Modeling of oscillations in endocrine networks with feedback.

Publisher Summary This chapter focuses on the mathematical approximation of endocrine oscillations in the framework of a modeling process structured in three formal phases. The mathematical methods presented are tailored to quantitatively interpret formal endocrine networks with (delayed) feedbacks. The goal is to illustrate different conditions, under which oscillations can emerge. The formal network itself consists of nodes and conduits, and is based on a qualitative analysis of available experimental data. In the presentation, the nodes are hormone concentrations in abstract pools, in which hormones are released or synthesized, under the control of other hormones. The conduits specify how the nodes interact within the network. The quantitative analysis of the formal network is based on approximation of the rate of change of a single system node. This essentially means that the dynamics of the hormone concentration is described with a single (delayed) ODE. A single half-life elimination model is used and the control of the synthesis is expressed as a combination of sigmoid Hill functions, depending on the related nodes. The derivation of the ODE is demonstrated, along with a brief analysis of the properties of its solution to facilitate the actual determination of all system parameters.