Biology Reference
In-Depth Information
the actual hormone axis. Typically, this is measured by the extent to
which the hypothesized connectivity explains selected experimental
findings. However, it is unlikely the initial intuitive construct will
provide satisfactory results. Therefore, additional assumptions are
formulated that refine and expand the initial physiological hypothesis.
We specifically target the question of pulsatility in hormone release. The
main sources of oscillations in endocrine physiology are (delayed)
negative feedback loops; however, not every network with feedback
generates periodic behavior. In this chapter, we illustrate different
conditions under which oscillations emerge and perform quantitative
analysis on various abstract endocrine networks, interpreted as dynamic
systems. We shall be mainly concerned with phase 3 (above) and its
relations to phases 1 and 2.
We begin by describing, through differential equations, an
approximation of the evolution of the concentration of a single hormone
secreted in the circulation under the control of one or more other
regulators. We further simulate and analyze the interactions between
system components (nodes) organized in different feedback networks.
The main concepts are illustrated on two two-node models. System
parameters are introduced on the basis of their physiologic meaning,
and the effect of their modification is appraised. Oscillations caused by
perturbations of systems with damped periodicity are distinguished
from oscillations of systems with a genuine periodic behavior. In
addition, we discuss the simulation of basic laboratory experimental
techniques, point out some of their limitations, and suggest alternatives
that reveal more network details.
In most of our examples, the underlying mathematical theory is not
trivial. This is especially true for those models that explicitly include
delays in the core system. Abstract mathematical details are generally
avoided, and the focus is placed on numerical solutions and
interpretations. As a rule, the simulated networks are abstract and do
not correspond to a specific endocrine system. However, the constructs
and the modeling techniques are fairly general and can be easily adapted
to fit a particular physiology.
III. EVOLUTION AND CONTROL OF HORMONE
CONCENTRATION
A. Rate of Change of Hormone Concentration
We begin by describing the quantitative approximation of the
concentration dynamics of a single hormone secreted in its releasable
pool. Recall from Chapter 9 that the rate of change of hormone
concentration depends on two processes: Secretion and ongoing
