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International audience; The theory of hybrid systems allows us to model biological functions with many interactive processes, describe complexity and hierarchy levels, and consider behavior law changes. However, we need to develop an implementation to simulate these models. The BioRica framework allows a non-ambiguous implementation, and, as shown here, the QSS method (Quantized States Systems) helps us to approach complex systems in a more efficient way. This method allows us to numerically solve stiff differential equations by separately choosing the temporal partition for each sub-model and variable, depending on how fast it changes over time. With that, one obtains more accurate solutions and decreases the number of computations compared to classic methods. Moreover, QSS does not need to store trajectories and interpolate when mode transitions occur between partition times. Herein, we exhibit a translation from BioRica to QSS models, which preserves the semantics. We implement QSS method with BioRica, and illustrate with applications in Biology, the Tyson model of cell cycle, and examples in Engineering.

The main aim of this thesis is to develop an approach that allows us to describe biological systems with theoretical sustenance and good results in practice. Biological functions are the result of the interaction of many processes, that connect different hierarchy levels going from macroscopic to microscopic level. Each process works in different way, with its own goal, complexity and hierarchy level. In addition, it is common to observe that changes in the conditions, such as nutrients or environment, modify the behavior of the systems. So, to describe the behavior of a biological system over time, it is convenient to combine different types of models: continuous models for gradual changes, discrete models for instantaneous changes, deterministic models for completely predictable behaviors, and stochastic or non- deterministic models to describe behaviors with imprecise or incomplete information. In this thesis we use the theory of Composition and Hybrid Systems as basis, and the BioRica framework as tool to model biological systems and analyze their emergent properties in silico. With respect to Hybrid Systems, we considered continuous models given by sets of differential equations or more general dynamics. We used Stochastic Transition Systems to describe the dynamics of model changes, allowing coe fficient switches that control the parameters of the continuous model, and strong switches that choose different models. Composition, reconciliation and reusing of models allow us to build complete and consistent descriptions of complex biological systems by combining them. Compositions of hybrid systems are hybrid systems, and the re nement of a model forming part of a composed system results in a re nement of the composed system. To implement our approach ideas we complemented the theory of our approach with the improving of the BioRica framework. We contributed to do that giving a BioRica speci cation of Hybrid Systems that assures integrity of models, allowing composition, reconciliation, and reuse of models with SBML speci cation. We applied our approach to describe two systems: wine fermentation kinetics, and cell fate decisions leading to bone and fat formation. In the case of wine fermentation, we reused known models that describe the responses of yeasts cells to different temperatures, quantities of resources and toxins, and we reconciled these models choosing the model with best adjustment to experimental data depending on the initial conditions and fermentation variable. The resulting model can be applied to avoid process problems as stuck and sluggish fermentations. With respect to cell fate decisions the idea is very ambitious. By using accurate models to predict the bone and fat formation in response to activation of pathways such as the Wnt pathway, and changes of conditions affecting these functions such as increments in Homocysteine, one can analyze the responses to treatments for osteoporosis and other bone mass disorders. We think that here we are giving a first step to obtain in silico evaluations of medical treatments before testing them in vivo or in vitro.; Les Fonctions biologiques sont le résultat de l'interaction de beaucoup de processus, avec differents objectives, complexités, niveaux d'hiérarchie, et changements de conditions que modi ent le comportement de systèmes. Nous utilisons des équations diferenciales ou dynamiques plus générales, et Stochastic Systèmes de Transition pour décrire la dynamique de changements des modèles. La composition, réconciliation et reutilisation des modèles nous permettent d'obtenir des descriptions de systèmes biologiques complètes et compatibles et leur combiner. Notre spéci cation de Systèmes Hybrides avec BioRica assures l'intégrité de modèles, et implement notre approche. Nous appliquons notre approche pour décrire in-silico deux systèmes: la dynamique de la fermentation du vin, et des décisions cellulaires associées à la formation de tissu d'os.