Das Verhalten adhärenter Zellen hängt stark von den chemischen, topographischen und mechanischen Eigenschaften ihrer Umgebung ab. Experimentelle Untersuchungen der letzten Jahre haben gezeigt, dass adhärente Zellen aktiv die elastischen Eigenschaften ihrer Umgebung erkunden, indem sie an dieser ziehen. Der resultierende Kraftaufbau hängt von den elastischen Eigenschaften der Umgebung ab und wird an den Adhäsionskontakten in entsprechende biochemische Signale umgewandelt, die zelluläre Programme wie Wachstum, Differenzierung, programmierten Zelltod und Zellbewegung mitbestimmen. Im Allgemeinen sind Kräfte wichtige Einflussgrößen in biologischen Systemen. Weitere Beispiele dafür sind Hör- und Tastsinn, Wundheilung sowie die rollende Adhäsion von weißen Blutkörperchen auf den Wänden der Blutgefäße. In der Habilitationsschrift von Ulrich Schwarz werden mehrere theoretische Projekte vorgestellt, die die Rolle von Kräften und Elastizität in der Zelladhäsion untersuchen.<br /> (1) Es wurde eine neue Methode entwickelt, um die Kräfte auszurechnen, die Zellen an den Kontaktpunkten auf mikro-strukturierte elastische Substrate ausüben. Das Hauptergebnis ist, dass Zell-Matrix-Kontakte als Mechanosensoren funktionieren, an denen interne Kräfte in Proteinaggregation umgewandelt werden.<br /> (2) Eine Ein-Schritt-Master-Gleichung, die die stochastische Dynamik von Adhäsionsclustern als Funktion von Clustergröße, Rückbindungsrate und Kraft beschreibt, wurde sowohl analytisch als auch numerisch gelöst. Zudem wurde dieses Modell auf Zell-Matrix-Kontakte, dynamische Kraftspektroskopie sowie die rollende Adhäsion angewandt.<br /> (3) Im Rahmen der linearen Elastizitätstheorie und mit Hilfe des Konzepts der Kraftdipole wurde ein Modell formuliert und gelöst, das die Positionierung und Orientierung von Zellen in weicher Umgebung vorhersagt. Diese Vorhersagen sind in guter Übereinstimmung mit zahlreichen experimentellen Beobachtungen für Fibroblasten auf elastischen Substraten und in Kollagen-Gelen. / The behaviour of an adhering cell is strongly influenced by the chemical, topographical and mechanical properties of the surface it attaches to. During recent years, it has been found experimentally that adhering cells actively sense the elastic properties of their environment by pulling on it through numerous sites of adhesion. The resulting build-up of force at sites of adhesion depends on the elastic properties of the environment and is converted into corresponding biochemical signals, which can trigger cellular programmes like growth, differentiation, apoptosis, and migration. In general, force is an important regulator of biological systems, for example in hearing and touch, in wound healing, and in rolling adhesion of leukocytes on vessel walls. In the habilitation thesis by Ulrich Schwarz, several theoretical projects are presented which address the role of forces and elasticity in cell adhesion.<br /> (1) A new method has been developed for calculating cellular forces exerted at sites of focal adhesion on micro-patterned elastic substrates. The main result is that cell-matrix contacts function as mechanosensors, converting internal force into protein aggregation.<br /> (2) A one-step master equation for the stochastic dynamics of adhesion clusters as a function of cluster size, rebinding rate and force has been solved both analytically and numerically. Moreover this model has been applied to the regulation of cell-matrix contacts, to dynamic force spectroscopy, and to rolling adhesion.<br /> (3) Using linear elasticity theory and the concept of force dipoles, a model has been introduced and solved which predicts the positioning and orientation of mechanically active cells in soft material, in good agreement with experimental observations for fibroblasts on elastic substrates and in collagen gels.

Afin d'estimer les forces statiques équivalentes du vent, qui produisent les réponses quasi-statiques et dynamiques extrêmes dans les structures soumises au champ de pression instationnaire induit par les effets du vent, une nouvelle méthode probabiliste est proposée. Cette méthode permet de calculer les forces statiques équivalentes du vent pour les structures avec des écoulements aérodynamiques complexes telles que les toitures de stade, pour lesquelles le champ de pression n'est pas gaussien et pour lesquelles la réponse dynamique de la structure ne peut être simplement décrite en utilisant uniquement les premiers modes élastiques (mais nécessitent une bonne représentation des réponses quasi-statiques). Généralement, les mesures en soufflerie du champ de pression instationnaire appliqué à une structure dont la géométrie est complexe ne suffisent pas pour construire une estimation statistiquement convergée des valeurs extrêmes des réponses dynamiques de la structure. Une telle convergence est nécessaire pour l'estimation des forces statiques équivalentes afin de reproduire les réponses dynamiques extrêmes induites par les effets du vent en tenant compte de la non-gaussianité du champ de pression aléatoire instationnaire. Dans ce travail, (1) un générateur de réalisation du champ de pression instationnaire non gaussien est construit en utilisant les réalisations qui sont mesurées dans la soufflerie à couche limite turbulente; ce générateur basé sur une représentation en chaos polynomiaux permet de construire un grand nombre de réalisations indépendantes afin d'obtenir la convergence des statistiques des valeurs extrêmes des réponses dynamiques, (2) un modèle d'ordre réduit avec des termes d'accélération quasi-statique est construit et permet d'accélérer la convergence des réponses dynamiques de la structure en n'utilisant qu'un petit nombre de modes élastiques, (3) une nouvelle méthode probabiliste est proposée pour estimer les forces statiques équivalentes induites par les effets du vent sur des structures complexes décrites par des modèles éléments finis, en préservant le caractère non gaussien et sans introduire le concept d'enveloppes des réponses. L'approche proposée est validée expérimentalement avec une application relativement simple et elle est ensuite appliquée à une structure de toiture de stade pour laquelle des mesures expérimentales de pressions instationnaires ont été effectuées dans la soufflerie à couche limite turbulente / In order to estimate the equivalent static wind loads, which produce the extreme quasi-static and dynamical responses of structures submitted to random unsteady pressure field induced by the wind effects, a new probabilistic method is proposed. This method allows for computing the equivalent static wind loads for structures with complex aerodynamic flows such as stadium roofs, for which the pressure field is non-Gaussian, and for which the dynamical response of the structure cannot simply be described by using only the first elastic modes (but require a good representation of the quasi-static responses). Usually, the wind tunnel measurements of the unsteady pressure field applied to a structure with complex geometry are not sufficient for constructing a statistically converged estimation of the extreme values of the dynamical responses. Such a convergence is necessary for the estimation of the equivalent static loads in order to reproduce the extreme dynamical responses induced by the wind effects taking into account the non-Gaussianity of the random unsteady pressure field. In this work, (1) a generator of realizations of the non-Gaussian unsteady pressure field is constructed by using the realizations that are measured in the boundary layer wind tunnel; this generator based on a polynomial chaos representation allows for generating a large number of independent realizations in order to obtain the convergence of the extreme value statistics of the dynamical responses, (2) a reduced-order model with quasi-static acceleration terms is constructed, which allows for accelerating the convergence of the structural dynamical responses by using only a small number of elastic modes of the structure, (3) a novel probabilistic method is proposed for estimating the equivalent static wind loads induced by the wind effects on complex structures that are described by finite element models, preserving the non-Gaussian property and without introducing the concept of responses envelopes. The proposed approach is experimentally validated with a relatively simple application and is then applied to a stadium roof structure for which experimental measurements of unsteady pressures have been performed in boundary layer wind tunnel

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

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