Computational modeling for systems biology and physiology through examples

Although recent enthousiasm has emerged for Systems Biology, it is of major importance to identify the roots it has with computational (mathematical) modeling. In fact, major contributions have been made for decades with the aim to quantitatively analyze and model the function of living systems in order, ultimately, to better understand the underlying constituents and collective behaviors and use them for diagnosis and therapeutic purposes. However, the impressive evolution of technological resources and methods allows today to revisit these early attempts and to bring to light new concepts, targets, and expectations. This chapter, after a tentative definition of the generic elements behind Systems Biology and Physiology, will provide a review of current efforts devoted to multimodal, multilevel, multiresolution approaches, all being addressed from the joint observational, modeling and information processing points of view. The several theoretical frames at our disposal will also be addressed, in particular the capability to handle multiple modeling for- malisms. Examples from the literature and the research conducted by the authors will exemplify these multidisciplinary developments and results. The forthcoming challenges to be faced will then be outlined