ODE Models for Systems Biological Networks

This chapter presents basics of mathematical modelling in systems biology. In Sect. 1.1, a brief introduction to the topic is given, mainly in terms of examples such as problems from population dynamics or from drug administration. In Sect. 1.2, the assembly of large ODE networks from simple chemical and physiological mechanisms, given in terms of chemical reaction modules, is described. Reasons are given, why the so-called Michaelis-Menten kinetics is no longer needed in the numerical simulation of such systems. For reaction diagram parts, where only the properties “stimulating” or “inhibiting” are known, the formulation in terms of Hill functions is presented. Finally, in Sect. 1.3, necessary mathematical background material is collected as far as it seems important for the class of applications in question. Main topics are the uniqueness and sensitivity of solutions as well as asymptotic stability. Mathematical contents are typically explained by examples rather than by theorems, while emphasis is laid on consequences for practical calculations.