In this chapter we introduce a new term, the "Mathematical Microscope", as a method of using mathematics in accessing information about reality when this information is otherwise inaccessible. Furthermore, we discuss how models and experiments are related: none of which are important without the other. In the sciences and medicine, a link that is often missing in the chain of a system can be made visible with the aid of the mathematical microscope. The mathematical microscope serves not only as a lens to clarify a blurred picture but more important as a tool to unveil profound truths. In reality, models are most often used in a detective-like manner to investigate the consequences of different hypothesis. Thus, models can help clarify connections and relations. Consequently, models also help to reveal mechanisms and to develop theories. Case studies are presented and the role of mathematical modeling is discussed for type 1 and type 2 diabetes, depression, cardiovascular diseases and the interactions between the combinations of these, the so-called gray triangle in the metabolic syndrome.
Betasys: Systems Biology of Regulated Exocytosis in Pancreatic Β-cells, 2011, p. 97-118
Mathematical Modeling; Diabetes; Depression; Cardiovascular Regulation; Systems Biology; Measurements; Experiments