Flux organizations and control modes in antagonistically combined negative feedback loops

The purpose of this paper is to show the different compensatory responses and control models towards environmental perturbations when two antagonistic integral controllers are combined at the level of the controlled variable. Dependent on the controllers' relative setpoints two types of compensatory flux regulations occur, which have been termed delegated and isolated control. In delegated control one of the feedbacks submits its entire compensatory flux to the system, while the other feedback is the actual controller by neutralizing the excess flux of its antagonistic partner. In isolated control the compensatory flux of one of the controllers is negligible while the other feedback regulates the controlled variable alone. One of the findings is that these interacting feedbacks can exhibit environmentally driven setpoint changes known as rheostasis. A striking example is the photoperiodic control of Siberian hamsters' body weights, which can be rationalized by the interacting feedbacks between circadian morning (M) and evening (E) oscillators. A third control type is metastable control. Here, additions or removals of the controller variable can cause a switch to the antagonistic partner's control regime, but resets to its original control mode once additions or removals stop. Integral windup can induce temporary metastable setpoint changes or even lead to robust perfect adaptation without integral feedback! How the setpoint in blood glucose homeostasis arises is still debated. A dual-controller approach with two setpoints can describe many properties of blood glucose homeostasis and the roles of insulin, glucagon, and somatostatin.