Heart disease, cancer, diabetes and other complex diseases account for more than half of human mortality in the United States. Other diseases such as AIDS, asthma, Parkinson’s disease, Alzheimer’s disease and cerebrovascular ailments such as stroke not only augment this mortality but also severely deteriorate the quality of human life experience. In spite of enormous financial support and global scientific effort over an extended period of time to combat the challenges posed by these ailments, we find ourselves short of sighting a cure or vaccine. It is widely believed that a major reason for this failure is the traditional reductionist approach adopted by the scientific community in the past. In recent times, however, the systems biology based research paradigm has gained significant favor in the research community especially in the field of complex diseases. One of the critical components of such a paradigm is computational systems biology which is largely driven by mathematical modeling and simulation of biochemical systems. The most common methods for simulating a biochemical system are either: a) continuous deterministic methods or b) discrete event stochastic methods. Although highly popular, none of them are suitable for simulating multi-scale models of biological systems that are ubiquitous in systems biology based research. In this work a novel method for simulating biochemical systems based on a deterministic solution is presented with a modification that also permits the incorporation of stochastic effects. This new method, through extensive validation, has been proven to possess the efficiency of a deterministic framework combined with the accuracy of a stochastic method. The new crossover method can not only handle the concentration and spatial gradients of multi-scale modeling but it does so in a computationally efficient manner. The development of such a method will undoubtedly aid the systems biology researchers by providing them with a tool to simulate multi-scale models of complex diseases.

Le mémoire est consacré à l'étude numérique des phénomènes survenant à l'interface solide-fluide. Trois processus ont été étudiés: auto-organisation de films moléculaires sur un substrat solide, adsorption du gaz moléculaires dans un matériau nanoporeux et la cristallisation à l'interface organique/inorganique. L'étude de l'auto-organisation et des transitions de phase dans des multicouches de l'azote moléculaires adsorbées sur graphite est présentée dans le chapitre III. L'analyse est focalisée sur l'hétérogénéité spatiale du système et son influence sur le mécanisme et température de transitions ordre/désordre et la fusion des couches. Elle complète ainsi l'étude numérique du diagramme de phase de l'azote moléculaire, bien connu pour le matériau massif (3D) et les monocouches (2D) adsorbées sur un substrat. Le chapitre IV présente une étude de cinétique du mélange des gaz (méthane et méthyle-mercaptan) confiné dans les nanopores de carbone (pores en forme de fentes, de dimensions latérales finies et largeur nanométrique). L'étude porte sur la capacité de stockage de pores, la dynamique des composantes du mélange des gaz sous confinement et l'évaluation de la quantité de l'odorant nécessaire pour une détection facile en cas de fuite. Chapitre V résume les résultats de l'étude préliminaire ayant pour but la mise en place des simulations de biomineralization à l'interface organique/inorganique. Les structures secondaires de deux biomolécules, human leucine-rich peptide hLRAP et full length amelogenin, rM179 ont été prédéterminées. Les plus probables configurations ont été optimisées dans un environnement aqueux. / The present work is devoted to computer simulations of phenomena occurring at solid-fluid interfaces. Three processes have been studied in details: auto organization of molecular films at a solid substrate, adsorption of molecular gas in confined geometry and crystal formation at organic-inorganic interface. Two classical simulation methods have been used: stochastic Monte Carlo and deterministic Molecular Dynamics.The study of self-organisation and phase transitions in molecular nitrogen multilayers adsorbed on the basal plane of graphite is presented in chapter III. It focusses on the systems' spatial heterogeneity and its influence on temperatures of order-disorder and melting transitions. This study completes the numerical analysis of molecular nitrogen phase diagram, well described and understood for 3d (bulk) and 2D (monolayer film) systems.The analysis of kinetics of fluid confined in nanopores is presented in chapter IV. The working case consists of methane-methyl mercaptan mixtures confined in slit-shaped carbon nanopores. Simulations focused on both: storage capacity of carbon pores of finite size and nanometric width, and dynamics of gas mixture components under confinement. An evaluation of odorant content necessary for easy gas leak detection is presented.Chapter V gathers the results of calculations performed to set up the simulations of biomineralization at the organic-inorganic interface. The secondary structures of two amelogenins (human leucine-rich peptide, hLRAP, and full length amelogenin, rM179) have been predicted. The most probable structures have been further refined and the chain folding optimized in aqueous environment.