Flux organizations and control modes in antagonistically combined negative feedback loops

Abstract

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 partners 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. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=183 SRC="FIGDIR/small/687434v2_ufig1.gif" ALT="Figure 1"> View larger version (46K): org.highwire.dtl.DTLVardef@1f984b9org.highwire.dtl.DTLVardef@78c409org.highwire.dtl.DTLVardef@8e6ab6org.highwire.dtl.DTLVardef@233_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LIA set of 16 inflow/outflow controllers (negative feedbacks) combined by a common controlled variable have been studied. C_LIO_LIDependent on the relationship between the inflow/outflow controllers setpoints two distinct regulatory modes termed delegated control and isolated control have been identified. C_LIO_LIRegions of control and their extensions are visualized by a perturbation phase diagram. C_LIO_LIMetastable control may temporarily occur when one of the controller variables are environmentally increased or decreased. C_LIO_LIRobust perfect or near-perfect adaptation may occur even in the absence of integral feedback. C_LIO_LIThe combined controllers can show homeostatic as well as rheostatic behaviors. A striking biological example of rheostasis is found in the photoperiodic regulation of the Siberian hamsters body weight. C_LIO_LIThe origin of the glycemic setpoint in blood glucose homeostasis is still debated. A glucagon- and insulin-based two-setpoint model suggests that in diabetic individuals the upper insulin-dependent setpoint increases with decreasing insulin generation rates. This setpoint is defended irrespective of its value, but the accuracy of regulation depends how tightly the insulin degrading enzyme (IDE, insulysin) binds to insulin. In addition, both glucagon- and insulin-based setpoints depend (rheostatically) on the level of somatostatin. C_LI