thesis is to demonstrate exponential decay of correlations above the critical temperature and study the Gibbs states of the mentioned models.

The theory of Gibbs measures belongs to the borderlandbetween statistical mechanics and probability theory. In thiscontext, the physical phenomenon of phase transitioncorresponds to the mathematical concept of non-uniqueness for acertain type of probability measures. The most studied model in statistical mechanics is thecelebrated Ising model. The Potts model is a natural extensionof the Ising model, and the beach model, which appears in adifferent mathematical context, is in certain respectsanalogous to the Ising model. The two main parts of this thesisdeal with the Potts model and the beach model,respectively. For theq-state Potts model on an infinite lattice, there areq+1 basic Gibbs measures: one wired-boundary measure foreach state and one free-boundary measure. For infinite trees,we construct "new" invariant Gibbs measures that are not convexcombinations of the basic measures above. To do this, we use anextended version of the random-cluster model together withcoupling techniques. Furthermore, we investigate the rootmagnetization as a function of the inverse temperature.Critical exponents to this function for different parametercombinations are computed. The beach model, which was introduced by Burton and Steif,has many features in common with the Ising model. We generalizesome results for the Ising model to the beach model, such asthe connection between phase transition and a certain agreementpercolation event. We go on to study aq-state variant of the beach model. Using randomclustermodel methods again we obtain some results on where in theparameter space this model exhibits phase transition. Finallywe study the beach model on regular infinite trees as well.Critical values are estimated with iterative numerical methods.In different parameter regions we see indications of both firstand second order phase transition. Keywords and phrases:Potts model, beach model,percolation, randomcluster model, Gibbs measure, coupling,Markov chains on infinite trees, critical exponent.

The main objective of the present thesis is to investigate: What are the properties of the Ising and Potts model coupled to a CDT emsemble? For that objective, we used two methods: (1) transfer matrix formalism and Krein-Rutman theory. (2) FK representation of the q -state Potts model on CDTs and dual CDTs. Transfer matrix formalism permite us to obtain spectral properties of the transfer matrix using the Krein-Rutman theorem [KR48] on operators preserving the cone of positive func- tions. This yields results on convergence and asymptotic properties of the partition function and the Gibbs measure and allows us to determine regions in the parameter quarter-plane where the free energy converges. Second methods permite us to determine a region in the quadrant of parameters , > 0 where the critical curve for the classical model can be located. We also provide lower and upper bounds for the innite-volume free energy. Finally, using arguments of duality on graph theory and hight-T expansion we study the Potts model coupled to CDTs. This approach permite us to improve the results obtained for Ising model and obtain lower and upper bounds for the critical curve and free energy. Moreover, we obtain an approximation of the maximal eigenvalue of the transfer matrix at lower temperature. / O objetivo principal da presente tese é pesquisar : Quais são as propriedades do modelo de Ising e Potts acoplado ao emsemble de CDT? Para estudar o modelo usamos dois métodos: (1) Matriz de transferência e Teorema de Krein-Rutman. (2) Representação FK para o modelo de Potts sobre CDT e dual de CDT. Matriz de transferência permite obter propriedades espectrais da Matriz de transferência utilizando o Teorema de Krein-Rutman [KR48] sobre operadores que conservam o cone de funções positivas. Também obtemos propriedades asintóticas da função de partição e das medidas de Gibbs. Esses propriedades permitem obter uma região onde a energia livre converge. O segundo método permite obter uma região onde a curva crítica do modelo pode estar localizada. Além disso, também obtemos uma cota superior e inferior para a energia livre a volume infinito. Finalmente, utilizando argumentos de dualidade em grafos e expansão em alta temperatura estudamos o modelo de Potts acoplado as triangulações causais. Essa abordagem permite generalizar o modelo, melhorar os resultados obtidos para o modelo de Ising e obter novas cotas, superior e inferior, para a energia livre e para a curva crítica. Além disso, obtemos uma aproximação do autovalor maximal do operador de transferência a baixa temperatura.

The main objective of the present thesis is to investigate: What are the properties of the Ising and Potts model coupled to a CDT emsemble? For that objective, we used two methods: (1) transfer matrix formalism and Krein-Rutman theory. (2) FK representation of the q -state Potts model on CDTs and dual CDTs. Transfer matrix formalism permite us to obtain spectral properties of the transfer matrix using the Krein-Rutman theorem [KR48] on operators preserving the cone of positive func- tions. This yields results on convergence and asymptotic properties of the partition function and the Gibbs measure and allows us to determine regions in the parameter quarter-plane where the free energy converges. Second methods permite us to determine a region in the quadrant of parameters , > 0 where the critical curve for the classical model can be located. We also provide lower and upper bounds for the innite-volume free energy. Finally, using arguments of duality on graph theory and hight-T expansion we study the Potts model coupled to CDTs. This approach permite us to improve the results obtained for Ising model and obtain lower and upper bounds for the critical curve and free energy. Moreover, we obtain an approximation of the maximal eigenvalue of the transfer matrix at lower temperature. / O objetivo principal da presente tese é pesquisar : Quais são as propriedades do modelo de Ising e Potts acoplado ao emsemble de CDT? Para estudar o modelo usamos dois métodos: (1) Matriz de transferência e Teorema de Krein-Rutman. (2) Representação FK para o modelo de Potts sobre CDT e dual de CDT. Matriz de transferência permite obter propriedades espectrais da Matriz de transferência utilizando o Teorema de Krein-Rutman [KR48] sobre operadores que conservam o cone de funções positivas. Também obtemos propriedades asintóticas da função de partição e das medidas de Gibbs. Esses propriedades permitem obter uma região onde a energia livre converge. O segundo método permite obter uma região onde a curva crítica do modelo pode estar localizada. Além disso, também obtemos uma cota superior e inferior para a energia livre a volume infinito. Finalmente, utilizando argumentos de dualidade em grafos e expansão em alta temperatura estudamos o modelo de Potts acoplado as triangulações causais. Essa abordagem permite generalizar o modelo, melhorar os resultados obtidos para o modelo de Ising e obter novas cotas, superior e inferior, para a energia livre e para a curva crítica. Além disso, obtemos uma aproximação do autovalor maximal do operador de transferência a baixa temperatura.

Epithelial-mesenchymal transition (EMT) regulates the cellular processes of migration, growth, and proliferation - as well as the collective cellular process of tissue remodeling - in response to mechanical and chemical stimuli in the cellular microenvironment. Cells of the epithelium form cell-cell junctions with adjacent cells to function as a barrier between the body and its environment. By distributing localized stress throughout the tissue, this mechanical coupling between cells maintains tensional homeostasis in epithelial tissue structures and provides positional information for regulating cellular processes. Whereas in vitro and in vivo models fail to capture the complex interconnectedness of EMT-associated signaling networks, previous computational models have succinctly reproduced components of the EMT program. In this work, we have developed a computational framework to evaluate the mechanochemical signaling dynamics of EMT at the molecular, cellular, and tissue scale. First, we established a model of cell-matrix and cell-cell feedback for predicting mechanical force distributions within an epithelial monolayer. These findings suggest that tensional homeostasis is the result of cytoskeletal stress distribution across cell-cell junctions, which organizes otherwise migratory cells into a stable epithelial monolayer. However, differences in phenotype-specific cell characteristics led to discrepancies in the experimental and computational observations. To better understand the role of mechanical cell-cell feedback in regulating EMT-dependent cellular processes, we introduce an EMT gene regulatory network of key epithelial and mesenchymal markers, E-cadherin and N-cadherin, coupled to a mechanically-sensitive intracellular signaling cascade. Together these signaling networks integrate mechanical cell-cell feedback with EMT-associated gene regulation. Using this approach, we demonstrate that the phenotype-specific properties collectively account for discrepancies in the computational and experimental observations. Additionally, mechanical cell-cell feedback suppresses the EMT program, which is reflected in the gene expression of the heterogeneous cell population. Together, these findings advance our understanding of the complex interplay in cell-cell and cell-matrix feedback during EMT of both normal physiological processes as well as disease progression.

L'adhérence cellulaire est un processus vital impliqué dans de nombreux phénomènes biologiques fondamentaux comme la diérenciation, la réparation tissulaire ou encore le développement cellulaire. Cette thèse porte sur une étude alliant expériences et modélisation de cellules uniques en adhérence sur des supports micro-structurés Les résultats montrent que la contrainte géomé- trique imposée par les supports à contraste adhésif limite l'adhérence. Au-delà de cette limitation, une organisation reproductible du cytosquelette d'actine est observée cela suggère l'existence de lois physiques simples régissant ce processus. Nous avons développé une méthode de classication des formes géométriques élémentaires observées expérimentalement nous permettant d'obtenir des statistiques robustes. En nous basant sur le modèle de Potts Cellulaire, nous avons pu reproduire les résultats expérimentaux. Ce modèle énergétique démontre que les formes élémentaires sont des états métastables utilisés par les cellules au cours de l'adhérence. Les paramètres du modèle sont reliés aux paramètres biologiques pertinents. Nous présentons des résultats qui relient la courbure des interfaces aux paramètres biologiques. Nous montrons que la mesure expérimentale de cette courbure est une représentation de la compétition entre la contractilité des bres de stress et l'élasticité du gel d'actine. Une correspondance entre les propriétés physiques issues du modèle et les processus biochimiques régulant et organisant l'adhérence cellulaire est ainsi possible.