Biology Reference
In-Depth Information
during the infusion of C the secretion of B is suppressed (but not the
synthesis), and the concentration in the storage pool is increased. The
concentration of A also increases, because low B levels cannot effectively
block its release. Thus, the model explains the rebound jointly, by the
augmented concentration in the storage pool and the increased
secretion of A.
We would like to note that a network may incorporate a single feedback
loop in a more complex way (e.g., via a combination of two or more
nodes). Stability analysis of the steady state of such three-node networks
with one feedback loop shows that these systems are capable of
sustaining periodicity even without an explicit delay in the feedback
loop, if the Hill coefficients are relatively high. The specific calculations
can be found in Richelle (1977) and Thomas (1973).
In the case of two nodes and one negative feedback loop, the systems
considered in this section always have only one fixed point (steady
state), which is either a repellor or an attractor (Figure 10-15). In the first
instance, the system has a unique limit cycle—a periodic solution, which
attracts all trajectories in the phase space and thereby generates stable
periodic behavior (Figure 10-16). In the second instance, the steady state
is either a focus or a node and attracts all trajectories in the phase space.
The construct displays damped periodic behavior only in the case of a
focus. An external perturbation can initiate a waning train of pulses
(Figure 10-1 , right panel; Figure 10-21) by removing the system from
its steady state. Therefore, oscillations might be generated even by a
system that does not have a periodic solution, and its fixed point is
asymptotically stable. However, an external energy source should exist.
The frequency of such oscillations is largely independent of the external
perturbation (Figure 10-21).
V. NETWORKS WITH MULTIPLE FEEDBACK LOOPS
The available experimental data might suggest that the release of a
particular hormone B is controlled by multiple mechanisms, with
different periodicity in the timing of their action. This implies that
probably more than one (delayed) feedback loop regulates the secretion
of B and the formal endocrine network may include more than two
nodes. In determining the elements to be included in the core construct,
it is important to keep track of the length of the delays in the feedback
action of all nodes of interest. For example, if the goal were to explain
events recurring every one to three hours, the natural candidates to
include in the formal network would be nodes involved in feedback
relations with B with delays shorter than three hours. Long feedback
delays cannot account for high-frequency events. In particular, if we
hypothesize that a certain feedback is responsible for a train of pulses in
